Post on 23-Aug-2019
Optimización del cálculo de lentes intraoculares monofocales, acomodativas y multifocales mediante la corrección del error queratométrico empleando óptica paraxial
Verónica Mateo Pérez
DepartamentodeÓptica,FarmacologíayAnatomía
FacultaddeCiencias
TESISDOCTORAL
OPTIMIZACIÓNDELCÁLCULODELENTES
INTRAOCULARESMONOFOCALES,
ACOMODATIVASYMULTIFOCALES
MEDIANTELACORRECCIÓNDELERROR
QUERATOMÉTRICOEMPLEANDOÓPTICA
PARAXIAL
Doctoranda:VerónicaMateoPérez
TesispresentadaparaaspiraralgradodeDOCTORAPORLAUNIVERSIDADDEALICANTE
DOCTORADOENTECNOLOGÍASPARALASALUDYELBIENESTAR
(VISIÓNYOPTOMETRÍA)
Dirigidapor:D.DavidP.PiñeroLlorensD.VicenteJ.CampsSanchís
Julio2016
D.VICENTEJESÚSCAMPSSANCHÍS,DoctorporlaUniversidaddeAlicanteyD.DAVID
PABLOPIÑEROLLORENS,DoctorporlaUniversidaddeAlicanteyProfesorAsociado
(Acreditado para titular en el área de Óptica) del Departamento de Óptica,
FarmacologíayAnatomíadelaFacultaddeCienciasdelaUniversidaddeAlicante:
CERTIFICA: Quelapresentememoriatitulada“Optimizacióndelcálculodelentes
intraocularesmonofocales,acomodativasymultifocalesmediante
lacorreccióndelerrorqueratométricoempleandoópticaparaxial”
ha sido realizada bajo su dirección por Doña VERÓNICA MATEO
PÉREZenelDepartamentodeÓptica,FarmacologíayAnatomíadela
Facultad de Ciencias de la Universidad de Alicante y constituye su
TesisDoctoralparaoptaralGradodeDoctor.
Y para que conste, y en cumplimiento de la legislación vigente, firman el presente
certificadoenAlicanteaveintisietedejuniodedosmildieciséis.
Fdo.VicenteJCampsSanchís Fdo.DavidPPiñeroLlorens
Agradecimientos: AvosotrosDavidyVicent,tutoresycompañerosdefatigas,portenerestetoque
delocuraalpensarqueseríaunabuenaideatutelarmedespuésdesupervisarmeelTFM
y TFG, dejándome de esta manera continuar aprendiendo de vosotros (espero no
haberosdefraudado…)
Al Hospital Internacional Medimar (Alicante), por darme la oportunidad de
elaborarlasbasesdedatosconsuspacientes.
ADolo,porsuinestimableayudaenlaprogramacióndeMatlab.
A mis compañeros y amigos del máster (Silvia, Esteban, Esther, Eli, Blanca,
Oscar,Vicenta,Maite)quedesdeelprincipiodemiandadurahanestadopreocupándose
pormisavancesyesperanansiososelgrandía.
Amifamilia,porvuestrocariñoysobretodograciasporlaconfianzaquehabéis
depositadosiempreenmí,hacéisquemeatrevaaemprendercualquierproyectoporque
séquesiemprevaisaestarallíparaapoyarme.
MuchasGracias
ÍNDICE Índiceabreviaturas
Capítulo0: Artículosqueconformanlatesis 13
Capítulo1:Introducciónyaspectosgenerales
1.a.Fórmulasdecálculodelentesintraoculares
19
21
1.a.1.Fórmulasde1ªgeneración. 21
1.a.2.Fórmulasde2ªgeneración 23
1.a.3.Fórmulasde3ªgeneración 26
1.a.4.Fórmulasde4ªgeneración 29
1.b.FactoresdeerrorenelcálculodelaPIOL 31
1.b.1.Longitudaxial(AL) 32
1.b.2.Posiciónefectivadelalente(ELP) 33
1.b.3.Potenciacorneal(Pc) 35
1.c.Antecedentesyestadoactual 36
1.d.Diseñosdelentesintraoculares 39
1.d.1.Lentesintraocularesacomodativas 40
1.d.2.Lentesintraocularesmultifocales 41
1.d.3.Lentesintraocularesasféricas 44
Capítulo2: Hipótesisyobjetivos 47
2.a.Hipótesis 49
2.b.Objetivos 49
Capítulo3: Materialesymétodos
3.a.Cálculodelapotenciacornealgaussiana(𝑃!!"#$$)y
queratométrica(Pk)
53
53
3.b.Diferenciasentrelapotenciacornealgaussianay
queratométrica(ΔPc) 54
3.c.Obtencióndelíndicequeratométricoexacto(nkexacto)y
ajustado(nkadj) 54
3.d.Obtenciónpotenciadelalenteintraocularqueratométrica
(𝑃!"#! )yGaussiana(𝑃!"#!"#$$) 56
3.e.Obtenciónpotenciadelalenteintraocularajustada
(PIOLadj) 59
3.f.Estimaciónposiciónefectivadelalenteajustada(ELPadj) 61
3.g.Seleccióndepacientes 62
3.h.Protocolodeexamendelospacientes 62
3.i.SistemaPentacam® 62
3.j.Lentesintraocularesutilizadasenlosestudios 64
3.k.Técnicaquirúrgica 66
3.l.Examenpreypostoperatorio
3.m.Análisisestadísticodelosresultados
67
67
Capítulo4: Resultadosydiscusión
4.a.ResultadosenrelaciónconelobjetivoA
69
71
4.b.ResultadosenrelaciónconelobjetivoB 76
4.c.ResultadosenrelaciónconelobjetivoC 86
4.d.ResultadosenrelaciónconelobjetivoD 95
4.e.ResultadosenrelaciónconelobjetivoE 106
Capítulo5: Conclusionesyperspectivasdefuturo 119
5.a.Conclusiones 121
5.b.Perspectivasdefuturo 122
Capítulo6: Referencias 125
Apéndice 143
Trabajo1 145
Clinicalvalidationofanalgorithmtocorrecttheerrorinthekeratometric
estimationofcornealpowerinnormaleyes
Trabajo2 151
MinimizingtheIOLpowererrorinducedbykeratometricpower
Trabajo3 163
Positional accommodative intraocular lens power error induced by the
estimationofthecornealpowerandtheeffectivelensposition
Trabajo4 171
Error induced by estimation of the corneal power and the effective lens
position with a rotationally asymmetric refractive multifocal
intraocularlens
Trabajo5 179
Preliminary evaluation of an algorithm to minimize the power error
selection of an aspheric intraocular lens by optimizing the
estimationofthecornealpowerandtheeffectivelensposition
ÍNDICEDEABREVIATURAS
ΔPc:DiferenciaentrelapotenciacornealqueratométricaylapotenciacornealcalculadaporelmétododeGauss
ΔPIOL: Diferencia entre la potencia de lente intraocular queratométrica y lapotenciadelalenteintraocularcalculadaporelmétododeGauss
ACA: Astigmatismodelacaraanterior
ACP: Astigmatismodelacaraposterior
ACD: Profundidaddelacámaraanterior(AnteriorChamberDepth)
ACDpost: Profundidaddelacámaraanteriorpostoperatoria
ACDpre: Profundidaddelacámaraanteriorpreoperatoria
AEN: Aberraciónesféricanegativa
AEP: Aberraciónesféricapositiva
AL: Longitudaxial(AxialLength)
BCVA: Agudezavisualconlamejorcorrección(BestCorrectionVisualAcuity)
CA: Astigmatismocorneal(cornealastigmatism)
ec: Espesorcorneal
eL: Espesordelcristalino
eLcorr: Espesorcorregidodelcristalino
ELP: Posiciónefectivadelalente(EffectiveLensPosition)
ELPadj: Posiciónefectivadelalenteajustada
ELPHaigis: PosiciónefectivadelalentecalculadamediantelafórmuladeHaigis
ELPHolladay: PosiciónefectivadelalentecalculadamediantelafórmulaHolladay
ELPHofferQ: PosiciónefectivadelalentecalculadamediantelafórmulaHofferQ
ELPSRK/T: PosiciónefectivadelalentecalculadamediantelafórmulaSRK/T
F: PotenciavariableenfuncióndelalongitudaxialenlafórmulaSRKII
factorS: Factor variable debido a la forma de la lente intraocular, fabricación,técnicadelcirujanoydispositivodemedida
FIV: Factorinflacióndelavarianza
H: Alturacorneal(distanciaentreelvérticecorneal-planodeliris)
Hc,H´c: Planosprincipalesdelacórnea
HIOL,H´IOL: Planosprincipalesdelalenteintraocular.
IOL: Lenteintraocular(IntraocularLens)
k: Razónentreradiocaraanterioryposteriorcorneal(𝑟!!/𝑟!!)
L: Grosorretiniano
LoA: Límitesdeacuerdo(LimitsofAgreement)
nc: Índicederefraccióndelacórnea
nha: Índicederefraccióndelhumoracuoso
nhv: Índicederefraccióndelhumorvítreo
nk: Índicederefracciónqueratométrico
nkadj: Índicederefracciónqueratométricoajustado
nkexact: Índicederefracciónqueratométricoexacto
P1c: Potenciacaraanteriordelacórnea
P2c: Potenciacaraposteriordelacórnea
Pc: Potenciacorneal
PcHaigis:PotenciacornealcalculadaparalafórmuladeHaigiscuandoseutilizaunvalordeíndicequeratométrico1.3315
𝑷𝒄𝑮𝒂𝒖𝒔𝒔 PotenciacornealcalculadaporelmétododeGauss
PIOL: Potencialenteintraocular
𝑷𝑰𝑶𝑳𝒌 : Potencialenteintraocularqueratométrica
PIOLadj: Potencialenteintraocularajustada
PIOLadjSRK/T:Potencia lente intraocular ajustada, cuando se usa el valor de ELPobtenidomediantelafórmulaSRK/T
𝑷𝑰𝑶𝑳𝑮𝒂𝒖𝒔𝒔: Potencialenteintraocularqueratométrica
PIOLHaigis: PotencialenteintraocularcalculadamediantelafórmuladeHaigis
PIOLHofferQ: PotencialenteintraocularcalculadamediantelafórmuladeHofferQ
PIOLHolladay: PotencialenteintraocularcalculadamediantelafórmuladeHolladay
PIOLSRK/T: PotencialenteintraocularcalculadamediantelafórmulaSRK/T
PIOLReal: Potencialenteintraocularimplantada
Pk: Potenciacornealqueratométrica
Pk(1.3375):Potencia corneal queratométrica calculada con el índice queratométrico1.3375
Pkadj: Potenciaqueratométricacalculadaconelíndicequeratométricoajustado
r1c: Radiocaraanteriorcorneal
r2c: Radiocaraposteriorcorneal
rc: Radiocorneal
Rdes: Refraccióndeseada
Rpre: Refracciónpreoperatoria
Rpost: Refracciónpostoperatoria
S: Vérticecorneal
SD: Desviaciónestándar(StandardDeviation)
SE: Equivalenteesférico(Sphericalequivalent)
SEpre: Equivalenteesféricopreoperatorio
SEpost: Equivalenteesféricopostoperatorio
WTW: Blancoablanco(WhitetoWhite)
Capítulo0
ARTÍCULOSQUECONFORMANLATESIS
15
ARTÍCULOSQUECONFORMANLATESIS
Lapresentetesis, laconformanuntotalde5artículospublicadosenrevistas
deimpactoanivelinternacional.Dichosartículosseenumeranacontinuaciónsegún
suordendedesarrollodurantelainvestigación:
1. Piñero DP, Camps VJ, Mateo V, Ruiz-Fortes P. Clinical validation of an
algorithm to correct the error in the keratometric estimation of corneal
power in normal eyes. J Cataract Refract Surg. 2012 Aug; 38(8): 1333-
1338.
2. CampsVJ,PiñeroDP,deFezD,MateoV.Minimizing the IOLpowererror
inducedbykeratometricpower.OptomVisSci.2013Jul;90(7):639-49.
3. PiñeroDP,CampsVJ,RamonML,MateoV,Pérez-CambordíRJ.Positional
accommodativeintraocularlenspowererrorinducedbytheestimationof
the corneal power and the effective lens position. Indian J Ophthalmol
2015May;63(5):438-44.
4. Piñero DP, Camps VJ, Ramon ML, Mateo V, Pérez-Cambordí RJ. Error
induced by the estimation of the corneal power and the effective lens
position with a rotationally asymmetric refractive multifocal intraocular
lens.IntJOphthalmol2015Jun18;8(3):501-7.
5. Piñero DP, Camps VJ, Ramon ML, Mateo V, Soto-Negro R. Preliminary
evaluation of an algorithm to minimize the power error selection of an
aspheric intraocular lens by optimizing the estimation of the corneal
powerandtheeffectivelensposition.IntEyeSci2016Jun;16(6):1001-8
15
Capítulo1
INTRODUCCIÓN
19
1.INTRODUCCIÓN
El cristalino en su forma natural es transparente y actúa como una lente
enfocandolaluzqueentraenelojo.Debidoalpasodelosaños,elcristalinopuedeir
perdiendoesa transparencianaturaly convertirseenuna lenteopaca,produciendo
unadisminuciónde la visiónque en casos avanzadospuededar lugar a ceguera.A
este fenómeno de opacificación se le denomina catarata. En estadíos avanzados de
opacificación, es necesario la extracción de la catarata y la sustitución del poder
dióptricodelcristalinoporeldeunalenteintraocular.
Lacatarataeslaprincipalcausadeceguerareversible.Lastécnicasquirúrgicas
para su extracciónhan idoevolucionando conelpasode los años.Hacemásde50
años,noserealizabaningúncálculodelenteintraocular,únicamenteserealizabauna
extracciónintracapsulardelcristalino.Elproblemaquepresentabaestemétodoera
queelpacientequedabaafáquico,precisandounacorrecciónópticahipermetrópica
elevada (fig.1)parapoderdesarrollarunavidanormal.Estemétododecorrección
provocabaaberracionesydebidoalelevadopesodelaslenteshacíaqueestasolución
nofueralaideal.
Figura1:Gafaparaafaquia.(Fuente:www.qvision.es)
La técnica quirúrgica evolucionó hasta poder realizar extracciones
extracapsulares,permitiendoinsertarunalenteintraoculardentrodelojo,conelfin
deproporcionarimágenesretinianassimilaresaltamañofisiológico,consiguiéndose
así una corrección óptica más adecuada. A partir de este momento, comienzan a
Capítulo1
Introducción
20
implantarselentesencirugíadecataratasdeigualpotenciaparatodoslospacientes
(por ejemplo +18 D)(1), lo que provocaba ametropías elevadas, debido a que la
longitudaxialylapotenciacornealnotienenelmismovalorentodoslosojos.
En las últimas décadas, se ha experimentado una enorme evolución en la
cirugíadecataratas,conelfindeconseguirincisionescornealesparalainserciónde
la lente intraocular cada vez más pequeñas, disminuir las complicaciones
postoperatorias, mejorar la recuperación visual del paciente y la realización del
cálculo correcto de la potencia de la lente intraocular (PIOL). En la actualidad, los
estudios van orientados a analizar los posibles parámetros susceptibles de inducir
errorenelcálculodelapotenciadelalenteintraocularparaintentaroptimizarlosy
asíreducirloserroresrefractivosqueaparecenenelpostoperatorio.
Antes de 1975, existía una única fórmula para el cálculo de la potencia de la
lente intraocular basada en la historia clínica(2). Esta fórmula tenía la siguiente
expresión*:
𝑃!"# = 18+ 1.25 ∙ 𝑅!"# [1]
Donde𝑃!"#eslapotenciadelalenteintraocularyRpreeslarefracciónpreoperatoria.
*Nota:Dadoqueensudíanoexistióunconsensoa lahoradeestandarizarparámetrosyesta
circunstanciapuedeinduciraconfusiónendeterminadosmomentos,sehadecididounificartérminosen
todaslasfórmulascitadasenlapresentetesis.
Porlotanto,sielpacienteeraemétropepreviamente(Rpre=0),seutilizabauna
lenteintraocularde18D.Seobservabanerroressuperioresa1.0Denel50%delos
casos,siendoenalgunoscasosestoserrorestanaltosqueseleasignaronelnombre
de “sorpresa refractiva”(3). Estos grandes errores llevaron a muchos autores a
investigar sobre el valor de la potencia de la lente intraocular que se debería
implantarenunpacienteconcataratasydesdeentoncessehanpublicadounaserie
de fórmulas de cálculo de la potencia de la lente intraocular (PIOL). Todas estas
fórmulas tienencomopuntodepartidaelmodelodeojo simplificado, enel cual se
consideraelojocomounsistemaformadoporundioptrioesféricoyunalenteplana
Capítulo1
Introducción
21
correspondientesalacórneayalcristalino,respectivamente,ycuyafocalimagendel
sistemacorrespondealaretina(2,4).
1.a.Fórmulasdecálculodelentesintraoculares
Alolargodelahistoriahanidoapareciendonumerosasfórmulasparaelcálculo
de la potencia de lentes intraoculares. Desde que se comenzó a realizar
intervencionesquirúrgicas,sehanutilizadobásicamentedosconjuntosde fórmulas
decálculo(5); teóricasyempíricas.LasteóricasaplicanlasecuacionesdeGausspara
ópticaparaxialenelmodelodeojoteórico,cuyaimagenfinal focalizaenretina.Las
fórmulas empíricas o de regresión lo que hacen es analizar los resultados de la
refracciónpostoperatoriademúltiplesintervencionesycalculanunoscoeficientesde
ajusteenlafórmuladecálculodela lenteparaobtenerlarefracciónpostoperatoria
deseada.
1.a.1.Fórmulasde1ªgeneración(fórmulasteóricasoriginales)
Estas fórmulas presentan una constante única para cada tipo de lente
intraocular, denominada ACD (profundidad de la cámara anterior) donde su
posicionamientodentrodelojoesconstante.Aestaprimerageneraciónpertenecen
las fórmulas de Fyodorov (1967)(6), Colenbrander (1973)(7), Thijssenn (1975)(8),
Binkhorst(1975)(9)yVanderHeijde(1976)(10)(vertabla1).Aunqueaparentemente
sondiferentes,esfácilcomprobarquetodasestánbasadasenelcálculodelapotencia
deunalenteintraocularenaproximaciónparaxialapartirdelasecuacionesdeGauss.
Fyodorov(6) [ec.2] fue el primer autor enpublicaruna fórmula teóricapara el
cálculodelaPIOLaimplantarenfuncióndelalongitudaxial(AL),lapotenciacorneal
(Pc) y la posición que adopta la lente intraocular al ser insertada en el ojo,
denominadaposiciónefectivadelalente(ELP).
EnlasfórmulasdeprimerageneraciónelvalordelaELPseconsiderabacomo
unaconstanteindependientementedecualquierotroparámetroocular.Enladécada
de los 70, las lentes intraoculares implantadas eran de fijación iridiana, donde la
Capítulo1
Introducción
22
profundidad de la cámara anterior o distancia de vértice corneal al plano del iris
coincidía respecto a la posición efectiva de la lente (ELP). Por esta razón, laELP o
ACDcte (para fórmulas de primera generación) adoptóun valormedio inicial de 4.0
mm,aumentandoalolargodeltiempoamedidaquelaslentesintraocularespasaron
aimplantarseenelsulcus(4.5mm)yposteriormenteenelsacocapsular(5.25mm).
El índice de refracción del humor acuoso y humor vítreo para los cálculos era
consideradosiempreelmismovalor(1.336)[ec.2].
Unosañosdespués,Colenbrander(7) [ec.3]publicóuna fórmulasimilara lade
Fyodorov,con laúnicadiferenciade la incorporacióndeunaconstante0.05mm, la
cual se añadía en losdosdenominadores. Lahipótesisque sebarajaba sobredicha
constanteeraqueelautorconsiderabaestevalorcomoladistanciaentrelosplanos
principalesdelacórneayelvérticecorneal.
Dosañosdespués,en1975,Thijssen(8)presentósufórmula[ec.4],muysimilara
lafórmuladeColenbrander(7).LaúnicadiferenciaconlaecuacióndeFyodorovesque
añadió unas constantes al primer y segundo denominador (Const1 y Const2
respectivamente),quesonconstantespropiasdecadatipode lente.Esemismoaño
Binkhorst(9) [ec.5] introdujoa la fórmuladecálculoun factor4Rcen lugardelradio
corneal,loquesuponíaunadiferenciade0.50Daproximadamenteenrelaciónconlas
demásformulas.VanderHeijde(10)[ec.6]porsupartepublicólamismafórmulaque
ladeFyodorovperoexpresadaendostérminos(verTabla1).
Capítulo1
Introducción
23
Tabla1.Fórmulasde1ªgeneración
𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔 − 𝑨𝑳 ∙ 𝑷𝒄
(𝑨𝑳 − 𝑬𝑳𝑷)(𝟏 − 𝑬𝑳𝑷 ∙ 𝑷𝒄𝟏𝟑𝟑𝟔 ) FórmuladeFyodorov(1967)(6)[2]
𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔
𝑨𝑳 − 𝑬𝑳𝑷 − 𝟎.𝟎𝟓−
𝟏𝟑𝟑𝟔𝟏𝟑𝟑𝟔𝑷𝒄
− 𝑬𝑳𝑷 − 𝟎.𝟎𝟓 FórmuladeColenbrander(1973)(7)[3]
𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔
𝑨𝑳 − 𝑬𝑳𝑷 + 𝑪𝒕𝒆𝟏−
𝟏𝟑𝟑𝟔𝟏𝟑𝟑𝟔𝑷𝒄
− 𝑬𝑳𝑷 + 𝑪𝒕𝒆𝟐 FórmuladeThijssen(1975)(8)[4]
𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔(𝟒𝒓𝒄 − 𝑨𝑳)
(𝑨𝑳 − 𝑬𝑳𝑷)(𝟒𝒓𝒄 − 𝑨𝑳) FórmuladeBinkhorst(1975)(9)[5]
𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔
𝑨𝑳 − 𝑬𝑳𝑷−
𝟏𝟏𝑷𝒄
− 𝑬𝑳𝑷𝟏𝟑𝟑𝟔
FórmuladeVanderHeijde(1975)(10)[6]
DondePIOL:potenciadelalenteintraocular;AL:longitudaxial;Pc:potenciacorneal;ELP:posiciónefectiva
delalente;Cte1yCte2:constantesdelafórmuladeThijssen;rc:radiocorneal
1.a.2.Fórmulasteóricasyempíricasde2ªgeneración
Dadoque seasumíaque laposiciónefectivade la lenteera igual en todos los
ojos independientemente de su longitud axial, surgieron una gran cantidad de
sorpresasrefractivas,observándoseque losojos largosquedabanhipercorregidosy
los ojos cortos hipocorregidos, de tal manera que se dedujo que el valor de la
profundidaddelacámaraanteriordebíavariardependiendodelalongitudaxial.Por
esta razón, en la década de los 80, se pasó de una ELP constante a una ELP
modificable proporcionalmente en función de la longitud axial. Estas fórmulas se
desarrollaron paralelamente a las fórmulas empíricas basadas en fórmulas de
regresiónmúltiple(vertabla2),lascualesprecisabandeunaconstantepropiadela
lente(A)ademásdelosdatosdelalongitudaxial(AL)ypotenciacorneal(Pc),basadas
enunaecuacióndeltipo:
Capítulo1
Introducción
24
𝑃!"# = 𝐴 − 𝐵 ∙ 𝐴𝐿 − 𝐶 ∙ 𝑃! [7]
EnconcretoSanders,RetzlaffyKraffintrodujeronunosvaloresalasconstantes
B=2.5yC=0.9alaecuación7,denominandoaestafórmulaSRKI(11,12).LaconstanteA
eravariableenfuncióndelaformayfabricacióndelalenteintraocular[ec.8].
Binkhorst,(13)en1981,utilizósupropiafórmulaoriginal[ec.5],peroajustando
la ELP para la posición de la lente dentro del ojo (fijada al iris, en la cápsula, en
sulcus,…)enrelaciónalalongitudaxial[ec.9](13–15).Cuandolalenteestácolocadaen
la cámara posterior, el valor deELPse reduce 0.17mmpor cadamilímetro deAL
inferiora23.45mmyse incrementa0.17mmporcadamilímetrodeAL superiora
23.45mm.LaELPsemodificabaenidénticaproporciónalaAL.
Shammas,(16) en 1982, publicó una fórmula basada en la modificación de la
fórmula de Colenbrander [ec. 3]. Además como sugería Binkhorst, este autor hacía
unavariaciónenel índicederefraccióncornealde1.3375a4/3por loque laPc se
reduceunfactor1.0125,ademásdeintroducirunfactorligadoalaAL[ec.10].
La fórmula de Hoffer(17) [ec.11] está fundamentada en la fórmula de
Colenbrander, al igual que la fórmula anterior. El error postoperatorio esperado
(Rpost)seañadealapotenciacorneal(Pc).Elvalordelaposiciónefectivadelalente
(ELP)seexpresaenfuncióndela longitudaxial(AL)ylaprofundidaddelacámara
anterior(ACD),correspondienteaunaconstantequevaríaenfuncióndelalongitud
axial.
ComparandolafórmulaSRKIderegresiónconlasfórmulasteóricasoriginales
talescomoVanderHeijde(10),Thijssen(8),Binkhorst(9),Colenbrander(7)yFyodorov(6)
,seobservaqueestasfórmulasderegresiónsonválidasenojosdemedidasestándar
yson labasede las fórmulasmodernas(Holladay IyHolladay II,SRK/T,HofferQ).
Sin embargo, debido a los errores que surgían en la medida de la PIOL, Sanders,
Retzlaff y Kraff, en 1988,modificaron su fórmula a la cual denominaron SRK II(18)
[ec.12]. Esta nueva fórmula añade a la potencia calculada con SRK I una cierta
potencia(F),queesvariableenfuncióndelalongitudaxialdelojo,dondeFtomaba
valoresdesde-0.5DparaAL>24.5mmhasta+3.0DparaAL<20.0mm.
Capítulo1
Introducción
25
Olsen,(4) basándose en la fórmula SRK y en un análisis de regresiónmúltiple,
publicóunafórmulautilizandoelmétododelosmínimoscuadrados[ec.13].Usando
estaecuaciónseobservóqueelerrormediocometidoenlarefracciónpostoperatoria
fuede0.00±0.64D.
Tabla2.Fórmulasde2ªgeneración
𝑷𝑰𝑶𝑳 = 𝑨 − 𝟐.𝟓𝑨𝑳 − 𝟎.𝟗𝑷𝒄 FórmuladeSRKI(1980)(12)[8]
𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔(𝟒𝒓𝒄 − 𝑨𝑳)
(𝑨𝑳 − 𝑬𝑳𝑷)(𝟒𝒓𝒄 − 𝑬𝑳𝑷)
• SiAL>26:ELPcorr=ELP·(26/23.45)
• SiAL≤26:ELPcorr=ELP·(AL/23.45)
FórmuladeBinkhorst(1984)(14)[9]
𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔
𝑨𝑳 − 𝟎.𝟏 𝑨𝑳 − 𝟐𝟑 − 𝑬𝑳𝑷 − 𝟎.𝟎𝟓−
𝟏𝟏.𝟎𝟏𝟐𝟓𝑷𝒄
− 𝑬𝑳𝑷 + 𝟎.𝟎𝟓𝟏𝟑𝟑𝟔
FórmuladeShammas(1982)(16)[10]
𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔
𝑨𝑳 − 𝑬𝑳𝑷 − 𝟎.𝟎𝟓−
𝟏𝟑𝟑𝟔𝟏𝟑𝟑𝟔
𝑷𝒄 + 𝑹𝒑𝒐𝒔𝒕− 𝑬𝑳𝑷 + 𝟎.𝟎𝟓𝟏𝟎𝟎𝟎
FórmuladeHoffer(1981)(19)[11]
𝑷𝑰𝑶𝑳 = 𝑷𝑰𝑶𝑳 𝑺𝑹𝑲 𝑰 + 𝑭FórmuladeSRKII(1988)(18)[12]
𝑷𝑰𝑶𝑳 = 𝟏𝟓𝟏.𝟑 − 𝟏.𝟐𝑷𝒄 − 𝟑.𝟑 ∙ 𝑨𝑳FórmuladeOlsen(2007)(4)[13]
DondePIOL:potenciadelalenteintraocular;A:constatedelalenteintraocular;AL:longitudaxial;Pc:
potencia corneal; rc: radio corneal;ELP:posiciónefectivade la lente;ELPcorr: posiciónefectivade la
lente corregida ; Rpost: refracción postoperatoria; PIOL(SRK I): Potencia lente intraocular calculada
mediantelafórmulaSRKI;F:potenciavariableenfuncióndelalongitudaxialparalafórmulaSRKII
Capítulo1
Introducción
26
1.a.3.Fórmulasde3ªgeneración
EstageneracióndefórmulassurgióalobservarquelaELPnosecorrelacionaba
con laACD preoperatoria, considerandoque laELP se incrementaba en ojos largos
(mayor AL) y decrecía en ojos cortos (menor AL). Como se ha comentado
anteriormente, este incrementonoeraproporcional a laAL comoconsideraban las
ecuaciones de segunda generación y laELP se correlacionaba con la posición de la
lente intraocular,yaseaencámaraanterior, sulcusosacocapsular.Poresta razón,
surgieronlasfórmulasdetercerageneración,lascualestratandepredecirlaposición
efectiva de la lente a implantar en el ojo (ELP) en función de dos parámetros, la
longitudaxialylaqueratometría(atendiendoacurvaturayespesorcorneal).Aesta
generaciónpertenecenlafórmuladeHolladayI(1988)(20),SRK/T(1990)(21)yHoffer
Q(1993)(17)(vertabla3).
Holladay (20) en 1988 desarrolló una fórmula empírica [ec.21] a partir de la
modificacióndelasecuacionesdeFyodorov[ec.2]yVanderHeijde[ec.6],queincluía
criterios de selección para identificarmedidas improbables de queratometría y de
longitudaxial,unamayorprecisiónenlaestimacióndelaprofundidadqueadquiere
lacámaraanteriorcuandoseintroducíaunalenteintraocular(ACDpost)equivalentea
ELP[ec.14],quenoeramásquelasumadelaprofundidaddelacámaraanteriordel
ojo(ACD)yladistanciaexistenteentreelplanoanteriordelirisyelplanoópticodela
lenteintraocular(Ꮪ).
𝐸𝐿𝑃 = 𝐴𝐶𝐷 + 𝑆 [14]
Aunque el factor Ꮪ es un valor medible definido como la distancia entre el
vérticecornealyelplanodeliris,realmentesecalculaapartirderesolverdemanera
inversaunafórmulaqueutilizacomovariableslalongitudaxial(AL),elpropiovalor
de la lente intraocular implantada (PIOL) y el valor de la refracción postoperatoria
(Rpost)(22).ElfactorᏚesvariabledebidoalaformadelalente,lafabricación,latécnica
del cirujano y de los dispositivos de medida. Esta distancia se predice con mayor
precisiónmediante el uso de una fórmulamatemática donde suma el valormedio
empleadoparaelgrosorcorneal(0.56mm)ylaalturacorneal(H).
Capítulo1
Introducción
27
LarelaciónquedioHolladayentreelfactorᏚylaconstanteAqueaparecíaenla
fórmulaSRKfue:
𝑆!"#$%& = 𝐴 − 𝐶𝑡𝑒 ∙ 0.5663 − 65.60 [15]
OenfuncióndelvalordelaACD:
𝑆!"#$%& = 𝐴𝐶𝐷 ∙ 0.9704 − 3.595 [16]
PorlaestrecharelaciónexistenteentreelfactorᏚyELP(casi1:1),uncambiode
una unidad en el factorᏚ es idéntico al cambio de 1.0mm en el valor deELP y la
refracciónpostoperatoriasemodificaalrededorde1.5D.
LafórmulaSRK/T(21)[ec.22],alcontrarioquelasfórmulasSRKI[ec.8]ySRKII
[ec.12], era una fórmula teórica basada en la fórmula de Fyodorov(6) [ec.2], que
utilizabalametodologíaderegresiónparalaoptimizacióndelaprediccióndelaELP,
delespesordelaretinaydelacorreccióndelíndicederefraccióncorneal.Elcálculo
estimadodelaACDpostoperatoriaveníadadopor:
𝐸𝐿𝑃 = 𝐻 + 𝑑𝑒𝑠𝑝𝑙𝑎𝑧𝑎𝑚𝑖𝑒𝑛𝑡𝑜 [17]
𝑑𝑒𝑠𝑝𝑙𝑎𝑧𝑎𝑚𝑖𝑒𝑛𝑡𝑜 = 𝐴𝐶𝐷 𝑐𝑡𝑒 − 3.336 [18]
Donde: H es la distancia entre la córnea y el plano del iris y ACD(cte) puede ser
medidaapartirdelacontanteA:
𝐴𝐶𝐷 𝑐𝑡𝑒 = 0.62467 ∙ 𝐴 − 68.747 [19]
LafórmulaSRK/TutilizabalamismaconstanteAdiseñadaoriginalmentepara
laecuaciónSRK.LaconstanteAabarcamúltiplesvariablesdel fabricante,elestiloy
colocación del implante dentro del ojo, la técnica del cirujano y los equipos de
medición.
Hoffer Q(17) después de publicar su fórmula [ec.11], continuó estudiando la
relaciónexistenteentreELPyAL,encontrandounarelaciónnolineal,loqueresultaba
contradictorioconlopublicadoporélmismoen1984,porloquemodificósupropia
fórmulaconunanuevaprediccióndeELP[ec.23].Hofferestudiólarelaciónexistente
entreELPyAL,encontrandoquesurelaciónseajustabaaunacurvatangenteenlugar
de a una recta. Hizo muchas variaciones de la fórmula en función de la AL y el
promedio de lecturas queratométricas hasta que encontró una fórmula que se
ajustabaalacurvadeseada.Lafórmulaconsistíaen:
Capítulo1
Introducción
28
• UnvalorpersonalizadodeELP (quedenominópACD)desarrolladoapartirde
cualquieradelasseriesdelestilodeunalenteintraocular.
• UnfactorqueaumentaELPcuandoaumentaAL.
• UnfactorqueaumentaELPcuandoaumentalacurvaturacorneal.
• UnfactorquemoderaloscambiosenelvalordeELPparaojosextremadamente
largos(>26mm)oextremadamentecortos(<22mm).
• UnaconstanteañadidaaELP.
ELP = pACD + 0.3 AL − 23.5 + (tan𝑃!)! + (0.1M(23.5 − A)!(tan 0.1 G − A)! − 0.99166
[20]
• SiAL≤23 M=1 G=28
AL>23 M=-1 G=23.5• SiELP>6.5 ELP=6.5
ELP<2.5 ELP=2.5
Tabla3.Fórmulasde3ªgeneración
𝑷𝑰𝑶𝑳 =𝟏𝟎𝟎𝟎𝒏𝒉𝒂 𝒏𝒉𝒂𝒓𝟏𝒄 − 𝒏𝒌 − 𝟏 𝑨𝑳 − 𝟎.𝟎𝟎𝟏𝑹𝒑𝒐𝒔𝒕(𝜹𝒗(𝒏𝒉𝒂𝒓𝟏𝒄 − 𝒏𝒌 − 𝟏 𝑨𝑳 + 𝑨𝑳 ∙ 𝒓𝟏𝒄
(𝑨𝑳 − 𝑬𝑳𝑷)(𝒏𝒉𝒂𝒓𝟏𝒄 − 𝒏𝒌 − 𝟏 𝑬𝑳𝑷 − 𝟎.𝟎𝟎𝟏𝑹𝒑𝒐𝒔𝒕(𝜹𝒗 𝒏𝒉𝒂𝒓𝟏𝒄 − 𝒏𝒌 − 𝟏 𝑬𝑳𝑷 + 𝑬𝑳𝑷 ∙ 𝒓𝟏𝒄
FórmuladeHolladay(1988)(20)[21]
𝑷𝑰𝑶𝑳 =𝟏𝟎𝟎𝟎𝒏𝒉𝒂(𝒏𝒉𝒂𝒓𝒄 − 𝒏𝒄 − 𝟏 𝑨𝑳)
(𝑨𝑳 − 𝑬𝑳𝑷)(𝒏𝒉𝒂𝒓𝒄 − 𝒏𝒄 − 𝟏 𝑬𝑳𝑷) FórmuladeSRK/T(1990)(21)[22]
𝑷𝑰𝑶𝑳 =𝟏𝟑𝟑𝟔
(𝑨𝑳 − 𝑬𝑳𝑷 − 𝟎.𝟎𝟓)−
𝟏𝟑𝟑𝟔𝟏𝟑𝟑𝟔
𝑷𝒄 + 𝑹𝒅𝒆𝒔− 𝑬𝑳𝑷 + 𝟎.𝟎𝟓
𝟏𝟎𝟎𝟎
FórmuladeHofferQ(1993)(17)[23]
DondePIOL:potenciadelalenteintraocular;nha:índicehumoracuoso;;r1c:radiocornealanterior;nk:
índicequeratométrico;AL:longitudaxial;Rpost:refracciónpostoperatoria;δv:distanciaalvértice;ELP:
posiciónefectivadelalente;rc:radiocorneal;nc:índicecorneal;Pc:potenciacorneal;Rdes:refracción
deseada
Capítulo1
Introducción
29
1.a.4.Fórmulasde4ªgeneración
Apesardequeactualmentenoesunacategoríauniversalmenteaceptada,en
losúltimosañossehanpropuestonuevasfórmulas quesepodríanincluirdentrode
unanuevageneración.Estasfórmulasempleanmásdedosfactoresparapredecirla
ELP,teniendoencuentaademásdelaALylapotenciacorneal(Pc),variablescomoel
grosordelcristalino(eL),larefracciónpostoperatoria(Rpost),etc.(vertabla4).
LafórmuladeOlsen(23–25)[ec.25]fuedesarrolladaen1980enunaépocaenla
que las fórmulas de regresión fuerondominantes y las fórmulas ópticasno estaban
bien consideradas, por lo que esta fórmula no se publicó hasta añosmás tarde. El
objetivoeradesarrollaruna fórmula conelmenornúmerodesuposicionesposibles
en el ámbito de la óptica Gaussiana para intentar hacer elmodelo aplicable al ojo
pseudofáquico.En1990,decidió incluirhastacuatro factoresmásde los tenidosen
cuentaanteriormente: longitudaxial(AL),profundidaddelacámaraanterior(ACD),
potenciacorneal(Pc)ygrosorretiniano(L).LafórmulaquedeterminalaELPesuna
ecuaciónderegresiónque incluyeelparámetroH, el cualesobtenidomediante las
ecuaciones ya utilizadas para las fórmulas Holladay I [ec.21] o SRK/T [ec.22], el
espesor del cristalino y el valor ACDcte determinado para cada tipo de lente
intraocularunavezestudiadoretrospectivamenteunnúmerodecasosutilizandoun
índicequeratométricode1.3315.
La fórmuladeHolladay II fuedesarrolladaen1996paramejorar lacapacidad
predictivadelaELPenojosmuycortos(AL<22.0mm).Loquepretendeespredecir
de una forma más precisa la posición efectiva de la lente (ELP) mediante la
incorporación de la medida blanco-blanco (WTW), la ACD fáquica, el espesor del
cristalino(eL),laedaddelpacienteyelsexo.Estafórmulanohasidopublicadapero
seencuentradisponiblecomopartedelsoftwareHolladayIOLConsultant(26,27).
Haigis(28)demostróqueparacaracterizarlaslentes,enlugardeunaconstante,
eramásconvenienteutilizarunaexpresiónquerelacionaralalongitudaxial(AL)con
laprofundidaddelacámaraanterior(ACD).LafórmuladeHaigis[ec.26]noempleala
potencia corneal para la predicción de ELP, sino que utiliza tres constantes para
ajustarlaposiciónylaformadelacurvadeprediccióndelapotencia.
Capítulo1
Introducción
30
𝐸𝐿𝑃 = 𝑎! + 𝑎!𝐴𝐶𝐷 + (𝑎!𝐴𝐿) [24]
Lasconstantesa0,a1ya2seobtienenapartirdelosdatosderegresióndeunos
200casos.Laconstantea0variadelamismamaneraqueelfactorᏚolaconstanteA
enlasfórmulasdeHolladayySRK/T,respectivamente.
Tabla4.Fórmulasde4ªgeneración
𝑷𝑰𝑶𝑳 =𝒏!𝑷𝒄𝑳𝒄𝒐𝒓
𝑳𝒄𝒐𝒓!𝑬𝑳𝑷 𝟏!𝑬𝑳𝑷∙𝑷𝒄𝒏
donde:FórmuladeOlsen(2004)(23–25)[25]
𝑬𝑳𝑷 = 𝑨𝑪𝑫𝒄𝒕𝒆 − 𝟒.𝟎𝟑 + 𝟎.𝟏𝟗𝑨𝑳 + 𝟎.𝟒𝟗𝑨𝑪𝑫𝒑𝒓𝒆 + 𝟎.𝟐𝟖𝑳 − 𝟎.𝟒𝟏𝒓𝒄 + 𝟎.𝟎𝟐𝟖𝑹𝒑𝒓𝒆
𝑷𝑰𝑶𝑳 =𝒏
𝑨𝑳 − 𝑬𝑳𝑷−
𝒏𝟏.𝟑𝟑𝟔𝒁 − 𝑬𝑳𝑷
donde: 𝒛 = 𝑷𝒄 +𝑹𝒅𝒆𝒔
𝟏 − 𝑹𝒅𝒆𝒔δ𝒗
FórmuladeHaigis(2003)(28)[26]
DondePIOL:potenciadelalenteintraocular;n:índicequeratométrico;Pc:potenciacorneal;Lcorr:espesor
del cristalino corregido; ELP: posición efectiva de la lente; ACDcte: profundidad de la cámara anterior
constante; AL: longitud axial; ACDpre: profundidad de la cámara anterior preoperatoria; L: espesor
cristalino; rc: radio corneal, Rpre: refracción preoperatoria; Rdes: refracción deseada;δ𝒗: distancia del
planodelagafaalvérticecorneal
Sehademostradoque las fórmulasmodernasofrecenmejores resultadosque
lasfórmulasteóricasoriginales(Colenbrander(7)yBinkhorst(9))yquelasfórmulasde
regresión (SRK y SRK II). En ojos con valores promedio, no existen diferencias
significativas entre las fórmulas de Holladay, SRK/T y Hoffer Q. No obstante, la
fórmula de Holladay II mejora la precisión en ojos cortos, con un error absoluto
menor que en la fórmula de Holladay (21,27). La desventaja que presentaban las
fórmulasderegresiónesquesólofuncionabanparaelconjuntodedatosdelcualse
derivaba.Porejemplo,silalongitudaxialsemideportécnicasdiferentes,laconstante
(ytalvezloscoeficientesderegresión)cambiarían.
Capítulo1
Introducción
31
Acontinuaciónsevaaanalizarlaimportanciadeesteyotrosfactoresclave,que
son necesarios para el cálculo preciso tanto de la potencia como de la posición
efectivadelalente,asícomosuniveldeinfluenciaenelcálculodelaPIOL.
1.b.Factoresdeerrorenelcálculodelapotenciadelalenteintraocular
Estudios clínicos han demostrado que el uso de una única potencia de lente
intraocular (PIOL) dejaría a un 5% de los pacientes con errores refractivos no
coincidentes con su refracción en más de 5.0 D(4). Estudios más recientes(29,30)
demuestran los errores cometidos en el cálculo de la PIOL a pesar de los avances
tecnológicos y las nuevas fórmulas. Estos errores alcanzan hasta 3.0 D en algunos
casos. En concreto, en el estudio realizado porNarváez et al.(29)se comparó cuatro
fórmulasdecálculodePIOL,HolladayI,HolladayII,HofferQySRK/Tparaobtenery
comparar los erroresque se cometían con cadaunade estas fórmulas.Observaron
quetodaslasfórmulascomprendíanunoserroresdesdeaproximadamente0Dhasta
másde3.0D.LafórmuladeHofferQeralaqueobteníaelrangodeerrorinferiorcon
unosvaloresde0,02Da3,03D.Enotroestudio realizadoporTerzietal.(30)donde
también se compararon las predicciones de errores cometidas mediante cuatro
fórmulasmodernas, talescomoHofferQ,SRK/T,HaigisyHolladay IIenojos largos
conlongitudesaxiales>26,0mmyenojoscortos<22,0mmobservaronqueenojos
miópicos existía una tendencia a la hipermetropización. Zaldivar et al.(31) en su
estudio con 50 ojos utilizando las mismas fórmulas que Terzi et al.(30) también
concluyeronquecontodaslasfórmulasseobteníaunvalorinferiordePIOLrespectoa
lacorrecta.
En el artículo publicado por Olsen(4) se indica que la precisión que se puede
lograr en la predicción de la refracción promedio con lametodologíamoderna, es
decir, en condiciones óptimas y con los algoritmos de última generación de
predicciónenelcálculodeACD,es<±0.5D,conunadesviaciónestándar<0,6D.Aún
contodoesto,alrededordel10%deloscasossiguenestandofueradelrangode±1.0
D,por loque todavía sigue siendo importanteencontraruna fórmula con laque se
puedanminimizarestoserrores.Olsenconcluyóqueestaprediccióneramásprecisa
Capítulo1
Introducción
32
enojoslargosqueenojoscortos.
Sepuedededucirportantoqueelerrorenlaprediccióndelcálculototaldela
PIOL es la suma de los errores asociados con las variables principales. Tal y como
hemoscomentadoanteriormentesepuedecomprobarenla literaturaexistenteque
losparámetrosquepresentanunamayorinfluenciaenelerrordelcálculodelalente
intraocularson:
1. Medidadelalongitudaxial(AL)
2. Medidadelaposiciónefectivadelalente(ELP)
3. Medidadelapotenciacorneal(Pc)
1.b.1.Longitudaxial
Entre los factores que pueden influir en el error del cálculo de la PIOL, la
medicióndelalongitudaxialsiguesiendounodelosfactoresmásrelevantes,puesto
queunerrorde0.1mmdeALesequivalenteaunerrorde0.27Denelplanodelas
gafas(enelsupuestodeojosnormales).
Antiguamente, a la hora de decidir qué fórmula o fórmulas eran las más
adecuadas en funcióndeAL, no existíaun criterio general. Enun estudio realizado
porNarváezetal(29)seutilizócomoreferencialafórmulaHolladayIIconunfactorde
cirujano personalizado. Para un mejor análisis, la muestra de ojos del estudio fue
divididaengruposdependiendodelalongitudaxial:ojoscortos(<22.0mm),medios
(entre22.0y24.5mm),medianamentelargos(entre24.5y26.0mm)ymuylargos(>
26.0mm).En losresultadosnoseobtuvierondiferenciassignificativasdeprecisión
respecto a la predicción del error refractivo postoperatoriomedido con las cuatro
fórmulasdeestudioytampocoseobtuvierondiferenciasconlalongitudaxial,porlo
que concluyeron que las cuatro fórmulas de estudio eran igualmente válidas
independientemente de la longitud total del ojo. Sin embargo, Donoso et al(32)
evaluaron en212 ojos la precisión alcanzada con las fórmulas SRK II, Binkhorst II,
Hoffer Q, Holladay II y SRK/T y concluyeron que las fórmulas de Binkhorst II y la
HofferQeranlasqueproporcionabanmejoresresultadosenlaprediccióndelaPIOL
enojospequeños(<22.0mm),mientrasquelaSRK/Teramásprecisaenojoslargos
Capítulo1
Introducción
33
(> 28.0 mm). En un estudio realizado por Tsang et al(33) con longitudes axiales
grandes (>25.0mm), sepudodemostrarque la fórmuladeHofferQ siempredaba
mejorresultadoenlaprediccióndelaPIOL,mientrasquelaHolladayIySRK/Tdaban
resultadoscomparablesentreellas,peropeoresquelaHofferQ.Hoffer(27)examinóel
errorabsolutomedioen317ojosusandolasfórmulasSRKII,BinkhorstII,HofferQ,
Holladay IIySRK/T.Elerrorenvalorabsoluto tendíaaser inferiorenojosmedios
(entre22.0y24.5mm)conlas fórmulasdeHolladayIyHofferQ.Enojoscortos(<
22.0 mm), las fórmulas Hoffer Q y Holladay II proporcionaban un error absoluto
medioinferior.LafórmulaSRK/Tmostrabaunatendenciamásbajadelamediapara
elerrorabsolutoenojosmedianamentelargos(entre24.5y26.0mm)ymuylargos
(>26.0mm).
1.b.2.Posiciónefectivadelalente.
Eltérminodeposiciónefectivadelalente(ELP)fuerecomendadoporlaFDAen
1995 para describir la posición que adoptaba la lente intraocular cuando era
insertada en el ojo(34) (ya sea en cámara anterior, iris, sulcus o en la cápsula del
cristalino). EstaELPeraequivalentealaACDpostdefinidapordiversosautoresenla
bibliografíayvienedeterminadaporladistanciaexistenteentreelvérticecornealyla
caraanteriordelalenteintraocular.(verfig.2)
Figura2.Distanciasusadasenlaprediccióndelaposiciónefectivadelalente
(ELP)oACDpostoperatoria(ACDpost)(4)
LpreACDpre
ELP
AL
H Ojo Fáquico
Ojo Pseudofáquico
Capítulo1
Introducción
34
LaELPpara lentes intraoculares antes de 1980 era una constante de 4.0mm
paratodoslostiposdelentesyentodoslospacientes(fórmulasde1ªgeneración).La
mayoríadelaslentesimplantadaseranfijadasaliris,dondeladistanciapromediode
suplanoprincipalposterioralvérticecornealeradeaproximadamente4.0mm.En
1981, Binkhorst mejoró la predicción de la ELP utilizando un factor variable de
predicción,lalongitudaxial,comounfactordeescalaparaELP(fórmulasteóricasde
2ªgeneración)(13).Enlospacientesconunalongitudaxial10%superioralanormal
(>23.45mm),aumentaba laELPenun10%.Posteriormente, el valorpromediode
ELPfueaumentadoa4.5mmporqueel implantede la lente intraocularseprefería
hacer en el sulcus, aproximadamente 0.5mmmás que el plano del iris, y además
había que tener en cuenta que muchas lentes eran convexo-planas, con formas
similares a la de las lentes de apoyo iridiano. El promedio de ELP en 1996 se
incrementóa5.25mm.Esteaumentodedistanciasediopordosrazones:lamayoría
delosimplantesdelentesintraoculareseranbiconvexos,desplazándosemáselplano
principaldelalentedentrodelojo,ylalocalizacióndeseadadelalenteenlacápsula
era0.25mmmayorqueensulcus(35).
Actualmente,hayfuertesindiciosdequelaACDpostoperatoriasecorrelaciona
positivamenteconlalongitudaxial(4).Cuandoenunmodelodecálculodepotenciade
lenteintraocularsedejabafijoelvalordelaACD,seobservabaquelamedidadeACD
era demasiado corta cuando semedía en ojos largos ymuy grandes comparado a
cuandose tratabadeojoscortos.Comoconsecuencia,seproducíaunerrormiópico
en ojos cortos y un error hipermetrópico en ojos largos. Para evitar este efecto, la
predicción de la ACD postoperatoria debía de alguna manera corregir la longitud
axial.
Hoyendía,laestimacióndelaposiciónefectivadelalenteELPestábasadaen
las observaciones de las asociaciones estadísticas entre varias medidas
preoperatoriasdelojoydelaposiciónefectivadeACD.Porlotanto,laestimaciónde
laELPsiguesiendoelverdaderocontenidoempíricodecadafórmuladecálculodela
lenteintraocularylosmodelosdiferentesqueseutilizanpararealizarelcálculodela
PIOLsonlacausadeladiferenciaenlaprecisión.
Capítulo1
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35
1.b.3.Potenciacorneal.
Elcálculodelvalorexactodelapotenciacornealesunparámetroclaveparala
obtencióndelaPIOL,además,talycomosehacomentadoanteriormente,lasfórmulas
de3ªy4ªgeneraciónutilizanlaPcparapredecirlaposiciónefectivadelalente(ELP).
Hoyendía, todavía seutiliza lapotenciade la córneamedidaapartirdeun índice
queratométrico,denominadapotenciacornealqueratométrica(Pk).Sinembargo,son
numerosos losautoresquehandemostrado loserroresqueseproducencuandose
utilizalamedidadelapotenciacornealqueratométrica(4,34,36–51).
Lascarasanterioryposteriordelacórneacontribuyenalapotenciatotaldela
córnea. Sin embargo, en el cálculo de la potencia corneal utilizando un índice
queratométrico,tansóloseconsideraelradiodelacaraanteriordelacórnea(r1c).El
índice queratométrico (nk) proviene de la adopción de unmodelo simple, con una
sola superficie de refracción y omitiendo la caraposterior de la córnea, y su valor
varía dependiendo del queratómetro(36,50). Los más comunes son: 1.3375, (Haag-
Streit,Bausch&Lomb),1.336(AmericanOptical),1.333y1.332(Zeiss).
Enel cálculode laPIOL, las razonesque llevaronaseleccionarunnkparticular
fueronvarias.Olsen(37)optóporelvalor1.3315,yaqueobtuvolosmejoresresultados
paraelcálculodelaPIOL.BinkhorstyHolladayeligieronelvalorde4/3(1.333)como
elnk normalizado en sus fórmulas de cálculo dePIOL (fórmula de Binkhorst II y la
fórmula Holladay I)(34,36). La fórmula SRK/T utiliza 1.333 como el índice
queratométrico estandarizado(21). La fórmula Hoffer Q(17) no designó un índice
queratométrico específico si no que utilizaba el valor de Pk medido por el
queratómetro, por tanto, el índice real queratométrico utilizado depende del
queratómetro que utilizara el clínico. Actualmente se dispone de nuevos
instrumentos como el sistema Pentacam® (Pentacam system, Oculus Optikgeräte),
Sirius(CSO)yOrbscanII(Orbscamsystem,Bausch&Lomb), loscualespuedenmedir
losradiosanterioresyposterioresdelacórneay,portanto,puedenaportarunvalor
de la potencia corneal basada en sus dos superficies. De todos modos, también
ofrecenlaposibilidaddeutilizarunapotenciacornealqueratométricacalculadacon
elíndicequeratométrico1.3375,lacualsiguesiendomuyutilizadaenlasfórmulasde
Capítulo1
Introducción
36
cálculodelaspotenciasdelaslentesintraoculares.
1.c.Antecedentesyestadoactualdeltema
Alolargodelahistoria,sehaobservadounaclaratendenciaasobrestimarla
potenciacorneal(Pc)cuandoseusaelvalordeuníndicequeratométrico(nk)parasu
cálculo(37,39–46),peroestatendenciavaríaentreindividuoseinclusoenlamayoríade
losestudiosquecomparan lapotenciacornealobtenidamedianteunqueratómetro
(Pk) y la potencia obtenida teniendo en cuenta las dos superficies corneales
considerando la óptica gaussiana (𝑃!!"#$$). Muchos de estos estudios comparativos
utilizanelmodelodeojodeGullstrandpararealizarestoscálculos.Porejemplo,Hoet
al.(44) comparando ojos derechos de 114 hombres y 107 mujeres calcularon la
potenciacornealGaussiana(denominadaPactual)basadaenelmodelodeojo teórico
de Gullstrand, la potencia corneal usando el índice queratométrico de 1.3315
(denominado PGullstrand) y la potencia corneal con índice queratométrico de 1.3375
(quedenominaronPconv).Encontraronqueladiferenciadepotenciacornealentrela
PactualylaPGullstrandvariabademedia0.43±0.23D,fluctuandoentre-0.64y+1.27D,y
ladiferenciaentrelaPactualylaPconvvariabademedia1.21±0.24D,oscilandoentre
+0.17y+1.99D.Enotroestudiosimilar,Shammasetal(45)con32ojosnormales(con
una media de r1c = 7.76 mm) y usando solamente nk = 1.3375, encontraron una
sobrestimación de la potencia corneal queratométrica en comparación con la
𝑃!!"#$$ basadaenelmodelodeojodeGullstrand,conunadiferenciamediade-1.17±
0.71 D (rango de -2.95 a +0.03 D). Fam et al(39) realizaron el mismo estudio que
Shammas et al(45) pero con una población distinta, obteniendo un rango de
diferenciasquevariabaentre-1.29y+0.49D.
Unfactorqueexplicaestavariabilidadentreautoreseslasuposiciónerrónea
dequelasuperficieanterioryposteriordelacórneatieneunarelaciónlineal(39,40).La
relaciónentreelradiodelacaraanterior(r1c)yposterior(r2c)delacórnea(k=r1c/r2c)
no es constante para el rango de curvatura de un ojo sano. De hecho, se ha
encontrado que el valor de k en población normal puede variar entre 1.157 y
1.295(47–50).
Capítulo1
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37
Conelfindeminimizarloserroresdecálculodelapotenciacornealdebidoal
uso de índices queratométricos, varios autores con diferentes técnicas han
recalculadoelvalordel índicequeratométrico. En1992,Dunneetal(51)observando
80 ojos sanos propusieron un valor de nk de 1.3283, con un rango asociado entre
1.3251 y 1.3305. Gobbi et al(43) hallaron un valor de nk de 1.3241 a partir de 20
córneas humanas normales. Dubbelman et al(52) con el estudio de 114 ojos
propusieronunvalormediodenkde1.329±0.001,Tangetal.(46)evaluando32ojos
obtuvieronunvalorde1.3278,FamyLim(39)en2429sujetosdescribieronunvalor
de nk= 1.3273 ± 0.0013, en un rango comprendido entre 1.3248 y 1.3298. Mas
recientementeHoetal.(44)enunestudiocon221ojosnormalesrealizadoenelaño
2008 obtuvieron una media calculada de nk de 1.328 ± 0.0018, con un rango de
1.3209a1.3363.Estosautoresdeterminaronquelosdiferentesvaloresdenkquese
obteníanvariabanenfuncióndeláreadecórneaanalizada:1.3278±0.0027,1.3284±
0.0021,1.3284±0.0031,1.3280±0.0038y1.3277±0.0042paraunamedidacentral
delacórneade3.0,5.0,6.0,7.0,y7.5mmrespectivamente.Shammasetal.(45)enun
artículopublicadoenelaño2009,sugirieronqueenrealidadelíndicederefracción
efectivoestabamascercade1.329quede1.3315usadoenalgunosqueratómetros.
Por tanto, sehandescritodiferentes enfoquesdenk condiscrepancias importantes
entre ellos. Estas discrepancias pueden deberse a los diferentes estudios entre los
aparatos utilizados en la medición del radio anterior corneal, del área de córnea
analizada,delmodelodeojousadoparaloscálculosydelapoblaciónevaluada(edad
yrefracción).
Elprimertrabajopublicadoenlalíneadeinvestigaciónalacualperteneceesta
tesis,Campsetal.(53)determinaronlasdiferenciasexistentesentrelapotenciacorneal
medida conun índicequeratométrico (Pk) y laque seobtendría apartirde lasdos
superficiescornealespormediodelasecuacionesdeGauss(𝑃!!"#$$),demaneraque
cuando se calculaba la diferencia entre ambas potencias corneales (∆𝑃! = 𝑃! −
𝑃!!"#$$) se consideraban las posibles variaciones de k en la población normal, sin
ningúntipodepatologíanicirugíaprevia.Observandoestasdiferenciasencontraron
quelaestimaciónqueratométricaPksobrestimabaosubestimabaelpodercornealdel
modelodeGauss𝑃!!"#$$ entre-0.75Dy+1.79DparaelmodelodeojodeGullstrandy
Capítulo1
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38
enelmodelodeojodeLeGrand,entre-1.12Dy+1.47D,dependiendodelosvalores
deradioscornealestantoanteriorcomoposterior(r1cyr2c,respectivamente).Cuando
elpoderqueratométricosecalculóutilizandounnkde1.3375,elvalordeΔPcresultó
sersiemprepositivo(hasta2.50DenelmodelodeojoGullstrandyhasta2.30Denel
modelodeLeGrand),revelandolapresenciadeunasobreestimaciónsistemáticaen
elcálculodelapotenciacorneal.TambiéndemostraronqueesasdiferenciasdeΔPcse
ajustabanperfectamenteaecuacioneslinealesdependientesdelarelaciónkoauna
expresióncuadráticadependienteder2C,conloqueresultamuysencillopredecirel
valor del error cometido. Estas ecuaciones se utilizaron para calcular el error
asociado con el uso de la potencia corneal queratométrica cuando se consideraba
únicamente la primera superficie corneal. Todos estos hallazgos revelaron la
necesidaddeunmodeloprecisoparadeterminarelíndicequeratométricoapropiado
paraelcálculodelapotenciacornealqueratométricasinasumirunerrorimportante.
Dehechoencontraronquelosvaloresdenk=1.3315delmodelodeojodeGullstrand,
nk= 1.3304 del modelo de ojo de Le Grand y el valor de nk =1.3375 no eran los
adecuados para el cálculo de la potencia corneal correspondiente a una población
normalyaqueloserrorescometidos(∆Pc)eransuperioresa0.5Denlamayoríade
loscasosanalizados.
Debido a todas las discrepancias encontradas entre los diversos autores(39,43–
46,51,52), Camps et al.(53) propusieron dos opciones para la selección del nk más
apropiadoparacadacaso.Laprimeraopcióneraobtenerelvalorexactodel índice
queratométrico(nkexacto)conelcualseigualabaelvalordelapotenciaqueratométrica
(Pk)yelvalordelapotenciacornealGaussiana(𝑃!!"#$$),esdecirseobteníantodoslos
posiblesvaloresdenkquecumplíanque∆𝑃! = 𝑃! − 𝑃!!"#$$=0,enfuncióndetodoslos
posiblesvaloresquepudierantomarr1cyr2c.Sinembargo,estemétodonosepodría
aplicar clínicamente si no se conocía el valor exacto de los radios de las dos
superficies corneales. La segunda opción era obtener el valor de un índice
queratométricoajustado (nkadj).Estemétodoeramás rápidoy fácildeaplicaren la
práctica clínica porque solo era necesario conocer el valor de r1c para realizar su
cálculo.Paracalcularelvalordenkadjsedesarrollóunalgoritmoparaelmodelodeojo
teóricodeGullstrandyLeGrand,válidoparaunrangodevaloresdecaraanteriory
Capítulo1
Introducción
39
posterior pertenecientes a una población normal sin ninguna patología ni cirugía
previa.
A lo largo de la historia han existido una gran variedad de autores que han
determinado el radio anterior corneal en ojos normales, no patológicos(39,44,45,47,50,51,54–72).Analizandotodosestosestudiosseestablecieronunrangonormal
para la cara anterior de la córnea entre 7.00 y 8.50 mm, siendo este rango
independiente del instrumento demedida, la edad, la refracción y el sexo. Para la
medida de la curvatura de la cara posterior se analizaron diferentes estudios
realizados por el sistema Pentacam® (Pentacam system, Oculus Optikgeräte)(57)
puesto que la repetibilidad de las medidas era mayor que con otros aparatos de
medida (57). Se estableció como rango normal para el radio de la cara posterior de
córneaelintervaloentre5.5y7.00mm(53).
Con este algoritmo, se obtuvo unos valores variables denkadj entre 1.32224 y
1.33188paraelmodelodeGullstrandyentre1.32383y1.33334paraelmodelode
Le Grand. Con este valor ajustado del índice queratométrico se estimó de forma
teóricaun errormáximode0.7D en el cálculode∆Pc tomando como referencia la
potenciacornealobtenidamedianteópticagaussianaapartirde lasdossuperficies.
Además esta condición de error máximo se observó en los valores máximos y
mínimosder2cenunrangodepoblaciónnormal(5.5,5.6,6.9y7.0mm),siendopara
el resto de los casos el error inferior a 0.5 D lo cual no representa un valor
clínicamentesignificativo.Estasdosopcionesconfirmaronqueunvalorparticularde
nknoeraválidoparatodosloscasosenlosquesequieracalcularlapotenciacorneal
yportantoningunodelosvaloresaportadosenlabibliografíapodríaserválidopara
elcálculodelapotenciacornealenpoblaciónnormalcomonormageneral.
1.d.Diseñosdelentesintraocularesafáquicas
Con el avance de las nuevas tecnologías, han surgido una gran variedad de
dispositivos tales como tabletas, libros electrónicos, teléfonos inteligentes, etc, que
precisan de una visión óptima en media y corta distancia. Por esta razón, los
Capítulo1
Introducción
40
pacientesprésbitasestándemandandosolucionesque lepermitancontinuarconsu
actividaddiariaenelmanejodeestosdispositivos.
Ademásde la correcciónmediante lentes oftálmicas y lentes de contacto, se
han desarrollado diferentes opciones quirúrgicas para la corrección de la
presbicia(73), como la sustitución del cristalino por una lente intraocular. Cuando
optamos por la inserción de una lente intraocular, el ojo pasa a denominarse
pseudofáquico,elcualestácompuestopordossuperficiesrefractivas(córneaylente
intraocular), cinco medios con sus respectivos índices de refracción (aire, córnea,
humos acuoso, lente intraocular y humor vítreo) y la distancia entre las diferentes
superficies refractivas (espesor corneal, cámara anterior pseudofáquica, espesor
lenteintraocularycámaravítreapseudofáquica).
Dentrodelosdiferentestiposdelentesintraocularesafáquicasquesepueden
implantarnosvamosacentrarenelestudiode3tiposdelentesintraoculares:
1. Lentesintraocularesacomodativas
2. Lentesintraocularesmultifocalesasimétricas
3. Lentesintraocularesasféricas
1.d.1.Lenteintraocularacomodativa
Laslentesintraocularesacomodativassonlentesmonofocalesdiseñadaspara
corregir el defecto refractivo de lejos. Estas lentes pretenden imitar la acción
fisiológicadel cristalinomediante la contracciónmusculardel cuerpo ciliar,poseen
unas pequeñas bisagras oscilantes dentro del saco capsular simulando la
acomodación natural del ojo. Al cambiar de posición, la lente hace que los rayos
enfoquen a una distancia más cercana de la posición original, aunque tiene un
movimiento limitado (fig. 3). Por lo que este tipo de lente intraocular intenta
proporcionarunavisióncercana funcional,dandounavisión lejanae intermediade
alta calidad sin distorsión óptica debido a la formación de una sola imagen en
retina(74).Sonvarioslosmodelosdelentesintraocularesacomodativasdesarrolladas
como la Crystalens AT-45 (Eyeonics)(75,76), 1CU (HumanOptic)(77–80) o la Tetraflex
Capítulo1
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41
(Lenstec)(75,81).Dadoqueestosmodelospreliminaresmostrabanunavisióndecerca
limitada(75,81),sedesarrollaronnuevosmodelos,deópticadual(82)enlacuallalentese
basaenelprincipiodecontraccióndelmúsculociliarpermitiendoquelasdosópticas
se separen incrementando así el poder total de la lente intraocular, permitiendo al
pacienteenfocardecercayotrasposicionesacomodativas(83)estetipodelentesson
rígidasdepotenciafijaconunmovimientohaciadelanteyhaciaatrásconsiguiendo
asíuncambioenelplanofocaldelalente.
Figura3.MecanismodeacciónCrystalensHDTM(Bausch&Lomb)
(Fuente:www.nuevocristalino.es)
Para nuestro estudio utilizamos la lente intraocular acomodativa Crystalens
HDTM (Bausch&Lomb). Estudios relativamente recientes(84) en los que se compara
con unamonofocal estándar, concluyeron que la CrystalensHD proporcionaba una
visión aceptable en lejos, con una mejoría significativa en cerca siendo la calidad
óptica similar a la monofocal convencional. Sin embargo, también se observaron
erroresrefractivospostoperatoriosinesperados.
1.d.2.Lenteintraocularmultifocal
Este tipo de lentes son capaces de recuperar la capacidad de enfocar a
distintasdistancias(85–87).
Las lentes intraocularesmultifocalessedividenendostiposbásicossegúnel
modoconelqueconsiguenlamultifocalidad:endifractivasyrefractivas.
LEJOS INTERMEDIO CERCA
Capítulo1
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42
1. Lentes intraoculares multifocales difractivas, consiguen su capacidad
multifocal a través de una serie de anillos concéntricos que forman una red de
difracción.Esta característicaóptica tiene la capacidaddedirigir los rayosde luz a
dosfocosdistintosalmismotiempocreandodospuntosfocalesseparados,unopara
lejosyotroparacerca(fig.4.a).Estetipodelentesofrecenbuenaagudezavisualde
cerca y lejos, además de experimentar menos problemas de visión nocturna(88,89).
Variosmodeloscomerciales sehayandentrodeestegrupocomosonTecnisZM900
(AMO)yAcrySofReSTOR(AlconLab.).
2. Lentes intraocularesmultifocales refractivas, emplean un método refractivo
multizonal,esdecir, sedefinendospotencias incorporadasdentrodeanillosozonas
refractivas circulares condiferente índice de refracción (fig. 4.b). Este tipode lentes
ofrecen muy buena visión intermedia y una mayor transmisión de la luz(90) pero
puedenprovocarsíntomasdisfotópsicosrelacionadoscon lavisiónnocturna,además
deunaagudezavisualinferioralaqueofrecenlaslentesintraocularesdifractivas(91–93).
Dentro este tipo de lentes se encuentran las rotacionales simétricas compuestas de
círculosozonasconcéntricasquepermitenunavisiónde lejosydecercademanera
alternativa y las rotacionales asimétricas, compuesta de una superficie asférica y
asimétrica para visión lejana junto a una superficie de visión cercana. Una de las
característicasmásimportantesdeestaslentesesquesonlentespupilodependientesy
necesitanundiámetrodepupilamínimoparaquelaluzpuedaatravesarlasdiversas
zonasdelalente(94).Dentrodeestetipodelentesintraocularessonvarioslosmodelos
comerciales desarrollados como son Array (AMO),ReZoom NXG (AMO), LentisMplus
LS-312(OculentisGmbH).
Capítulo1
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43
Figura4a.Lenteintraocularmultifocaldifractiva
(Fuente:www.nuevocristalino.es)
Figura4b.Lenteintraocularmultifocalrefractiva
(Fuente:www.oculentis.com)
Sehademostradoquetantoconlaslentesintraocularesmultifocalesdifractivas
como refractivas se obtiene una visión de cerca eficaz, con un rendimiento visual
cercano a J3 entre el 92% y 99% de los pacientes(86,95–98). Sin embargo, existen
autores(89) que afirman que las lentes multifocales difractivas proporcionan mejor
visióncercanaencomparaciónconmodelosdelentesmultifocalesrefractivas,siendo
la distribución de potencias de lejos y cerca en las lentes multifocales difractivas
cuestionadaporalgunosexpertos(99).
Otros estudios indican una mejora en el rendimiento visual después de la
implantaciónunalentemultifocaldifractivaconbajaonuladisminucióndelacalidad
visualencomparaciónconunalenteintraocularmonofocal(5,100–103).
El tipode lente intraocularquevamosautilizarparanuestroestudioesuna
lentemultifocal refractiva de rotación asimétrica. En concreto se realizó el estudio
con la Lentis Mplus LS-312 (Oculentis GmbH), la cual presenta una zona de visión
lejanaasféricacombinadaconunazonaenformadesectorenlazonainferiordela
lenteparalavisióndecerca(fig.5).
Capítulo1
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44
Fig.5.GeometríadelalenteMplusLS-312,dondeseobservaelaumentode
curvaturadelsegmentoinferior.(Fuente:www.windsoreyeclinic.zendesk.com)
Los estudios sobre esta lente demuestran buenos resultados visuales en
visióndelejosycerca,conunasensibilidadalcontrastepostoperatoriadentrodelos
rangos fisiológicos, obteniendo además un impacto positivo en la calidad de
vida(84,85,104–110). Algunos estudios también han reportado unos buenos niveles de
visiónintermediaconestetipodelente(84,104).Sinembargo,apesardeestosestudios,
se ha demostrado un cierto nivel de variabilidad en la corrección
refractiva(84,104,105,108–110).
1.d.3.Lenteintraocularasférica
El ojo humano está compuesto de dos lentes asféricas (córnea y cristalino),
quesonlosquedeterminanengranmedidalacalidaddeimagenópticaquellegaala
retina.Lacórneacompuestapordossuperficiesprolatas,inducenaberraciónesférica
positiva (AEP) que aumenta con la edad(111). El cristalino compuesto por dos
superficiesasféricasproducenaberraciónesféricanegativa(AEN)(112).Conlaedad,la
diferencia entre la aberración esférica de la córnea y el cristalino disminuye
progresivamente,reduciendoasíelniveldecalidaddeimagenretiniana(96–98,113).Las
Capítulo1
Introducción
45
lentes intraoculares asféricas tratan de imitar el cristalino joven, con el fin de
minimizarlasaberraciones,enlaquealmenosunasuperficieópticaesasféricapara
asímejorarelcontrastedelaimagenylacalidadvisual(114,115).Laslentesasféricasse
basan en una superficie prolata (más curva en el centro y plana en la periferia)
modificada(fig.6).Estediseñoprolatopuedeincorporarseenlacaraanterior,como
eselcasodelaAMOTecnisoposteriordelalentecomoenlaAlconSN60WF.
Figura6.ComparacióndeRayosdeluzcruzandoópticasEsféricayAsférica
(Fuente:https://www.syscom.com.m)
Son numerosos los autores(114,116–124) que compararon la agudeza visual
obtenida con una lente intraocular asférica con una esférica, los cuales o no
encontrarondiferenciasentreambostiposde lentesó lascondicionesen lasquese
realizaronesasmedicionesnoeranlosuficientementeprecisasparadetectarcambios
visualesdebidoalareduccióndeaberraciónesféricaaconsecuenciadelareducción
de la asfericidad.Otros, sin embargo, observaron unamenor aberración esférica al
implantarunalenteintraocularasféricaencomparaciónconunaesférica(122,125,126).
Encuantoasensibilidadalcontrasteserefiere,existenestudios(116–118,124,127–
129) en los cuales muestran una mejoría en los resultados al utilizar una lente
intraocular asférica en comparación con una esférica. Sin embargo, otros
autores(114,121,123) no encontraron diferencias significativas entre ambos tipos de
Capítulo1
Introducción
46
lentes.Estasdiscrepanciaspuedenserdebidasalasdiferenciasenmaterialydiseño
delenteexistenteentreestudios.
El tipo de lente escogida para este estudio fue la lente monofocal asférica
LentisL-313(OculentisGmbH).
Capítulo2
HIPÓTESISYOBJETIVOS
49
2.HIPÓTESISYOBJETIVOS
2.aHipótesis
La hipótesis de trabajo de la presente tesis doctoral es la siguiente: La
optimizacióndelcálculodelapotenciadelalenteintraocular,dependiendodeltipode
lenteintraocularaimplantar,yaseamonofocal,acomodativaomultifocalmediantela
minimizacióndelerrorenelcálculodelapotenciacorneal.
2.b.Objetivos
Losobjetivosdeltrabajoparacorroborarlahipótesisplanteadayquesehan
tratadodeconseguirconlosartículossonlossiguientes:
A. Validar clínicamente en una población sana el algoritmo diseñado
paraminimizar el error cometido en la estimación de la potencia
cornealbasándonosenelusodeuníndicequeratométricoajustado
(nkadj).
B. Evaluardeformateóricaenojosnormaleslainfluenciadelerroren
el cálculode la potencia corneal en el cálculode laPIOL cuando se
utiliza un valor queratométrico nk y analizar y validar de forma
preliminarelusodeuníndicequeratométricoajustado(nkadj)enel
cálculodelapotenciadelalenteintraocular(PIOLadj).
C. Evaluar la predictibilidad de diferentes fórmulas comerciales de
cálculodelapotenciadeunalenteintraocularydelaPIOLadjenuna
lenteacomodativa.
D. Evaluar la predictibilidad de diferentes fórmulas comerciales de
cálculodelapotenciadeunalenteintraocularydelaPIOLadjenuna
lentemultifocalrefractivaderotaciónasimétrica.
E. Evaluar la predictibilidad de diferentes fórmulas comerciales de
cálculodelapotenciadeunalenteintraocularydelaPIOLadjenuna
lenteasférica.
Capítulo2
HipótesisyObjetivos
50
Acontinuaciónsedetallanlaspublicacionesincluidasenlapresentetesis,en
relaciónconcadaunodelosobjetivospropuestos:
ObjetivoA:
Clinical validation of an algorithm to correct the error in the
keratometricestimationofcornealpowerinnormaleyes.(JCataractRefractSurg)
ObjetivoB:
MinimizingtheIOLpowererrorinducedbykeratometricpower.(Optom
VisSci)
ObjetivoC:
Positional accommodative intraocular lens power error induced by the
estimationofthecornealpowerandtheeffectivelensposition.(IndianJOphthalmol)
ObjetivoD:
Error induced by the estimation of the corneal power and the effective
lenspositionwitharotationallyasymmetricrefractivemultifocalintraocularlens.(IntJ
Ophthalmol)
ObjetivoE:
Preliminary evaluation of an algorithm to minimize the power error
selection of an aspheric intraocular lens by optimizing the estimation of the corneal
powerandtheeffectivelensposition.(IntEyeSci)
Capítulo3
MATERIALYMÉTODOS
53
3.MATERIALYMÉTODOS
3.a.CálculodelaPotenciacornealGaussiana(𝑷𝒄𝑮𝒂𝒖𝒔𝒔)yqueratométrica(Pk)
La córnea es un tejido que permite que la luz se refracte y se transmita. Su
formaconsistebásicamenteenunalentecóncavo-convexaconunacaraanterior,en
contactoíntimoconlapelículalagrimalprecornealyotracaraposterior,bañadapor
elhumoracuoso.Elpoderdióptricototaldelacórneasesitúaentre42.0y42.5Dy
representa aproximadamente el 70% del poder dióptrico del ojo por lo que es un
elementoesencialparaelcálculodelapotenciadelalenteintraocular.Elpoderdela
córneasepuedecalcularmedianteópticagaussiana,enlaaproximaciónparaxialdela
siguientemanera:
𝑃!!"#$$ = 𝑃!! + 𝑃!! − 𝛿𝑃!!𝑃!! =!!!!!!!!
+ !!!!!!!!!
− !!!!∙ !!!!!
!!!∙ !!!!!!
!!![27]
donde𝑃!!"#$$eslapotenciatotaldelacórneaobtenidaporelmétododeGauss,
P1ceslapotenciadelacaraanteriordelacórnea,P2clapotenciadelacaraposterior
delacórnea,r1celradioanteriorcorneal,r2celradioposteriorcorneal,naelíndicede
refraccióndelaire,ncel índicederefraccióndelacórnea,nhael índicederefracción
delhumoracuosoyecelespesorcorneal.
Para nuestros estudios siempre hemos considerado los parámetros
correspondientesalmodelodeojoteóricodeGullstrandydeLeGrand(vertabla5).
Tabla5.ParámetrosocularesparalosmodelosdeojosteóricosdeLeGrandyGullstrand
na nc nha nhv
ec
(mm)
r1c
(mm)
r2c
(mm)k nk
AL
(mm)
ACD
(mm)
LeGrand 1 1.3771 1.3374 1.336 0.55 7.80 6.50 1.20 1.3304 24.197 3.05
Gullstrand 1 1.376 1.336 1.366 0.50 7.70 6.80 1.132 1.3315 24.385 3.10
Capítulo3
MaterialyMétodos
54
La medida de la potencia queratométrica (Pk) nos viene definida por la
siguienteecuación:
𝑃! =!!!!!!!
[28]
Dondenkeselvalordelíndicequeratométricoyr1celradiodelacaraanterior
delacórnea.
Elvalordekvienedefinidocomoelcocienteorazóndadaentreelradiodela
caraanterioryposteriordelacórnea:
𝑘 = !!!!!![29]
3.b.Diferenciasentrelapotenciacornealgaussianayqueratométrica(ΔPc)
Usandolasecuaciones[27]y[28],podemoscalcularladiferencia(ΔPc)quese
obtieneentrelamedidadelapotenciacornealmedidaconelqueratómetro(Pk)yla
Gaussiana(𝑃!!"#$$)mediantelaexpresión:
Δ𝑃! = 𝑃! − 𝑃!!"#$$ =!!!!!!!
− !!!!!!!!
+ !!!!!!!!!
− !!!!∙ !!!!!
!!!∙ !!!!!!
!!![30]
Siusamoslaecuación[29],podemosmodificarlaecuación[30]delasiguiente
manera:
Δ𝑃! = 𝑃! − 𝑃!!"#$$ =!!!!!!!
− !!!!!!!!
∙ !!!!!!!!!!
− !!!!∙ !!!!!
!!!∙ !!!!!!!!!
![31]
3.c. Obtención del índice queratométrico exacto (nkexacto) y del índice
queratométricoajustado(nkadj)
Paraelcálculodelíndicequeratométricoexactocorrespondienteaunmodelo
deojoteórico(nkexacto),sedebenigualarlasecuaciones[30]o[31]acero,conloque
obtenemoslassiguientesexpresiones:
Capítulo3
MaterialyMétodos
55
𝑛!"#$%&' =!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!![32]
o
𝑛!"#$%&' =!!!!"!!!!!!!!!!!!"!!!!!!"!!!!!!!!!!!!!"!!!!!!!!!!!!!!!
!!!!![33]
Como se ha mencionado anteriormente, nuestro grupo de investigación ha
propuestorecientementeelusodeuníndicequeratométricovariable(nkadj)(53).Este
valorseobtuvoalconsiderarparacadavalorder1cymodelodeojoteórico,elvalor
que igualaba ΔPc con los valores extremos de r2c(53). Una vez obtenidos todos los
valores de nkadj, se comprobó que todos los valores de nkadj se ajustaban
perfectamenteaunaecuaciónlineal(R2:0.99)
ModeloGullstrand:𝑛!"#$ = −0.0064286𝑟!! + 1.37688[34]
ModeloLeGrand:𝑛!"#$ = −0.0063804𝑟!! + 1.37806[35]
Donder1cestáexpresadoenmm.
Medianteestealgoritmo,definimosunanuevapotenciacornealqueratométrica,
denominada potencia corneal queratométrica ajustada (Pkadj), la cual puede ser
calculadaapartirdelaecuación28utilizandocomoíndicequeratométricoelvalorde
nkadjobtenidomediantelasecuaciones[34]y[35].
Los datos clínicos del valor de los parámetros relacionados con la córnea se
obtuvieronconelsistemaPentacam®.Además,seutilizólaTrueNetPower(explicada
endetalleenelapartado3.h)quenosproporcionaelvalorde lapotenciacorneala
partir del valor de los radios corneales de la primera y segunda cara de la córnea,
despreciandoelespesorcornealytomandoparaelcálculodelaspotenciascorneales
decadacaralosvaloresproporcionadosporelmodelodeojoteóricodeGullstrand.
Portanto,paranuestroestudioclínicoseutilizólaecuacióndenkadjcorrespondiente
almodelodeojoteóricodeGullstrand[ec.34].
Capítulo3
MaterialyMétodos
56
3.d. Obtención de la potencia de la lente intraocular queratométrica (𝑷𝑰𝑶𝑳𝒌 ) y
Gaussiana(𝑷𝑰𝑶𝑳𝑮𝒂𝒖𝒔𝒔)
Comosehamencionadoanteriormente, lagranmayoríadefórmulasteóricas
existentes para el cálculo de la potencia de una lente intraocular, se basan en el
modelodeojosimplificadoenel cual seconsideraelojocomounsistema formado
porundioptrioesféricoyunalenteplanacorrespondientesalacórneayalcristalino
respectivamenteycuyafocalimagendelsistemacorrespondealaretina(2,4).
Siguiendo el esquema de la figura 7, se puede calcular fácilmente el valor
correspondiente a la potencia de la lente intraocular que sustituye al cristalino
mediantelaecuacióndeGaussparaópticaparaxialsuponiendoquesequieredejaral
paciente con una refracción deseada (Rdes). Este esquema presenta una serie de
limitaciones claras, puesto que realmente la córnea y el cristalino tienen espesor y
ademáslaópticaparaxialsoloesválidaparaángulospequeños.
Figura7.Modelodeojosimplificado
Enelesquemadelafigura,ACDeslaprofundidaddelacámaraanterior,AL
longitudtotaldelojo,O1objetosituadoenelpuntoremotodeseado(prdes),Selvértice
Córnea IOL
Retina
O´1=O2
prdes
Hc = H´c HIOL = H´IOL
O´2
ACD
AL
nhv
S
nha
O1
Capítulo3
MaterialyMétodos
57
delacórnea,Hc=H´closplanosprincipalesdelacórnea,nhaelíndicedelhumor
acuoso,IOLlalenteintraocular,nhvelíndicedelhumorvítreoyHIOL=H´IOLlosplanos
principalesdelalenteintraocular,O´1=O2imagendadaporlacórnea,O´2imagen
finalformadaenretina.
BasándonosenesteesquemasepuedeobtenermedianteelmétododeGauss,la
fórmulaquedeterminalapotenciadelalenteintraocular:
𝑃!"# =!!!
!"!!"#− !!!
!!!!!"#!!!
!!"# [36]
Donde:PIOLeslapotenciadelalenteintraocular,nhvelíndicederefraccióndelhumor
vítreo, nha el índice de refracción del humor acuoso, AL la longitud axial, Rdes la
refracción deseada, Pc la potencia corneal y ELP la posición efectiva de la lente
(ELP=ACD).
Estafórmulaestáexpresadaenfuncióndelaposiciónefectivadelalente(ELP)
en lugar de la profundidad de la cámara anterior (ACD), esto es debido a que es
preferiblehablarde laposiciónqueadopta la lentecuandose implantaenelojoen
lugar de hablar de profundidad de cámara anterior (ya que dependiendo del lugar
dondeseimplantelalenteintraocular,elvalordeELPserádiferente).
Comosehamencionadoenelapartado3.a,vamosaconsiderarquelapotencia
cornealpuedemedirsea travésdeunqueratómetro (Pk)oporelmétododeGauss
(𝑃!!"#$$). Es por esta razónquepara realizar el cálculo de la potencia de una lente
intraocular teniendo en cuenta la ec. 36, se han definido dos fórmulas de cálculo
diferentesdependiendodelapotenciacornealescogida(Pk)o(𝑃!!"#$$).
Si para la medida de la potencia corneal se utiliza Pk, la ecuación
correspondientealcálculodePIOLserá:
𝑃!"#! = !!!!"!!"#
− !!!!!!
!!"#!!!!!!!!
!!"# [37]
ysipararealizarelcálculodelapotenciacornealseutiliza𝑃!!"#$$,laecuaciónparael
cálculodelaPIOLserá:
Capítulo3
MaterialyMétodos
58
𝑃!"#!"#$$ =!!!
!"!!"#− !!!
!!!!!"#!
!!!!!!!!!
!!!!!!!!!!
!!!!!∙!!!!!!!!
∙!!!!!!!!!
!!"#[38]
Donde:nhvíndicedelhumorvítreo,ALlongitudaxial,ELPposiciónefectivadelalente,
nha índice refracción del humor acuoso, Rdes refracción deseada, nk es el índice
queratométrico, r1c radio corneal anterior, r2c radio corneal posterior, na índice
refraccióndelaire,ncíndicerefraccióndelacórneayecelespesordelacórnea.
Esimportanteseñalarqueenlasecuaciones[37]y[38]lapotenciacornealestá
referenciada desde diferentes planos debido al modelo de córnea considerado (de
unasolasuperficie[ec.37]ydedossuperficies[ec.38]).
Siutilizamoslaecuación29podemosvolverareescribirlaecuación[38]comosigue:
𝑃!"#!"#$$ =!!!
!"!!"#− !!!
!!!
!!"#!!!!!!!!!!
!!!!!!!!!!!
!!!!!∙!!!!!!!!
∙!!!!!!!!!!
!!"#[39]
La diferencia que existe entre realizar el cálculo de la PIOL con el valor de la
potencia corneal queratométrica (Pk) [ec.37] oGaussiana (𝑃!!"#$$) [ec.38]nosda la
siguienteexpresión:
Δ𝑃!"# = 𝑃!"#! − 𝑃!"#! = !!!!!!
!!"#!!!!!!!!
!!"#− !!!
!!!!!"#!
!!!!!!!!!
!!!!!!!!!!
!!!!!∙!!!!!!!!
∙!!!!!!!!!
!!"#[40]
Siintroducimoslavariablekenla[ec.40],obtenemoslasiguienteexpresión:
Δ𝑃!"# =!!!
!!!!!"#!
!!!!!!!
!!"#− !!!
!!!
!!"#!!!!!!!!!!
!!!!!!!!!!!
!!!!!∙!!!!!!!!
∙!!!!!!!!!!
!!"#[41]
ElvalordeΔPIOLsecalculóparaunrangodecurvaturacornealpertenecientea
una población normal, que corresponde a un rango de curvatura corneal anterior
entre 7.0 y 8.5mm(39,44,45,52,53,64,130,131) y de cara posterior entre 5.6 y 7.0mm. Por
tanto,ennuestrosestudiosteóricos,seasumieronunosvaloresdekvariabledesde1
hasta 1.51. Además, se consideró una ELP variable entre 2 y 6 mm, acorde a la
bibliografíaencontrada(4,13,20).TambiénseoptóporunosvaloresdeRdesvariablesde
Capítulo3
MaterialyMétodos
59
0,-1.0y+1.0D.
Mediante la ecuación 36 podemos explicar y entender las primeras fórmulas
que aparecieron para el cálculo de potencia de lentes intraoculares denominadas
fórmulas de primera generación. Por ejemplo, Van der Heijde(10) introdujo esta
fórmulaparalarealizacióndelcálculodelapotenciadelalenteintraocularenelcaso
de cataratas y suponiendo que el paciente quedaba emetropizado. La fórmula era
idéntica a la ecuación 36, donde sustituyó nha=nhv=1.336, las multiplicó por 1000,
consideróquelaRdes=0ylaACDpasóallamarseACDpost.Enelcasodelasfórmulasde
segunda generación, realmente son desarrollos en serie de Taylor de la ecuación
teórica 36 hasta el primer orden en función de AL y Pc, entorno a valores
determinados de AL y Pc. Por lo tanto derivan realmente de la expresión teórica
obtenidaanteriormente.
3.e.Obtencióndelapotenciadelalenteintraocularajustada(PIOLadj)
Siparaelcálculode lapotenciade la lente intraocular introducimoselvalorde
Pkadjobtenidomedianteelcálculodenkadjpertenecientesalosmodelosdeojoteórico
deGullstrandoLeGrand[ec.34yec.35,respectivamente]enla[ec.36],obtenemosla
siguienteexpresión:
𝑃!"#$%& =!!!
!"!!"#− !!!
!!!!!"#!!!"#$
!!"#[42]
Elvalorteóricodelapotenciadelalenteintraocularajustada(PIOLadj)secalculó
paralosdiferentestiposdelentesintraocularesestudiadasmediantelaecuación36,
usandoelvalordenkadjparalaestimacióndelapotenciacorneal(Pkadj),asícomolos
valores de nha y nhv correspondientes al modelo de ojo teórico de Gullstrand y Le
Grand(vertabla5).Paraelvalordelarefraccióndeseadaesprácticahabitualquese
pretenda dejar al paciente con una refracción determinada (Rdes) después de
implantar la lente intraocular,por loqueesmuy importantequeel clínicoconozca
bien las necesidades de su paciente. Debe saber si su paciente prefiere quedarse
miopepara así poder leer sin gafas o si por el contrario desea ser emétrope y por
Capítulo3
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60
tanto, deberá usar gafas de cerca. En algunos casos se opta por una distancia
intermedia (-1.00 D)(35) para un mejor compromiso. Para nuestro estudio,
seleccionamoselequivalenteesféricopostoperatoriomedidodesdeelvérticecorneal
(Rdes=SEpost).EstacondiciónfueelegidaparapodercomprobarsielvalordelaPIOLadj
eraintercambiableconlalenteimplantada(PIOLReal),paraelloseasumióqueelclínico
realmente quería dejar al paciente con una cierta refracción residual [ec.42]. Este
valordepotenciadelenteintraocular(PIOLadj)secomparóconelvalorrealdelalente
intraocularimplantada(PIOLReal)encadacaso.
En primer lugar, se realizó una prevalidación clínica de la PIOLadj en la cual se
obtuvo una relación de ΔPIOL con ΔPc para el rango de curvatura corneal
pertenecienteaunapoblaciónnormalsincirugíaprevia(r1crangoentre7.0y8.5mm,
r2centre5.6y7.0mm).PararealizarestacomparativaseconsideróRdes=0,siendoel
valor del índice queratométrico el propuesto para cada modelo (1.3304 y 1.3315,
paraelmodelodeLeGrandyGullstrandrespectivamente)ademásde incorporarel
valor queratométrico de 1.3375. El valor de ELP considerado en este primer
momentofueeldescritoparacadamodelo(3.05mmparaelmodelodeLeGrandy
3.10 mm para el modelo de Gullstrand, ver Tabla 5), así como un valor de ELP
variable entre 2.0 y 6.0mm, puesto que dependiendo del tipo de lente intraocular
implantadasuposiciónpuedevariar.
Acontinuación,seprocedióarealizarunavalidaciónclínicaprevia.Enestecaso,
se comparó la PIOLadj con la PIOL obtenida mediante el cálculo de cuatro fórmulas
comerciales como la fórmula de Haigis (PIOLHaigis) [ec. 26], fórmula de Hoffer Q
(PIOLHofferQ) [ec. 23], fórmula SRK/T (PIOLSRK/T) [ec. 22] y fórmula de Holladay I
(PIOLHolladay) [ec.21], en las que se consideró para cada paciente el valor de ELP
definidoparacadafórmulayRdes=SEpost.
En los estudios donde se utilizaron datos de lentes reales, para realizar las
comparativas entre la potencia real implanta (PIOLReal) en cada tipo de lente
intraocular analizada y la potencia ajustada (PIOLadj) obtenida mediante nuestro
algoritmo, se procedió a calcular el valor de laPIOLadj utilizando el valor de laELP
siguiendo las directrices de la fórmula SRK/T (a la que se le denominóPIOLadjSRK/T),
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61
debido a la elección en todos los casos por parte del clínico del valor de la PIOL
obtenidamedianteelIOLMaster®correspondientealaobtenidamediantelafórmula
SRK/T. También se desarrolló un nuevo método de cálculo de ELP usando una
expresiónmatemáticaobtenidamedianteregresiónmúltiple(alaqueseledenominó
ELPadj)enlaqueseexplicarádetalladamenteenelsiguienteapartado.Estosvalores
dePIOLsecompararonconlasfórmulascomercialesdeHofferQ,HaigisyHolladayI,
en las cuales se consideró el valor de ELP definido para cada fórmula, siendo
Rdes=SEpost.
3.f.EstimaciónELPadj
Sondiversas lasposibles fuentesdeerrorpara la realizacióndel cálculode la
potencia deuna lente intraocular, como son la potencia corneal, longitud axial y la
posiciónefectivadelalente.Lapotenciacornealseanalizómedianteelusodelvalor
de nkadj para minimizar el error cometido en la estimación de la potencia de la
córnea(53,132).Dadoqueestevalorsehaminimizado,otraposiblefuentedeerrorera
la obtención de la longitud axial. Puesto que la exactitud del IOLMaster® para el
cálculo de la longitud axial ha sido ampliamente demostrada(133), se consideró el
cálculodeELPcomofactorcríticoporlapresenciadeunalimitadapredictibilidaden
elcálculodeunalenteintraocular.Enlosestudiosrealizadosconlentescomerciales
setratódecalcularcuáldeberíaserelvalordelaELPexacto.Paraello,seconsideróla
ecuación 36, PIOLReal, Pkadj y la Rdes=SEpost y se obtuvo el valor de la ELP para cada
paciente. Una vez obtenidos los valores de ELP para cada paciente se realizó un
análisis de regresión múltiple de pasos hacia atrás (backwards) para obtener una
expresión matemática que relacionara la variable ELP a partir de diferentes
parámetros anatómicos y clínicos preoperatorios. Una vez obtenida la ecuación, el
valor que se obtenía para cada paciente se denominó posición efectiva de la lente
ajustada(ELPadj).EstevalordeELPadjsecomparóconotrosvaloresdeELPobtenido
conotrasfórmulasconvencionalesdecálculodeELP.
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62
3.g.Seleccióndepacientes
El criterio de inclusión en todos los estudios fueron pacientes con catarata
significativa o présbitas/pre-présbitas candidatos para la implantación de lentes
intraocularesqueexigíanunavisiónóptimaa todas lasdistancias.Comocriteriode
exclusiónseconsiderólapresenciadepatologíaocularactiva,elanalfabetismo,ojos
quehubieransidosometidosacualquierprocedimientoquirúrgicoprevio,asícomo
la presencia de astigmatismos superiores a 1.5 D. Todos los voluntarios leyeron y
firmaronpreviamenteunconsentimiento informadoacordecon loestablecidoen la
DeclaracióndeHelsinki,quefueaprobadoporelcomitédeéticalocal.
3.h.Protocolodeexamendelospacientes
Entodosloscasosserealizóunexamenoftalmológicocompletoenlosquese
incluíanlarefracción,lamejoragudezavisualcorregida(BCVA),biomicroscopíacon
lámpara, tonometría de Goldman, evaluación del fondo de ojo y un análisis de la
estructura corneal por medio de una fotografía basada en la tomografía de
Scheimpflug, conel sistemaOculusPentacam®(OculusOptikgeräteGmbH,Germany).
Enconcreto,losdatosdelosparámetrosrecogidosyanalizadosfueron:radiocorneal
delacaraanterior(r1c)yposterior(r2c)pertenecientealos3mmdeáreacentraldela
córnea,elastigmatismocornealanterior(ACA)yposterior(ACP)enlos3mmdeárea
central de la córnea, la potencia corneal real calculada teniendo en cuenta la cara
posterior de la córnea denominada “true net power”, la profundidad de la cámara
anterior(ACD)yelespesorcorneal(ec).
3.i.SistemaPentacam
ElOculusPentacam® esunsistemano invasivopara lamedidaycaracterización
delsegmentoanteriorutilizandounacámararotatoriadeScheimpflug(64,134)figura(8).
Capítulo3
MaterialyMétodos
63
A
B
C
Figura8.SistemadetopografíacornealPentacam®.A:Pantallavisualizacióndedatos.B.BasedelfuncionamientodelsistemaPentacam®medianteproyección/reflexiónencórnea.C.Montajedispositivo
Pentacam®(Fuente:www.pentacam.com)
El procedimiento de examen rotatorio genera imágenes Scheimpflug
tridimensionalesatiemporealdelsegmentoanteriorocular,conunamatrizdepunto
demallafinaenelcentrodebidoalarotación.Serecogenuntotalde100imágenes
con500puntos demedidade la cara anterior y posterior de la córnea durante un
movimientorotatoriode360º.Losdatosdeelevaciónobtenidosdecada imagense
combinan con el fin de generar una reconstrucción tridimensional de la estructura
corneal(135). Este sistema necesita unmáximo de 2 segundos en tomar una imagen
completadelacaraanteriordelojo.Cualquiermovimientodelojoserácaptadopor
una segunda cámara y se corregirá durante el proceso de examen. El Oculus
Pentacam® calcula un modelo tridimensional de la cara anterior del ojo con un
examenrealdehasta25.000puntosdeelevación.LasimágenesScheimpflugtomadas
durante el examen son digitalizadas en una unidad y todas esas imágenes son
transferidasalordenador.Elsoftwarenosproporcionaunagrancantidaddemapas
de códigos de colores, una variedad de parámetros geométricos de la superficie
Capítulo3
MaterialyMétodos
64
anterior y posterior, un análisis aberrométrico así comomedidas volumétricas de
espesores.ElOculusPentacam®mide lasdos superficiesde la córneayusa losdos
mapas de curvatura para calcular el mapa de potencia real (true net power). Los
valores refractivosde la caraanteriorde la córnease calculanusando ladiferencia
entreelíndicederefraccióndelaire(n=1),elíndicederefraccióndeltejidocorneal
(n=1.376) y el índice de refracción del humor acuoso (n=1.336). Los valores
refractivosmostrados en elmapa de la true net power se obtienen a partir de las
potenciascornealesdelaprimeraysegundacaradespreciandoelespesorcorneal.La
expresiónutilizadaeslasiguiente(135):
𝑇𝑟𝑢𝑒𝑁𝑒𝑡𝑃𝑜𝑤𝑒𝑟 = !.!"#!!!!!
×1000+ !.!!"!!.!"#!!!
𝑥1000 [43]
Para la toma demedidas en todos los casos se ha utilizado el software del
OculusPentacam®versión1.14r01.
3.j.Lentesintraocularesutilizadasenlosestudios
Para laelaboracióndelArtículo3, seutilizó la lenteCrystalensHD(Bausch&
Lomb)(fig.9),unalentecondiseñobiconvexo.Estalenteesdesiliconabiocompatible
de tercera generación (Biosil) con un índice de refracción de 1.427. Tiene una
modificaciónbi-asféricaenlazonacentralparaaumentarlaprofundidaddefocoyasí
proporcionarunamejorvisiónenlazonaintermediaycerca.Estádisponibleendos
tamañosdependiendodelapotencianecesaria,elmodelode12.0mm(HD520)para
potenciascomprendidasentre10.00y16.75Dyelmodelode11.5mm(HD500)para
potenciascomprendidasentre17.00y33.00D.Segúnlasindicacionesdelfabricante,
lalenteintraoculartieneundoblemecanismoparamejorarlafunciónvisualdecerca:
movimiento axial como consecuencia del musculo ciliar y variación del radio de
curvaturadelasuperficieanteriordelalenteintraocular(arqueamientoóptico)(136).
Capítulo3
MaterialyMétodos
65
Figura9.CrystalensHD500(Bausch&Lomb)
(Fuente:www.eyepress.ru)
ParaelArtículo4,seutilizólaLentisMplusLS-312(OculentisGmbH)lacuales
una lente multifocal refractiva de rotación asimétrica compuesta por una zona de
visiónde lejosasféricacombinadaconunazonade3.00D(quesecorrespondecon
+2.50Denelplanodegafa)(109)enformadesectorparavisióndecercaparapermitir
latransiciónentrezonas.Compuestadeuncopolímeroacrílicoconcomponentesde
filtrado UV y con una superficie hidrofóbica. Tiene un diseño biconvexo con una
ópticade6.0mm, conuna longitud totalde11.0mmyundiseñodehápticosde0
grados.Disponibleenunrangodepotenciasde-10.00a-1.00D(enpasosde1.0D)y
entre0.00y+36.00D(enpasosde0.5D).
Figura10.LentisMplusLS-312(OculentisGmbH)
(Fuente:www.nuevocristalino.es)
Capítulo3
MaterialyMétodos
66
EnelArticulo5,seestudiólaLentisL-313(OculentisGmbH).Unalentedeuna
solapiezaacrílica(copolímerodeHydroSmart)conunasuperficiehidrofóbicayfiltro
ultravioleta.Tieneundiseñobiconvexoconunaópticade6.0mm,unalongitudtotal
de11.0mmyundiseñodehápticosde0grados.Lasuperficieposteriorde lalente
intraoculares asférica y proporciona un nivel negativo de aberración esférica para
compensarlaaberraciónesféricapositivadelacórnea.Estádisponibleenpotencias
de -10.00a+35.00Denpasosde1.00Dyde+10.50a+29.50Denpasosde0.50
D(137).
Figura1.LentisL-313(OculentisGmbH)
(Fuente:www.nuevocristalino.es)
3.k.Técnicaquirúrgica
Todaslascirugíasfueronrealizadasporunacirujanaexperimentada(MLR).En
todaslasintervencionesseusóunatécnicaestándardefacoemulsificación,enlosque
seadministróanestesiatópicaydilataciónpupilarinducidaconunacombinaciónde
tropicamida y fenilefrina al 10% cada 15 minutos, media hora antes de la
intervención.Diezminutosantesdelaoperaciónseinstiló5%desoluciónyodada.Se
realizóunaclaraincisiónde2.75mmconunacuchilladediamanteenelmeridiano
mayorparaminimizar el astigmatismopostquirúrgico. Se creóunaparacentesis en
sentido horario de 60-90º desde la incisión principal y donde el compartimiento
anteriorestaballenodematerialviscoelástico.Despuésdelaextraccióndelcristalino
lalenteintraocularseimplantóatravésdelaincisiónenelsacocapsularutilizando
Capítulo3
MaterialyMétodos
67
un inyector específico para cada tipo de lente. Finalmente la cirujana procedió a
recuperarelmaterialviscoelásticoutilizandoelsistemade irrigacióndeaspiración.
Se prescribieron una combinación de esteroides tópicos y antibióticos (Tobradex,
Alcon, Fort Worth, TX, USA) así como un antiinflamatorio no esteroideo en gotas
(Dicloabak, Laboratorios Thea, Barcelona, España) para aplicar cuatro veces al día
duranteunasemanadespuésde lacirugíay tresvecesaldíaen lasegundasemana
postoperatoria. Además, las gotas antiinflamatorias no esteroideas también fueron
prescritasparaaplicartresvecesaldíadurante2semanasmásdespuésdelacirugía.
3.l.Examenpreypostoperatorio
Previamente,serealizóunexamenoftalmológicocompletoenelqueseincluía
unaevaluacióndelestadorefractivo,tomadeagudezasvisualestantodelejoscomo
de cerca, un examen con lámpara de hendidura, biometría óptica (IOL-Master,Carl
ZeissMeditec, Jena,Alemania), tonometría deGoldman y fundoscopia. Las agudezas
visualesenvisióndelejos(a4m)yvisióncercana(a40cm)seevaluaronmediante
lascartasETDRS.Postoperatoriamente,lospacientesfueronevaluadosdespuésde1
día,1semana,1mesy3mesesdelacirugía.Entodaslasvisitas,seevaluólaagudeza
visual,larefracciónylaintegridaddelsegmentoanterior.Lafundoscopiatambiénse
realizóenlarevisiónpostoperatoriadelos3meses.
3.m.Análisisestadístico
El análisis estadísticoen los artículos1 a3 se realizómedianteelprograma
SPSSversión19.0paraWindows(IBM,Amonk,NY,USA),enelcasodelosartículos4y
5 se utilizó el programa SPSS versión 21.0.0.0 paraMac (IBM, Amonk, NY, USA). La
normalidad de las variables fue evaluadamediante el testKolmogorov-Smirnov, se
utilizóunniveldeconfianzadel95%yniveldesignificancia(α)del5%.Seconsideró
quelosdatosseguíanunadistribuciónnormalenaquelloscasosenlosqueelp-valor
erasuperiora0.05.
Para comparar los distintos valores de las PIOL obtenidos se utilizó el test
estadístico t-Student para datos pareados en el supuesto de que se cumpliera la
Capítulo3
MaterialyMétodos
68
condición de normalidad, en caso contrario se utilizó el test de los rangos de
Wilcoxon. En cualquiera de losmétodos utilizados para contrastar las variables se
aceptóquenoexistíandiferenciasestadísticamente significativasentre lasmedidas
cuandoseobtuvounp-valor>0.05.
Para evaluar la intercambiabilidad entre métodos analizados se realizó un
análisis Bland Altman, en el que se muestran las diferencias entre los métodos
evaluados frente a la media de los mismos. Los límites de acuerdo (LoA) vienen
definidoscomolamedia±1.96ladesviaciónestándar(SD)delasdiferencias.
Se valoró la presencia de correlaciones entre distintos tipos de variables
mediantes los coeficientes de Pearson o Spearman, dependiendo si la condición de
normalidadsecumplíaonorespectivamente.
También se realizó un análisis de regresión múltiple de pasos hacia atrás
(backwards) para obtener una expresión matemática que relacionara la variable
ELPadj a partir de diferentes parámetros anatómicos y clínicos preoperativos. Para
evaluarlaslimitacionesdelmodelomatemáticoobtenido,seanalizólanormalidadde
los residuosnoestandarizados (homoscedasticidad)y lasdistanciasdeCookconel
fin de detectar outliers. Además, se comprobó la ausencia de correlación entre
errores con el test de Durbin-Watson y la presencia de multicolinealidad con la
toleranciadecolinealidadyelfactordeinflacióndelavarianza(FIV).
Capítulo4
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4.RESULTADOSYDISCUSIÓN
4.a.ResultadosdelostrabajosenrelaciónconelobjetivoA
Validaciónclínicadeunalgoritmoparalacorreccióndelaestimacióndel
error queratométrico de la potencia corneal en ojos normales. [Piñero DP,
CampsVJ,MateoV,Ruiz-FortesP. Clinical validationof an algorithm to correct the
errorinthekeratometricestimationofcornealpowerinnormaleyes.JCataractSurg
2012;38:1333-1338]
EnesteestudiosevalidódeformaclínicaelalgoritmodefinidoporCampset
al.(53) para la corrección del error en la estimación queratométrica de la potencia
corneal en personas con ojos sanos sin cirugía previa, basándonos en el uso de un
índice queratométrico variable (nkadj). Para ello, de acuerdo con la literatura
revisada(39,44,45,52,53,64,130,131), se consideró un rango de radio corneal anterior
pertenecienteaojossanosvariableentre7.0y8.5mm,siendoelrangoparalacara
posteriordelacórneaentre5.6y7.0mm.
Elalgoritmoutilizadoparaelestudiosecorrespondeconelmodelodeojoteóricode
Gullstrand[ec.34],conunrangodevaloresdesuperficieanterioryposteriorcorneal
pertenecientesapoblaciónnormal(53).
𝑛!"#$ = −0.0064286𝑟!! + 1.37688[34]
Este valor de nkadj se ha utilizado para realizar el cálculo de la Pkadj y así poder
comparar este valor con el obtenido por el método de Gauss(𝑃!!"#$$) . A las
diferenciasentreambasmedidasselehadesignadocomoΔPc.
Sevaloraronun totalde92ojosde92pacientes conunaedadmediade36.7
años (rango de 15 a 64 años) de los cuales 47 (51.1%) eranmujeres. Lamuestra
estabacompuestapor49ojosderechos(53.3%).Latabla6muestralosparámetrosde
losojosevaluados.
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72
Tabla6.Parámetrosocularesevaluados
Parámetro Media±SD Rango
SE(D) -2.80±3.89 -15.75a+4.00
r1c(mm) 7.67±0.01 7.19a8.43
r2c(mm) 6.30±0.21 5.87a6.82
ACA(D) 1.13±0.98 0.00a5.80
ACP(D) 0.36±0.24 0.00a1.60
𝑷𝒄𝑮𝒂𝒖𝒔𝒔 (𝑫) 42.76±1.30 38.80a45.50
Pkadj(D) 42.74±1.47 38.28a45.99
ΔPc(D) -0.02±0.22 -0.55a+0.52
ACD(mm) 3.08±0.38 2.21a4.96
ec(ìm) 559.0±33.8 485.0a665.0
Donde: SE= equivalente esférico; r1c= radio caraanterior de la córnea; r2c= radio cara
posterior de la córnea; ACA= astigmatismo anterior corneal; ACP= astigmatismo
posteriorcorneal;=potenciacornealcalculadaporelmétododeGaussparaelmodelo
de ojo de Gullstrand; Pkadj= potencia corneal queratométrica calculada con el índice
queratométricoajustado;ÄPc=diferenciaentrelapotenciacornealqueratométricayla
potencia corneal calculada por el método de Gauss; ACD=profundidad de la cámara
anterior;ec=espesorcorneal
Losprincipaleshallazgosyconsideracionessobrelosresultadosobtenidosse
exponenacontinuación:
Capítulo4
ResultadosyDiscusión
73
1. No se encontraron diferencias estadísticamente significativas entre la
potencia queratométrica ajustada (Pkadj) y la potencia corneal gaussiana
(𝑃!!"#$$) (P=.43, t-Student).Comoseobservaen la figura12, se encontró
unafuertecorrelaciónentreambasmedidasdepotenciacorneal(r=0.994,
P<.01)
Figura12.Diagramadispersióndondesemuestralarelaciónentre𝑃!!"#$$yPkadj
2. En el análisis de Band-Altman (fig.13) se obtuvo que la media de las
diferencias entre ambas medidas fue de -0.02 D, con unos límites de
concordanciainferiorde–0.46Dysuperiorde+0.42D, loscualesnoson
clínicamenterelevantes.Seaprecióunapequeña tendenciaasobrestimar
elvalordePcconelusodenkadjencórneascurvasyasubestimarsuvalor
encórneasplanas.
38,0
40,0
42,0
44,0
46,0
38,0 40,0 42,0 44,0 46,0
P kadj(D)
PcGauss(D)
Capítulo4
ResultadosyDiscusión
74
Figura13.DiagramadepuntosBlandAltmancorrespondientealasdiferenciasentrelaPkadjyla𝑃!!"#$$frentealamediadelasdiferencias
3. No se encontraron correlaciones significativas entre laΔPc (Pkadj-𝑃!!"#$$)
conlaedad(r=0.13;P=.21),equivalenteesférico(SE)(r=-0.045;P=.67),
agudeza visual con la mejor corrección (BCVA)(r = 0.04; P =.73),
profundidad de la cámara anterior (ACD) (r = -0.05; P =.64), espesor
corneal (ec) (r = -0.09; P =.41), astigmatismo corneal anterior (ACA) (r =
0.07;P=.52)yastigmatismocornealposterior(ACP)(r=0.08;P=.43).Por
contra, se observó una fuerte correlación estadísticamente significativa
entre ΔPc y el radio corneal posterior (r2c) (r = -0.96; P <.01) (fig. 14).
También se encontró una correlación estadísticamente significativa,
aunqueenmenorgrado,entrelaΔPcyelradiocornealanterior(r1c)(r=-
0.79;P<.01).
+0,42D
-0,46D-0,02D
-2,5
-1,5
-0,5
0,5
1,5
2,5
38,0 39,0 40,0 41,0 42,0 43,0 44,0 45,0 46,0 47,0
DiferenciasP
kadj-P
cGauss (D)
MediaPkadj-PcGauss(D)
Capítulo4
ResultadosyDiscusión
75
Figura14.Diagramadedispersióndondesemuestralarelacióndeladiferencia(ΔPc)entrelapotenciacornealqueratométricaajustada(Pkadj)ylapotenciacornealgaussiana(PcGauss)conelvalordelradiodelacaraposteriordelacornea(r2c)
En un estudio de simulación previo(53) realizado por nuestro grupo de
investigación, al analizar losmodelosdeojosdeGullstrandyLeGrandseencontró
quelaestimaciónqueratométricasubestimabaosobrestimabaelvalordelapotencia
corneal gaussiana, siendo este error dependiente de ambos radios corneales y por
consiguiente del cociente k(53). La sobrestimación de la potencia corneal estuvo
siemprepresenteenambosmodeloscuandoseempleóelvalordenk=1.3375.Estos
resultados(53) junto con los estudios previos(39,44,45) muestran la necesidad de un
modeloprecisoparadeterminarelvalormásapropiadodenkparacalcularelvalorde
lapotenciacornealqueratométrica.Porestarazóndesarrollamosunmétodorápido,
fácil y clínicamente aplicable para la determinación del nk más adecuado para la
estimaciónqueratométricaencadacasoconcreto(53).Paraelloseutilizóunaecuación
linealparadeterminarelvalordenk (nkadj)dependienteúnicamenteder1c.Elerror
máximocalculadoasociadoaesteenfoque(ΔPc) fuede0.70D, correspondientesa
losdosvaloresdecadaextremoder2cdefinidosparaunapoblaciónnormalysana(
5.5,5.6mmy6.9,7.0mm)paraelrestodevaloresder2c,elerrorasociadoconeluso
de nkadj se situó por debajo de 0.5 D independiente del valor r1c. Como cabía de
esperar se encontró una fuerte correlación entre Pkadj y𝑃!!"#$$(true net power),
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
5,8 6,0 6,2 6,4 6,6 6,8 7,0
ΔPc(D)
r2c(mm)
Capítulo4
ResultadosyDiscusión
76
apreciándosediferenciasnosignificativasestadísticamente(-0,02±0.22D,rangode-
0,55a0,52D),confirmándosedeestemodolaintercambiabilidaddeambosmétodos
demedidadepotenciacornealobtenidosenlosresultadosteóricosprevios(53).Enla
práctica clínica, se consideran aceptables diferencias de hasta 0,50 D entre Pkadj y
𝑃!!"#$$portanto,lasdiferenciasqueseobtuvieronnofueronclínicamenterelevantes.
ElanálisisdeBlandyAltman(138)confirmólavalidezclínicadelalgoritmodenkadj,se
apreció una pequeña tendencia a sobrestimar el valor dePc con el uso delnkadj en
córneascurvasyasubestimarsuvalorencórneasplanas,siendoelrangodeacuerdo
entre ambas medidas de potencia corneal de 0,44 D. Es decir, el 95% de las
diferenciasentrelapotenciagaussianayloscálculosqueratométricosteníanunvalor
≤0,44D.
4.2.ResultadosdelostrabajosenrelaciónconelobjetivoB
Minimizacióndelerrordelapotenciadeunalenteintraocularinducida
por la potencia queratométrica. [Camps VJ, Piñero DP, de Fez D, Mateo V.
MinimizingtheIOLpowererrorinducedbykeratometricpower.OptomVisSci.2013
Jul;90(7):639-49.]
Enesteestudioseevaluódeformateóricaenunapoblacióndeojossanosla
influencia del error en el cálculo de la potencia corneal debido al uso de un índice
queratométrico(nk)enelcálculodelapotenciadelalenteintraocular(PIOL).Además
seanalizóyvalidódeformapreliminarelusodeuníndicequeratométricoajustado
(nkadj)enelcálculodelapotenciadelalenteintraocular(PIOLadj).
Lapotencia corneal se calculó, al igualqueenel estudioanterior,paraunos
rangosdecaraanterioryposteriorcornealcorrespondientesacórneassanas,rango
deradiocornealanteriorentre7.0y8.5mm,siendoelrangoparalacaraposteriorde
lacórneaentre5.6y7.0mm[ec.37y38].Paraelvalordenkseeligieronlosvalores
correspondientes al modelo de ojo de Gullstrand(139) y Le Grand(140,141) (1.3315 y
1.3304,respectivamente)yelvalorclásicode1.3375.SeconsideróRdes=0yelvalor
deELPteóricoqueseintrodujoparaelcálculodelapotenciadelalenteintraocular
Capítulo4
ResultadosyDiscusión
77
correspondió al valor de la profundidad de cámara anterior teórica proporcionada
por los dosmodelos de ojo teórico utilizados (3.05 y 3.10 para losmodelos de Le
GrandyGullstrandrespectivamente)así comounvalordeELP variableentre2.0y
6.0mm,parasimularlasdistintasposicionesquepuedeadoptarlalenteintraocular
alserinsertada.Conlosvaloresdepotenciadelenteintraoculargaussiana(𝑃!"#!"#$$)y
queratométrica(𝑃!"#! )obtenidas,seprocedióaanalizarlarelacióndeΔPIOLrespectoa
ΔPc.
Acontinuación,seprocedióarealizarunavalidaciónclínicaprevia.Enestecaso,
se analizó en primer lugar la intercambiabilidad existente entre PIOLadj [ec 42] y
𝑃!"#!"#$$[ec 38]. Al confirmar su intercambiabilidad se procedió a comparar nuestra
PIOLadjconlaPIOLobtenidamedianteelcálculodecuatrofórmulascomercialescomo
son la fórmuladeHaigis (PIOLHaigis) [ec.26], fórmuladeHofferQ(PIOLHofferQ) [ec.23],
fórmulaSRK/T(PIOLSRK/T)[ec.22]y fórmuladeHolladayI(PIOLHolladay)[ec.21],en las
que se consideró para cada paciente el valor deELP definido para cada fórmula y
Rdes=SEpost
Los algoritmos de nkadj utilizados para este estudio clínico previo, son los
correspondientesalmodelodeGullstrandyalmodelodeLeGrandpropuestospor
nuestro grupo de investigación(53) dependientes únicamente del radio anterior
corneal[ec.34y35]
ModeloojodeGullstrand:nkadj=-0.0064286r1c+1.37688 [34]
ModeloojodeLeGrand:nkadj=-0.0063804r1c+1.37806 [35]
Estos algoritmos, se utilizaron para calcular la potencia corneal queratométrica
ajustada (Pkadj) mediante el uso de la fórmula clásica de la potencia corneal
queratométrica[ec.28].
Para la validación preliminar de la PIOL con el algoritmo propuesto en este
estudio se consideró unamuestra de ojos normales conAL entre 22.0 y 26.0mm.
Específicamenteseescogióunamuestrade81ojoscorrespondientesa81pacientes
candidatos a cirugía refractiva que fueron examinados en elHospital Internacional
Capítulo4
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Medimar (Alicante). Únicamente se escogió un ojo por paciente para realizar el
estudio.
Los principales hallazgos y consideraciones sobre los resultados obtenidos se
exponenacontinuación:
1. Secompararonlasdiferenciasteóricas(ΔPIOL)encontradasentrelamedidade
lapotenciadelalenteintraocularqueratométrica(𝑃!"#! )obtenidaapartirdela
potenciacornealqueratométrica(Pk)y lagaussiana(𝑃!"#!"#$$) obtenidapartir
delapotenciacornealgaussiana(𝑃!!"#$$).Estasdiferenciasfueronanalizadas
en función de las diferencias entre la potencia corneal queratométrica y la
gausiana (ΔPc) para un rango normal de r1c (valores de 7.0 a 8.5mm) en el
modelo de ojo de Le Grand y Gullstrand y distintos valores de nk (1.3304,
1.3315y1.3375).Comosepuedeapreciarenlatabla7,existeunatendenciaa
subestimarelvalordelaPIOLcuandoseutilizaPkenelcálculo(𝑃!"#! )enlugar
de𝑃!"#!"#$$ (ΔPIOL<0). Esta tendencia proviene de la sobreestimación de Pk
respecto a𝑃!!"#$$ en el cálculo de la potencia corneal (ΔPc>0). La mayor
sobrestimaciónhalladaseencontróenlacombinaciónder1c=7.0mmyr2c=
7.0mm con unos valores de +1.41 y +0.95D para elmodelo de LeGrand y
Gullstrand respectivamente. La mayor subestimación se situó en la
combinaciónder1c=8.5mmyr2c=5.60mm,conunosvaloresde-1.76y-2.16
DparaelmodelodeojodeLeGrandyGullstrandrespectivamente.Cuandose
usónk= 1.3375para losdosmodelos, se observóuna subestimaciónde𝑃!"#!
respecto a𝑃!"#!"#$$ . El valor máximo de subestimación se encontró en la
combinaciónder1c=8.5mmyr2c=5.60mm,conunosvaloresde-3.01y-2.77
DparaelmodelodeGullstrandyLeGrand,respectivamente.
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Tabla 7. Resumen de las diferencias obtenidas entre la potencia de la lente intraocularqueratométrica y gaussiana (ΔPIOL) obtenidos dentro de un rango de curvatura de radioanteriornormal(r1cde7.0a8.5mm)paralosmodelosdeojodeLeGrandyGullstrand,asícomoparalosdiferentesvaloresdenkutilizados(1.3304,1.3315y1.3375)
LeGrand Gullstrand
nk:1.3304 nk:1.3375 nk:1.3315 nk:1.3375
r1c(mm) ΔPc(D) ΔPIOL(D) ΔPc(D) ΔPIOL(D) ΔPc(D) ΔPIOL(D) ΔPc(D) ΔPIOL(D)
7.00 0.26;-1.12 -0.33;1.41 1.28;-0.11 -1.61;0.14 0.65;-0.75 -0.81;0.95 1.50;0.10 -1.90;-0.13
7.10 0.36;-1.03 -0.45;1.29 1.36;-0.03 -1.71;0.03 0.74;-0.66 -0.93;0.84 1.58;0.18 -1.99;-0.23
7.20 0.45;-0.93 -0.57;1.17 1.44;0.05 -1.80;-0.07 0.83;-0.57 -1.03;0.72 1.66;0.26 -2.08;-0.32
7.30 0.55;-0.84 -0.68;1.05 1.52;0.13 -1.89;-0.16 0.91;-0.49 -1.14;0.61 1.73;0.33 -2.17;-0.42
7.40 0.63;-0.75 -0.78;0.94 1.59;0.20 -1.98;-0.25 1.00;-0.40 -1.24;0.50 1.81;0.41 -2.25;-0.51
7.50 0.72;-0.67 -0.89;0.83 1.67;0.28 -2.06;-0.34 1.08;-0.32 -1.34;0.40 1.88;0.48 -2.33;-0.59
7.60 0.80;-0.59 -0.99;0.72 1.74;0.35 -2.14;-0.43 1.16;-0.24 -1.43;0.30 1.95;0.55 -2.41;-0.68
7.70 0.89;-0.50 -1.09;0.62 1.81;0.42 -2.22;-0.51 1.24;-0.17 -1.52;0.20 2.02;0.61 -2.49;-0.76
7.80 0.96;-0.42 -1.18;0.52 1.87;0.48 -2.30;-0.60 1.31;-0.09 -1.61;0.11 2.08;0.68 -2.56;-0.84
7.90 1.04;-0.35 -1.27;0.43 1.94;0.55 -2.37;-0.67 1.39;-0.02 -1.70;0.02 2.15;0.74 -2.63;-0.91
8.00 1.12;-0.27 -1.36;0.33 2.01;0.61 -2.44;-0.75 1.46;0.05 -1.78;-0.07 2.21;0.80 -2.70;-0.99
8.10 1.19;-0.20 -1.44;0.24 2.07;0.68 -2.51;-0.82 1.53;0.12 -1.86;-0.15 2.27;0.86 -2.76;-1.06
8.20 1.26;-0.13 -1.53;0.15 2.13;0.74 -2.58;-0.90 1.60;0.19 -1.94;-0.23 2.33;0.92 -2.83;-1.13
8.30 1.33;-0.06 -1.61;0.07 2.19;0.80 -2.64;-0.97 1.66;0.26 -2.01;-0.31 2.39;0.98 -2.89;-1.19
8.40 1.40;0.01 -1.69;-0.01 2.25;0.85 -2.71;-1.03 1.73;0.32 -2.09;-0.39 2.44;1.04 -2.95;-1.26
8.50 1.47;0.08 -1.76;-0.09 2.30;0.91 -2.77;-1.10 1.79;0.39 -2.16;-0.47 2.50;1.09 -3.01;-1.32
2. Seencontróque ladiferenciaΔPIOL conk(r1c/r2c),seajustabaaunaecuación
linealenfunciónder1c(vertabla8).
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Tabla8.Ecuacioneslineales(R2=0.99)deΔPIOLenrelaciónakenfunciónder1cenpasosde0.1
mmparalosmodelosdeojoteóricodeGullstrandydeLeGrand
Gullstrand LeGrand
nk=1.3315 nk=1.3375 nk=1.3304 nk=1.3375
r1c(mm) ΔPIOL(D)=ak+b ΔPIOL(D)=ak+b ΔPIOL(D)=ak+b ΔPIOL(D)=ak+b
7.00 ΔPIOL=-7.07k+8.03 ΔPIOL=-7.07k+6.94 ΔPIOL=-6.99k+8.40 ΔPIOL=-6.99k+7.12
7.10 ΔPIOL=-6.95k+7.88 ΔPIOL=-6.95k+6.82 ΔPIOL=-6.86k+8.25 ΔPIOL=-6.86k+6.99
7.20 ΔPIOL=-6.8k+7.74 ΔPIOL=-6.83k+6.70 ΔPIOL=-6.74k+8.10 ΔPIOL=-6.74k+6.87
7.30 ΔPIOL=-6.71k+7.61 ΔPIOL=-6.71k+6.58 ΔPIOL=-6.63k+7.96 ΔPIOL=-6.63k+6.75
7.40 ΔPIOL=-6.60k+7.48 ΔPIOL=-6.60k+6.47 ΔPIOL=-6.52k+7.83 ΔPIOL=-6.52k+6.63
7.50 ΔPIOL=-6.49k+7.35 ΔPIOL=-6.49k+6.36 ΔPIOL=-6.41k+7.69 ΔPIOL=-6.41k+6.52
7.60 ΔPIOL=-6.38k+7.23 ΔPIOL=-6.38k+6.25 ΔPIOL=-6.31k+7.57 ΔPIOL=-6.31k+6.41
7.70 ΔPIOL=-6.28k+7.11 ΔPIOL=-6.28k+6.15 ΔPIOL=-6.20k+7.45 ΔPIOL=-6.20k+6.31
7.80 ΔPIOL=-6.18k+7.00 ΔPIOL=-6.18k+6.05 ΔPIOL=-6.11k+7.33 ΔPIOL=-6.11k+6.21
7.90 ΔPIOL=-6.09k+6.89 ΔPIOL=-6.09k+5.95 ΔPIOL=-6.01k+7.21 ΔPIOL=-6.01k+6.11
8.00 ΔPIOL=-5.99k+6.78 ΔPIOL=-5.99k+5.86 ΔPIOL=-5.92k+7.10 ΔPIOL=-5.92k+6.02
8.10 ΔPIOL=-5.90k+6.68 ΔPIOL=-5.90k+5.77 ΔPIOL=-5.83k+6.99 ΔPIOL=-5.83k+5.92
8.20 ΔPIOL=-5.81k+6.58 ΔPIOL=-5.81k+5.68 ΔPIOL=-5.75k+6.89 ΔPIOL=-5.75k+5.83
8.30 ΔPIOL=-5.73k+6.48 ΔPIOL=-5.73k+5.60 ΔPIOL=-5.66k+6.78 ΔPIOL=-5.66k+5.75
8.40 ΔPIOL=-5.65k+6.38 ΔPIOL=-5.65k+5.52 ΔPIOL=-5.58k+6.68 ΔPIOL=-5.58k+5.66
8.50 ΔPIOL=-5.57k+6.29 ΔPIOL=-5.57k+5.44 ΔPIOL=-5.50k+6.59 ΔPIOL=-5.50k+5.58
3. Se analizó la dependencia deΔPIOLcon variaciones deELP. Los distintos
valores de ELP que se utilizaron para el estudio son: el valor de ACD
anatómica (ACDa) la cual corresponde aunos valoresde3.05 y3.10mm
paralosmodelosdeojoteóricodeLeGrandyGullstrand,respectivamente,
además de un rango de variación entre 2.0 y 6.0 mm. Con todo esto se
observó que en términos generales este valor de ELP no influyó
clínicamente en el error cometido en el cálculo de la lente intraocular,
siendo el valormáximode variaciónΔPIOL encontrado correspondiente a
un valor de ELP= 6.0 mm, no superando en ningún caso 0.48 D en
comparaciónconelvalorobtenidodeACDaparacadamodelodeojo.
4. AlcompararlosvaloresdeΔPIOLconsiderandounrangodeRdesentre-1.0y
+1.0D,siendolosdemásparámetrosconstantes,seobservóquelaRdesno
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eraun factor influyenteen laobtencióndelerrordecálculode laPIOL,ya
que las diferencias máximas que se encontraron respecto a considerar
Rdes=0fueronde0.02D.
5. Utilizandoelvalordenkadjcalculadoapartirdelasecuaciones34y35para
laobtencióndelapotenciacornealqueratométricaycalculandoelvalorde
PIOLadj, el error máximo teórico de ΔPIOL que se obtuvo fue de ± 0.9 D
medido desde el vértice corneal, independientemente delmodelo de ojo
analizado. Si consideramos que 1.0 D de variación de PIOL induce una
variacióndeaproximadamentede0.9Dmedidodesdeelvérticecorneal,se
observóqueelerrorcometidoparaelcálculodePIOLqueseobtuvoconel
valordenkadj,noexcedióde±0.6Dmedidodesdeelplanodelalenteó±
0.5 D desde el vértice corneal para un rango de r2c de 5.8 y 6.7mm. Al
utilizarlavariacióndeELP,seobservóqueparavaloresdeELP>4.0mm,
el error en el cálculo de la PIOL no excedió de ± 0.5 D medido desde el
vérticecornealenningunodeloscasos.
6. Lavalidaciónpreliminarclínica,serealizó(talycomosehacomentadoenelapartado3.e)mediantelacomparativadediferentesfórmulasdecálculo
dePIOL,talescomoSRK/T(PIOLSRK/T),Haigis(PIOLHaigis),HofferQ(PIOLHofferQ)y
Holladay (PIOLHolladay) con la obtenida con nuestro algoritmo para una
población normal (PIOLadj), siendoRdes=SEpost y ELP el definido para cada
fórmula. Se observaron diferencias clínicamente relevantes y
estadísticamentesignificativas(tabla9).SiendolafórmulaPIOLHaigislaque
presentómenosdiferenciasalcompararlaconnuestraPIOLadj (0.39±0.33
SD) y la fórmulaPIOLHofferQ la quemostró lasmayores diferencias (1.92±
0.58 SD) llegando a alcanzar diferencias de hasta 3.07 D. En todas las
comparativasseobtuvounafuertecorrelacióndeladiferenciaencontrada
conelvalordePIOLadjcalculadaconnkadj.
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Tabla 9. Resumen comparativa de análisis de PIOL obtenida con diferentes fórmulascomercialesynuestroalgoritmo
SRK/T HAIGIS HOFFER-Q HOLLADAY
Diferenciademedias conPIOLcalculadaconnkadj(SD)
1.01(0.26) 0.39(0.33) 1.92(0.58) 1.04(0.77)
p-valor <0.01 <0.01 <0.01 <0.01
CoeficientedecorrelaciónconPIOLcalculadaconnkadj
0.997 0.996 0.993 0.977
Límites de acuerdo con PIOLcalculadaconnkadj
0.50a1.52 -0.27a1.04 0.78a3.07 -0.50a2.50
7. El análisis Bland-Altmanmuestra las diferencias clínicamente relevanteshalladas (fig. 15 A a D), las cuales fueron positivas en lamayoría de los
casos,porloqueelvalordePIOLobtenidomediantenuestroalgoritmofue
mayor que el encontrado con otras fórmulas estándar de cálculo dePIOL.
Además se observaron diferencias clínicamente significativas entre las
fórmulas de cálculo comerciales analizadas en este estudio. Se encontró
quelasdiferenciasentrePIOLadjyPIOLSRK/Tsecorrelacionabaconlapotencia
cornealgaussiana(𝑃!!"#$$)(r=-0.81,p<0.01),radioposteriordelacórnea
(r2c) (r = -0.81, p < 0.01), con la diferencia entre la potencia corneal
obtenida mediante índice queratométrico ajustado y la potencia
queratométrica(nk=1.3375)(r=-0.81,p<0.01), posiciónefectivade la
lente(ELP)(r=-0.46,p<0.01)yradioanteriorcorneal(r1c)(r=-0.81,p<
0.01).UnatendenciasimilarseobservóentrePIOLadjyPIOLHaigis,siendoestas
diferenciascorrelacionadasconlapotenciacornealgaussiana(𝑃!!"#$$)(r=
-0.75,p<0.01),radioposteriorcorneal(r2c)(r=0.54,p<0.01),diferencia
entre la potencia corneal obtenida mediante índice queratométrico
ajustadoy lapotenciaqueratométrica (nk=1.3375)(r=0.75,p<0.01)y
radioanteriordelacórnear1c(r=0.75,p<0.01).
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A
B
1,04D
-0,27D0,39D
-4,0
-3,0
-2,0
-1,0
0,0
1,0
2,0
3,0
4,0
5,0 10,0 15,0 20,0 25,0 30,0
DiferenciasP
IOLadj-P
IOLHaigis(D)
MediaPIOLadj-PIOLHaigis(D)
1,52D
0,50D
1,01D
-4,0
-3,0
-2,0
-1,0
0,0
1,0
2,0
3,0
4,0
5,0 10,0 15,0 20,0 25,0 30,0
DiferenciasP
IOLadj-P
IOLSRK/T(D)
MediaPIOLadj-PIOLSRK/T(D)
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C
D
Figura15.ComparativaB-AentrelaPIOLobtenidausandolaPkadjylaobtenidautilizandolasdistintasfórmulasdecálculo.(A)diferenciasentrePIOLadjyPIOLobtenidamediantelafórmulaSRK/T(PIOLSRK/T).(B)diferenciasentrePIOLadjyPIOLobtenidamediantelafórmulaHaigis(PIOLHaigis).(C)diferenciasentrePIOLadjyPIOLobtenidamediantelafórmulaHofferQ(PIOLHofferQ).(D)diferenciasentrePIOLadjyPIOLobtenidamediantelafórmula
Holladay(PIOLHolladay)
Con los resultados obtenidos, se observó que en una simulación teórica
considerandoun rangonormalde curvatura cornealperteneciente aunapoblación
2,50D
-0,50D
1,04D
-4,0
-3,0
-2,0
-1,0
0,0
1,0
2,0
3,0
4,0
5,0 10,0 15,0 20,0 25,0 30,0DiferenciasP
IOLadJ-P
IOLHolladay(D)
MediaPIOLadj-PIOLHolladay(D)
3,07D
0,78D
1,92D
-4,0
-3,0
-2,0
-1,0
0,0
1,0
2,0
3,0
4,0
5,0 10,0 15,0 20,0 25,0
DiferenciasP
IOLadj-P
IOLHofferQ(D)
MediaPIOLadj-PIOLHofferQ(D)
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85
sana, optimizando el valor denk para el cálculo de la potencia corneal, éste puede
conducir a errores clínicamente relevantes en el cálculo de la PIOL en cirugía de
cataratas(hastade3Dsink=1.3375).Sisobrestimamoselpodercornealconelusode
un valor único de nk, esta sobrestimación nos conducirá a una subestimación del
correspondiente valor queratométrico de la potencia de la lente intraocular y
viceversa. Se encontró una ecuación cuadrática dependiente del valor de r2c y una
lineal dependiente de k para la predicción del valor de ΔPIOL. Para minimizar los
errores cometidos en las estimacionesde laPIOL debido al error en el cálculode la
potencia cornealqueratométrica, sepropusounanueva fórmulapara la estimación
de la potencia de la lente intraocular usando óptica paraxial y aproximación
queratométricateniendoencuentaunnkvariable(nkadj)deacuerdoconelalgoritmo
desarrollado(53)yvalidadoclínicamente(143)pornuestrogrupodeinvestigaciónyque
denominamospotenciade la lente intraocularajustada(PIOLadj).En lassimulaciones
teóricas, la diferencia entre la PIOLadj y la𝑃!"#!"#$$ (ΔPIOL) nunca superó las 0.90 D
medidodesdeelvérticecorneal,independientementedelmodelodeojoutilizado,del
valorder1cydelaRdes.Estemargendeerrornoresultóserclínicamentesignificativo
en la mayoría de las posibles combinaciones r1c – r2c para ojos normales y sanos.
Además,seobservóquelavariacióndeELPteníaunainfluencia,aunquemínima,en
laΔPIOL.EspecíficamentesielvalordeELPerainferioralaprofundidaddelacámara
anterior anatómica (ACDa), las diferencias entre PIOLadj y𝑃!"#!"#$$ disminuyeron y
viceversa,siendoestasdiferenciasentodos loscasos inferiora0.50D locualnoes
clínicamentesignificativo.
En la prevalidación clínica se encontraron diferencias estadísticamente
significativas entre nuestra fórmula de cálculo y otras fórmulas comerciales, tales
comoHaigis,HofferQ,HolladayySRK/T.LamáximadiferenciarespectoalaPIOLadjse
obtuvo al compararla con la fórmula de Hoffer Q (PIOLHofferQ) (1.92 ± 0.58 SD) y la
menordiferenciaconlafórmuladeHaigis(PIOLHaigis)(0.39±0.33SD).Aunqueeneste
últimocasolos intervalosdeconfianzaresultabanclínicamentesignificativos[-0.27,
1.04]D.
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4.3.ResultadosdelostrabajosenrelaciónconelobjetivoC
Error inducido en la estimación de la potencia corneal y la posición
efectivaenlapotenciadeunalenteintraocularacomodativa.[PiñeroDP,Camps
VJ, RamónML, Mateo V, Pérez-Cambordi RJ. Positional accommodative intraocular
lens power error inducedby the estimation of the corneal power and the effective
lensposition.IndJOphthal2015May;63(5):438-44]
En este estudio se evaluó la predictibilidad de la PIOLadj y de las diferentes
fórmulas de cálculo comerciales de PIOL para el cálculo de la lente acomodativa
CrystalensHD (B&L), desarrollando una fórmula predictiva de cálculo de ELP para
minimizar los errores asociados a la estimación queratométrica de la potencia
corneal.
Para la obtención de la potencia de la lente intraocular (PIOLadj) se calculó
medianteelusodelaecuacióndeGaussparaópticaparaxial(132)[ec.36].Delosdos
algoritmos para el cálculo de nk propuestos recientemente por nuestro grupo de
investigación(53), se escogió para este estudio el correspondiente al modelo de
Gullstrand[ec.34],puestoqueparalaobtencióndelapotenciadelalenteintraocular
implantada,elclínicosebasóenelvalordePcproporcionadoporelPentacam,elcual
sebasaenelmodelodeojoteóricodeGullstrandpararealizarloscálculos.
nkadj=-0.0064286r1c+1.37688 [34]
Con el uso de este algoritmo se calculó el valor de la potencia corneal
queratométrica (Pkadj) [ec. 28], con el uso de nkadj y los valores de nha y nhv
correspondientesalmodelodeojodeGullstrand(1.336paraambosíndices).Parael
equivalenteesférico, sepensóqueel clínicoqueríadejar alpaciente conuna cierta
refracción residual, por lo cual se consideró el equivalente esférico postoperatorio
igual a la refracción deseada (SEpost= Rdes). Este valor de PIOLadj se comparó con la
PIOLReal implantada, siendo el valor de PIOLadj calculada mediante dos métodos
diferentesdecálculodeELP.EnprimerlugarsecalculóelvalordeELPmediantelas
directricesdecálculodelafórmulaSRK/T(PIOLadjSRK/T)puestoqueparalaobtención
de la lente implantada por parte del clínico, se basó en la obtenida mediante la
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fórmula SRK/T. En segundo lugar se calculó el valor de ELP mediante el uso del
algoritmoobtenidoporregresiónmúltiple(ELPadj).Talycomosehaexplicadoenel
apartadodemétodos,pararealizarestecálculo,enprimerlugarsecalculóelvalorde
ELPexactoparacadapacienteapartirdeigualarlaexpresióndelaPIOLadjalvalorde
la lente implantada (PIOLadj=PIOLReal). Con todos los valores obtenidos para cada
paciente se realizó un análisis de regresión múltiple teniendo en cuenta todas las
variables preoperatorias medidas. De todas las ecuaciones obtenidas se escogió
aquellaquepresentóausenciadecorrelaciónentreerroresmedianteeltestDurbin-
Watsonypresentóunamulticolinealidadconlatoleranciadecolinealidadyfactorde
inflación de la varianza (FIV), teniendo presente también, cual es la ecuación que
presentó mejores resultados al analizar la normalidad de los residuos no
estandarizados (homocesdasticidad) y distancias de Cook. A la ecuación que se
obtuvo se le denominóELPadj y se utilizó para calcular denuevo el valor dePIOLadj.
Este valor de potencia de lente intraocular se comparó con el valor obtenido por
diversasfórmulascomercialesdecálculo,comoHaigis,HofferQyHolladay,siendoel
valordeELPeldefinidoparacadafórmulaylaRdes=SEpost..
Sevaloraronuntotalde25ojosde14pacientesconunaedadmediade65.9
años (rango de 52 a 79 años) de los cuales 16 (64%) eran hombres. La muestra
estabacompuestapor13ojosizquierdos(52%).Latabla10muestralosparámetros
evaluados
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88
Tabla10.Medidasvisuales,refractivas,biométricasydatosdecálculodelaPIOL
Parámetros Media±SD RangoSEpre(D) 0.81±2.77 -5.50a5.38SEpost(D) -0.36±0.76 -3.13a1.14r1c(mm 7.80±0.26 7.35a8.25ACD(mm) 3.27±0.30 2.63a3.84AL(mm) 23.21±0.89 21.65a25.04ELPSRK/T(mm) 5.21±0.34 4.78a6.17ELPadj(mm) 4.18±0.27 3.70a4.83ELPHaigis(mm) 5.41±0.18 5.12a5.82ELPHofferQ(mm) 5.25±0.23 4.88a5.83ELPHolladay(mm) 4.95±0.30 4.31a5.52nkadj 1.327±0.02 1.324a1.330Pk(1.3375)(D) 43.29±1.44 40.91a45.89PcHaigis(1.3315)(D) 42.52±1.42 40.18a45.07Pkadj(D) 41.91±1.61 39.25a44.82PIOLReal(D) 22.53±2.70 16.00a28.00PIOLadjSRK/T(D) 24.51±2.91 17.69a32.09PIOLadj(D) 22.53±2.79 15.86a29.07PIOLHofferQ(D) 22.94±3.14 15.43a30.89PIOLHolladay(D) 23.03±2.98 16.00a30.80PIOLHaigis(D) 24.33±3.36 16.53a33.25Donde:SEpre=equivalenteesféricopreoperatorio; SEpost= equivalenteesféricopostoperatorio; r1c= radiocara anterior de la córnea; ACD=profundidad de la cámara anterior; AL= longitud axial; ELPSRK/T=posiciónefectivade la lentecalculadamediante la fórmulaSRK/T;ELPadj=posiciónefectivade la lenteajustada; ELPHaigis= posición efectiva de la lente calculada mediante la fórmula de Haigis; ELPHofferQ=posiciónefectivadelalentecalculadamediantelafórmuladeHofferQ;ELPHolladay=posiciónefectivadelalente calculadamediante la fórmula de Holladay; nkadj= índice de refracción queratométrico ajustado;Pk(1.3375)= potencia corneal queratométrica calculada con el índice queratométrico 1.3375; PcHaigis=potenciacornealcalculadaparalafórmuladeHaigisconunvalordeíndicequeratométrico1.3315;Pkadj=potencia queratométrica calculada con el índice queratométrico ajustado; PIOLReal= potencia lenteintraocularimplantada;PIOLadjSRK/T=potencialenteintraocularcalculadaparalafórmulaSRK/T;PIOLadj=potencia lente intraocularajustada;PIOLHofferQ=potencia lente intraocularcalculadapara la fórmuladeHofferQ;PIOLHolladay=potencialenteintraocularcalculadaparalafórmuladeHolladay;PIOLHaigis=potencialenteintraocularcalculadaparalafórmuladeHaigis
Losprincipaleshallazgosyconsideracionessobrelosresultadosobtenidosseexponenacontinuación:
1. SeencontrarondiferenciasestadísticamentesignificativasentrePIOLadjSRK/T
y PIOLReal cuando se usó el valor de ELP calculado mediante la fórmula
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89
SRK/T(p<0.01,t-Student).Comoseobservaenlafigura16,seencontró
una fuerte correlación entre ambas medidas de potencia de lente
intraocular(r=0.960,P<.01)
Figura16.DiagramadedispersióndondesemuestralarelaciónentrelaPIOLadjSRK/TylaPIOLReal
2. EnelanálisisdeBand-Altman(fig.17)seobservóunasobrestimacióndel
valordePIOLSRK/TrespectoalvalordePIOLReal(r=0.960;P<0.01).Lamedia
delasdiferenciasentreambasmedidasfuede1.97D,conunoslímitesde
concordancia inferior de 0.36 D y superior de 3.39 D, los cuales fueron
clínicamenterelevantes.
15
20
25
30
35
15 20 25 30 35
P IOLadjSRK/T(D)
PIOLReal(D)
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90
Figura17.DiagramadepuntosdeBlandAltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/TylaPIOLRealfrentealamediadelasdiferencias
3. Medianteunanálisisderegresiónmúltiple,seobtuvoqueelvalordeELPadj
estabacorrelacionadoconlalongitudaxial(AL),profundidaddelacámara
anterior (ACD), lapotenciaqueratométrica ajustada (Pkadj) y la edad (p<
0.001):
𝐸𝐿𝑃!"# = −9.549+ 0.422 ∙ 𝐴𝐿 + 0.164 ∙ 𝑃!"#$ − 1.612 ∙ 𝐴𝐶𝐷 − 0.014 ∙ 𝐸𝑑𝑎𝑑
[44]
Lahomocedasticidaddelmodeloseconfirmóal realizarelanálisisde los
residuos no estandarizados (p=0.20) y la ausencia de valores atípicos
(distanciadeCook:0.049±0.081).Conestemodelo,el72%delosresiduos
tuvieron un valor ≤ 0.30 y el 80% se encontraron por debajo de 0.40.
También se confirmó la pobre correlación existente entre residuos (test
Durbin-Watson: 2.165) y la falta demulticolinealidad (tolerancia0.486 a
0.992,FIV2.056a1.008).
4. Cuando se comparó este valor de ELPadj con el valor de ELP obtenido
mediante la fórmula SRK/T (ELPSRK/T), se observaron diferencias
estadísticamente significativas entre ambas medidas (p < 0.01, test T-
3,39D
0,36D
1,97D
-4,0
-3,0
-2,0
-1,0
0,0
1,0
2,0
3,0
4,0
10,0 15,0 20,0 25,0 30,0 35,0
DiferenciasP
IOLadjSRK/T-P IOLReal(D)
MediaPIOLadjSRK/T-PIOLReal(D)
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91
Student), siendoELPadj el demenor valor (4.18± 0.27mm, rango3.70 a
4.83)(vertabla10).
5. Al comparar la PIOLReal con PIOLadj cuando se utilizó el valor de ELPadj
calculada mediante la ecuación 39, no se observaron diferencias
estadísticamentesignificativas(p=0.10,t-Student).Seencontróunafuerte
correlación estadísticamente significativa entre ambas medidas de PIOL
(r=0.97,p<0.01)(figura18).
Figura18.DiagramadedispersióndondesemuestralarelaciónentrelaPIOLadjyla
PIOLReal
6. De acuerdo con en el análisis de Band Altman (fig.19), la media de las
diferencias entre ambas medidas fue de 0.002 D, con unos límites de
concordancia inferior de -1.225 D y superior de 1.229 D, valores
clínicamentesignificativos.
15
20
25
30
35
15 20 25 30 35
P IOLadj(D)
PIOLReal(D)
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92
1,229D
-1,225D
0,002D
-4
-2
0
2
4
10 15 20 25 30 35
DiferenciaPIOLadj-P
IOLReal(D)
MediaPIOLadj-PIOLReal(D)
Figura19.DiagramadepuntosBlandAltmancorrespondientealasdiferenciasentrelaPIOLadjylaPIOLRealfrentealamediadelasdiferencias
7. Se comparó el valor de PIOLadj con las distintas fórmulas de cálculo másusadasenlaactualidad,comosonlafórmuladeHaigis(PIOLHaigis),HofferQ
(PIOLHofferQ) y Holladay (PIOLHolladay). Se encontraron diferencias
estadísticamente significativas con cada una de las fórmulas (p<0.01, t-
Student).Seencontróunafuertecorrelaciónestadísticamentesignificativa
entrePIOLHaigisyPIOLadj (r=0.983, p<0.01), entrePIOLHofferQyPIOLadj (r=0.992,
p<0.01) y entre PIOLHolladay y PIOLadj (r=0.987, p<0.01). En la tabla 11 se
muestran los análisis Bland-Altman correspondientes, donde se observa
que todas las diferencias son clínicamente significativas y que la mayor
diferenciasedioentrePIOLHaigisyPIOLadj.
Tabla11.AnálisisBland-AltmanentrePIOLadjyPIOLobtenidoconfórmulascomerciales
ΔPIOL±SD(D) LoA(D) p-valor
Haigis 1.77±0.79 3.33a0.21 <0.01
HofferQ 0.40±0.52 1.40a-0.64 <0.01
HolladayI -0.47±0.50 1.44a-0.50 <0.01
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93
8. Comosepuedeapreciarenlatabla10,elvalordeELPadj(4.18±0.27mm,
rango3.70a4.83)essignificativamentemenorqueelvalordeELPquese
obtuvo con cualquiera de las fórmulas comerciales usadas (p<0.01, t-
Student).
Enelpresenteestudio,setratódeminimizarelerrordecálculodelapotencia
de la lente intraocular a implantar para el modelo específico de lente intraocular
acomodativaCrystalensHD(Bausch&Lomb). Para ello, por una parte de utilizó el
algoritmo de cálculo del índice queratométrico ajustado (nkadj) para minimizar el
errorenelcálculodelapotenciacornealqueratométricayporotraparteseoptimizó
elcálculode laELPen funcióndevalorespreoperatorioscomolaAL,Pkadj,ACDy la
edad.
En este estudio los pacientes presentaban en algunos casos un error
postoperatorio miópico o hipermetrópico inesperado. Este error postoperatorio
(SEpost)presentóunrangode-3.13a+1.14D,confirmándoseunatendenciamiópica
significativa, lo cual inducía a pensar en la necesidad de la realización de algunas
optimizaciones en el cálculo de la potencia de la lente intraocular acomodativa a
implantar.
Lasposibles fuentesdeerrorparaelcálculode lapotenciadeestetipode lente
intraocularacomodativa,podíanserdebidoalasumirerroresenlapotenciacorneal,
enlaobtencióndelalongitudaxialoenlainexactitudenlaestimacióndelaposición
efectivadelalenteparaestalenteintraocularespecífica.Enprimerlugar,elimpacto
del error queratométrico se analizó mediante el cálculo de la potencia corneal
mediante el valor denkadj paraminimizar el error cometido en la estimación de la
potencia de la córnea(53,132,144). Sin embargo, aún seguían apreciándose diferencias
estadísticamente significativas y clínicamente relevantes entre el cálculo de la
potencia de la lente intraocular ajustada y la real (obtenida de acuerdo con los
resultados de la fórmula SRK/T). Puesto que la exactitud del IOLMaster® para el
cálculodela longitudaxial fueampliamentedemostrada(143),seconsideróelcálculo
deELP comounfactorcríticopara lapresenciadeunaprevisibilidadrelativamente
limitadade la lente intraocularacomodativaevaluada.Porestarazón,sedesarrolló
unaexpresiónmatemáticaparalaestimaciónyoptimizacióndeELPdeacuerdocon
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94
parámetrospreoperatorios (ELPadj),obtenidamedianteregresión linear.Elvalorde
PIOLadjobtenidoconelusodeesteELPadjsecomparóconlosobtenidosmedianteotros
algoritmosdeprediccióndeELP(17,20,21,145,146). Revelando este análisis queELPadj es
significativamente menor comparado con los valores obtenidos con las fórmulas
comerciales.
Respecto a la intercambiabilidad entre PIOLReal y PIOLadj, no se encontraron
diferenciassignificativasentre lasmedias (media0.002±0.67D),aunquepresentó
unos límites de acuerdo clínicamente relevantes (LoA 1.229 a -1.225D), lo cual es
clínicamente significativo, siendoestevalor limitado si tenemosen cuentaqueeste
tipode lente intraocularestádisponibleenpasosdemediadioptría. Estoconfirma
queaunsiendolaposicióndelalenteintraocularmásanterior,éstapuedecontribuir
a errores de ELP en el cálculo de la lente intraocular acomodativa, así como la
inestabilidad posicional que puede aparecer en este tipo de lente cuando se sitúa
dentro de la bolsa capsular. Estos resultados concuerdan con los obtenidos por
algunosestudiosquerevelanlapresenciadeposicionesinesperadasconestetipode
lenteintraocularacomodativa(147–149).Posteriormente,sepasóacomprobarsiexistía
intercambiabilidad entre PIOLadj y las distintas fórmulas de cálculo comerciales. Se
obtuvierondiferenciasestadísticamentesignificativasentrelosparesPIOLadj-PIOLHaigis,
PIOLadj-PIOLHofferQyPIOLadj-PIOLHolladay(p<0.01,testT-Student),siendoestasdiferencias
máximasparalacombinaciónPIOLadjyPIOLHaigis(rangoacuerdo1.77±0.79D,LoA3.33
a-0.21D).Enlatabla10semuestranlosvaloresBlandAltmancorrespondientes.Con
estosdatosseobservóquelaparejaPIOLReal-PIOLadjeralaqueproporcionóelmenor
intervalorespectoalasdemásfórmulasdecálculoanalizadas,indicandoqueseríala
fórmulamásadecuadaparatratardereproducirlosvaloresdelaPIOLReal.
Se obtuvo una relación entreELP y algunos factores preoperativos como laAL,
Pkadj,ACDy laedad.Enojoslargos,elvalormáselevadosecorrespondióalvalorde
ELPadj, lo cual concuerda con los resultados anteriormente obtenidos por otros
autores como Olsen et al.(25), quienes observaron una tendencia en ojos cortos a
presentarunacámaraanteriormenorqueenojoslargos.Comoyareportaronotros
autoresdemanerasimilarenotromodelodelenteintraocularacomodativa,laedad
también resultó ser un factor influyente(150). Uno de los principales factores que
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ResultadosyDiscusión
95
pueden explicar estos hallazgos es la posición más anterior que adopta la lente
acomodativaCrystalensHDdebidoasushápticosflexibles.
Elpresenteestudiopresentaunaseriede limitaciones,comoel tamañolimitado
de la muestra o el seguimiento de corta duración realizado. Otra limitación es la
determinacióndelarefracciónconestalenteacomodativa.LalenteCrystalensHDes
una lente con una óptica central bi-asférica modificada, generando una ligera
aberración esférica negativa la cual contribuye al aumento de la profundidad de
foco(151,152). Se han reportado pequeños niveles de aberración esférica primaria en
este tipo de lentes intraoculares acomodativas(152) y de signo positivo en algunos
casos(151). Errores refractivos residualesdemasde -0.50Dno sepuedenatribuir a
estosniveleslimitadosdeaberraciónesférica,ademásdeencontrarcasosconerrores
refractivos residuales hipermetrópicos clínicamente significativos. Otro factor que
puedehaber contribuido a la variabilidad en la estimaciónde la refracción sería la
presenciadeunalenteintraocularmalposicionada,yaseainclinadaodescentrada,la
cual conduciría a una degradación de la calidad visual y por tanto limitaría la
exactitud de refracción manifiesta. Algunos autores han reportado casos de lentes
malposicionadasobasculantes(153).Ennuestroestudionoseobservóenelexamen
conlámparadehendiduraningunadesalineaciónniinclinación.
4.4.ResultadosdelostrabajosenrelaciónconelobjetivoD
Error inducido en la estimación de la potencia corneal y la posición
efectiva en la potencia de una lente intraocular multifocal rotacional
asimétrica. [Piñero DP, Camps VJ, RamónML, Mateo V, Pérez-Cambordí RJ. Error
inducedbytheestimationofthecornealpowerandtheeffectivelenspositionwitha
rotationallyasymmetricrefractivemultifocalintraocularlens.IntJOphthalmol2015
Jun18;8(3):501-7]
En este estudio seha evaluado lapredictibilidadde lasdiferencias entre las
fórmulas de cálculo de la potencia de la lente intraocular multifocal refractiva de
rotaciónasimétricaMplusLS-312(OculentisGmbH,Germany)y laPIOLadj, así comoel
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ResultadosyDiscusión
96
impactodelerrorcometidoenlaestimaciónqueratométricadelapotenciacornealy
lafórmulapredictivadecálculodelaELP.
Paralaobtencióndelapotenciadelalenteintraocular(PIOL),aligualquecon
el objetivo C, se calculó mediante el uso de la ecuación de Gauss para óptica
paraxial(132)[ec.36].Escogiendoparaelcálculodenkelcorrespondientealmodelode
Gullstrand[ec.34],propuestopornuestrogrupodeinvestigación(53),porlasrazones
quesehanexpuestoanteriormente.
Con el uso de este algoritmo se calculó el valor de la potencia corneal
queratométricaajustada(Pkadj),conelusodenkadjparalaestimacióndelaPkadjylos
valores de nha y nhv correspondientes al modelo de ojo de Gullstrand (1.336 para
ambos índices). Para el equivalente esférico, se consideró igual a la refracción
deseada (SEpost= Rdes). Este valor de PIOLadj se comparó con la PIOLReal implantada,
siendo el valor de PIOLadj calculada mediante los dos métodos de cálculo de ELP,
detalladosanteriormente.Estevalordepotenciadelenteintraocularsecomparócon
elvalorobtenidopordiversasfórmulascomercialesdecálculo,comoHaigis,HofferQ
yHolladay,siendoelvalordeELPeldefinidoparacadafórmula.
Sevaloraronuntotalde25ojosde13pacientesconunaedadmediade65.6
años(rangode50a83años)deloscuales7(53.8%)eranmujeres.Lamuestraestaba
compuestapor13ojosizquierdos(52%).Latabla12muestralosparámetrosdelos
ojosevaluados.
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97
Tabla11.Medidasvisuales,refractivas,biométricasydatosdecálculodelaPIOL
Parámetros Media±SD Rango SEpre(D) -1.27±2.87 -7.50a3.00 SEpost(D) -0.11±0.56 -1.83a0.76 r1c(mm) 7.61±0.25 7.19a8.01 ACD(mm) 3.31±0.28 2.61a3.79 AL(mm) 23.52±1.04 22.02a27.36 ELPSRK/T(mm) 5.12±0.45 4.60a6.83 ELPadj(mm) 4.31±0.50 3.39a5.34 ELPHaigis(mm) 5.01±0.16 4.77a5.46 ELPHofferQ(mm) 5.00±0.27 4.63a6.01 ELPHolladay(mm) 4.59±0.27 3.89a5.07 nkadj 1.328±0.02 1.325a1.331 Pk(1.3375)(D) 44.37±1.44 42.14a46.95 PcHaigis(D) 43.57±1.41 41.39a46.11 Pkadj(D) 43.11±1.61 40.62a45.99 PIOLReal(D) 19.78±2.32 12.50a23.50 PIOLadjSRK/T(D) 21.18±2.74 12.51a25.46 PIOLadj(D) 19.71±2.55 11.02a23.53 PIOLHaigis(D) 20.40±3.15 10.16a24.99 PIOLHofferQ(D) 19.30±3.04 9.50a23.90 PIOLHolladay(D) 19.57±2.99 9.40a23.90 Donde:SEpre=equivalenteesféricopreoperatorio; SEpost= equivalenteesféricopostoperatorio; r1c= radiocara anterior de la córnea; ACD=profundidad de la cámara anterior; AL= longitud axial; ELPSRK/T=posiciónefectivade la lentecalculadamediante la fórmulaSRK/T;ELPadj=posiciónefectivade la lenteajustada; ELPHaigis= posición efectiva de la lente calculada mediante la formula de Haigis; ELPHofferQ=posiciónefectivadelalentecalculadaconlafórmuladeHofferQ;ELPHolladay=posiciónefectivadelalentecalculada con la fórmula de Holladay; nkadj= índice de refracción queratométrico ajustado; Pk(1.3375)=potenciacornealqueratométricacalculadaconelíndicequeratométrico1.3375;PcHaigis=potenciacornealcalculadapara la fórmuladeHaigis cuando seutilizaunvalorde índicequeratométrico1.3315;Pkadj=potencia queratométrica calculada con el índice queratométrico ajustado; PIOLReal= potencia lenteintraocular implantada;PIOLadjSRK/T=potencia lente intraocularcalculadacon la fórmulaSRK/T;PIOLadj=potencia lente intraocular ajustada; PIOLHofferQ= potencia lente intraocular calculada con la fórmula deHofferQ;PIOLHolladay=potencialenteintraocularcalculadaconlafórmuladeHolladay;PIOLHaigis=potencialenteintraocularcalculadaconlafórmuladeHaigis
Losprincipaleshallazgosyconsideracionessobrelosresultadosobtenidosse
exponenacontinuación:
1. Se encontraron diferencias estadísticamente significativas entre PIOLadjSRK/T y
PIOLRealcuandoseusóelvalordeELPcalculadomediantelafórmulaSRK/T(p<
0.01,Wilcoxontest).Comoseobservaenlafigura20,seencontróunafuerte
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98
correlaciónentreambasmedidasdepotenciadelenteintraocular(r=0.860,P
<.01)
Figura20.Diagramadedispersióndondesemuestralarelaciónentrela
PIOLadjSRK/TylaPIOLReal
2. EnelanálisisdeBand-Altman(fig.21)seobservóunatendenciaasobrestimar
elvalordePIOLSRK/TrespectoalvalordePIOLReal(r=0.960;P<0.01).Lamedia
de las diferencias entre ambas medidas fue de 1.41 D, con unos límites de
concordancia inferior de -0.48 D y superior de 3.29 D, los cuales son
clínicamenterelevantes.
5
10
15
20
25
5 10 15 20 25
P IOLadjSRK/T(D)
PIOLReal(D)
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99
Figura21.DiagramadepuntosBlandAltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/TylaPIOLRealfrentealamediadelasdiferencias
3. Mediante un análisis de regresiónmúltiple, se obtuvoque el valor deELPadj
estaba correlacionado con la longitud axial (AL), profundidad de la cámara
anterior(ACD),ypotenciaqueratométricaajustada(Pkadj)(p<0.01):
𝐸𝐿𝑃!"# = −17.333+ 0.612 ∙ 𝐴𝐶𝐷 + 0.360 ∙ 𝐴𝐿 + 0.268 ∙ 𝑃!"#$ [45]
La homocedasticidad del modelo se confirmó al realizar el análisis de los
residuos no estandarizados (p=0.20) y la ausencia de valores atípicos
(distancia deCook: 0.155±0.528). Con estemodelo, el 56%de los residuos
tuvieron un valor de ≤ 0.20 y el 76% se encontraron por debajo de 0.50.
También se confirmó la pobre correlación existente entre residuos (test
Durbin-Watson: 1.629) y la falta de multicolinealidad (tolerancia 0.805 a
0.560,FIV1.785a1.243).
4. Seencontrarondiferenciasestadísticamentesignificativasalcompararelvalor
de ELPadj con el valor de ELP obtenido con cualquiera de las fórmulas
comercialesanalizadas(p<0.01,Wilcoxontest).Comoseapreciaenlatabla12,
el valormínimodeELPcorrespondeaELPadj (4.31± 0.50mm, rango3.39 a
5.34).
3,29D
-0,48D
1,41D
-5
-3
-1
1
3
5
10 15 20 25
DiferenciasP
IOLadjSRK/T-P IOLReal(D)
MediaPIOLadjSRK/T-PIOLReal(D)
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100
5. Al comparar laPIOLadjcuandoseutilizóel valor calculadodeELPadj, obtenida
mediante la ec. 40, con el valor de PIOLReal no se encontraron diferencias
estadísticamente significativas (p=0.65, test t-Student). Además se encontró
una fuerte correlación estadísticamente significativa entre ambas medidas
(r=0.95,p<0.01)(figura22).
Figura22.RelaciónentrelaPIOLadjylaPIOLReal
6. En el análisis de Bland Altman (fig.23) se observó que la media de las
diferencias entre ambas medidas fue de -0.07 D, con unos límites de
concordancia inferior de -1.61 D y superior de 1.47 D, los cuales son
clínicamentesignificativos.
5
10
15
20
25
5 9 13 17 21 25
P IOLadj(D)
PIOLReal(D)
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101
Figura23.DiagramadepuntosBlandAltmancorrespondientealasdiferencias
entrelaPIOLadjylaPIOLRealfrentealamediadelasdiferencias
7. Posteriormente se comprobaron las diferencias entre PIOLadj y las distintas
fórmulas de cálculo comerciales, obteniéndose diferencias estadísticamente
significativas entre PIOLadj y PIOLHaigis y entre PIOLadj y PIOLHofferQ (p<0.01, test
Wilcoxon),peronoentrePIOLadjyPIOLHolladay(p=0.20,testWilcoxon).Enlatabla
13semuestranlosvaloresBlandAltmancorrespondientes.
Tabla12.AnálisisBland-AltmanentrePIOLadjyPIOLobtenidaconfórmulascomerciales
ΔPIOL± SD(D) LoA(D) p-valor
Haigis 0.68±0.72 2.09a-0.73 <0.01
HofferQ -0.43±0.75 1.05a-1.90 <0.01
Holladay1 -0.13±0.67 1.01a-1.28 0.20
8. Como se aprecia en la figura 24 se obtuvo una fuerte correlación
estadísticamentesignificativaentrePIOLadjyPIOLHolladay(r=0.96,p<0.01).
1,47D
-1,61D
-0,07D
-5
-3
-1
1
3
5
10 15 20 25
DiferenciasP
IOLadj-P
IOLReal(D)
MediaPIOLadj-PIOLReal(D)
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102
Figura24.RelaciónentrelaPIOLHolladayylaPIOLadj
9. En el análisis de Band-Altman (fig.25) se observó que la media de las
diferencias entre la potencia de la lente intraocular ajustada (PIOLadj) y la
obtenidamediantelafórmuladeHolladay(PIOLHolladay)fuede-0.13D,conunos
límitesdeconcordanciainferiorde-1.28Dysuperiorde1.01D.
Figura25.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLHolladayylaPIOLadjfrentealamediadelasdiferencias
5791113151719212325
5 7 9 11 13 15 17 19 21 23 25
P IOLHolladay(D)
PIOLadj(D)
1,01D
-1,28D
-0,13D
-5
-3
-1
1
3
5
10 15 20 25
DiferenciasP
IOLHolladay-P
IOLadj(D)
MediaPIOLHolladay-PIOLadj(D)
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10. Al comprobar la intercambiabilidad entre nuestra PIOLadj y PIOLHolladay , se
decidió comprobar, la posible intercambiabilidad entrePIOLRealy las distintas
fórmulas de cálculo comerciales. En este caso, se obtuvieron diferencias
estadísticamentesignificativasentrePIOLRealyPIOLHaigisyentrePIOLRealyPIOLHofferQ
(p<0.05 test Wilcoxon), pero no entre PIOLReal y PIOLHolladay (p=0.29, test
Wilcoxon)(vertabla14).
Tabla13.AnálisisBland-AltmanentrePIOLRealyPIOLobtenidaconfórmulascomerciales
ΔPIOL± SD(D) LoA(D) p-valor
Haigis 0.62±1.15 2.88a-1.64 0.01
HofferQ -0.43±1.13 1.73a-2.69 0.03
Holladay1 -0.21±1.10 1.96a-2.37 0.29
11. En el análisis de Band-Altman (fig.26) al comparar PIOLReal y PIOLHolladay se
observaquelamediadelasdiferenciasenestecasofuede-0.21D,conunos
límitesdeconcordanciainferiorde-2.37Dysuperiorde1.96D,siendoestos
límitessuperioresalosobtenidosentrePIOLRealyPIOLHolladay.
Figura26.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLHolladayylaPIOLRealfrentealamediadelasdiferencias
1,96D
-2,37D
-0,21D
-5
-3
-1
1
3
5
10 12 14 16 18 20 22 24 26 28DiferenciaPIOLHolladay-P
IOLReal(D)
MediaPIOLHolladay-PIOLReal(D)
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Ennuestroestudio,setratódeminimizarelerrordecálculodelapotenciade
la lente intraocular a implantar para el modelo específico de lente intraocular
multifocalderotaciónasimétricaMplusLS-312(OculentisGmbH,Germany).Paraello,
por unaparte deutilizó el algoritmode cálculo del índice queratométrico ajustado
(nkadj)paraminimizarelerrorenelcálculode lapotenciacornealqueratométricay
porotraparteseoptimizóelcálculode laELPen funciónde lapotenciade la lente
intraocular.
A partir de este estudio, se observó en los pacientes una significantiva
variabilidadenelvalordelequivalenteesféricopostoperatorio(-0.11±0.56D,rango
-1.83 a 0.76D), con una ligera tendenciamiópica tal y como ya indicaban algunos
estudiospreviosdelmismotipodelenteintraocularmultifocal(84,85,110).Estoconfirmó
la necesidad de optimizar un algoritmo para el cálculo de la potencia de la lente
intraocular con el fin de afinar los resultados refractivos y visuales de este tipode
lenteintraocularmultifocalpremium.Lalimitaciónrelativaenlaprevisibilidaddela
correcciónrefractivaenalgunoscasosimplantadosconla lenteMplusLS-312puede
ser atribuible al sesgo asociado del uso de la potencia corneal queratométrica, los
erroresenladeterminacióndelalongitudaxialoenlainexactituddelaestimaciónde
laELP.Lapotenciacornealqueratométricafueanalizadaycalculadaconelusodeun
índicequeratométricoajustadoconelfindeminimizarelerrorenlaestimacióndela
potenciacorneal(Pkadj)(53,132).EstaPkadj seutilizópara laobtenciónde laestimación
de la potencia lente intraocular considerando la longitud axial y la ELP calculada
segúnlasdirectricesdelafórmulaSRK/T(PIOLadjSRK/T)(21).Alanalizarlosresultadosse
encontraron diferencias estadísticamente significativas y clínicamente relevantes
entreestamedidadepotenciadelenteintraocularylarealdelalenteimplantada.La
ELPesunafactorcríticoporlapresenciadela limitadapredictibilidadenelcálculo
deestetipodelenteintraocular.ElcálculodelvalordeELPoptimizada,conseguido
mediante regresión lineal, sedenominó comoposición efectivade la lente ajustada
(ELPadj). Se obtuvo que este valor de ELP estaba relacionado con algunos factores
anatómicos,comolaAL,PkadjylaACD.AlcompararlaintercambiabilidadentrePIOLadj
y PIOLReal, no se encontraron diferencias entre las medias (p<0.05) sin embargo el
Capítulo4
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105
intervalodeconfianzasiresultóserclínicamentesignificativo(rangoacuerdo-0.07D,
conunosLoAinferiorysuperior-1.61y1.47D,respectivamente).
El valor deELPadj se comparó con otros obtenidosmediante otras fórmulas de
cálculo de ELP(21,146,154). Se encontró un valor significativamente menor de ELPadj
comparadoconlosvaloresestimadosdelasfórmulasdeHaigis,HofferQyHolladay
(ELPHaigis,ELPHofferQyELPHolladay, respectivamente)(146,154).Ladiferenciamáspequeña
correspondióa laencontradaentreELPadjyELPHolladay,estopuedeserlarazóndela
ausenciadediferenciasestadísticamentesignificativasentrePIOLHolladayyPIOLadj(rango
de acuerdo 0.13± 0.67D, LoA -1.28 a 1.01D). Aún sin la presencia de diferencias
significativasentreambasmedidas,seobtuvounintervalodeconfianzaclínicamente
relevante.Porelcontrario,seencontrarondiferenciasestadísticamentesignificativas
y clínicamente relevantes al comparar nuestro valor calculado de lente intraocular
(PIOLadj)conlasfórmulasdeHaigisyHofferQ(PIOLHaigisyPIOLHofferQ,respectivamente).
DadalafaltadediferenciaentrelasmediasdelosparesPIOLReal-PIOLadjyPIOLHolladay-
PIOLadj, se analizó la intercambiabilidad entre PIOLReal y PIOLHolladay, sin apreciarse
diferencias significativas entre ambas medidas aunque el intervalo de confianza
resultóserclínicamentesignificativo(rangodeacuerdo-0.13D,LoA1.96a-2.37D).
Con estos datos se observó que la parejaPIOLReal -PIOLadj era la que proporcionó el
menorintervalorespectoalasdemásfórmulasdecálculoanalizadas, indicandoque
seríalafórmulamásadecuadaparatratardereproducirlosvaloresdelaPIOLReal.
Elpresenteestudiopresentaunaseriede limitaciones,comoel tamañolimitado
de la muestra o el seguimiento de corta duración realizado. Otra limitación es la
determinacióndelarefracciónconestalentemultifocal.Ciertasdificultadeshansido
descritasenlaobtencióndelarefraccióndespuésdelaimplantacióndelosdiferentes
modelosdelenteintraocular,conunatendenciaclaraalasobrestimaciónesféricacon
signo positivo(155). La refracción manifiesta se obtuvo mediante el mismo
procedimiento descrito para la obtención de la refracción en lentes intraoculares
multifocales(156) y sin el uso del autorrefractómetro como base, dado que se ha
demostradoel falloqueapareceenojos implantadoscon la lente intraocularMplus
LS-312(157).
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4.5.ResultadosdelostrabajosenrelaciónconelobjetivoE
Error inducido en la estimación de la potencia corneal y la posición
efectiva en lapotenciadeuna lente intraocular asférica. [PiñeroDP,CampsVJ,
Ramon ML, Mateo V, Soto-Negro R. Preliminary evaluation of an algorithm to
minimizethepowererrorselectionofanasphericintraocularlensbyoptimizingthe
estimationofthecornealpowerandtheeffectivelensposition.IntEyeSci2016Jun;
16(6):1001-8]
Enesteestudioseevaluó lapredictibilidaddediferentes fórmulasdecálculo
delapotenciadelalenteintraocularasféricaLentisL-313ydelaPIOLadjdesarrollando
unafórmulapredictivadecálculodelaELP.
El cálculode lapotenciade la lente intraocular (PIOL) secalculóde lamisma
manera que en los artículos anteriores, escogiendo para el cálculo de nk el
correspondientealmodelodeGullstrand,elmotivodeestaelecciónhasidodetallado
anteriormente.
Con el uso de este algoritmo se calculó el valor de la potencia corneal
queratométricaajustada(Pkadj),conelusodenkadjparalaestimacióndelaPkadjylos
valores de nha y nhv correspondientes al modelo de ojo de Gullstrand (1.336 para
ambos índices). Se consideró el equivalente esférico igual a la refracción deseada
(SEpost=Rdes).SecomparóelvalordePIOLadjconlaPIOLReal implantada,siendoelvalor
de PIOLadj calculada mediante los dos métodos de cálculo de ELP detallados
anteriormente. Este valor depotencia de lente intraocular se comparó con el valor
obtenido por diversas fórmulas comerciales de cálculo, como Haigis, Hoffer Q y
Holladay,siendoelvalordeELPeldefinidoparacadafórmula.
Enprincipioseoptóporhacerunestudiocontodoslospacientessometidosa
estudio.Dadolosmalosresultadosobtenidosydebidoalbeneficiomáslimitadoque
presentanlaslentesintraocularesasféricasenojosmáslargos(158)seoptópordividir
a lamuestraanalizadaen funciónde lapotenciade la lente intraocular implantada,
conelfindeoptimizarelvalordeELPmásadecuadoparacadapaciente.
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Lamuestrasedividióportantoendosgruposdeacuerdoconlapotenciadela
lenteintraocularimplantada.EnelgrupoA(PIOL≥23.0D),sevaloraronuntotalde12
ojosde8pacientesconunaedadmediade68.2años(rangode56.0a80.0años)de
loscuales11(91.7%)erandehombres.EnelgrupoB(PIOL<23.0D),sevaloraronun
totalde53ojosde35pacientesconunaedadmediade72.2años(rangode57.0a
92.0 años) de los cuales 29 (54.7%) eran de mujeres. La tabla 15 muestra los
parámetrosdelosojosevaluados.
Tabla14.Medidasvisuales,refractivas,biométricasydatosdecálculodelaPIOL Parámetro PIOLReal>23.0D PIOLReal<23.0D
Media±SD Rango Media±SD Rango SEpre(D) 1.04±1.64 -2.38a2.75 -0.84±3.05 -12.38a3.38 SEpost(D) -0.02±0.40 -0.75a0.75 -0.25±0.44 -1.38a0.75 r1c(mm) 7.54±0.24 7.13a7.86 7.61±0.23 7.14a8.21 ACD(mm) 2.95±0.33 2.41a3.35 3.32±0.34 2.48a4.15 AL(mm) 22.33±0.55 21.30a23.09 23.70±1.13 22.20a28.33 ELPadjSRK/T(mm) 4.60±0.13 4.37a4.86 5.17±0.78 4.65a9.24 ELPadj(mm) 4.44±0.31 3.93a5.01 4.61±0.53 3.82a6.24 ELPHaigis(mm) 4.75±0.14 4.54a4.90 5.04±0.21 4.66a5.65 ELPHofferQ(mm) 4.68±0.08 4.59a4.88 5.06±0.33 4.74a6.42 ELPHolladay(mm) 3.77±0.42 3.08a4.29 4.24±0.43 3.17a5.31 nkadj 1.328±0.002 1.326a1.331 1.328±0.002 1.324a1.331 Pk(1.3375)(D) 44.79±1.44 42.92a47.34 44.37±1.35 41.09a47.28 PcHaigis(D) 43.99±1.41 42.16a46.50 43.58±1.33 40.35a46.43 Pkadj(D) 43.58±1.61 41.50a46.44 43.12±1.51 39.45a46.36 PIOLReal(D) 23.75±0.69 23.00a25.00 19.72±3.10 7.50a22.50 PIOLadjSRK/T(D) 24.18±0.98 21.85a25.87 20.69±3.00 9.81a24.31 PIOLadj(D) 23.82±1.02 22.16a25.76 19.74±3.11 728a22.91 PIOLHaigis(D) 23.95±1.16 21.25a26.14 19.95±3.58 6.35a24.05 PIOLHofferQ(D) 22.68±1.47 20.24a25.07 17.94±4.15 4.55a22.47 PIOLHolladay(D) 22.90±1.00 20.51a24.61 19.19±3.37 5.58a23.01 Donde:SEpre=equivalenteesféricopreoperatorio;SEpost=equivalenteesféricopostoperatorio;r1c=radiocara anterior corneal; ACD=profundidad cámara anterior; AL= longitud axial; ELPSRK/T= posiciónefectivadelalentecalculadamediantefórmulaSRK/T;ELPadj=posiciónefectivadelalenteajustada;ELPHaigis= posición efectiva de la lente calculada mediante fórmula de Haigis; ELPHofferQ= posiciónefectivade la lentecalculadamediante fórmuladeHofferQ;ELPHolladay=posiciónefectivade la lentecalculadamediantefórmuladeHolladay;nkadj=índicederefracciónqueratométricoajustado;Pk(1.3375)=potencia corneal queratométrica calculada con índice queratométrico 1.3375; PcHaigis= potenciacorneal calculada para la fórmula de Haigis cuando se utiliza un valor de índice queratométrico1.3315; Pkadj= potencia queratométrica calculada con índice queratométrico ajustado; PIOLReal=potencia lente intraocular implantada; PIOLadjSRK/T= potencia lente intraocular calculada mediantefórmula SRK/T; PIOLadj= potencia lente intraocular ajustada; PIOLHofferQ= potencia lente intraocularcalculadamediante fórmula de Hoffer Q; PIOLHolladay= potencia lente intraocular calculadamediantefórmuladeHolladay;PIOLHaigis=potencialenteintraocularcalculadamediantefórmuladeHaigis
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Losprincipaleshallazgosyconsideracionessobrelosresultadosobtenidosse
exponenacontinuación:
1. En el grupo A, no se encontraron diferencias estadísticamente significativas
(aunque por poco) entre PIOLadjSRK/T y PIOLReal cuando se usó el valor deELP
calculado mediante la fórmula SRK/T (p = 0.06, test t-Student). Como se
apreciaen la figura27a,existeunacorrelaciónestadísticamentesignificativa
entreambasmedidas(r=0.680,p<0.01).
EnelgrupoB,seencontrarondiferenciasestadísticamentesignificativasentre
PIOLadjSRK/T y PIOLReal cuando se usó el valor de ELP calculado mediante la
fórmula SRK/T (p < 0.01, testWilcoxon). Como se aprecia en la figura 27b,
existe una fuerte correlación estadísticamente significativa entre ambas
medidas(r=0.898,p<0.01).
Fig.27a.(GrupoA)RelaciónentrelaPIOLadjSRK/TylaPIOLReal.
20
22
24
26
28
20 21 22 23 24 25 26 27
P IOLadjSRK/T(D)
PIOLReal(D)
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109
Fig27b.(GrupoB)RelaciónentrelaPIOLadjSRK/TylaPIOLReal
2. AlrealizarelanálisisdeBland-AltmanenelgrupoA(fig.28a)seobtuvoquela
mediadelasdiferenciasentreambasmedidasfuede0.43D,conunoslímites
de concordancia inferior de -0.98 D y superior de +1.84 D, lo cual resulta
clínicamente significativo. En el análisis de Bland-Altman en el grupo B
(fig.28b)seobtuvoquelamediadelasdiferenciasentreambasmedidasfuede
0.97 D, con unos límites de concordancia inferior de -0.30 D y superior de
+2.24D.
Fig.28a.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/TylaPIOLReal
frentealamediadelasdiferenciasenelGrupoA
5
10
15
20
25
30
5 10 15 20 25 30
P IOLadjSRK/T(D)
PIOLReal(D)
1,84D
-0,98D
0,43D
-5
-3
-1
1
3
5
22 23 24 25 26 27
DiferenciaPIOLadjSRK/T-P IOLReal(D)
MediaPIOLadjSRK/T-PIOLReal(D)
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110
Fig.28b.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/TylaPIOLRealfrentealamediadelasdiferenciasenelGrupoB
3. Mediante un análisis de regresiónmúltiple, se obtuvoque el valor deELPadj
paraelgrupoA,estabacorrelacionadoconlaedadyelastigmatismocorneal
(AC)(p<0.01):
𝐸𝐿𝑃!"#!!" = 5.983− 0.015 ∙ 𝐸𝑑𝑎𝑑 − 0.460 ∙ 𝐶𝐴 [46]
La homocedasticidad del modelo se confirmó al realizar el análisis de los
residuos no estandarizados (p=0.20) y la ausencia de valores atípicos
(distanciadeCook:0.146±0.259).Conestemodelo,el58.33%delosresiduos
no estandarizados tenían un valor ≤ 0.20. También se confirmó la pobre
correlaciónexistenteentreresiduos(testDurbin-Watson:2.320)ylafaltade
multicolinealidad(tolerancia0.971a0.971,FIV1.029a1.029).
No se encontraron diferencias estadísticamente significativas entre ELP
calculadamediantelafórmulaSRK/TylaELPadj(p=0.07,testt-Student).
En el grupo B, se descubrió que el valor de ELPadj en este caso estaba
correlacionado con la edad, la profundidad de la cámara anterior (ACD),
longitudaxial(AL)yradiocornealanterior(r1c)(p<0.01):
2,24D
-0,30D
0,97D
-5
-3
-1
1
3
5
7 11 15 19 23
DiferenciaPIOLadjSRK/T-P IOLReal(D)
MediaPIOLadjSRK/T-PIOLReal(D)
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111
𝐸𝐿𝑃!"#!!" = 5.327 + 0.015 ∙ 𝐸𝑑𝑎𝑑 + 0.346 ∙ 𝐴𝐶𝐷 + 0.334 ∙ 𝐴𝐿 − 1.430 ∙ 𝑟!! [47]
La homocedasticidad del modelo se confirmó al realizar el análisis de los
residuos no estandarizados (p=0.20) y la ausencia de valores atípicos
(distanciadeCook:0.04±0.13).Conestemodelo, el84.91%de los residuos
teníanunvalorde≤0.50.Lapobrecorrelaciónexistenteentreresiduos(test
Durbin-Watson: 2.208) y la falta de multicolinealidad (tolerancia 0.733 a
0.926,FIV1.080a1.364)fueconfirmada.
Para este grupo, se encontraron diferencias estadísticamente significativas
entre ELP calculada mediante la fórmula SRK/T y la ELPadj (p < 0.01, test
Wilcoxon),siendoelvalormenorelcorrespondienteaELPadj(vertabla15).
4. Enambosgrupos,seencontrarondiferenciasestadísticamentesignificativasal
compararelvalordeELPadjconelvalordeELPobtenidoconcualquieradelas
fórmulas comerciales analizadas (p<0.01, test T-Student para el grupo A y
p<0.01,testWilcoxonparaelgrupoB).Comoseapreciaenlatabla15,elvalor
mínimodeELPcorrespondeaELPHolladayparaambosgrupos(3.77±0.42mm,
rango3.08a4.29mmy4.24±0.43mm,rango3.17a5.31mm,pertenecientes
alosgruposAyB,respectivamente).
5. Noseencontrarondiferenciasentrelasmediasestadísticamentesignificativas
entrePIOLadjyPIOLRealalanalizarlaintercambiabilidadentreambasmedidasen
losdosgruposdeestudios(GrupoA:p=0.64,testt-Student;GrupoB:p=0.82,
test Wilcoxon). Se encontró una fuerte correlación estadísticamente
significativaentrePIOLadjyPIOLRealtantoparaelGrupoA(r=0.88,p<0.01)como
paraelGrupoB(r=0.91,p<0.01)(Figura29ay29b,respectivamente).
Capítulo4
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112
Fig.29a.(GrupoA)RelaciónentrelaPIOLadjylaPIOLReal
Fig.29b.(GrupoB)RelaciónentrelaPIOLadjylaPIOLReal
6. AlrealizarelanálisisBland-Altman,paraelGrupoA(figura30a)seobtuvoun
valorde0.08Ddelamediadelasdiferenciasentreambasmedidas,conunos
límitesdeconcordanciainferiorde-0.96Dysuperiorde+1.11D.EnelGrupo
B, el valorde lamediade lasdiferencias fuede -0.02D conunos límitesde
concordancia inferiory superiorde -1.18y+1.14D, respectivamente (figura
30b).
0
5
10
15
20
25
0 5 10 15 20 25
P IOLadj(D)
PIOLReal(D)
21
22
23
24
25
26
21 22 23 24 25 26
P IOLadj(D)
PIOLReal(D)
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113
Fig.30a.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/Ty
laPIOLRealfrentealamediadelasdiferenciasenelGrupoA
Fig.30b.Bland-AltmancorrespondientealasdiferenciasentrelaPIOLadjSRK/T
ylaPIOLRealfrentealamediadelasdiferenciasenelGrupoB
1,14D
-1,18D
-0,02D
-5
-3
-1
1
3
5
7 11 15 19 23
DiferenciasP
IOLadj-P
IOLReal(D)
MediaPIOLReal-PIOLadj(D)
1,11D
-0,96D0,08D
-5
-3
-1
1
3
5
22 23 24 25 26 27
DiferenciasP
IOLadj-P
IOLReal(D)
MediaPIOLadj-PIOLReal(D)
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114
7. Al comprobar la intercambiabilidad existente entre PIOLadj y las distintas
fórmulas de cálculo comerciales, se obtuvo en el Grupo A, diferencias
estadísticamente significativasentre todas las combinaciones (p<0.01, test t-
Student), excepto para la combinación de PIOLadj y PIOLHaigis (p=0.53, test t-
Student),conunamediade0.13±0.69yunintervalodeconfianzade1.47a-
1.22D.LamáximadiferenciaseobtuvoentrePIOLadjyPIOLHofferQ(-1.14±1.15D,
rangode+1.11a-3.40D).Seencontróunafuertecorrelaciónestadísticamente
significativa entrePIOLadjyPIOLHaigis(r=0.81, p<0.01) y entrePIOLHolladayyPIOLadj
(r=0.82, p<0.01). Además de una moderada correlación estadísticamente
significativaentrePIOLHofferQyPIOLadj(r=0.63,p=0.03).
Al analizar el Grupo B, se encontraron diferencias estadísticamente
significativas entre PIOLadj y todas las fórmulas analizadas (p<0.01, test
Wilcoxon). Coincidiendo estas diferencias máximas, como en el grupo A, al
comparar PIOLadj con PIOLHofferQ (-1.76 ± 1.84 D, rango de +1.84 a -5.36 D).
AparecióunafuertecorrelaciónestadísticamentesignificativaentrePIOLHaigisy
PIOLadj (r=0.99, p<0.01), entrePIOLHolladayyPIOLadj (r=0.98, p<0.01), siendo esa
correlaciónmasmoderadaentrePIOLHofferQyPIOLadj(r=0.66,p<0.01).Enlatabla
16semuestraunresumendelosvaloresBlandAltmancorrespondientes.
Tabla15.AnálisisBland-AltmanentrePIOLadjyPIOLobtenidoconfórmulascomerciales
GRUPOA GRUPOB
ΔPIOL± SD(D) LoA(D) p-value ΔPIOL± SD(D) LoA(D) p-value
Haigis 0.13±0.69 1.47to-1.22 <0.01 0.25±0.50 1.24to-0.73 <0.01
HofferQ -1.14±1.15 1.11to-3.40 <0.01 -1.76±1.84 1.84to-5.36 <0.01
HolladayI -0.93±0.61 0.26to-2.12 0.53 -0.50±0.36 0.20to-1.20 <0.01
Ennuestroestudio,setratódeminimizarelerrordecálculodelapotenciade
lalenteintraocularaimplantarparaelmodeloespecíficodelenteintraocularasférica
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Lentis L-313. Para ello, por una parte de utilizó el algoritmo de cálculo del índice
queratométricoajustado (nkadj)paraminimizarel errorenel cálculode lapotencia
cornealqueratométricayporotraparteseoptimizóelcálculodelaELPenfunciónde
lapotenciade la lente intraocular,hechoquehastaahoranohabíamosrealizadoen
losanterioresartículos.
Los pacientes presentaban un rango de valores de esfera equivalente
postoperatoriaentre-0.75y+0.75DenojosconPIOL≥23Dyentre-1.38y+0.75Den
ojos conPIOL<23D.Observándoseuna ligera tendenciaa lamiopíaen los casosde
ojosconpotenciadelenteintraocularmenoryenconsecuenciaenojoslargos.Estoes
coherente con los estudiosdonde sehan reportadouna tendencia a lamiopización
con lentes intraoculares asféricas, especialmente en casos de extrema miopía
preoperatoria(159).
Seevaluólaslimitacionesenlapredictibilidaddelerrorrefractivoenestetipo
de lente. Dado que los errores en la estimación de la AL eran mínimos y de bajo
impacto en la predicción del error(133), se evaluó la influencia del error
queratométrico mediante el cálculo de la potencia corneal con el valor de índice
queratométricoajustado(nkadj)conelfindeminimizarelerrorcorneal(53,132,143).Este
valor dePkadj se utilizó para obtener el valor de la potencia de la lente intraocular
considerandoAL,Rdes=SEpost yELP calculadomediante las directrices de la fórmula
SRK/T(PIOLadjSRK/T)(21).Paralosdosgruposdeestudio(ojosimplantadosconPIOL≥23
DyPIOL<23D)seobservarondiferenciasclínicamenterelevantesentrelaPIOLadjSRK/T
yPIOLReal siendomayores lasdiferenciasenojos implantadosconpotenciasbajasde
lente intraocular. De acuerdo con los resultados obtenidos, se observó que la
estimación de la ELP parecía ser el factor más crítico para la presencia de una
previsibilidad relativamente limitadaen la lente intraocular asférica, especialmente
enojos cortos. Conel finde confirmar esto, seobtuvopormediodeunanálisisde
regresión múltiple, una expresión para la estimación del valor de ELP optimizado
(ELPadj)deacuerdo conalgunosparámetrospreoperatorios.EstevalordeELPadj se
utilizó para calcular la potencia de la lente intraocular (PIOLadj) considerandoRdes =
SEpost,conelobjetivodecomprobarsiestanuevaestimacióneracapazdereproducir
el resultado clínico real. Con este enfoque, no se encontraron diferencias
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116
estadísticamentesignificativasyclínicamenteaceptablesentrePIOLadjyPIOLRealenlos
dosgrupos.
Ennuestroanálisis,seencontróqueELPadjestabarelacionadocondiferentes
factores en los grupos A y B. La edad es el único factor que compartían ambos
modelos.Estopuedeserdebidoalarelaciónexistenteconladependenciadelaedad
del comportamiento capsular después de la cirugía de cataratas. Un estudio reveló
que la edad podría estar asociada con el síndrome de distensión de la bolsa
capsular(160). En el grupo B, que incluyó los ojos con mayor AL, los factores
anatómicos fueron cruciales en el cálculo de la ELP para el cálculo de la lente
intraocularevaluada.ElvalordeELPadj fuemayorenojosconmayorALyACD,que
resulta ser consistente con la dependencia lineal de la posición final de la lente
intraocular en elAL reportado por diversos autores(161–163). También se incluyó un
factorcornealentérminosdemagnituddeastigmatismocornealenelgrupoAyde
radiodecurvaturade laprimerasuperficiecornealenelgrupoB.Siendoenambos
grupos nuestro valor de ELPadj< ELPadjSRK/T (ELPadj 4.44 ± 0.31 mm y 4.61 ± 0.53,
correspondientesalgrupoAyB,respectivamente)
Por último, se comparó la PIOLadj con las diversas fórmulas de cálculo de
potencia de lente intraocular. En ambos grupos, se encontraron diferencias
clínicamente relevantes entre PIOLadj y los valores de potencia de lente intraocular
obtenidos con la fórmula de Haigis, Hoffer Q y Holladay. Estas diferencias fueron
estadísticamente significativas, salvo la diferencia entre PIOLadj y PIOLHaigis que no
alcanzó una significación estadística, posiblemente debido a la limitación en el
tamaño de la muestra de este grupo. Estas diferencias entre las fórmulas parecen
estarenrelaciónconlasdiferentesestimacionesdeELPproporcionadosporcadauno
deellos,conelresultadomásprecisoparaELPadj.AlcompararnuestraELPadjconel
restodeELPcalculadas,seencontróquelafórmuladeHolladay(ELPHolladay)fuelaque
dioelvalormásbajodeELPpara losdosgrupos(3.77±0.42,rangode3.08a4.29
mmy4.24± 0.43, rangode3.17a5.31,parael grupoAyB, respectivamente). Sin
embargo,nuestraPIOLadjfuecapazdereproducirconmásprecisiónelvalorrealdela
potenciadelalenteintraocularimplantada.Estosugierequenuestroenfoquepuede
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117
ser un método útil para el cálculo de potencia de la lente intraocular asférica
evaluada.
Existenvariaslimitacionesenelestudioactual,talescomoeltamañolimitado
delamuestraoelcortoseguimientorealizado.Debetenerseencuenta,aunqueson
poco frecuentes, los cambios en la posición de la lente intraocular descritos en
pacientes de más de tres meses después de la cirugía, sobre todo después de la
capsulotomíaposteriorconlaserYAG(164).Otraposiblelimitaciónpuedeserdebidoa
que la fórmula Holladay II no se utilizó en nuestra comparación ya que no era
disponibleennuestraclínica.Posiblemente,nuestroenfoquepudierasermássimilar
a losresultadosde la fórmulaHolladayIIyaqueambostiposdecálculoutilizanun
algoritmo optimizado para la estimación de laELP, que deberá ser confirmado en
estudiosfuturos.
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121
5.CONCLUSIONESYPERSPECTIVASDEFUTURO
5.a.Conclusiones
Con estos resultados, se deduce que la imprecisión en el cálculo de Pc,
pertenecientes a una población sana sin cirugía previa, con la estimación
queratométrica puede serminimizada en la práctica clínicamediante el uso de un
índicequeratométricovariabledependientede r1c,al cualhemosdenominadonkadj.
Siendo esta estimación válida únicamente cuando sea inviable la obtención de r2c,
dado que la mejor opción para la realización del cálculo es obtener el valor de la
potenciacornealgaussianaconsiderandoambassuperficiescorneales.Por loquese
concluyequeelusodeunúnicovalordenkparaelcálculodePIOLpuededarlugara
imprecisiones las cuales pueden ser minimizadas mediante el uso de un valor
variabledenkdependientedelasuperficieanteriorcorneal.
Los resultados refractivos obtenidos después de la cirugía de cataratas
mediante el implante de la lente intraocular acomodativa Crystalens HD, pueden
optimizarsemedianteunalgoritmodecálculodenkadjparaminimizarelerrorenel
cálculodelapotenciacornealqueratométrica,ademásdeunaoptimizacióndelvalor
de ELP, dependiente de AL, Pkadj, ACD y la Edad. Siendo nuestro valor de ELPadj
significativamente menor comparado con los valores obtenidos con el resto de
fórmulas comerciales analizadas. No se obtuvieron errores clínicamente
significativos,aunquesifueronclínicamenterelevantesloslímitesdeacuerdo,entre
nuestra PIOLadj y la PIOLReal, pero sí entre nuestra PIOLadj y el resto de fórmulas
comerciales. Concluyendo que la PIOLadj es la que mejor reproduce los valores de
PIOLReal.
Los resultados refractivos obtenidos en el caso de implante de la lente
intraocularmultifocalLentisMplusLS-312despuésdecirugíadecatarata,aligualque
enel estudioanterior,puedeoptimizarsemedianteunalgoritmodecálculodenkadj
paraminimizarelerrorenelcálculodelapotenciacornealqueratométrica,además
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122
de una optimizacióndel valor deELP, en este casodependiente deAL,Pkadj yACD.
Siendo en este caso también significativamente menor nuestro valor de ELPadj
comparadoconlosvaloresobtenidosconelrestodefórmulascomercialesanalizadas,
siendo estas diferencias mínimas para la pareja ELPadj – ELPHolladay. En este caso,
tampoco se obtuvieron errores clínicamente significativos, aunque si fueron los
límitesdeacuerdoentrenuestraPIOLadjy laPIOLRealyentrePIOLadjyPIOLHolladay.Siendo
para la pareja PIOLadj - PIOLReal la que proporcionó un menor intervalo de acuerdo
respectoalrestodefórmulascomercialesanalizadas,indicandoqueseríalafórmula
másadecuadaparareproducirlosvaloresdePIOLReal.
Los resultados refractivos obtenidos en el caso de implante de la lente
intraocular asféricaLentisL-313después de cirugía de catarata, al igual que en los
estudiosanteriores,tambiénpuedeoptimizarsemedianteunalgoritmodecálculode
nkadj para minimizar el error en el cálculo de la potencia corneal queratométrica,
ademásdeunaoptimizacióndelvalordeELP.Sinembargo,enestaocasiónsedividió
lamuestraendosgruposenfuncióndelvalorde lapotenciade la lente intraocular
implantada, siendo el valor de ELPadj dependiente de la Edad y el astigmatismo
corneal,paralamuestraPIOLadj>23DydependientedelaEdad,ACD,ALyr1cparala
muestraPIOLadj<23D.SiendoelvalordeELPadjmayorenojosconmayorALyACD.
Sin embargo, el valor más bajo de ELP para ambos grupos, se correspondió con
ELPHolladay. Al igual que en los estudios anteriores, no se obtuvieron errores
clínicamente significativos entre nuestra PIOLadj y PIOLReal, en ninguno de los dos
grupos. Al comparar PIOLadj con el resto de fórmulas comerciales, se encontraron
diferencias significativas excepto cuando se comparó con PIOLHaigis, posiblemente
debidoallimitadotamañodelamuestra.NuestraPIOLadjfuecapazdereproducircon
más precisión el valor de la indicando de este modo que sería la fórmula más
adecuadaparareproducirlosvaloresdePIOLReal.
5.bPerspectivasdefuturo
Variossonlosobjetivosplanteadosparafuturosestudios,comoson:
Evaluarelimpactodelaestimaciónqueratométricaenpacientessometidosa
cirugíapreviaparaconfirmarel inadecuadousodeunúnico índicequeratométrico,
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123
ademásdecomprobarelbeneficiodeestealgoritmoparaoptimizarelcálculode la
potenciadelalenteintraocular.
Es necesario confirmar todos los resultados obtenidos teóricamente en el
cálculo de la potencia de la lente intraocular con diferentes tipos de lentes
intraocularesyporconsiguientecondiferentesconstantesA.
Sedebeanalizar la influenciade lapotenciaqueratométricaajustadaparael
cálculodelapotenciadecadalenteintraocularanalizada,comosonlaacomodativa,
multifocalyasférica,sobreunamuestramásgrandeincluyendocasosextremos(ojos
largosycortos).
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127
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APÉNDICE
ARTICLE
Clinical validation of
an algorithm to correctthe error in the keratometric estimationof corneal power in normal eyesDavid P. Pi~nero, PhD, Vicente J. Camps, PhD, Ver�onica Mateo, MSc, Pedro Ruiz-Fortes, OD
Q 2012 A
Published
SCRS an
by Elsev
PURPOSE: To validate clinically in a normal healthy population an algorithm to correct the error inthe keratometric estimation of corneal power based on the use of a variable keratometric index ofrefraction (nk).
SETTING: Medimar International Hospital (Oftalmar) and University of Alicante, Alicante, Spain.
DESIGN: Case series.
METHODS: Corneal power was measured with a Scheimpflug photography–based system (Penta-cam software version 1.14r01) in healthy eyes with no previous ocular surgery. In all cases,keratometric corneal power was also estimated using an adjusted value of nk that is dependenton the anterior corneal radius (r1c) as follows: nkadj Z �0.0064286 r1c C1.37688. Agreementbetween the Gaussian (Pc
Gauss) and adjusted keratometric (Pkadj) corneal power values wasevaluated.
RESULTS: The study evaluated 92 eyes (92 patients; age range 15 to 64 years). The mean differencebetween Pc
Gauss and Pkadj was �0.02 diopter (D)G 0.22 (SD) (PZ.43). A very strong, statisticallysignificant correlation was found between both corneal powers (r Z .994, P<.01). The rangeof agreement between Pc
Gauss and Pkadj was 0.44 D, with limits of agreement of �0.46 andC0.42 D. In addition, a very strong, statistically significant correlation of the difference betweenPc
Gauss and Pkadj and the posterior corneal radius was found (r Z 0.96, P<.01).
CONCLUSION: The imprecision in the calculation of corneal power using keratometric estimationcan be minimized in clinical practice by using a variable keratometric index that depends on theradius of the anterior corneal surface.
Financial Disclosure: No author has a financial or proprietary interest in any material or methodmentioned.
J Cataract Refract Surg 2012; 38:1333–1338 Q 2012 ASCRS and ESCRS
Accuratemeasurement of corneal power (Pc) in clinicalpractice is crucial because this parameter is used forseveral purposes, such as intraocular lens (IOL) powercalculation, contact lens management, and keratoco-nus diagnosis. However, the total Pc is usually calcu-lated considering only the radius of curvature of theanterior corneal surface measured using a keratometeror a topography system.1 This simplification arisesbecause in the past, it has been difficult to measurethe posterior corneal surface because of technologicallimitations. In addition, there was an assumptionthat this surface contributes little to the ocular refrac-tive power because of the small difference in therefractive index at this surface.1 In an attempt to mini-mize the error caused by this simplification, the
d ESCRS
ier Inc.145
keratometric index of refraction (nk) was defined.Themost commonly used approach in a clinical settingis to estimate Pc by considering only the radius ofcurvature of the anterior corneal surface and the nkvalue of 1.3375, which is used by most commerciallyavailable keratometers and topography systems. Aclear trend toward Pc overestimation has been re-ported with the estimation obtained with this specificvalue of nk.2–10 Several recalculations of nk have beenproposed to compensate for the keratometric Pc esti-mation error.2,3,5,6,9,11 However, differences betweenkeratometric and Gaussian corneal powers in normalhealthy populations have been reported even withthe use of some of these recalculations (Ho et al.,3 range�1.10 to 0.87 D; Fam and Lim,4 range�1.29 to 0.49 D).
0886-3350/$ - see front matter 1333doi:10.1016/j.jcrs.2012.03.026
1334 ALGORITHM TO CORRECT KERATOMETRIC ERROR IN NORMAL EYES
Today, new advanced devices, such as the Scheimp-flug photography–based tomographers,12,13 are avail-able that allow clinicians to measure the anterior andposterior corneal surfaces simultaneously and reliably.These devices normally provide the true net power,which considers the real optical conditions of thecornea. Specifically, the true net power is calculatedusing the Gaussian equation and therefore consideringthe measured values of the anterior corneal radius ofcurvature (r1c), posterior corneal radius of curvature(r2c), central corneal thickness (ec), and conditionsof the Gullstrand eye model (corneal refractiveindex nc Z 1.376; aqueous humor refractive indexnha Z 1.336). Despite the adequacy of this approachfor Pc calculation, these devices are not alwaysavailable in clinical practice. For this reason, Pc estima-tions based on r1c only are commonly used. Ourresearch group recently proposed the use of a variablenk (nkadj) that depends on the radius of curvature ofthe anterior corneal surface.1 Specifically, the mostappropriate value of nk to use in each specific case isderived from a simple linear equation that requiresonly the r1c value in millimeters. This approachprovides Pc estimations differing from the Gaussiancalculation a maximum of 0.70 diopter (D) and lessthan 0.50 D in most of the probable combinations ofr1c and r2c.1
The aim of the current study was to clinicallyvalidate this algorithm based on the use of a variablenk developed to correct the error in the keratometricestimation of Pc in a normal healthy population.
PATIENTS AND METHODS
This study comprised candidates for corneal refractive sur-gery who were screened at the Department of Ophthalmol-ogy (Oftalmar) of the Medimar International Hospital,Alicante, Spain. For the study, 1 eye of each patient waschosen according to a random-number sequence (dichoto-mic sequence, 0 and 1). Eyes with active ocular pathologyor previous ocular surgery were excluded from the study.All patients were informed about the study and signed an
Submitted: December 19, 2011.Final revision submitted: February 15, 2012.Accepted: March 5, 2012.
From Grupo de �Optica y Percepci�on Visual (Pi~nero, Camps, Mateo),the Department of Optics, Pharmacology and Anatomy, Universityof Alicante, the Department of Ophthalmology, Oftalmar (Pi~nero,Ruiz-Fortes), Medimar International Hospital, and the Foundationfor the Visual Quality (Pi~nero), Alicante, Spain.
Corresponding author: David P. Pi~nero, PhD, Department of Optics,Pharmacology and Anatomy, University of Alicante, Carretera SanVicente del Raspeig s/n, 03690 San Vicente del Raspeig, Alicante,Spain. E-mail: david.pinyero@ua.es.
J CATARACT REFRACT SURG -
146
informed consent document in accordance with the Declara-tion of Helsinki.
Clinical Evaluation
A comprehensive ophthalmologic examination was per-formed in all cases. It included refraction, corrected distancevisual acuity (CDVA), slitlamp biomicroscopy, Goldmanntonometry, fundus evaluation, and analysis of the cornealstructure using a Scheimpflug photography–based tomogra-pher (Pentacam system, software version 1.14r01, OculusOptikger€ate GmbH). Specifically, the following parameterswere recorded and analyzed: anterior corneal radius (r1c)and posterior corneal radius (r2c) in the central 3.0 mm cor-neal area; anterior corneal astigmatism (ACA) and posteriorcorneal astigmatism (PCA) in the central 3.0 mm cornealarea; the true net power, which is the Pc calculated usingthe Gaussian equation with the Gullstrand eye model(Pc
Gauss); anterior chamber depth (ACD), defined as the dis-tance from corneal epithelium to lens surface; and centralcorneal thickness (ec).
Scheimpflug System
The Pentacam is a noninvasive system for measuring andcharacterizing the anterior segment using a rotatingScheimpflug camera.12,13 The rotational measuring proce-dure generates Scheimpflug images in 3 dimensions, withthe dot matrix fine-meshed in the center due to the rotation.It takes a maximum of 2 seconds to generate a completeimage of the anterior eye segment. Any eye movement isdetected by a second camera and corrected for in the process.The system calculates a 3-dimensional model of the anterioreye segment from as many as 25 000 true elevation points.The Scheimpflug images taken during the examination aredigitized in the main unit, and all image data are transferredto a computer.
Correction of Keratometric Estimation Error
As previously stated, the use of a variable keratometricindex (nkadj) has been proposed for Pc calculation; the vari-able is dependent on the radius of the anterior corneal sur-face (r1c).1 Specifically, the following expression wasdefined assuming the ocular conditions of the Gullstrandeye model and the range of anterior and posterior curvaturefor the normal healthy population1:
nkadjZ � 0:0064286 r1c þ 1:37688 (1)
The Pc valuewas calculated considering nkadj to determinewhether it minimizes the error associated to the keratometricestimation of Pc (DPc) as follows:
PkadjZnkadj � 1
r1c(2)
The difference between Pkadj and the true net powerprovided directly by the Scheimpflug photography–basedsystem, which is the Pc derived from the Gaussian equation(Pc
Gauss), was calculated (DPc). The agreement between Pkadjand PGauss
c was carefully evaluated.
Statistical Analysis
Statistical analysis was performed using the SPSS forWindows software (version 19.0, SPSS, Inc.). Normality of
VOL 38, AUGUST 2012
1335ALGORITHM TO CORRECT KERATOMETRIC ERROR IN NORMAL EYES
data distributions was first evaluated using theKolmogorov-Smirnov test. Only the variables Pc
Gauss, Pkadj,DPc, and ec followed a normal distribution. Thus, parametricstatistics were applied for statistical analysis involving thesevariables. Specifically, the unpaired Student t test was usedfor comparing the 2 approaches for Pc calculation. Bland-Altman analysis14 was used to evaluate the interchangeabil-ity of the 2 methods used for obtaining Pc, the Gaussiancalculation (true net power), and the adjusted keratometricestimation. Specifically, Bland-Altman plots show the differ-ences between the methods evaluated plotted against themean of the 2 methods. The limits of agreement are definedas the mean G1.96 standard deviation (SD) of the differ-ences. Pearson or Spearman correlation coefficients, depend-ing on whether the normality condition could be assumed,were used to assess the correlation between DPc and allanalyzed parameters.
Figure 1. Relationship between the Gaussian corneal power (PcGauss)
and the adjusted keratometric corneal power (Pkadj).
RESULTSThis study comprised 92 eyes of 92 patients (47women[51.1%]) with a mean age was 36.7 years G 10.3 (SD)(range 15 to 64 years). The sample comprised 49 righteyes (53.3%). Table 1 shows the mean ocular featuresof the eyes evaluated.
Agreement of Pkadj and PGaussc
No statistically significant differences were foundbetween Pkadj and Pc
Gauss (true net power) (PZ.43,unpaired Student t test). A very strong, statisticallysignificant correlation was found between Pkadj andPc
Gauss (r Z 0.994, P!.01) (Figure 1). According tothe Bland and Altmanmethod, the range of agreementbetween Pkadj and Pc
Gauss was 0.44 D, with limits ofagreement of �0.46 and C0.42 D. Figure 2 shows theBland and Altman plot corresponding to this
Table 1. Mean ocular features.
Parameter Mean G SD Range
SE (D) �2.80 G 3.89 �15.75, C4.00r1c (mm) 7.67 G 0.01 7.19, 8.43r2c (mm) 6.30 G 0.21 5.87, 6.82ACA (D) 1.13 G 0.98 0.00, 5.80PCA (D) 0.36 G 0.24 0.00, 1.60PGaussC ðDÞ 42.76 G 1.30 38.80, 45.50Pkadj (D) 42.74 G 1.47 38.28, 45.99DPc (D) �0.02 G 0.22 �0.55, C0.52ACD (mm) 3.08 G 0.38 2.21, 4.96ec (mm) 559.0 G 33.8 485, 665
DPc Z difference between Pkadj and PGaussc ; ACAZ anterior corneal astig-matism; ACD Z anterior chamber depth; ec Z central corneal thickness;PCA Z posterior corneal astigmatism; PGaussc Z true net or Gaussianpower; Pkadj Z corneal power obtained using the adjusted keratometricindex; r1c Z radius of the anterior corneal surface; r2c Z radius of theposterior corneal surface; SE Z spherical equivalent
J CATARACT REFRACT SURG -
147
agreement analysis. There was a trend toward Pc over-estimation with the use of nkadj for steep corneas,whereas the opposite trend was present for flatcorneas; the trends were not clinically relevant.
Correlation of DPc with Other Clinical Variables
The correlations of DPc with several variables werepoor and not significant; the variables included age(r Z 0.13, PZ.21), spherical equivalent (r Z �0.045,PZ.67), CDVA (r Z 0.04, PZ.73), ACD (r Z �0.05,PZ.64), ec (r Z �0.09, PZ.41), ACA (r Z 0.07,
Figure 2. Differences between the adjusted keratometric cornealpower (Pkadj) and the Gaussian corneal power (Pc
Gauss) plottedagainst the mean value of both. The upper and the lower linesrepresent the limits of agreement calculated as mean of differencesG1.96 SD.
VOL 38, AUGUST 2012
Figure 3. Relationship of the difference (DPc) between the Gaussiancorneal power (Pc
Gauss) and the adjusted keratometric corneal power(Pkadj) with the radius of the posterior corneal surface (r2c). Theadjusting line to the data obtained by means of the least-squares fitis shown in the 2 graphs as follows:DPcZ 6.46� 1.03 r2c (R2Z 0.92).
1336 ALGORITHM TO CORRECT KERATOMETRIC ERROR IN NORMAL EYES
PZ.52), and PCA (r Z 0.08, PZ.43). However, a verystrong, statistically significant correlation was foundbetween DPc and r2c (r Z �0.96, P!.01) (Figure 3).Furthermore, a statistically significant correlationwas found between DPc and r1c (r Z �0.79, P!.01),although the correlation was of less magnitude.
DISCUSSION
Numerous approaches for defining a keratometric in-dex (nk) have been developed, allowing the clinician toobtain an estimation of Pc by considering the cornea asa single refractive surface.2–4,9,11 The classic nk value of1.3375 was proposed for convenience rather than foroptical significance because it provided an agreementbetween a specific value of the anterior radius of cur-vature and the total Pc (7.5 mm and 45.0 D).10 Othernk values have been derived from schematic eyemodels, such as the value of 1.3315, whichwas derivedfrom the Gullstrand schematic eye and recommendedby Olsen.10 Several authors have provided other nkvalues obtained from normal and healthy populations.For example, Shammas et al.2 defined an effectiveindex of refraction closer to 1.329. Ho et al.3 obtaineda mean calculated nk of 1.328 G 0.0018 (range 1.3209to 1.3363) and propose using different nk valuesdepending on the corneal area analyzed (1.3278G 0.0027, 1.3284 G 0.0021, 1.3284 G 0.0031, 1.3280G 0.0038, and 1.3277 G 0.0042 for the central3.0 mm, 5.0 mm, 6.0 mm, 7.0 mm, and 7.5 mm zones,respectively). All these approaches attempted to
J CATARACT REFRACT SURG -
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minimize the difference between the keratometricand Gaussian corneal power (DPc) using a single nkvalue with the SD or range as a general solution. How-ever, differences between keratometric and Gaussianpowers have been reported despite the use of someof the proposed nk values; some differences werehigher than 1.0 D.3,4 One factor accounting for this isthe incorrect assumption of a constant and linearrelationship1,4,5 between the curvature of the anteriorand the posterior corneal surface. The k ratio, whichis defined as the ratio of r1c to r2c, is not constant inthe range of curvatures of the normal healthy cornea,which range from 1.157 to 1.295.15–17
In a previous simulation study performed by ourresearch group using the Gullstrand and Le Grandeye models,1 we found that keratometric estimationcan significantly overestimate or underestimate theGaussian corneal power. This error (DPc) was foundto be dependent on both r1c and r2c, and therefore onthe k ratio.1 Corneal power overestimation wasalways found in both eye models when an nk valueof 1.3375 was used. These findings1 and those in previ-ous studies2–4 show there is a need for a precise modelto determine the most appropriate nk value forcalculating Pc with the keratometric approach. We de-veloped and reported a fast, easy, and clinicallyapplicable method for determining the most appropri-ate nk for the keratometric estimation in each specificcase.1 It uses a linear equation to determine nk (nkadj),which is dependent only on r1c, a parameter easilymeasurable in the clinical setting with a variety of de-vices. The maximum calculated error associated withthis approach (DPc) was 0.70 D, corresponding to the2 highest and 2 lowest r2c values of the range definedfor the normal and healthy population (5.5 mm,5.6 mm, 6.9 mm, and 7.0 mm). For the remaining r2cvalues, the error associated with the use of nkadj wasbelow 0.50 D, independent of the r1c value. The aimof the current study was to validate clinically the nkadjalgorithm developed to correct the error in thekeratometric estimation of Pc in a normal healthypopulation.
As expected, the corneal powers Pkadj and PcGauss
(true net power)were strongly correlated.Mean differ-ence between Pkadj and Pc
Gauss in the analyzed samplewas�0.02 D (range�0.55 toC0.52 D), confirming ourprevious theoretical results. This difference did notreach statistical significance, confirming the similarityof both Pc calculation methods. Differences up to0.50 D between Pkadj and Pc
Gauss might be consideredacceptable in clinical practice and thus not clinicallyrelevant. A variation of 0.50 D is equivalent to mini-mum differences in r1c (!0.1 mm), which are equiva-lent to or slightly higher than the curvature steps ofcurrently available contact lenses. In addition, an error
VOL 38, AUGUST 2012
1337ALGORITHM TO CORRECT KERATOMETRIC ERROR IN NORMAL EYES
of 0.50 D in Pc estimation induces errors in IOL powerestimation by only as much as 0.50 D at the cornealvertex according to optical simulations,1 which isthe minimum IOL power step provided by mostmanufacturers. Bland and Altman analysis14 con-firmed the clinical validity of the nkadj algorithm,with a range of agreement between Pkadj and Pc
Gauss
of 0.44 D. Therefore, 95% of differences between theGaussian and adjusted keratometric calculationswere 0.44 D or less. This excellent outcome confirmsthe interchangeability of the 2 approaches for calculat-ing Pc for clinical purposes.
The linear equation defining nkadj was obtained byconsidering the magnitude of DPc for all the combina-tions of r1c and r2c in the range of Pc in the normalhealthy population, including combinations of flatanterior and steep posterior corneal curvatures andvice versa. This is the reason for the trend observedin the Bland and Altman plot toward Pc overestima-tion by using nkadj for steep corneas and the oppositetrend for flat corneas. The curvature of both cornealsurfaces is correlated in normal eyes18,19; therefore, ifthe anterior corneal surface is steep, the posterior isalso expected to be steep. This potential correlationwas not considered in the definition of the nkadjalgorithm. In concordance with this, DPc was foundto be strongly correlated with r2c (r Z 0.96). In anycase, these trends toward Pc overestimation for steepcorneas and underestimation for flat corneas werenot clinically relevant. Indeed, the range of agreementbetween Pkadj and Pc
Gauss was 0.44 D. All these find-ings confirm the relevance of the curvature of theposterior corneal surface in the error of the keratomet-ric estimation, even minimizing it by consideringa variable nk (nkadj).
In summary, the imprecision in the calculation ofPc with keratometric estimation can be minimizedin clinical practice by using a variable keratometricindex that depends on the radius of the anteriorcorneal surface. This approach is valid only whenthe curvature of the posterior corneal surface is notavailable clinically because the best option is to calcu-late the Gaussian corneal power considering thecurvature of both corneal surfaces. The potentialimprovement of our algorithm, including the profileof correlation between anterior and posterior cornealcurvature, should be evaluated. In addition, futurestudies evaluating the impact of posterior corneal sur-face changes after different types of corneal surgeryon the keratometric estimation should be evaluatedto confirm the inadequacy of using such simplifica-tion in these cases. In addition, the potential benefitof using this algorithm in IOL power calculationto optimize the refractive outcomes should beevaluated.
J CATARACT REFRACT SURG - V
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WHAT WAS KNOWN
� A clear trend toward corneal power overestimation hasbeen reported with the estimation obtained with thekeratometric refractive index of 1.3375.
� Theoretical simulations have demonstrated that this over-estimation can be minimized by using a linear adjustmentbased on the curvature of the anterior corneal surface.
WHAT THIS PAPER ADDS
� The imprecision in the calculation of corneal power usingthe keratometric estimation in normal healthy eyes can beminimized in the clinical practice by using a variablekeratometric index that depends on the radius of theanterior corneal surface, with a level of agreement withthe Gaussian corneal power below 0.50 D.
REFERENCES1. Camps V, Pi~nero Llorens DP, de Fez D, Coloma P,
Caballero MT, Garc�ıa C, Miret JJ. Algorithm for correcting the
keratometric estimation error in normal eyes. Optom Vis Sci
2012; 89:221–228
2. ShammasHJ, Hoffer KJ, ShammasMC. Scheimpflug photogra-
phy keratometry readings for routine intraocular lens power
calculation. J Cataract Refract Surg 2009; 35:330–334
3. Ho J-D, Tsai C-Y, Tsai RJ-F, Kuo L-L, Tsai I-L, Liou S-W.
Validity of the keratometric index: evaluation by the Pentacam
rotating Scheimpflug camera. J Cataract Refract Surg 2008;
34:137–145
4. Fam H-B, Lim K-L. Validity of the keratometric index: large
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5. Borasio E, Stevens J, Smith GT. Estimation of true corneal
power after keratorefractive surgery in eyes requiring cataract
surgery: BESSt formula. J Cataract Refract Surg 2006;
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6. Tang M, Li Y, Avila M, Huang D. Measuring total corneal power
before and after laser in situ keratomileusis with high-speed
optical coherence tomography. J Cataract Refract Surg 2006;
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7. Canarim de Oliveira �EC, Arce CG, Campos M, Schor PO.
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8. Espinosa J, Rouarch J, P�erez J, Illueca C, Mas D. Geometrical
approximations for accurate evaluation of refraction in the
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9. Gobbi PG, Carones F, Brancato R. Keratometric index, video-
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10. OlsenT.On the calculation of power fromcurvature of the cornea.
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11. Dunne MCM, Royston JM, Barnes DA. Normal variations of the
posterior corneal surface. Acta Ophthalmol (Copenh) 1992;
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12. Shankar H, Taranath D, Santhirathelagan CT, Pesudovs K.
Anterior segment biometry with the Pentacam: comprehensive
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13. Pi~nero DP, Saenz Gonz�alez C, Ali�o JL. Intraobserver and
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VOL
38, AUGUST 2012First author:David P. Pi~nero, PhD
Department of Optics, Pharmacologyand Anatomy, University of Alicante,Alicante, Spain
Minimizing the IOL Power Error Induced byKeratometric Power
Vicente J. Camps*, David P. Pinero*, Dolores de Fez*, and Veronica Mateo†
ABSTRACTPurpose. To evaluate theoretically in normal eyes the influence on IOL power (PIOL) calculation of the use of a keratometricindex (nk) and to analyze and validate preliminarily the use of an adjusted keratometric index (nkadj) in the IOL powercalculation (PIOLadj).Methods. A model of variable keratometric index (nkadj) for corneal power calculation (Pc) was used for IOL power cal-culation (named PIOLadj). Theoretical differences ($PIOL) between the new proposed formula (PIOLadj) and which is obtainedthrough Gaussian optics (PIOL
Gauss) were determined using Gullstrand and Le Grand eye models. The proposed new formula for IOLpower calculation (PIOLadj) was prevalidated clinically in 81 eyes of 81 candidates for corneal refractive surgery and compared withHaigis, HofferQ, Holladay, and SRK/T formulas.Results. A theoretical PIOL underestimation greater than 0.5 diopters was present in most of the cases when nk = 1.3375 wasused. If nkadj was used for Pc calculation, a maximal calculated error in $PIOL of T0.5 diopters at corneal vertex in most caseswas observed independently from the eye model, r1c, and the desired postoperative refraction. The use of nkadj in IOL powercalculation (PIOLadj) could be valid with effective lens position optimization nondependent of the corneal power.Conclusions. The use of a single value of nk for Pc calculation can lead to significant errors in PIOL calculation that mayexplain some IOL power overestimations with conventional formulas. These inaccuracies can be minimized by using thenew PIOLadj based on the algorithm of nkadj.(Optom Vis Sci 2013;90:639Y649)
Key Words: intraocular lens, IOL power, IOL power calculation, HofferQ, Holladay, Haigis, SRK-T
Unsatisfactory visual outcomes after cataract surgery as aresult of a residual refractive error can be obtained be-cause of inaccuracies in biometric analysis,1 inadequate
calculation and selection of the intraocular lens (IOL) power,1 orlongitudinal IOL positional errors.2 Some studies have evidencedthat some errors are still possible in the calculation of the IOLpower (PIOL) for a normal eye (no pathology or previous ocularsurgeries) despite the technological diagnostic advances and thelatest formulas developed for PIOL calculation.3 The most im-portant sources of these errors are the axial length (AL), the ef-fective lens position (ELP), and the corneal power (Pc).
3
An accurate calculation of the corneal optical power is crucialfor an optimized IOL power calculation. It is even relevant for theprediction of the ELP in some of the third- and fourth-generationformulas.3 In clinical practice, total corneal power is still calcu-lated only considering the radius of curvature of the anteriorcorneal surface measured by means of a keratometer or a topog-raphy system. Specifically, the cornea is assumed to have a singlespherical surface with the radius of curvature of the epithelialsurface and an adjusted index of refraction, the keratometric in-dex (nk), providing a correction for such simplification. Severalauthors have analyzed such simplification, some of them reveal-ing that the keratometric corneal power (Pk) can lead to an over-estimation of the corneal optical power.4Y6
Different values of nk have been defined as useful for PIOL
calculations, such as the value of 1.3315 described by Olsen,7
the value of 4/3 described by Holladay,8 or the value of 1.333used in the SRK/T formula.9 Other authors have also performedrecalculations of the nk with the aim of defining a more accu-rate approach to overcome the errors introduced by the cor-neal keratometric power.6,10,11 Our research group has recently
1040-5488/13/9007-0639/0 VOL. 90, NO. 7, PP. 639Y649
OPTOMETRY AND VISION SCIENCE
Copyright * 2013 American Academy of Optometry
ORIGINAL ARTICLE
Optometry and Vision Science, Vol. 90, No. 7, July 2013
*PhD†MSc
Grupo de Optica y Percepcion Visual, Department of Optics, Pharmacology
and Anatomy, University of Alicante, Alicante, Spain (VJC, DPP, DdF, VM); and
Foundation for the Visual Quality (Fundacion para la Calidad Visual-FUNCAVIS),
Alicante, Spain (DPP).
151
proposed the use of a variable nk for normal and nonpathologicalpopulations, depending on the radius of curvature of the anteriorcorneal surface.4,5 Specifically, the most appropriate value of nk touse in each specific case is derived from a simple linear equationonly requiring the anterior corneal radius (r1c) in millimeters andwith a maximal associated error in the calculation of the cornealpower of 0.5 diopters (D).4 These theoretical results were vali-dated clinically.5
The aim of the current study was to evaluate in a normalpopulation (no pathology and previous ocular surgeries) thetheoretical influence on IOL power (PIOL) calculation of the errorin the calculation of corneal power ($Pc) caused by the use of thekeratometric index (nk) and to develop and validate preliminarilyan algorithm to avoid this influence.
METHODS
Corneal power was calculated for the range of anterior andposterior curvatures of the healthy cornea according to the peer-reviewed literature by using nk and also by using the Gaussianequation that considers the contribution of two corneal surfaces.The nk values corresponding to the Gullstrand12 and Le Grandeye13,14 models (1.3315 and 1.3304, respectively) and the clas-sical value of 1.3375 were used. Differences in the IOL powercalculation obtained with a simplified formula using the ker-atometric and Gaussian corneal power were determined andmodeled by regression analysis. All calculations and simula-tions were performed by Matlab software (MathWorks Inc.,Natick, MA).
Calculation of the Gaussian and Keratometric IOLPower
The starting point of almost all theoretical formulas for IOLpower calculation is the classical vergence equation based on theuse of a simplified eye model, with thin cornea and lens models.3
According to such scheme, the power of the IOL (PIOL) thatreplaces the lens can be easily calculated using the Gauss equationsin paraxial optics:
PIOL ¼ nhvðALjELPÞj
nhanha
Rdes þ PcjELP
� � ð1Þ
The first term after the equal sign is an expression for the vergencethat must leave the effective lens position (ELP) to focus on theretina. The second term is the vergence arriving at the ELP, sothe difference between those two yields is the required power ofthe IOL. In this equation, Pc represents the total corneal power,ELP, the effective lens position, AL, the axial length, nha, theaqueous humor refractive index, nhv, the vitreous humor refractiveindex, and Rdes represents the postoperative desired refraction cal-culated at corneal vertex.
The IOL power when a keratometric corneal power (Pk) wasused for its estimation was defined as Pk
IOL and the IOL powerwhen a Gaussian corneal power P c
Gauss was used as defined asP IOL
Gauss. The calculation of Pk and P cGauss was described in detail in
a previous article of our research group.4 The calculation of P kIOL
and P IOLGauss was performed as follows:
PkIOL ¼
nhvALjELF
jnha
nha
Rdes þ nkj1
r1c
jELPð2Þ
PGaussIOL ¼
nhvALjELP
� nhanha
Rdes þ ncjna
r1cþ nhajnc
r2cj
ec
ncqncjna
r1cqnhajnc
r2c
� �jELPð3Þ
It is important to note here that in equations 2 and 3, thecorneal power is referenced from different planes because of theone-surface and two-surface corneal models considered. However,the secondary principle plane for corneas in the normal range isonly around a fraction of millimeter from the corneal vertex.Therefore, the use of these relatively different reference planes inequations 2 and 3 could not introduce any significant bias in thecalculations proposed. For example, in the complete Le Grand eyemodel, a distance of only 0.06 mm is present between the sec-ondary principle plane and the corneal vertex.13
We defined the k ratio as the relation between the anteriorcorneal radius and the posterior corneal radius (k = r1c/r2c). Whenthis parameter was used in equation 3, we obtained the followingexpression:
PGaussIOL ¼
nhvALjELP
jnha
Rdes þ ncjna
r1cþ nhajnc
r1ck
jec
ncqncjna
r1cqnhajnc
r1ck
0@
1A
jELP ð4Þ
In all these expressions, nk is the keratometric index, r1c, theanterior corneal surface radius, r2c, the posterior corneal radius, na
is the refractive index of air, nc, the refractive index of the cornea,nha, the refractive index of the aqueous humor, and ec is the centralcorneal thickness.
Difference between the Gaussian and KeratometricIOL Power
The difference between the keratometric and Gaussian IOLpower calculation ($PIOL) was obtained by using equations 2 and4 as follows:
$PIOL ¼ PkIOLjPGauss
IOL ¼nha
nha
Rdes þ ncjna
r1cþ nhajnc
r2cj
ec
ncqncjna
r1cqnhajnc
r2c
� �jELP
jnha
nha
Rdes þ nkj1
r1c
jELPð5Þ
If the k ratio was used in equation 5, we obtained the followingexpression:
$PIOL ¼ nhanha
Rdes þ ncjna
r1cþ nhajnc
r1c
k
jec
ncqncjna
r1cqnhajnc
r1c
k
0BBB@
1CCCA
jELPj
nhanha
Rdesþnkj1
r1c
jELPð6Þ
As can be seen in equations 5 and 6, $PIOL was not depen-dent on AL.
640 Minimizing IOL Power Error Induced by Keratometric PowerVCamps et al.
Optometry and Vision Science, Vol. 90, No. 7, July 2013
152
The $PIOL was calculated for the range of corneal curvatureof the normal population. According to the peer-reviewedliterature,4,6,10,15Y19 we considered that the anterior corneal ra-dius in the healthy normal population ranged between 7 and8.5 mm, whereas the posterior corneal radius ranged between 5.6and 7 mm. Therefore, we assumed k ratio values ranging from 1 to1.51 in our theoretical calculations. In addition, we considered inthe calculations performed in the current study that ELP could varybetween 2 and 6 mm according to previous authors dealing with thisissue.3,20,21 The desired postoperative refraction was also varied inthe calculations, performing an analysis of $PIOL for values of Rdes
of 0, +1, and j1 D.
Difference between the Gaussian and KeratometricIOL Power Using the Adjusted Keratometric Index
As previously commented, our research group recently pro-posed the use of a variable keratometric index (nkadj) depending onthe radius of the anterior corneal surface (r1c) expressed in mil-limeters for corneal power calculations.4 Specifically, two differentexpressions were defined depending on the eye model used:
Gullstrand eye model; nkadj ¼ j0:0064286 r1c
þ 1:37688ð7Þ
Le Grand eye model; nkadj ¼ j0:0063804 r1cþ1:37806
ð8Þ
Using these algorithms, a new keratometric corneal power(named adjusted keratometric corneal power, Pkadj) can be cal-culated using the classical keratometric corneal power formula.4
Therefore, PIOLadj was defined as the IOL power calculated fromequation 2 using the nkadj value for the estimation of the cornealpower (Pkadj). After that, $PIOL was also calculated consideringthe adjusted IOL power (PIOLadj) and the Gaussian IOL powerðPGauss
IOL ).
Preliminary Clinical Validation
A preliminary validation of the IOL power calculation with thealgorithm proposed in this study was performed in a sample ofnormal eyes with AL between 22 and 26 mm to avoid in thispreliminary study the inclusion of highly myopic or hyperopiceyes. Specifically, 81 eyes of 81 candidates for corneal refractivesurgery who were screened at the Department of Ophthalmology(Oftalmar) of the Medimar International Hospital (Alicante,Spain) were included. Only one eye from each subject was chosenrandomly for the study according to a random number sequence(dichotomic sequence, 0 and 1). Eyes with active ocular pathol-ogies or previous ocular surgeries were excluded from the study.This clinical study was approved by the local ethics committee andhas therefore been performed in accordance with the ethicalstandards laid down in the 1964 Declaration of Helsinki. Writteninformed consent was obtained after explaining the nature of theprocedure before surgery in all cases.
A comprehensive ophthalmologic examination was performedin all cases, which included optical biometry (IOLMaster, Carl ZeissMeditec) and analysis of the corneal structure by means of aScheimpflug photographyYbased tomographer, the Pentacam system(software version 1.14r01, Oculus Optikgerate GmbH, Germany).
Intraocular lens power calculation was performed with the IOL-Master software using the SRK/T, Haigis, HofferQ, and Holladayformulas and also with our paraxial approximation using the nkadj
(PIOLadj). All calculations in all formulas were performed for only onesimulated IOL type with an A-constant of 118.0. A comparativeanalysis of our estimations with those obtained with the otherestablished formulas was performed by using the statistical softwareSPSS version 19.0 for Windows (IBM, Armonk, NY). Normality ofdata distributions was first evaluated by means of the Kolmogorov-Smirnov test. The unpaired Student t test was used for analyzingthe statistical significance of differences between IOL power calcu-lations, whereas the Bland-Altman method was used for evaluatingthe interchangeability of such calculations. In the Bland-Altmananalysis, differences between the different formulas evaluated in theIOL power to implant were considered as clinically relevant forvalues of more than 0.5 D because this value is the IOL power stepprovided currently by most manufacturers and has been shown to bethe optical neutralization tolerance since many years ago.13 Besidesall these analyses, Pearson correlation coefficients were used to assessthe correlation between differences among calculations and differentclinical parameters. Finally, it should be considered that the calcu-lations with our algorithm were performed using the values of ELPobtained with the estimation equations defined by the authors de-veloping each of the formulas used (Haigis, HofferQ, SRK/T, andHolladay).20,22,23
RESULTS
Relationship between $PIOL and $Pc
Table 1 summarizes the $PIOL outcomes obtained within thenormal range of anterior corneal curvature (r1c, from 7 to 8.5 mm)for each eye model and for the different nk values used. The in-terval shown for each value of $PIOL and $Pc corresponded to thevalues associated to the extreme values of the normality rangedefined for r2c, from 5.6 to 7 mm.
As shown in Table 1, there was an underestimation of the IOLpower by P k
IOL with respect to P GaussIOL ($PIOL 90) provided that
an overestimation of the corneal power was present and vice versa. Inboth theoretical eyes models, overestimations and underestimationsof IOL power were possible depending on the multiple combina-tions of r1c and r2c, although more underestimations were presentwith the Gullstrand eye model. Overestimations of IOL power byP k
IOL with respect to P GaussIOL higher than 0.5 D were present in
the Le Grand eye model (nk = 1.3304) from r1c =7 mm combinedwith r2c Z[6.2, 7] mm to r1c = 7.8 mm with r2c = 7 mm and in theGullstrand eye model (nk = 1.3315) from r1c = 7 mm combined withr2c Z[6.6, 7] mm to r1c = 7.40 mm with r2c = 7 mm. The highestoverestimation value was always found for the combination ofr1c = 7 mm with r2c = 7 mm (unlikely corneal curvature combi-nation), with values of +1.41 and +0.95 D for the Le Grand andGullstrand eye models, respectively. The higher underestimationswere found for r1c = 8.5 mm combined with r2c Z[5.60, 6.60] mmand for r1c = 8.5 mm combined with r2cZ[5.60, 6.90] for Le Grandand Gullstrand eye models, respectively. The highest underesti-mation value was found for the combination of r1c = 8.5 mm andr2c = 5.6 mm for both eye models, with values ofj1.76 andj2.16 Dfor the Le Grand and Gullstrand eye models, respectively.
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When nk = 1.3375 was used in both models, an underestimationof IOL power by P k
IOL with respect to P GaussIOL was almost always
observed. The magnitude of this underestimation was higher than0.5 D in almost all possible combinations of r1c and r2c. Themaximum underestimation was again found for the combination ofr1c = 8.5 mm with r2c = 5.6 mm, with values ofj3.01 andj2.77 Dfor Gullstrand and Le Grand eye models, respectively. It should beremarked that differences in $PIOL values between the two eyemodels used in the current study were below or equal to 0.27 D ifnk = 1.3375 was used and below or equal to 0.48 D if the theoreticalnk values (1.3304 and 1.3315) were used.
All these trends for $PIOL were modeled by means of linear re-gression analysis. Specifically, predictive linear equations (R2 = 0.99)relating $PIOL and k ratio as a function of r1c in 0.1-mm steps werefound for the two eye models used in this study (Tables 2, 3).Likewise, $PIOL data could also be adjusted by a quadratic ex-pression (R2 = 0.99) dependent on r2c (Fig. 1). As example, $PIOL
data corresponding to r1c = 8.5 mm using the Gullstrand eye modelwith nk = 1.3375 could be adjusted to the quadratic expression$PIOL = j0.188464 r 2
2c + 3.577053r2c + 17.130125, where r2c
is expressed in millimeters (Fig. 1). The equivalent equation de-pending on k was $PIOL = j5.566861Ik + 5.436452 (Table 2).
Relationship between $PIOL and ELP
A comparative analysis of $PIOL variation with the value of$PIOL obtained for the ELP values coincident with the anatomicalACD (ACDa) of the two eye models used in this study (3.05 and3.10 mm for Le Grand and Gullstrand eye models) was performed
considering a range of variation of ELP between 2 and 6 mm aswell as no variation in the rest of parameters. Differences in $PIOL
calculation did not become clinically significant because of ELP
TABLE 1.
Summary of the differences between the keratometric andGaussian IOL ($PIOL) obtainedwithin the normal range of anteriorcorneal curvature (r1c, from 7 to 8.5 mm) for the Le Grand and Gullstrand eye models as well as for the different nk valuesused (1.3304, 1.3315, and 1.3375)
Comparative $PIOL and $Pc
Le Grand Gullstrand
nk: 1.3304 nk: 1.3375 nk: 1.3315 nk: 1.3375
r1c, mm $Pc, D $PIOL, D $Pc, D $PIOL, D $Pc, D $PIOL, D $Pc, D $PIOL, D
7.00 0.26; j1.12 j0.33; 1.41 1.28; j0.11 j1.61; 0.14 0.65; j0.75 j0.81; 0.95 1.50; 0.10 j1.90; j0.137.10 0.36; j1.03 j0.45; 1.29 1.36; j0.03 j1.71; 0.03 0.74; j0.66 j0.93; 0.84 1.58; 0.18 j1.99; j0.237.20 0.45; j0.93 j0.57; 1.17 1.44; 0.05 j1.80; j0.07 0.83; j0.57 j1.03; 0.72 1.66; 0.26 j2.08; j0.327.30 0.55; j0.84 j0.68; 1.05 1.52; 0.13 j1.89; j0.16 0.91; j0.49 j1.14; 0.61 1.73; 0.33 j2.17; j0.427.40 0.63; j0.75 j0.78; 0.94 1.59; 0.20 j1.98; j0.25 1.00; j0.40 j1.24; 0.50 1.81; 0.41 j2.25; j0.517.50 0.72; j0.67 j0.89; 0.83 1.67; 0.28 j2.06; j0.34 1.08; j0.32 j1.34; 0.40 1.88; 0.48 j2.33; j0.597.60 0.80; j0.59 j0.99; 0.72 1.74; 0.35 j2.14; j0.43 1.16; j0.24 j1.43; 0.30 1.95; 0.55 j2.41; j0.687.70 0.89; j0.50 j1.09; 0.62 1.81; 0.42 j2.22; j0.51 1.24; j0.17 j1.52; 0.20 2.02; 0.61 j2.49; j0.767.80 0.96; j0.42 j1.18; 0.52 1.87; 0.48 j2.30; j0.60 1.31; j0.09 j1.61; 0.11 2.08; 0.68 j2.56; j0.847.90 1.04; j0.35 j1.27; 0.43 1.94; 0.55 j2.37; j0.67 1.39; j0.02 j1.70; 0.02 2.15; 0.74 j2.63; j0.918.00 1.12; j0.27 j1.36; 0.33 2.01; 0.61 j2.44; j0.75 1.46; 0.05 j1.78; j0.07 2.21; 0.80 j2.70; j0.998.10 1.19; j0.20 j1.44; 0.24 2.07; 0.68 j2.51; j0.82 1.53; 0.12 j1.86; j0.15 2.27; 0.86 j2.76; j1.068.20 1.26; j0.13 j1.53; 0.15 2.13; 0.74 j2.58; j0.90 1.60; 0.19 j1.94; j0.23 2.33; 0.92 j2.83; j1.138.30 1.33; j0.06 j1.61; 0.07 2.19; 0.80 j2.64; j0.97 1.66; 0.26 j2.01; j0.31 2.39; 0.98 j2.89; j1.198.40 1.40; 0.01 j1.69; j0.01 2.25; 0.85 j2.71; j1.03 1.73; 0 .32 j2.09; j0.39 2.44; 1.04 j2.95; j1.268.50 1.47; 0.08 j1.76; j0.09 2.30; 0.91 j2.77; j1.10 1.79; 0.39 j2.16; j0.47 2.50; 1.09 j3.01; j1.32
The interval shown for each value of r1c is the maximum and minimum values of $Pc and $PIOL corresponded to the values associatedwith the extreme values of the normality range defined for r2c, from 5.6 to 7 mm are also shown.
TABLE 2.
Linear equations (all R2 = 0.99) relating $PIOL and k ratioas a function of r1c in 0.1-mm steps using the Gullstrandeye model
nk = 1.3315 nk = 1.3375
r1c, mm $PIOL, D = a k + b $PIOL, D = a k + b
7.00 $PIOL = j7.07 k + 8.03 $PIOL = j7.07 k + 6.947.10 $PIOL = j6.95 k + 7.88 $PIOL = j6.95 k + 6.827.20 $PIOL = j6.83 k + 7.74 $PIOL = j6.83 k + 6.707.30 $PIOL = j6.71 k + 7.61 $PIOL = j6.71 k + 6.587.40 $PIOL = j6.60 k + 7.48 $PIOL = j6.60 k + 6.477.50 $PIOL = j6.49 k + 7.35 $PIOL = j6.49 k + 6.367.60 $PIOL = j6.38 k+ 7.23 $PIOL = j6.38 k + 6.257.70 $PIOL = j6.28 k + 7.11 $PIOL = j6.28 k + 6.157.80 $PIOL = j6.18 k + 7.00 $PIOL = j6.18 k + 6.057.90 $PIOL = j6.09 k + 6.89 $PIOL = j6.09 k + 5.958.00 $PIOL = j5.99 k + 6.78 $PIOL = j5.99 k + 5.868.10 $PIOL = j5.90 k + 6.68 $PIOL = j5.90 k + 5.778.20 $PIOL = j5.81 k + 6.58 $PIOL = j5.81 k + 5.688.30 $PIOL = j5.73 k + 6.48 $PIOL = j5.73 k + 5.608.40 $PIOL = j5.65 k + 6.38 $PIOL = j5.65 k + 5.528.50 $PIOL = j5.57 k + 6.29 $PIOL = j5.57 k + 5.44
The linear adjustment for the keratometric indexes of 1.3315 and1.3375 and for the range of normality defined for r1c is shown.
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changes in such conditions. The highest variation was found forELP = 6 mm, and it did not exceed more than 0.48 D in com-parison with the value obtained with the eye model ACDa.
Relationship between $PIOL and Rdes
For a range of Rdes between j1 and +1 D and considering theother parameters constant, the variation of $PIOL was not of morethan 0.02 D in comparison with the values obtained for Rdes = 0 Din any of the conditions simulated.
$PIOL Using nkadj for Minimizing $PC
If nkadj derived from equations 7 and 8 was used for the cal-culation of keratometric corneal power and then PIOLadj wascalculated, a maximal error of T0.9 D in $PIOL was observedindependently from the eye model used, r1c and Rdes (Fig. 2A, B).Considering that 1 D of variation of PIOL induced approximately0.9 D of change in subjects’ refraction at the corneal vertex,$PIOL obtained with the nkadj simulations did not exceed T0.60or T0.50 D at the corneal vertex for a range of r2c between 5.8 and6.7 mm (almost all the normality range for this parameter). Theanalysis of the effect on PIOL calculation when the nkadj was usedon the variation of ELP was also performed. For ELP values
higher than 4 mm, the range of r2c associated with $PIOL notexceeding T0.5 D at the corneal vertex was somewhat more re-duced, including the values between 5.9 and 6.6 mm.
Preliminary Clinical Validation
Table 4 summarizes the results of the comparative analysis ofthe IOL power obtained with different standard formulas andwith our optimized algorithm in a clinical population. As shown,clinically relevant and statistically significant differences betweenthe result obtained with our formula (PIOLadj) and the IOL powervalues obtained with the SRK/T (PIOLSRK/T), Haigis (PIOLHaigis),Holladay (PIOLHolladay), and HofferQ (PIOLHofferQ) formulas werefound. The Bland-Altman plots show these clinically relevantdifferences in Fig. 3A to D. These differences were positive inmost cases and, therefore, the PIOL obtained with our formula washigher than that obtained with the other standard IOL powercalculation formulas. In addition, clinically relevant differenceswere found between most of the standard formulas used for thecurrent comparative analysis, as shown in Bland-Altman plots ofFig. 4A to F.
The difference between PIOLadj and PIOLSRK/T was found tocorrelate significantly with the Gaussian corneal power (r = j0.81,p G 0.01), r2c (r = 0.81, p G 0.01), the difference between the
FIGURE 1.$PIOL data using the Gullstrand eye model with nk=1.3375 corresponding to three values of r1c (7, 7.70, and 8.5 mm) adjusted to quadratic expressionsdependent on r2c (R
2 = 0.99).
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corneal power obtained with the adjusted keratometric indexand the keratometric power (nk = 1.3375) (r = 0.81, p G 0.01), ELP(r =j0.46, p G 0.01), and r1c (r = 0.81, p G 0.01). A similar trend wasobserved for the difference between PIOLadj and PIOLHaigis thatcorrelated significantly with the Gaussian corneal power (r =0.j75, p G 0.01), r2c (r = 0.54, p G 0.01), the difference betweenthe corneal power obtained with the adjusted keratometric indexand the keratometric power (nk = 1.3375) (r = 0.75, p G 0.01), andr1c (r = 0.75, p G 0.01). In contrast, the difference between PIOLadj
and PIOLHofferQ correlated significantly with AL (r = 0.97, pG0.01)and ELP (r = 0.99, p G 0.01). Regarding the difference betweenPIOLadj and PIOLHolladay, it correlated significantly with the Gaussiancorneal power (r = j0.25, p = 0.02), the difference between thecorneal power obtained with the adjusted keratometric index andthe keratometric power (nk = 1.3375) (r = 0.25, p = 0.02),ELP (r = 0.64, p G 0.01), and r1c (r = 0.26, p = 0.02).
DISCUSSION
In the current study, we have observed in a theoretical simu-lation considering the range of corneal curvature of the normalhealthy population that the use of a nonoptimized nk for corneal
FIGURE 2.Comparison ofPIOL fornk = 1.3375andnkadj with P Gauss
IOL in the range of normality corresponding to r2c and for a) r1c = 7 mm and b) r1c = 8.5 mm.
TABLE 3.
Linear equations (all R2 = 0.99) relating $PIOL and k ratio as afunction of r1c in 0.1-mm steps using the Le Grand eye model
nk = 1.3304 nk = 1.3375
r1c, mm $PIOL, D = a k + b $PIOL, D = a k + b
7.00 $PIOL = j6.98 k + 8.40 $PIOL = j6.98 k + 7.127.10 $PIOL = j6.86 k + 8.25 $PIOL = j6.86 k + 6.997.20 $PIOL = j6.74 k + 8.10 $PIOL = j6.74 k + 6.877.30 $PIOL = j6.63 k + 7.96 $PIOL = j6.63 k + 6.757.40 $PIOL = j6.52 k + 7.83 $PIOL = j6.52 k + 6.637.50 $PIOL = j6.41 k + 7.69 $PIOL = j6.41 k + 6.527.60 $PIOL = j6.31 k + 7.57 $PIOL = j6.31 k + 6.417.70 $PIOL = j6.20 k + 7.45 $PIOL = j6.20 k + 6.317.80 $PIOL = j6.11 k + 7.33 $PIOL = j6.11 k + 6.217.90 $PIOL = j6.01 k + 7.21 $PIOL = j6.01 k + 6.118.00 $PIOL = j5.92 k + 7.10 $PIOL = j5.92 k + 6.028.10 $PIOL = j5.83 k + 6.99 $PIOL = j5.83 k + 5.928.20 $PIOL = j5.75 k + 6.89 $PIOL = j5.75 k + 5.838.30 $PIOL = j5.66 k + 6.78 $PIOL = j5.66 k + 5.758.40 $PIOL = j5.58 k + 6.68 $PIOL = j5.58 k + 5.668.50 $PIOL = j5.50 k + 6.59 $PIOL = j5.50 k + 5.58
The linear adjustment for the keratometric indexes of 1.3304 and1.3375 and for the range of normality defined for r1c is shown.
TABLE 4.
Summary of the comparative analysis of the IOL powerobtained with different standard formulas and with ouroptimized algorithm in a clinical population
SRKT Haigis HofferQ Holladay
Mean differencewith PIOL
calculatedwith nkadj (SD)
1.01 (0.26) 0.39 (0.33) 1.92 (0.58) 1.04 (0.77)
p G0.01 G0.01 G0.01 G0.01
Coefficient ofcorrelation withPIOL calculatedwith nkadj
0.997 0.996 0.993 0.977
Limits ofagreement withPIOL calculatedwith nkadj
0.50Y1.52 j0.27 to 1.04 0.78Y3.07j0.5 to 2.5
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power calculation can lead to relevant clinically errors in PIOL
calculation if cataract surgery is needed and consequently theimplantation of an IOL. We observed that if the corneal powerwas overestimated when a single nk was used, there was an un-derestimation of the corresponding value of P k
IOL and vice versa.Specifically, the higher the nk used, the higher was the level ofunderestimation observed, with a maximum value of 3.01 D whenthe Gullstrand model was used with nk = 1.3375. Several authorshave adjusted the keratometric index on the basis of posterior
corneal curvature for improving the IOL outcomes,6,10,11,17 butusing in most cases a single value of nk. Our results suggest that theuse of a single keratometric index for calculating Pc when it is usedfor PIOL calculations would not be adequate and it would lead tosignificant postoperative residual refractive errors (refractive sur-prise) after cataract surgery.
A quadratic equation dependent on r2c was found to be pre-dictive of the $PIOL value (Tables 2, 3). These equations may beuseful to calculate the magnitude of the error associated with IOL
FIGURE 3.Bland-Altman plots for the comparison between the PIOL obtained using our formula considering the potential influence of the keratometric error (PIOLadj)and that obtained with other calculation formulas. (A) Differences between PIOLadj and PIOL obtained with the SRK-T formula (PIOLSrk/t). (B) Differencesbetween PIOLadj and PIOL obtained with the Haigis formula (PIOLHaigis). (C) Differences between PIOLadj and PIOL obtained with the HofferQ formula(PIOLHofferQ). (D) Differences between PIOLadj and PIOL obtained with the Holladay formula (PIOLHolladay). Upper and lower lines represent the limits ofagreement calculated as mean of differences T1.96 SD.
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FIGURE 4.Bland-Altman plots for the comparison between the PIOL obtained with different calculation formulas. (A) Differences between the PIOL obtained with theHaigis formula (PIOLHaigis) and that obtained with the HofferQ formula (PIOLHofferQ). (B) Differences between the PIOL obtained with the Haigis formula(PIOLHaigis) and that obtained with the Holladay formula (PIOLHolladay). (C) Differences between the PIOL obtained with the Haigis formula (PIOLHaigis) and thatobtained with the SRK/T formula (PIOLSRK/T). (D) Differences between the PIOL obtained with the HofferQ formula (PIOLHofferQ) and that obtained with theHolladay formula (PIOLHolladay). (E) Differences between the PIOL obtained with the HofferQ formula (PIOLHofferQ) and that obtained with the SRK/T formula(PIOLSRK/T). (F) Differences between the PIOL obtained with the Holladay formula (PIOLHolladay) and that obtained with the SRK/T formula (PIOLSRK/T). Upperand lower lines represent the limits of agreement calculated as mean of differences T1.96 SD.
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power calculation when it is calculated using P kIOL or using
P GaussIOL . The group of equations obtained for predicting $PIOL
with the two eye models used in the study was practicallyequivalent, with minimal differences between models. Effectivelens position was found to have an influence on $PIOL, although itwas minimal. Specifically, if the ELP was lower than the ana-tomical chamber depth (ACDa), the differences between P k
IOL
and P GaussIOL decreased and vice versa. These variations were al-
ways found to be lower than 0.5 D. It should be considered that, inour simulations, the exact value of ELP was considered as mea-surable preoperatively and therefore totally predictable. However,it should be considered that the behavior of the IOL within thecapsular bag is not the same in each case in clinical practice and theELP value used in the IOL power calculations is obtained usingprediction formulas that are, in most of cases (except Haigisformula), dependent on corneal power.8,20,23
In an attempt of defining an algorithm minimizing the errors inIOL power estimations and with potential use in clinical practice, anew formula was proposed for IOL power estimation (PIOLadj) usingparaxial optics and the keratometric approximation but consideringa variable nk according to the algorithm developed4 and validatedclinically5 by our research group. In theoretical simulations, dif-ferences between PIOLadj and P Gauss
IOL never exceeded 0.9 D, inde-pendently from the theoretical eye model used, r1c and Rdes. Thiserror range did not result clinically significant in most of the po-tential combinations of r1c and r2c in the healthy normal eye atcorneal vertex plane and did not vary significantly with ELP vari-ations. When the formula was validated in a clinical population,statistically significant and clinically relevant differences were foundbetween our formula for IOL power estimation and other com-monly used (Haigis, HofferQ, Holladay, and SRK/T). Specifically,our formula always provided higher IOL power values, although itwas less evident when compared with those of the Haigis formula.Therefore, our formula cannot be used interchangeably with any ofthe formulas used in this comparative analysis. However, the in-terchangeability between the four formulas used currently in clinicalsetting was not possible either (Fig. 4A to E and D). This is con-sistent with previous studies performed by other authors.24Y26
Several factors may have accounted for the clinically relevantdifference between our formula and those evaluated and usedcommonly in clinical practice. Among them, the correction of thekeratometric error with our approach seems to be crucial. Indeed,differences between our PIOLadj and the SRK-T, Haigis, andHolladay formulas correlated significantly with the difference be-tween the corneal power obtained with the adjusted keratometricindex and the keratometric power. The higher the overestimation ofthe keratometric approach, the higher was the underestimation ofthe IOL power, as observed in the theoretical simulations. Thisconfirms the relationship between the keratometric overestimationand the presence of errors in IOL power calculation that may resultin very significant postoperative refractive errors. McEwan andcolleagues24 found in a previous study that inaccuracy in axial lengthmeasurements and keratometer readings were first-order determi-nants of postoperative spherical refractive error after cataract withIOL implantation. Specifically, measurement errors of 0.2 mmin axial length and 0.50 D in corneal curvature lead to IOL powererrors of T1.17 D using the modified Binkhorst, modifiedColenbrander, Holladay, Hoffer, and SRK II formulas.
Another factor influencing the postoperative refractive outcomeafter cataract surgery and leading to errors in IOL power calcu-lations is the postoperative position of the IOL,3,27 which can beassumed to be equivalent to ELP using the thin lens approxi-mation. In our clinical validation, a strong and significant cor-relation of ELP with the difference between the IOL powerobtained with our formula and those obtained with the HofferQand Holladay formulas was obtained. The higher the ELP, thehigher was the difference between formulas. With the SRK/Tformula, this correlation of ELP with the difference in IOL powercompared with our formula was also found, but it was weaker.One factor accounting for this finding may be that the calcula-tion of ELP with these three formulas requires the use of thekeratometric reading8,20,23 and therefore the overestimation as-sociated with the keratometric approach interferes with the cal-culation of IOL power. Shammas et al.6 and Savini et al.28Y30
groups performed an optimization of ELP depending on thecorneal power measurement and the IOL formula. With theseoptimizations, the mean refractive error outcome was 0 D,demonstrating that a compensation of errors introduced by cor-neal power measurements can be achieved by optimizing ELP.Indeed, the lower the corneal power, the lower was the A-constantvalue required.6,28Y30 This suggests that errors caused by theoverestimation of the keratometric cornea are minimized andcorrected with some formulas with the selection of the A-constant.In our study, the lower the A-constant value used for ELP cal-culation to estimate PIOLadj, the lower were differences betweenour formula and standard formulas evaluated. Specifically, clini-cally tolerable and not statistically significant differences werefound between PIOLadj obtained with an A-constant of 117 andPIOLSRK/T obtained with an A-constant of 118 (limits of agree-ment = j0.59 to 0.56 D, p = 0.66) as well as between PIOLadj
obtained with an A-constant of 117.6 and PIOLHaigis obtainedwith an A-constant of 118 (limits of agreement = j0.69 to 0.62 D,p = 0.3). Therefore, our formula for IOL power estimation (PIOLadj)can be used clinically after an appropriate estimation of the ELPand A-constant associated to each specific type of IOL, with theadvantage of a less dependence of this estimation on cornealpower. The selection of the A-constant to use for different designsof IOL should be investigated further in future studies.
Finally, it should be noted that there are some potentialweaknesses in the formula developed for IOL power calculationusing our adjusted keratometric approach for corneal power es-timation. Our formula is based on paraxial optics, not consideringthe effect of asphericity. Future studies evaluating the validity ofour model for nonparaxial optics as well as if there is an im-provement with clinical relevance when using a more complexoptical estimation are required. In any case, Einighammer et al.31
found that there was an agreement between the IOL power esti-mations obtained by ray tracing and Gaussian optics in normaleyes. Likewise, Jin et al.32 found that theoretical thin-lens for-mulas were as accurate as the ray-tracing method in IOL powercalculations in normal eyes. Besides the paraxial approximation,corneal thickness is not considered in our formula, which can beconsidered as a limitation. However, differences in PIOLadj weredemonstrated to be always below 0.036 D for the potential rangeof corneal thickness in the normal healthy population (centralcorneal thickness from 450 to 600 Km).33 Finally, the eye model
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selected can be considered as an additional limitation. We used inour study two theoretical eye models, Gullstrand and Le Grandmodels, both providing very similar results. Therefore, the choiceof one model or another is therefore not decisive and with smallclinical relevance for normal eyes.
Regarding the clinical study, the main limitation was the rangeof cases considered, including only eyes with AL between 22 and26 mm. It should be considered that Narvaez et al.34 found errorsin the postoperative manifest refraction higher to 2.00 D using theHofferQ, the SRK/T, and the Holladay 1 and 2 formulas in thistype of eyes. We have demonstrated that the correction of theerror associated with the keratometric approach in this AL range isable to minimize potential refractive surprises because of this fac-tor. Future studies should elucidate if the trends found here are alsoobserved in very short and long eyes or in eyes with previous lasercorneal refractive surgery. Furthermore, IOL power calculationswere performed in a large sample of eyes with a variety of formulas,but these eyes did not undergo cataract surgery, and therefore wewere not able to analyze the postoperative outcomes, which can besignificantly affected by the postoperative position of the IOLwithin the capsular bag and consequently by differences in ELPwith respect to the predicted. In our study, we assumed a pre-dictable ELP and an accurate AL measurement, being the error incorneal power the main source of error.
In conclusion, we have shown that the use of a single value of nk
for the calculation of IOL power can lead to inaccuracies that mayexplain some IOL power overestimations with conventionalformulas after cataract surgery in eyes with AL between 22 and26 mm. These inaccuracies in PIOL calculations can be minimizedtheoretically by using a variable nk depending on the radius ofcurvature of the anterior corneal surface. Future studies would benecessary to confirm all these outcomes in eyes undergoing cat-aract surgery and implanted with different types of IOL andtherefore having different A-constants. It should be consideredthat the algorithm proposed for the minimization of the impactof the keratometric error on IOL power calculation is under-standable and accessible for the clinician, uses a model that re-quires minimal computation time in comparison with morecomplex models or approaches such as ray tracing, and does notrequire the measurement of the radius of the posterior cornealsurface and, therefore, without the necessity of acquiring expen-sive systems, such as Scheimpflug photographyYbased systems oroptical coherence tomographers, which cannot be available in allclinical settings.
ACKNOWLEDGMENTS
The authors have no financial or proprietary interest in a product, method, ormaterial described herein.
All the authors have full control of all primary data, and they agree to allowOptometry and Vision Science to review the data of the current study ifrequested.
Received December 29, 2012; accepted April 4, 2013.
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David P. PineroDepartamento de Optica Farmacologıa y Anatomıa
Universidad de AlicanteCrta San Vicente del Raspeig s/n
03690 San Vicente del RaspeigAlicante, Spain
e-mail: david.pinyero@ua.es
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Original Article
Positional accommodative intraocular lens power error induced by the estimation of the corneal power and the effective lens position
David P Piñero1,2,3, Vicente J Camps1, María L Ramón2, Verónica Mateo1, Rafael J Pérez‑Cambrodí2,3
Purpose: To evaluate the predictability of the refractive correction achieved with a positional accommodating intraocular lenses (IOL) and to develop a potential optimization of it by minimizing the error associated with the keratometric estimation of the corneal power and by developing a predictive formula for the effective lens position (ELP). Materials and Methods: Clinical data from 25 eyes of 14 patients (age range, 52–77 years) and undergoing cataract surgery with implantation of the accommodating IOL Crystalens HD (Bausch and Lomb) were retrospectively reviewed. In all cases, the calculation of an adjusted IOL power (PIOLadj) based on Gaussian optics considering the residual refractive error was done using a variable keratometric index value (nkadj) for corneal power estimation with and without using an estimation algorithm for ELP obtained by multiple regression analysis (ELPadj). PIOLadj was compared to the real IOL power implanted (PIOLReal, calculated with the SRK‑T formula) and also to the values estimated by the Haigis, HofferQ, and Holladay I formulas. Results: No statistically significant differences were found between PIOLReal and PIOLadj when ELPadj was used (P = 0.10), with a range of agreement between calculations of 1.23 D. In contrast, PIOLReal was significantly higher when compared to PIOLadj without using ELPadj and also compared to the values estimated by the other formulas. Conclusions: Predictable refractive outcomes can be obtained with the accommodating IOL Crystalens HD using a variable keratometric index for corneal power estimation and by estimating ELP with an algorithm dependent on anatomical factors and age.
Key words: Accommodating intraocular lenses, Crystalens HD, effective lens position, intraocular lenses power, keratometry
1Department of Optics, Pharmacology and Anatomy, Group of Optics and Visual Perception, University of Alicante, 2Department of Ophthalmology, Medimar International Hospital, 3Foundation for the Visual Quality (FUNCAVIS), Alicante, Spain
Correspondence to: Dr. David P Piñero, Department of Ophthalmology (OFTALMAR), 1st Floor, Medimar International Hospital, C/Padre Arrupe, 20, 03016 Alicante, Spain. E‑mail: dpinero@oftalmar.es
Manuscript received: 17.05.14; Revision accepted: 24.05.15
With the advancement of new technologies, a great variety of devices have emerged requiring exigent demands at near and intermediate vision, such as tablets, E‑books, smartphones. For this reason, presbyopic patients and younger patients with cataract currently demand solutions allowing them to continue their daily activities with these devices. Besides spectacles glasses and contact lenses, different surgical options for the correction of presbyopia have been developed.[1] One of the surgical options that have gained popularity in the last decade is the implantation of accommodative intraocular lenses (IOLs) after cataract surgery. An accommodating IOL tries to provide a functional near vision, giving a high‑quality intermediate and distance vision without optical distortion because only one image at a time is formed on the retina.[2] Different single‑optic models were developed and marketed, such as the Crystalens AT‑45 (Eyeonics),[3,4] the 1CU (HumanOptic)[5‑8] or the Tetraflex (Lenstec).[3,9] However, these preliminary models of accommodating IOLs were shown to provide very limited near visual outcomes.[3,9] This was the main reason for the development of new models of accommodating IOLs, such as the dual‑optic[10] and other nonpositional accommodating models.[11]
Recently, Bausch and Lomb released the IOL Crystalens HD™ which theoretically overcomes the limitations of its predecessor, the Crystalens AT‑45. Specifically, a central bi‑aspheric optical modification has been added to increase depth of focus and some changes in the design and material of the IOL has been included that allow the variation of the radius of curvature of the anterior IOL surface (arching optic) with the contraction of the ciliary muscle.[12] A relatively recent study[12] comparing this IOL with a standard monofocal IOL concluded that the Crystalens HD provided a restoration of the distance visual function and a significant improvement of near vision, with an optical quality similar to that corresponding to the conventional monofocal IOL. However, in spite of these acceptable visual outcomes, the refractive predictability was observed to be limited in some cases showing an unexpected postoperative myopic or hyperopic postoperative refractive error. This may be due to an inappropriate IOL power calculation, mainly biased by an inaccurate estimation of the corneal power and ELP.[13]
The hypothesis of the current research is that an improvement of the refractive precision after cataract surgery with implantation of the Crystalens HD IOL may be achievable with a formula for IOL power calculation controlling the error induced by the keratometric approach for the estimation of the corneal power and the error associated with an inaccurate estimation of ELP. For testing such hypothesis, two main objectives were set up. The first objective was to evaluate the predictability of the refractive correction achieved with this positional accommodating IOL and consequently the range of error. The second objective was to develop an optimization of the predictability error by minimizing the error associated with the keratometric estimation of the corneal power and
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May 2015 Piñero, et al.: Errors in accommodative IOL power calculations 439
by developing a predictive formula of the effective lens position (ELP) for accommodating IOL evaluated.
Materials and MethodsPatientsThis retrospective study included a total of 25 eyes of 14 patients with ages ranging between 52 and 77 years old. All these eyes underwent cataract surgery with implantation of the accommodating IOL Crystalens HD (Bausch and Lomb). The inclusion criteria of this study were patients with visually significant cataract or presbyopic/pre presbyopic patients suitable for refractive lens exchange and demanding complete spectacle‑independence. The exclusion criteria were patients with active ocular diseases, ruptured posterior capsule, zonulodialysis, scotopic pupil size of more than 6.0 mm, illiteracy and topographic astigmatisms higher than 1.25 D. All volunteers were adequately informed and signed a consent form. The study adhered to the tenets of the declaration of Helsinki and was approved by the Local Ethical Committee.
Intraocular lensThe accommodating IOL used in this study was the Crystalens HD (Bausch and Lomb), which has a biconvex single‑optic design. The IOL is of a biocompatible third‑generation silicone (Biosil) with a refractive index of 1.428. It has a central bi‑aspheric modification (around 1.5‑mm diameter) to increase depth of focus and thus provide better intermediate and near foci. Two sizes are available depending on the required power, the 12.0 mm model (HD520) for powers between 10.00 and 16.50 D, and the 11.5 mm model (HD500) for powers between 17.00 and 33.00 D. According to the manufacturer, the IOL has a double mechanism to improve the near visual function: Axial movement of the optic as a consequence of the ciliary muscle changes and variation of the radius of curvature of the anterior IOL surface (arching optic). In the current study, the SRK/T formula and the IOL Master software (Carl Zeiss Meditec, Jena, Germany) were used in all cases for the IOL power calculation, with an A‑constant value of 118.8.
Surgical techniqueAll surgeries were performed by one of the experienced surgeons (MLR) us ing a s tandard technique of phacoemulsification. In all cases, topical anesthesia was administered, and pupillary dilation was induced with a combination of tropicamide and phenylephrine 10% every 15 min ½ h prior to the procedure. Povidone iodine solution 5% was instilled on the eye 10 min before the operation. A 2.75‑mm clear incision was made with a diamond knife on the steepest meridian to minimize post‑surgical astigmatism. A paracentesis was made 60–90° clockwise from the main incision and the anterior chamber was filled with viscoelastic material. A continuous curvilinear capsulorhexis between 5.5 and 6.0 mm was performed. After the crystalline lens removal, the IOLs were implanted through the incision into the capsular bag using a specific injector developed by the manufacturer for such purpose. Finally, the surgeon proceeded to retrieve the viscoelastic material using the irrigation‑aspiration system. A combination of topical steroid and antibiotic (Tobradex, Alcon, Fort Worth, TX, USA) as well as a nonsteroidal anti‑inflammatory drops (Dicloabak, Laboratorios Thea, Barcelona, Spain) were prescribed to be applied four times daily for a week after the surgery and
3 times daily the second postoperative week. In addition, the nonsteroidal anti‑inflammatory drops were also prescribed to be applying three times daily during 2 weeks more after surgery.
Calculation of the adjusted IOL power to minimize the keratometric errorAlmost all theoretical formulas for IOL power calculation are based on the use of a simplified eye model, with a thin cornea and crystalline lens model.[13] According to such approach, the power of the IOL (PIOL) can be easily calculated using the Gauss equation in paraxial optics:[14]
( )
hahv
IOL ha
des c
P = ELPAL ELP R + P
(1)
Where Pc is the total corneal power, ELP the effective lens plane, AL the axial length (AL), nha the aqueous humor refractive index, nhv the vitreous humor refractive index and Rdes is the postoperative desired refraction calculated at corneal vertex.
Our research group has recently proposed the use of a variable keratometric index (nkadj) depending on the radius of the anterior corneal surface (r1c) expressed in millimeters for minimizing the error associated to the keratometric approach for corneal power calculation.[15] Specifically, the following expression was defined according to the Gullstrand eye model:
nkadj = −0.0064286r1c + 1.37688 (2)
Using this algorithm, a new keratometric corneal power, named adjusted keratometric corneal power (Pkadj), can be calculated using the classical keratometric corneal power formula.[15] In the current study, the adjusted IOL power (PIOLadj) was calculated, defined as the IOL power calculated from the equation 1 using the nkadj value for the estimation of the corneal power (Pkadj), the nha and nhv values corresponding to the Gullstrand eye model (1.336 for both index). In such calculation, the postoperative spherical equivalent (SE) at corneal vertex was considered as the desired refraction (Rdes = SEpost). Afterward, this IOL power (PIOLadj) was compared with the real power of the IOL implanted (PIOLReal). The PIOLadj calculation was performed after estimating the ELP using two different approaches: ELP calculation following the SRK/T formula guidelines (named PIOLadjSRK/T) and ELP calculation using a mathematical expression obtained by multiple regression analysis (named PIOLadj), as explained carefully in the next section.
Furthermore, the PIOL was also calculated using three conventional formulae (Haigis, HofferQ and Holladay I) considering the ELP defined for each formula and that Rdes = SEpost. A comparative analysis was done between these values of PIOL and PIOLadj.
Estimation of adjusted ELPConsidering equation 1, PIOLreal, Pkadj and Rdes = SEpost in each case, ELP was obtained and named adjusted ELPadj. A multiple regression analysis was performed with the aim of obtaining a mathematic expression for predicting the ELPadj from different anatomical and clinical parameters.
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Preoperative and postoperative examinationsPreoperatively, all patients had a full ophthalmologic examination including the evaluation of the refractive status, the distance and near visual acuities, slit lamp examination, optical biometry (IOL‑Master, Carl Zeiss Meditec, Jena, Germany), Goldman tonometry and funduscopy. Distance (4 m) and near (40 cm) visual acuities were evaluated with ETDRS charts. Postoperatively, patients were evaluated at 1‑day, 1‑week, 1‑month, and 3 months after surgery. At all visits, visual acuity, refraction and the integrity of the anterior segment were evaluated. Funduscopy was also performed in the postoperative revision at 3 months.
Statistical analysisThe statistical analysis was performed using the SPSS statistics software package version 19.0 for Windows (IBM, Armonk, NY, USA). Normality of data samples was evaluated by means of the Kolmogorov‑Smirnov test. When parametric analysis was possible, the Student’s t‑test for paired data was used for comparing the different approaches for PIOL calculation and also for comparing preoperative and postoperative data. When parametric analysis was not possible, the Wilcoxon rank sum test was applied to assess the significance of such comparisons. Differences were considered to be statistically significant when the associated P < 0.05. Correlation coefficients (Pearson or Spearman depending if normality condition could be assumed) were used to assess the correlation between different variables. Regarding the interchangeability between pairs of methods used for obtaining PIOL, the Bland‑Altman analysis was used.[16] This is a graphical method for assessing if there is an agreement between two clinical procedures.[16] Specifically, Bland‑Altman plots show the differences between the methods plotted against the mean of the 2 methods. The limits of agreement (LoA) are defined as the mean ± 1.96 standard deviation (SD) of the differences.[16] If the limits are clinically relevant, the 2 methods cannot be used interchangeably. In the current study, differences in IOL power between the different formulas evaluated was considered as clinically relevant for values of more than 0.5 D because this value is the IOL power step provided currently by most of manufacturers and has been shown to be the optical neutralization tolerance since many years ago.[17]
A multiple regression analysis was used for predicting the ELPadj from different preoperative anatomical and clinical parameters. Model assumptions were evaluated by analyzing residuals, the normality of nonstandardized residuals (homoscedasticity), and the Cook distance to detect influential points or outliers. In addition, the lack of correlation between errors and multicollinearity was assessed using the Durbin–Watson test, the calculation of the colinearity tolerance, and the variance inflation factor.
ResultsThis study evaluated 25 eyes of 14 patients (16 men [64%]), with a mean age of 65.9 years ± 8.9 (SD) (range, 52–79 years). The sample comprised 13 left eyes (52%). Mean preoperative keratometry, AL and anterior chamber depth (ACD) were 43.29 D ± 1.45 (range, 40.91–45.89 D), 23.21 mm ± 0.89 mm (range, 21.65–25.04 mm), and 3.27 mm ± 0.30 mm (range, 2.63–3.84 mm), respectively. According to all these data and using the SRK‑T formula, mean IOL power implanted
was 22.53 D ± 2.70 (SD) (range, 16–28 D). Table 1 summarizes the preoperative and postoperative visual and refractive data, and Table 2 displays the biometric and IOL power calculation data of the eyes evaluated.
Agreement of PIOLReal and PIOLadj‑SRK/T
Statistically significant differences were found between PIOLadjSRK/T and PIOLReal when ELP was calculated with the SRK/T formula guidelines and Rdes = EEpost (P < 0.01, paired Student’s t‑test). A very strong and statistically significant correlation was found between PIOLadj‑SRK/T and PIOLReal (r = 0.960, P < 0.01) [Fig. 1]. According to the Bland and Altman method, the PIOLadj‑SRK/T was higher than PIOLReal (mean of differences 1.97 D), with clinically relevant LoA (3.39 and 0.36 D). Fig. 2 shows the Bland and Altman plot corresponding to this agreement analysis.
Estimation of ELPadj
The multiple regression analysis revealed that the ELPadj was significantly correlated with AL, ACD, Pkadj and age (P < 0.001):
= 9.549 + 0.422 × + 0.164 × 1.612 ×
0.014 ×
− −
−adj kadjELP LA P
ACD Age (3)
The homoscedasticity of the model was confirmed by the normality of the nonstandardized residuals distribution (P = 0.20) and the absence of influential points or outliers (mean Cook’s distance: 0.049 ± 0.081). With this model, 72% of nonstandardized residuals were 0.30 or lower and 80% were lower than 0.40. The poor correlation between residuals (Durbin‑Watson test: 2.165) and the lack of
Table 1: Comparative table showing the preoperative and postoperative visual and refractive outcomes. The corresponding P values for the comparison between the preoperative and postoperative data are shown for each parameter evaluated
Mean (SD)Median (range)
Preoperative Postoperative (3 months)
P
LogMAR UDVA ‑ 0.21 (0.24)0.15 (0.00 ‑ 0.80)
‑
Sphere (D) +1.09 (2.76)+2.25 (−5.25 - +6.00)
+0.03 (0.79)0.00 (−2.50 - +2.00)
0.06
Cylinder (D) −0.57 (0.54)−0.50 (−2.00-0.00)
−0.80 (0.56)−1.00 (−1.75 - 0.00)
0.04
SE (D) +0.81 (2.77)+2.00 (−5.50 - +5.38)
−0.37 (0.78)−0.25 (−3.25 - +1.13)
0.35
LogMAR CDVA 0.18 (0.21)0.10 (0.00 ‑ 0.80)
0.06 (0.07)0.05 (0.00 ‑ 0.22)
0.02
LogMAR UNVA ‑ 0.44 (0.23)0.30 (0.22 ‑ 1.00)
‑
LogMAR DCNVA ‑ 0.53 (0.18)0.52 (0.30 ‑ 1.00)
‑
Near addition (D) 2.55 (0.37)2.50 (2.00 ‑ 3.00)
1.68 (0.70)1.50 (0.00 ‑ 3.00)
0.03
LogMAR CNVA 0.11 (0.14)0.10 (0.00 ‑ 0.40)
0.10 (0.07)0.10 (0.00–0.30)
0.55
SD: Standard deviation, D: Diopters, UDVA: Uncorrected distance visual acuity, SE: Spherical equivalent, CDVA: Corrected distance visual acuity, UNVA: Uncorrected near visual acuity, DCNVA: Distance‑corrected near visual acuity, CNVA: Corrected near visual acuity
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May 2015 Piñero, et al.: Errors in accommodative IOL power calculations 441
multicollinearity (tolerance 0.486–0.992; variance inflation factors 2.056–1.008) was also confirmed.
A statistically significant difference was found between ELP calculated with the SRK/T formula guidelines and the
ELPadj (P < 0.01, paired Student’s t‑test), with the lowest value for the adjusted calculation [Table 1].
Agreement between PIOLReal and PIOLadj
No statistically significant differences were found between PIOLadj and PIOLReal when ELPadj was used and Rdes = SEpost were considered for PIOLadj calculation (P = 0.10, paired Student’s t‑test). A very strong and statistically significant correlation was found between PIOLadj and PIOLReal (r = 0.97, P < 0.01) [Fig. 3]. According to the Bland and Altman method, the mean difference between both PIOLadj and PIOLReal was 0.002 D, with LoA of 1.229 and −1.225 D. Fig. 4 shows the Bland and Altman plot corresponding to this agreement analysis.
Agreement of PIOLadj and other formulasStatistically significant differences were found between PIOLadj and each of the formulas studied (P < 0.01, paired Student’s t‑test). A very strong and statistically significant correlation was found between PIOLHaigis and PIOLadj (r = 0.983, P < 0.01), between PIOLHofferQ and PIOLadj (r = 0.992, P < 0.01) and between PIOLHolladay and PIOLadj (r = 0.987, P < 0.01). Table 3 shows the Bland and Altman analysis outcomes corresponding to all comparisons done. Furthermore, the ELPadj (mean ± SD: 4.18 ± 0.27 mm, range 3.70–4.83 mm) was significantly lower than the ELP obtained following the guidelines proposed by each of the formulas used (paired Student’s t‑test, P < 0.01) [Table 1].
DiscussionCurrently, a great variety of options are available for the correction of presbyopia, such as the replacement of the transparent crystalline lens by an accommodating IOL that theoretically provide a restoration of the visual function not only at distance, but also at intermediate and near. However, the various preliminary models of accommodating IOLs were found to provide limited near visual outcomes and the results with the new generation of accommodating IOLs are not completely successful. Beiko[17] concluded from a comparative study that the single‑optic accommodating IOLs, such as Crystalens HD and Tetraflex, did not offer a significant
Table 2: Mean biometric and IOL power calculation data
Parameter Mean±SD Range
SEpre (D) 0.81±2.77 −5.50-5.38
SEpost (D) −0.36±0.76 −3.13-1.14
r1c (mm) 7.80±0.26 7.35‑8.25
ACD (mm) 3.27±0.30 2.63‑3.84
AL (mm) 23.21±0.89 21.65‑25.04
ELPSRK/T (mm) 5.21±0.34 4.78‑6.17
ELPadj (mm) 4.18±0.27 3.70‑4.83
ELPHaigis (mm) 5.41±0.18 5.12‑5.82
ELPHoffer Q (mm) 5.25±0.23 4.88‑5.83
ELPHolladay (mm) 4.95±0.30 4.31‑5.52
nkadj 1.327±0.02 1.324‑1.330
Pk(1.3375) (D) 43.29±1.44 40.91‑45.89
PcHaigis(1.3315) (D) 42.52±1.42 40.18‑45.07
Pkadj (D) 41.91±1.61 39.25‑44.82
PIOLReal (D) 22.53±2.70 16.00‑28.00
PIOLadjSRK/T (D) 24.51±2.91 17.69‑32.09
PIOLadj (D) 22.53±2.79 15.86‑29.07
PIOLHoffer Q (D) 22.94±3.14 15.43‑30.89
PIOLHolladay (D) 23.03±2.98 16.00‑30.80PIOLHaigis (D) 24.33±3.36 16.53‑33.25
SEpre: Preoperative spherical equivalent, SEpost: Postoperative spherical equivalent, r1c: Radius of curvature of the anterior corneal surface, ACD: Anterior chamber depth, AL: Axial length, ELPSRK/T: Effective lens position for the SRK/T formula, ELPadj: Effective lens position for the adjusted formula, ELPHaigis: Effective lens position for the Haigis formula, ELPHoffer Q: Effective lens position for the Hoffer Q formula, ELPHolladay: Effective lens position for the Holladay formula, nkadj: Adjusted keratometric index, Pk(1.3375): Corneal power obtained using the IOL‑Master or keratometric power, PcHaigis(1.3315): Corneal power obtained for the Haigis formula, Pkadj: Corneal power obtained using the adjusted keratometric index, PIOLReal: Power of the intraocular lens implanted which was calculated using the SRK/T formula, PIOLadj: Intraocular lens power obtained using the adjusted formula, PIOLHofferQ: Intraocular lens power obtained using the Hoffer Q formula, PIOLHolladay: Intraocular lens power obtained using the Holladay formula, PIOLHaigis: Intraocular lens power obtained using the Haigis formula, IOL: Intraocular lens, SD: Standard deviation, D: Diopters
Table 3: Bland and Altman analysis outcomes of the comparison between PIOLadj and the IOL power obtained with other commonly used formulas
∆PIOL±SD (D) LoA (D) P
Haigis 1.77±0.795 3.33‑0.21 <0.01
Hoffer Q 0.40±0.52 1.40-−0.64 <0.01Holladay 1 −0.47±0.50 1.44-−0.50 <0.01
IOL: Intraocular lens, SD: Standard deviation, D: Diopters, PIOL: Power of the intraocular lens, LoA: Limits of agreement, PIOLadj: Intraocular lens power obtained using the adjusted formula
Figure 1: Scattergram showing the relationship between the adjusted intraocular lenses (IOL) power using the effective lens position estimated using the SRK‑T formula guidelines (PIOLadj‑SRK/T) and the real power of the IOL implanted (PIOLReal)
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advantage in near visual acuity over mini‑monovision with a monofocal IOL. Zamora‑Alejo et al.[18] concluded in another comparative study that the Crystalens HD was able to provide some benefit for intermediate visual function compared to a monofocal IOL. Likewise, Alió et al.[12] compared this IOL with a standard monofocal IOL and concluded that the intraocular optical quality achieved with this IOL was similar to that obtained with a conventional monofocal IOL. However, the refractive predictability was observed to be limited in some cases showing an unexpected postoperative myopic or hyperopic postoperative refractive error. In our study, the postoperative SE ranged from −3.13 to +1.14 D, which confirms the presence of a significant variability with a trend to postoperative myopia. According to all this evidence, some optimizations seem to be necessary in the calculation of the power required to be implanted with this accommodating IOL.
Possible sources of error in the calculation of this accommodation IOL might be the bias introduced by considering the corneal power assuming the keratometric error, errors in the determination of the AL or inaccuracy in the estimation of the ELP for this specific IOL. First, the potential impact of the keratometric error was analyzed by calculating the corneal power using an adjusted keratometric index aimed at minimizing the clinical error in the estimation of the corneal power.[14,15,19] However, we still obtained statistically significant and clinically relevant differences between the adjusted calculation, and the real power of the IOL implanted that was selected according to the SRK‑T formula outcomes. As the accuracy of the IOL‑Master for obtaining AL measurements has been widely demonstrated,[20] the ELP was thought to be a critical factor for the presence of a relatively limited predictability with the accommodating IOL evaluated. For such purpose, an expression for estimating an optimized ELP according to some preoperative parameters, designated as adjusted ELP, was obtained by means of multiple linear regression. The IOL power calculation was performed considering this adjusted ELP and the results were compared to those obtained with other predicting algorithms of ELP.[21‑25] This analysis revealed that the ELPadj was significantly lower compared to the values
estimated with the commonly used formulas. One of the main factors that may account for this finding is the potentially more anterior position of the optic of the evaluated accommodating IOL due to the flexible haptics. Indeed, considering equation 1, a longer ELP would lead to the calculation of a higher value of IOL power that may potentially lead to the presence of postoperative myopia. This may explain in part the trend to myopia observed in our sample. Indeed, when the calculation of IOL power was done correcting the keratometric power and also assuming the ELPadj value, no statistically significant differences were found between the implanted and the estimated IOL power. In contrast, significant differences in IOL power were observed with the other commonly used formulas, Haigis, HofferQ and Holladay, which used significantly higher values of ELP.
Regarding the clinical interchangeability of PIOLReal and PIOLadj, a range of agreement of 1.23 D was found which is limited considering that the evaluated IOL is available in half diopter steps. This confirms that although a potential more anterior position of the IOL may contribute to ELP errors with the accommodating IOL evaluated, some positional instability of this IOL within the capsular bag could also influence on them. This is consistent with the results of some ultrasonographic studies revealing the presence of unexpected positions with this type of accommodating IOL.[26‑28]
Finally, ELPadj was found to be related to some factors, such as the AL, the adjusted keratometric corneal power (Pkadj), the ACD and age. Specifically, the longer the eye, the higher was the ELPadj. This is consistent with previous outcomes reported by other authors such as Olsen et al.[29] who found that short eyes tended to have a shallow anterior chamber postoperatively and vice versa. These authors also found that myopic eyes with a large capsular bag showed less IOL movement postoperatively.[29] However, not only anatomical parameters influenced on ELP; age was also found to be an influencing factor. Similarly, other authors have reported a similar finding for another model of accommodating IOL.[30] The interaction between capsular bag fusion and the fibrotic reaction following IOL implantation that leads to capsular bag shrinkage seems to be the main factor accounting for this.
Figure 2: Bland–Altman plots for the comparison between the adjusted intraocular lenses (IOL) power using the effective lens position estimated using the SRK‑T formula guidelines (PIOLadj‑SRK/T) and the real power of the IOL implanted (PIOLReal). The dotted lines show the limits of agreement (±1.96 SD)
Figure 3: Scattergram showing the relationship between the adjusted intraocular lenses (IOL) power using the regression analysis adjusted effective lens position (PIOLadj) and the real power of the IOL implanted (PIOLReal)
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There are several limitations in the current research, such as the limited sample size or the short follow‑up. It should be considered that, although rare, changes in IOL position has been described more than 3 months after surgery, especially after Nd: YAG capsulotomy.[31] This requires further analysis and investigation in future studies. Another potential limitation is the determination of refraction with this accommodating IOL. As previously mentioned, the Crystalens HD IOL has a central bi‑aspheric optical modification generating theoretically some level of negative spherical aberration and therefore contributing to the increase of the depth of focus.[12,32] This may have led to some degree of myopia under pupillary constriction and therefore to some bias in the estimation of the refraction. However, it should be considered that small levels of intraocular primary spherical aberration have been reported with this accommodating IOL,[12] and of positive sign in some cases.[32] Residual myopic refractive errors of more than 0.50 D cannot be attributed to these limited levels of spherical aberration. Furthermore, there were several cases with clinically significant hyperopic residual refractive errors, not only myopic. Another factor that may have contributed to some variability and bias in the estimation of refraction would be the presence of IOL tilts or decentration leading to a degradation of the visual quality and therefore limiting the accuracy of manifest refraction. Some authors have reported cases of misalignment, tilting or bad positioning with previous models of the evaluated accommodating IOL leading to significant levels of visual deterioration.[33‑35] In our sample, IOL misalignment and tilt were not observed in the slitlamp examination, but a more detailed analysis with advanced imaging techniques, such as optical coherence tomography or ultrasonography would be recommendable. Future studies should be conducted to evaluate the position adopted by this IOL into the capsular bag and how it is relation to limitation in the precision of the refractive correction. Finally, it must be acknowledged as an additional limitation that intermediate visual acuity was not recorded in the current series.
ConclusionRefractive outcomes after cataract surgery with implantation of the accommodating IOL Crystalens HD can be optimized by
minimizing the keratometric error using a variable keratometric index for corneal power estimation and by estimating ELP using a mathematical expression dependent on anatomical factors and age. The correction only of the error associated with the keratometric estimation of the corneal power using a variable refractive index does not improve significantly the refractive precision achieved with the accommodating IOL evaluated. The optimization of the estimation of ELP is also necessary. Future studies should be performed to validate this model of IOL power calculation for the Crystalens HD IOL with larger sample of sizes including more extreme cases (long and short).
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Galal A. Near vision restoration with refractive lens exchange and pseudoaccommodating and multifocal refractive and diffractive intraocular lenses: Comparative clinical study. J Cataract Refract Surg 2004;30:2494‑503.
3. Brown D, Dougherty P, Gills JP, Hunkeler J, Sanders DR, Sanders ML. Functional reading acuity and performance: Comparison of 2 accommodating intraocular lenses. J Cataract Refract Surg 2009;35:1711‑4.
4. Patel S, Alió JL, Feinbaum C. Comparison of Acri. Smart multifocal IOL, crystalens AT‑45 accommodative IOL, and Technovision presbyLASIK for correcting presbyopia. J Refract Surg 2008;24:294‑9.
5. Harman FE, Maling S, Kampougeris G, Langan L, Khan I, Lee N, et al. Comparing the 1CU accommodative, multifocal, and monofocal intraocular lenses: A randomized trial. Ophthalmology 2008;115:993‑1001.e2.
6. Uthoff D, Gulati A, Hepper D, Holland D. Potentially accommodating 1CU intraocular lens: 1‑year results in 553 eyes and literature review. J Refract Surg 2007;23:159‑71.
7. Dogru M, Honda R, Omoto M, Toda I, Fujishima H, Arai H, et al. Early visual results with the 1CU accommodating intraocular lens. J Cataract Refract Surg 2005;31:895‑902.
8. Mastropasqua L, Toto L, Nubile M, Falconio G, Ballone E. Clinical study of the 1CU accommodating intraocular lens. J Cataract Refract Surg 2003;29:1307‑12.
9. Wolffsohn JS, Naroo SA, Motwani NK, Shah S, Hunt OA, Mantry S, et al. Subjective and objective performance of the Lenstec KH‑3500 “accommodative” intraocular lens. Br J Ophthalmol 2006;90:693‑6.
10. Ossma IL, Galvis A, Vargas LG, Trager MJ, Vagefi MR, McLeod SD. Synchrony dual‑optic accommodating intraocular lens. Part 2: Pilot clinical evaluation. J Cataract Refract Surg 2007;33:47‑52.
11. Alió JL, Ben‑nun J, Rodríguez‑Prats JL, Plaza AB. Visual and accommodative outcomes 1 year after implantation of an accommodating intraocular lens based on a new concept. J Cataract Refract Surg 2009;35:1671‑8.
12. Alió JL, Piñero DP, Plaza‑Puche AB. Visual outcomes and optical performance with a monofocal intraocular lens and a new‑generation single‑optic accommodating intraocular lens. J Cataract Refract Surg 2010;36:1656‑64.
13. Olsen T. Calculation of intraocular lens power: A review. Acta Ophthalmol Scand 2007;85:472‑85.
14. Camps VJ, Piñero DP, de Fez D, Mateo V. Minimizing the IOL power error induced by keratometric power. Optom Vis Sci 2013;90:639‑49.
Figure 4: Bland–Altman plots for the comparison between the adjusted intraocular lenses (IOL) power using the regression analysis adjusted effective lens position (PIOLadj) and the real power of the IOL implanted (PIOLReal). The dotted lines show the limits of agreement (±1.96 SD)
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15. Camps VJ, Pinero Llorens DP, de Fez D, Coloma P, Caballero MT, Garcia C, et al. Algorithm for correcting the keratometric estimation error in normal eyes. Optom Vis Sci 2012;89:221‑8.
16. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986;1:307‑10.
17. Le Grand Y, El Hage SG. Physiological Optics. Berlin: Springer‑Verlag; 1980.
18. Beiko GH. Comparison of visual results with accommodating intraocular lenses versus mini‑monovision with a monofocal intraocular lens. J Cataract Refract Surg 2013;39:48‑55.
19. Zamora‑Alejo KV, Moore SP, Parker DG, Ullrich K, Esterman A, Goggin M. Objective accommodation measurement of the Crystalens HD compared to monofocal intraocular lenses. J Refract Surg 2013;29:133‑9.
20. Piñero DP, Camps VJ, Mateo V, Ruiz‑Fortes P. Clinical validation of an algorithm to correct the error in the keratometric estimation of corneal power in normal eyes. J Cataract Refract Surg 2012;38:1333‑8.
21. Shammas HJ, Chan S. Precision of biometry, keratometry, and refractive measurements with a partial coherence interferometry‑keratometry device. J Cataract Refract Surg 2010;36:1474‑8.
22. Haigis W. The Haigis formula. In: Shammas HJ, editor. Intraocular Lens Power Calculations. Thorofare, NJ: Slack; 2004. p. 41‑57.
23. Hoffer KJ. The Hoffer Q formula: A comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19:700‑12.
24. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16:333‑40.
25. Holladay JT, Prager TC, Chandler TY, Musgrove KH, Lewis JW, Ruiz RS. A three‑part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17‑24.
26. Stachs O, Schneider H, Stave J, Guthoff R. Potentially accommodating intraocular lenses – An in vitro and in vivo study
using three‑dimensional high‑frequency ultrasound. J Refract Surg 2005;21:37‑45.
27. Marchini G, Pedrotti E, Sartori P, Tosi R. Ultrasound biomicroscopic changes during accommodation in eyes with accommodating intraocular lenses: Pilot study and hypothesis for the mechanism of accommodation. J Cataract Refract Surg 2004;30:2476‑82.
28. Koeppl C, Findl O, Menapace R, Kriechbaum K, Wirtitsch M, Buehl W, et al. Pilocarpine‑induced shift of an accommodating intraocular lens: AT‑45 Crystalens. J Cataract Refract Surg 2005;31:1290‑7.
29. Olsen T, Corydon L, Gimbel H. Intraocular lens power calculation with an improved anterior chamber depth prediction algorithm. J Cataract Refract Surg 1995;21:313‑9.
30. Li XM, Wang W. To observe clinical effect of accommodative IOL on different age patients. Zhonghua Yan Ke Za Zhi 2008;44:30‑2.
31. Findl O, Drexler W, Menapace R, Georgopoulos M, Rainer G, Hitzenberger CK, et al. Changes in intraocular lens position after neodymium: YAG capsulotomy. J Cataract Refract Surg 1999;25:659‑62.
32. Ramón ML, Piñero DP, Blanes‑Mompó FJ, Pérez‑Cambrodí RJ. Clinical and quality of life data correlation with a single‑optic accommodating intraocular lens. J Optom 2013;6:25‑35.
33. Yuen L, Trattler W, Boxer Wachler BS. Two cases of Z syndrome with the Crystalens after uneventful cataract surgery. J Cataract Refract Surg 2008;34:1986‑9.
34. Jardim D, Soloway B, Starr C. Asymmetric vault of an accommodating intraocular lens. J Cataract Refract Surg 2006;32:347‑50.
35. Cazal J, Lavin‑Dapena C, Marín J, Vergés C. Accommodative intraocular lens tilting. Am J Ophthalmol 2005;140:341‑4.
Cite this article as: Piñero DP, Camps VJ, Ramón ML, Mateo V, Pérez-Cambrodí RJ. Positional accommodative intraocular lens power error induced by the estimation of the corneal power and the effective lens position. Indian J Ophthalmol 2015;63:438-44.
Source of Support: Nil. Conflict of Interest: None declared.
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Error induced by the estimation of the corneal powerand the effective lens position with a rotationallyasymmetric refractive multifocal intraocular lens
窑Clinical Research窑
1Grupo de 魷ptica y Percepci佼n Visual (GOPV). Departmentof Optics, Pharmacology and Anatomy, University ofAlicante, San Vicente del Raspeig, Alicante 03690, Spain2Department of Ophthalmology (Oftalmar), Vithas MedimarInternational Hospital, Alicante 03016, Spain3Foundation for the Visual Quality (FUNCAVIS: Fundaci佼npara la Calidad Visual), Alicante 03016, SpainCorrespondence to: David P. Pi觡ero. Department ofOphthalmology (OFTALMAR), 1st floor, MedimarInternational Hospital, C/Padre Arrupe 20, Alicante 03016,Spain. dpinero@oftalmar.esReceived: 2014-09-02 Accepted: 2014-12-01
Abstract·AIM : To evaluate the prediction error in intraocular lens(IOL) power calculation for a rotationally asymmetricrefractive multifocal IOL and the impact on this error ofthe optimization of the keratometric estimation of thecorneal power and the prediction of the effective lensposition (ELP).
·METHODS: Retrospective study including a total of 25eyes of 13 patients (age, 50 to 83y) with previous cataractsurgery with implantation of the Lentis Mplus LS-312 IOL(Oculentis GmbH, Germany). In all cases, an adjusted IOLpower (PIOLadj) was calculated based on Gaussian opticsusing a variable keratometric index value (nkadj) for theestimation of the corneal power (Pkadj) and on a new valuefor ELP (ELPadj) obtained by multiple regression analysis.This PIOLadj was compared with the IOL power implanted(PIOLReal) and the value proposed by three conventionalformulas (Haigis, Hoffer Q and Holladay 玉).
·RESULTS: PIOLReal was not significantly different thanPIOLadj and Holladay IOL power ( >0.05). In the Bland andAltman analysis , PIOLadj showed lower mean difference(-0.07 D) and limits of agreement (of 1.47 and -1.61 D)when compared to PIOLReal than the IOL power valueobtained with the Holladay formula. Furthermore, ELPadj
was significantly lower than ELP calculated with otherconventional formulas ( <0.01) and was found to bedependent on axial length, anterior chamber depth and Pkadj.
· CONCLUSION: Refractive outcomes after cataractsurgery with implantation of the multifocal IOL LentisMplus LS -312 can be optimized by minimizing the
keratometric error and by estimating ELP using amathematical expression dependent on anatomicalfactors.
·KEYWORDS: Mplus;multifocal intraocularlens;keratometry;effective lens position; intraocular lens powerDOI:10.3980/j.issn.2222-3959.2015.03.12
Pi觡ero DP, Camps VJ, Ram佼n ML, Mateo V, P佴rez-Cambrod侏 RJ.
Error induced by the estimation of the corneal power and the effective
lens position with a rotationally asymmetric refractive multifocal
intraocular lens. 2015;8(3):501-507
INTRODUCTION
S everal studies[1-8] have confirmed the ability of multifocalintraocular lenses (IOLs) of providing a good near and
distance functional vision without the use of corrective lensesafter cataract surgery. One modality of IOL multifocality isthe use of a rotationally asymmetric refractive profilecontaining an aspheric distance-vision zone combined with asector-shaped near-vision zone in the inferior area of the IOL.This concept of multifocality is the basis of the multifocalIOL Lentis Mplus LS-312 (Oculentis GmbH). Studies on thisIOL have shown good near and distance visual outcomes,combined with postoperative contrast sensitivity withinphysiological ranges and positive impact on patient's qualityof life [1,2,9-15]. Even some studies have reported good levels ofintermediate visual acuity with this type of IOL[1,2].Despite the good visual outcomes reported with this IOL[1,2,9-15],some studies have shown some level of variability in therefractive correction achieved[1,2,9,13-15]. Ali佼 [15] found in aprospective comparative study evaluating a group of 21 eyesimplanted with the Mplus IOL a mean 3mo postoperativesphere of -0.34依0.93 D, ranging from -3.00 to +1.25 D. Inanother sample of 9366 eyes implanted with this type of IOL,Venter [9] found that 91.8% of eyes had a postoperativespherical equivalent (SE) within 依1.00 D. In the same line,Mu觡oz [13] found that 6 eyes (9.4%) from a sample of 64eyes had a postoperative myopic SE of more than 0.50 D(mean residual SE: -0.75依0.15 D). McAlinden and Moore [14]
reported in another series of cases a percentage of 86.4% ofeyes with an SE within 依0.50 D. Several factors may be inrelation to this variable level of predictability, such as some
501171
inaccuracies in IOL power calculation due to the use of notfully optimized formulae for this specific type of IOL.The aim of the current study was to evaluate thepredictability of the refractive correction achieved with thisrefractive multifocal IOL and to develop an optimization ofthe predictability error by minimizing the error associated tothe keratometric estimation of the corneal power and bydeveloping a predictive formula of the effective lens positionfor this specific type of IOL.SUBJECTS AND METHODSSubjects This retrospective study included a total of 25 eyesof 13 patients. All eyes underwent cataract surgery withimplantation of the rotationally asymmetric multifocal IOLLentis Mplus LS-312 (Oculentis GmbH). Inclusion criteriafor this study were patients with visually significant cataractor presbyopic/pre-presbyopic patients suitable for refractivelens exchange and demanding complete spectacleindependence. Exclusion criteria were patients with activeocular diseases, illiteracy and topographic astigmatismshigher than 1.5 D. All volunteers were adequately informedabout the surgery and signed a consent form. The studyadhered to the tenets of the Declaration of Helsinki and wasapproved by the Local Ethical Committee.MethodsIntraocular lens The Lentis Mplus LS-312 (OculentisGmbH, Germany) is a rotationally asymmetric multifocalIOL that contains an aspheric distance-vision zone combinedwith a 3.00 D posterior sector-shaped near-vision zone toallow good transition between the zones. It has biconvexdesign with a 6.0 mm optic, a 12.0 mm overall length, and aC-loop haptic design with 0-degree angulation. The IOL ismade of an acrylic copolymer comprising acrylates with ahydrophobic surface and ultraviolet-filtering components.Surgical technique All surgeries were performed by thesame experienced surgeon (Ram佼n ML) using a standardtechnique of phacoemulsification. In all cases, topicalanesthesia was administered and pupillary dilation wasinduced with a combination of tropicamide andphenylephrine 10% every 15min half an hour previous to theprocedure. Iodine solution 5% was instilled on the eye 10minbefore the operation. A 2.75-mm clear incision was madewith a diamond knife on the steepest meridian to minimizepost-surgical astigmatism. A paracentesis was made 60毅-90毅clockwise from the main incision and the anterior chamberwas filled with viscoelastic material. After the crystalline lensremoval, the IOLs were implanted through the incision intothe capsular bag using a specific injector developed by themanufacturer for such purpose. Finally, the surgeonproceeded to retrieve the viscoelastic material using theirrigation-aspiration system. A combination of topical steroidand antibiotic (Tobradex, Alcon, Fort Worth, TX, USA) as
well as a non-steroidal anti-inflammatory drops (Dicloabak,Laboratorios Thea, Barcelona, Spain) were prescribed to beapplied four times daily for a week after the surgery and threetimes daily the second postoperative week. In addition,non-steroidal anti-inflammatory drops were also prescribed tobe applied three times daily during 2 additional weeks aftersurgery.Calculation of an adjusted intraocular lens powerAlmost all theoretical formulas for IOL power (PIOL)calculation are based on the use of a simplified eye model,with thin cornea and lens models [16]. According to suchapproach, PIOL can be easily calculated using the Gaussequations in paraxial optics:[17]
(1)where, Pc is the total corneal power, ELP the effective lensplane, AL the axial length, nha the aqueous humour refractiveindex, nhv the vitreous humour refractive index, and Rdes thepostoperative desired refraction calculated at corneal vertex.Our research group proposed the use of a variablekeratometric index (nkadj) depending on the radius of theanterior corneal surface (r1c) expressed in millimetres forminimizing the error associated to the keratometric approachfor corneal power calculation [18]. Specifically, the followingexpression was defined according to the Gullstrand eyemodel:nkadj = -0.0064286r1c + 1.37688 (2)Using these algorithm, a new keratometric corneal power,named adjusted keratometric corneal power (Pkadj), can becalculated using the classical keratometric corneal powerformula [18]. In the current study, the adjusted IOL power(PIOLadj) was calculated, which was defined as the IOL powercalculated from the equation 1 using the nkadj value for theestimation of the corneal power (Pkadj), and the nha and nhv
values corresponding to the Gullstrand eye model (1.336 forboth indexes). In this IOL power calculation, thepostoperative SE at corneal vertex was considered as thedesired refraction (Rdes=SEpost). The PIOLadj calculation wasperformed by estimating the ELP using two differentapproaches: ELP calculation following the SRK/T formulaguidelines (named PIOLadjSRK/T) [19] and ELP calculation using amathematical expression obtained by multiple regressionanalysis (named PIOLadj), following a procedure described inthe next section. These values of IOL power (PIOLadj) werecompared with the real power of the IOL implanted (PIOLReal).An PIOL calculation was also performed using threeconventional formulae (Haigis [20], Hoffer Q [21] and Holladay
( )
−
+
−
−
=
ELPcPdesR
hanhan
ELPALhvn
IOLP
Optimization of lentis mplus IOL power calculation
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Ⅰ [22]) considering the ELP defined for each formula andRdes=SEpost. All these values of PIOL were also compared toPIOLadj. The calculation with the conventional IOL powerformulas was performed by implementing them in an Excelsoftware sheet version 14.0.0 for Mac.Estimation of adjusted effective lens positionConsidering the equation 1, PIOLreal, Pkadj and Rdes=SEpost, anestimation of ELP was obtained in each case. By means ofmultiple regression analysis, a mathematic expression wasobtained for predicting the ELP in each specific case. ThisELP was named as adjusted effective lens position (ELPadj).Preoperative and postoperative examinationsPreoperatively, all patients had a full ophthalmologicexamination including the evaluation of the refractive status,distance and near visual acuities, slit lamp examination,optical biometry (IOL-Master, Zeiss), applanation tonometryand funduscopy. Distance (4 m) and near (40 cm) visualacuities were evaluated with ETDRS charts. Postoperatively,patients were evaluated at 1d, 1wk, 1mo and 3mo aftersurgery. In all visits, visual acuity, refraction and the integrityof the anterior segment were evaluated. Funduscopy was alsoperformed in the postoperative revision at 3mo.Statistical Analysis The statistical analysis was performedusing the SPSS statistics software package version 21.0.0.0for Mac (IBM, Armonk, NY, USA). Normality of datasamples was evaluated by means of the Kolmogorov-Smirnov test. When parametric analysis was possible, theStudent test for paired data was used for comparing thedifferent approaches for PIOL calculation. When parametricanalysis was not possible, the Wilcoxon rank sum test wasapplied to assess the significance of such comparisons.Differences were considered to be statistically significantwhen the associated -value was of less than 0.05.Regarding the interchangeability between pairs of methodsfor obtaining PIOL, the Bland-Altman analysis was used[23].A multiple regression analysis was performed by using thebackward elimination method for obtaining a mathematicalexpression allowing the prediction of ELPadj from differentpreoperative anatomical and clinical parameters. Modelassumptions were evaluated by analysing residuals, thenormality of non-standardized residuals (homoscedasticity),and the Cook distance to detect influential points or outliers.In addition, the lack of correlation between errors andmulticolinearity was assessed using the Durbin-Watson test,the calculation of the colinearity tolerance, and the varianceinflation factor.RESULTSThis study evaluated 25 eyes of 13 patients [6 men (46.2%)and 7 women (53.8%)], with a mean age of 65.6y依7.6 SD(range, 50 to 83y). The sample comprised 12 (48%) and 13(52%) right and left eyes, respectively. Table 1 summarizessome preoperative visual, refractive and anatomical data of
the eyes evaluated as well as all the estimation performed forELP and IOL power. According to axial length (AL), anteriorchamber depth (ACD) and corneal power, and using theSRK-T formula, the mean power of the IOL implanted was19.78 D依2.32 SD (range, 12.50 to 23.50 D).Agreement of PIOLReal and PIOLadjSRK/T Statistically significantdifferences were found between PIOLadjSRK/T and PIOLReal,considering that ELP was calculated following the SRK/Tformula guidelines and considering Rdes=SEpost ( <0.01,Wilcoxon test). A very strong and statistically significantcorrelation was found between PIOLadj and PIOLReal ( =0.86,
<0.01, Figure 1). According to the Bland and Altmananalysis of interchangeability, the PIOLadjSRK/T was higher thanPIOLReal (mean difference: 1.41 D) and the limits of agreement
Table 1 Summary of several parameters involved in the study: mean preoperative anatomical and corneal power (calculated with the conventional keratometric index 1.3375, the Haigis approach[20] and the approach developed by our research group[18]) parameters, mean preoperative and postoperative SE, mean nkadj (calculated with our approach[18]), and mean ELP and IOL power calculated with different formulas
Parameters sx ± Range SEpre (D) -1.27± 2.87 -7.50 to 3.00 SEpost (D) -0.11±0.56 -1.83 to 0.76 r1c
[24] 7.61 ± 0.25 7.19 to 8.01 ACD[24] 3.31 ± 0.28 2.61 to 3.79 AL[24] 23.52 ± 1.04 22.02 to 27.36 ELPSRK/T
[24] 5.12 ± 0.45 4.60 to 6.83 ELPadj
[24] 4.31 ± 0.50 3.39 to 5.34 ELPHaigis
[24] 5.01 ± 0.16 4.77 to 5.46 ELPHofferQ
[24] 5.00 ± 0.27 4.63 to 6.01 ELPHolladay
[24] 4.59 ± 0.27 3.89 to 5.07 nkadj 1.328 ± 0.002 1.325 to 1.331 Pk(1.3375) (D) 44.37 ± 1.44 42.14 to 46.95 PcHaigis (D) 43.57 ± 1.41 41.39 to 46.11 Pkadj (D) 43.11 ± 1.61 40.62 to 45.99 PIOLReal (D) 19.78 ± 2.32 12.50 to 23.50 PIOLadjSRK/T (D) 21.18 ± 2.74 12.51 to 25.46 PIOLadj (D) 19.71 ± 2.55 11.02 to 23.53 PIOLHaigis (D) 20.40 ± 3.15 10.16 to 24.99 PIOLHofferQ (D) 19.30 ± 3.04 9.50 to 23.90 PIOLHolladay (D) 19.57 ± 2.99 9.40 to 23.90
SEpre: Preoperative spherical equivalent; SEpost: Postoperative spherical equivalent; r1c: Radius of curvature of the anterior corneal surface; ACD: Anterior chamber depth; AL: Axial length; ELPSRK/T: Effective lens position for the SRK/T formula; ELPadj: Effective lens position for the adjusted formula; ELPHaigis: Effective lens position for the Haigis formula; ELPHofferQ: Effective lens position for the Hoffer Q formula; ELPHolladay: Effective lens position for the Holladay formula; nkadj: Adjusted keratometric index; Pk(1.3375): Corneal power obtained using IOL-Master or keratometric power; PcHaigis: Corneal power obtained for the Haigis formula; Pkadj: Corneal power obtained using the adjusted keratometric index; PIOLReal: Power of the intraocular lens implanted which was calculated using the SRK/T formula; PIOLadjSRK/T: Power of the intraocular lens obtained using adjusted formula and ELP calculated with the SRK/T formula; PIOLadj: Intraocular lens power obtained using the adjusted formula and ELPadj; PIOLHaigis: Intraocular lens power obtained using the Haigis formula; PIOLHofferQ: Intraocular lens power obtained using the Hoffer Q formula; PIOLHolladay: Intraocular lens power obtained using the Holladay formula.
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were clinically relevant (3.29 and -0.48 D). Figure 2 showsthe Bland and Altman plot corresponding to this agreementanalysis.Estimation of ELPadj The multiple regression analysisrevealed that the ELPadj was significantly correlated with AL,ACD and Pkadj ( <0.01):ELPadj=-17.333+0.612伊ACD+0.360伊AL+0.268伊Pkadj(3)
The homoscedasticity of the model was confirmed by thenormality of the non-standardized residuals distribution( =0.20) and the absence of influential points or outliers(mean Cook's distance: 0.155依0.528). With this model, 56%of non-standardized residuals were 0.20 or lower and 76%were lower than 0.50. The poor correlation between residuals(Durbin-Watson test: 1.629) and the lack of multicolinearity(tolerance 0.805 to 0.560; variance inflation factors 1.785 to1.243) was also confirmed.A statistically significant difference was found between
ELPadj and the rest of ELP values obtained following theguidelines proposed by each of the formulas used ( <0.01,unpaired Wilcoxon test). ELPadj was the lowest ELP value(Table 1) among all values of ELP calculated (4.31依0.50 mm,range 3.39 to 5.34 mm).Agreement between PIOLReal and PIOLadj No statisticallysignificant differences were found between PIOLadj and PIOLReal
when ELPadj and Rdes=SEpost were considered for PIOLadj
calculation ( =0.65, unpaired Student's -test). A verystrong and statistically significant correlation was foundbetween PIOLadj and PIOLReal ( =0.95, <0.01) (Figure 3).According to the Bland and Altman [23] analysis, the meandifference between both PIOLadj and PIOLReal was -0.07 D, withlimits of agreement of 1.47 and -1.61 D. Figure 4 shows theBland and Altman plot corresponding to this agreementanalysis.Agreement of PIOLadj with other formulas Statisticallysignificant differences were found between PIOLadj and PIOLHaigis,
and between PIOLadj and PIOLHofferQ ( <0.01, Wilcoxon test), butnot between PIOLadj and PIOLHolladay ( =0.20, Wilcoxon test).
Figure 1 Relationship between the adjusted IOL power usingthe ELP estimated using the SRK/T formula guidelines(PIOLadjSRK/T) and the real power of the IOL implanted (PIOLReal).
Figure 2 Bland-Altman plots for the comparison between theadjusted IOL power using the ELP estimated using the SRK/Tformula guidelines (PIOLadjSRK/T) and the real power of the IOLimplanted (PIOLReal) The dotted lines show the limits of agreement(依1.96SD).
Figure 4 Bland-Altman plots for the comparison between theadjusted IOL power using the regression analysis adjustedELP (PIOLadj) and the real power of the IOL implanted (PIOLReal)The dotted lines show the limits of agreement (依1.96SD).
Figure 3 Relationship between the adjusted IOL power usingthe regression analysis adjusted ELP (PIOLadj) and the realpower of the IOL implanted (PIOLReal).
Optimization of lentis mplus IOL power calculation
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Table 2 shows the Bland and Altman analysis outcomescorresponding to all comparisons done. A very strong andstatistically significant correlation was found between PIOLadj
and PIOLHolladay ( = 0.96, <0.01, Figure 5). According to theBland and Altman [23] analysis, the mean difference betweenboth PIOLadj and PIOLHolladay was -0.13 D, with limits of agreementof 1.01 and -1.28 D. Figure 6 shows the Bland and Altmanplot corresponding to this agreement analysis.Agreement of PIOLreal with other formulas Statisticallysignificant differences were found between PIOLreal and PIOLHaigis,
and between PIOLreal and PIOLHofferQ ( <0.05, Wilcoxon test), butnot between PIOLreal and PIOLHolladay ( =0.29, Wilcoxon test).Table 3 shows the Bland and Altman analysis outcomescorresponding to all comparisons done. According to theBland and Altman method, the mean difference betweenPIOLHolladay and PIOLreal was -0.21 D, with limits of agreement of1.96 and -2.37 D (Figure 7).DISCUSSIONThe refractive results obtained after cataract surgery withimplantation of a multifocal IOL based on the concept ofrefractive rotationally asymmetry, the Lentis LS-312 IOL,have been evaluated in the current series. A significantvariability in the postoperative SE was observed in theanalyzed sample, with a mean value of -0.11 依0.56 D.Specifically, the SE at 3mo after surgery ranged from -1.83 to+0.76 D, with a slight trend to some level of residual myopia,as in some previous series evaluating the results of the same
type of multifocal IOL [2,11,15]. This confirms that anoptimization in the algorithm of IOL power calculation isnecessary in order to refine the refractive and visualoutcomes with this premium multifocal IOL. The relativelimitation of the predictability of the refractive correction insome cases implanted with the Mplus IOL may beattributable to the bias associated to the use of thekeratometric approach for the calculation of the cornealpower, errors in the determination of the axial length orinaccuracy in the estimation of the ELP for this specific IOL.However, the errors in the estimation of axial length with thetechnology used have been shown to be minimal and with avery limited impact on the refractive predictability [24].Therefore, in the current study, the potential contribution ofthe corneal power and ELP factors to the limitation of the
Table 2 Bland and Altman analysis outcomes of the comparison between PIOLadj and the IOL power obtained with other commonly used formulas
Comparison ∆PIOL ±SD (D) LoA (D) P PIOLHaigis - PIOLadj 0.68 ± 0.72 2.09 to -0.73 <0.01 PIOLHofferQ - PIOLadj -0.43 ± 0.75 1.05 to -1.90 <0.01 PIOLHolladay - PIOLadj -0.13 ± 0.67 1.01 to -1.28 0.20
Figure 6 Bland-Altman plots for the comparison between theadjusted IOL power using the regression analysis adjustedELP (PIOLadj) and the IOL power when using the Holladayformula (PIOLHolladay) The dotted lines show the limits of agreement
(依1.96 SD).
Figure 7 Bland-Altman plots for the comparison between theIOL power when using the Holladay formula (PIOLHolladay) andthe real power of the IOL implanted (PIOLHolladay) The dotted lines
show the limits of agreement (依1.96SD).
Table 3 Bland and Altman analysis outcomes of the comparison between PIOLreal and the IOL power obtained with other commonly used formulas
Comparison ∆PIOL ±SD (D) LoA (D) P PIOLHaigis - PIOLreal 0.62 ± 1.15 2.88 to -1.64 0.01 PIOLHofferQ - PIOLreal -0.43 ± 1.13 1.73 to -2.69 0.03 PIOLHolladay - PIOLreal -0.13 ± 1.10 1.96 to -2.37 0.29
Figure 5 Relationship between the adjusted IOL power usingthe regression analysis adjusted ELP (PIOLadj) and the IOLpower when using the Holladay formula (PIOLHolladay).
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refractive predictability with the multifocal IOL evaluatedhave been investigated.First, the potential impact of the keratometric error wasanalysed by calculating the corneal power using an adjustedkeratometric index aimed at minimizing the clinical error inthe estimation of the corneal power[17,18]. This adjusted cornealpower was used to obtain an estimation of the IOL powerconsidering the axial length and an ELP estimated followingthe algorithm established for the SRK-T formula [19]. With thisapproach, statistically significant and clinically relevantdifferences were found between the adjusted calculation(PIOLadjSRK/T) and the real power of the IOL implanted that wasselected according to the SRK-T formula (PIOLReal) [19].Therefore, the correction of this factor seems to have aminimal effect on the outcomes achievable with themultifocal IOL evaluated. Then, ELP was thought to be acritical factor for the presence of a relatively limitedpredictability with the IOL evaluated. For such purpose, anexpression for estimating an optimized ELP according tosome preoperative parameters was obtained by means ofmultiple linear regression. This new ELP estimation wasnamed adjusted ELP (ELPadj). The ELPadj were compared tothose ELP values obtained with other predicting algorithmsof ELP [19-21]. This analysis revealed that the ELPadj wassignificantly lower compared to the values estimated with theHaigis, Hoffer Q and Holladay Ⅰ formulas (ELPHaigis,ELPHofferQ and ELPHolladay respectively) [20,21]. In any case,differences between ELPadj and ELPHolladay were found to be thelowest in magnitude and this may be the reason for theabsence of statistically significant differences between PIOLadj
and PIOLHolladay. In contrast, the difference was statisticallysignificant and clinically relevant when our IOL power(PIOLadj) was compared to Haigis or Hoffer Q formulas (PIOLHaigis
and PIOLHofferQ, respectively). One factor attributable to thelower value of ELPadj compared to those ELP values obtainedwith conventional formulas is a more anterior position of theoptic of the multifocal IOL evaluated due to the flexibility ofthe haptics. This more anterior position was better predictedwith the Holladay formula and with our ELPadj calculationalgorithm (see equation 3). This may explain in part the trendtoward myopia observed in our sample, in which the IOLpower calculation was performed with the SRK-T formulathat uses higher estimated values of ELP. Indeed, consideringequation 1, a longer ELP would lead to the calculation of ahigher value of IOL power that may potentially lead to thepresence of postoperative myopia. Future studies shouldevaluate the real position of the IOL within the capsular bagby means of imaging techniques in order to confirm ourhypotheses, as has been done for other types of IOLs[25].In our linear regression analysis, ELPadj was found to berelated to some factors, such as the AL, Pkadj and the ACD.
The anatomical factors were crucial determinants of the finalposition of the IOL evaluated within the eye. ELPadj washigher in those eyes with longer AL and ACD, as happens inmoderate to high myopic eyes. This finding was consistentwith those reported by previous authors, reporting a lineardependence of the final position of the IOL on the AL [26-28].Considering that ELPadj and ELPHolladay were not significantlydifferent, this formula seems to be the most recommendableapproach for IOL power calculation with the multifocal IOLevaluated. More studies with larger samples sizes should beperformed to confirm all these outcomes.Finally, it should be mentioned that when all IOL powerformulas were compared with PIOLreal, PIOLadj and PIOLHolladay didnot differ significantly with PIOLreal. The Bland-Altman plotsshowed less clinically relevant level of agreement of PIOLreal
with PIOLadj than with PIOLHolladay (Figures 4, 7). Therefore, PIOLadj
was able to reproduce more accurately PIOLReal and therefore ofthe refractive outcome. This suggests that our approach maybe a useful method for IOL power calculation with themultifocal IOL evaluated. This should be corroborated infuture prospective studies.There are several limitations in the current research, such asthe limited sample size or the short follow-up. It should beconsidered that, although rare, changes in IOL position hasbeen described more than 3mo after surgery, especially afterNd:YAG capsulotomy [29]. This requires further analysis andinvestigation in future studies with the Mplus IOL. Anotherpotential limitation is the determination of refraction with thismultifocal IOL. Some difficulties have been described forobtaining an accurate refraction after implantation ofdifferent models of IOL, with a clear trend to overestimationof the sphere with positive sign [30]. In any case, the manifestrefraction was obtained using the same procedure describedfor refracting eyes with multifocal IOLs [31] and without usingthe autorrefraction as the basis because it has been shown tofail in eyes implanted with the Mplus IOL [32]. Finally, itshould be mentioned that the Holladay II formula was notused in our comparison as it was not available in our clinic.Possibly, our approach may be more similar to the results ofthe Holladay II formula as both types of calculation use anoptimized algorithm for the estimation of ELP, but thisshould be confirmed in future studies.In conclusion, refractive outcomes after cataract surgery withimplantation of refractive rotationally asymmetric IOL LentisMplus LS-312 may be optimized by minimizing thekeratometric error using a variable keratometric index forcorneal power estimation and by estimating ELP using amathematical expression dependent on anatomical factors.Future studies should be performed to validate this model ofIOL power calculation for the Lentis Mplus IOL with larger
Optimization of lentis mplus IOL power calculation
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sample of sizes including more extreme cases (long andshort AL).ACKNOWLEDGEMENTSConflicts of Interest: Pi觡ero DP, None; Camps VJ, None;Ram佼n ML, None; Mateo V, None; P佴rez-Cambrod侏 RJ,None.REFERENCES1 Ram佼n ML, Pi觡ero DP, P佴rez-Cambrod侏 RJ. Correlation of visual
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·Original article·
Preliminary evaluation of an algorithm to minimize thepower error selection of an aspheric intraocular lens byoptimizing the estimation of the corneal power and theeffective lens positionDavid P. Pi觡ero1,2, Vicente J. Camps1, Mar侏a L. Ram仵n2, Ver佼nica Mateo1, RobertoSoto-Negro2
1Group of Optical and Visual Perception, Department ofOptics, Pharmacology and Anatomy, University of Alicante,San Vicente del Raspeig, Alicante 03690, Spain2Department of Ophthalmology, Vithas Medimar InternationalHospital, Alicante 03016, SpainCorrespondence to: David P. Pi觡ero. Department ofOphthalmology, Vithas Medimar International Hospital,Alicante 03016, Spain. dpinero@ oftalmar. esReceived: 2015-07-23摇 摇 Accepted: 2016-03-17
非球面人工晶状体度数计算的最优化David P. Pi觡ero1,2, Vicente J. Camps1, Mar侏a L. Ram仵n2,Ver佼nica Mateo1, Roberto Soto-Negro2
(作者单位:1西班牙,阿利坎特 03690,圣维森特-德埃拉斯佩
奇,阿利坎特大学,视光学、药理学和解剖学系,光学和视觉知觉
组;2西班牙,阿利坎特 03016,Vithas Medimar 国际医院,眼科)通讯作者:David P. Pi觡ero. dpinero@ oftalmar. es
摘要目的:通过评价非球面人工晶状体( intraocular lens, IOL)屈光度的可预测性,初步开发一种计算屈光度(PIOL)的优
化算法。方法:本研究纳入植入非球 面 IOL ( LENTIS L - 313,Oculentis GmbH)65 眼,并分为 2 组:A 组 8 例 12 眼,PIOL逸23. 0D;B 组 35 例 53 眼,PIOL<23. 0D。 术后 3mo 进行屈光
度可预测性评价。 参考角膜屈光力估计所致的可变性屈
光指数计算出校正的 IOL 度数(PIOLadj)及屈光结果,根据
年龄和解剖学因素得出校正的有效晶状体位置( adjustedeffective lens position, ELPadj)。结果:术后 A、B 两组等效球镜度数分别为-0. 75 ~ +0郾 75D、-1. 38 ~ +0. 75D。 A、B 两组的 PIOLadj和实际晶状体屈光度
(PIOLReal)之间无统计学差异 ( P = 0. 64、0. 82)。 Bland -Altman 分析显示 A、B 两组 PIOLadj和 PIOLReal之间的一致性区
间分别为+1. 11 ~ -0. 96D 和+1. 14 ~ -1. 18D。 Hoffer Q公式和 Holladay I 公式计算 PIOLadj和 PIOL之间存在临床和
统计学上的显著差异(P<0. 01)。结论:植入非球面 IOL 白内障手术的屈光可预测性可通过
平行轴光学联合线性法则使角膜屈光力及晶状体位置相
关误差最小化。
关键词:非球面人工晶状体;人工晶状体屈光度计算;有效
晶状体位置
引用:Pi觡ero DP, Camps VJ, Ram仵n ML, Mateo V, Soto-NegroR. 非球面人工晶状体度数计算的最优化. 国际眼科杂志 2016;16(6):1001-1008
Abstract誗AIM: To evaluate the refractive predictability achievedwith an aspheric intraocular lens ( IOL) and to develop apreliminary optimized algorithm for the calculation of itspower (PIOL) .誗METHODS: This study included 65 eyes implanted withthe aspheric IOL LENTIS L - 313 (Oculentis GmbH) thatwere divided into 2 groups: 12 eyes (8 patients) with PIOL
逸23. 0 D (group A), and 53 eyes (35 patients) with PIOL<23. 0 D ( group B ) . The refractive predictability wasevaluated at 3mo postoperatively. An adjusted IOL power(PIOLadj ) was calculated considering a variable refractiveindex for corneal power estimation, the refractiveoutcome obtained, and an adjusted effective lens position(ELPadj) according to age and anatomical factors.誗 RESULTS: Postoperative spherical equivalent rangedfrom - 0. 75 to + 0. 75 D and from - 1. 38 to + 0. 75 D ingroups A and B, respectively. No statistically significantdifferences were found in groups A (P = 0. 64) and B (P =0. 82 ) between PIOLadj and the IOL power implanted(PIOLReal) . The Bland and Altman analysis showed rangesof agreement between PIOLadj and PIOLReal of +1. 11 to -0. 96D and +1. 14 to -1. 18 D in groups A and B, respectively.Clinically and statistically significant differences werefound between PIOLadj and PIOL obtained with Hoffer Q andHolladay I formulas (P<0. 01) .誗CONCLUSION: The refractive predictability of cataractsurgery with implantation of an aspheric IOL can beoptimized using paraxial optics combined with linearalgorithms to minimize the error associated to theestimation of corneal power and ELP.誗KEYWORDS:aspheric intraocular lens; intraocular lenspower calculation; effective lens positionDOI:10. 3980 / j. issn. 1672-5123. 2016. 6. 01
1001
Int Eye Sci, Vol. 16, No. 6, Jun. 2016摇 摇 http: / / ies. ijo. cnTel:029鄄82245172摇 82210956摇 摇 Email:IJO. 2000@163. com
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Citation:Pi觡ero DP, Camps VJ,Ram佼n ML, Mateo V, Soto-NegroR. Preliminary evaluation of an algorithm to minimize the powererror selection of an aspheric intraocular lens by optimizing theestimation of the corneal power and the effective lens position. GuojiYanke Zazhi( Int Eye Sci) 2016;16(6):1001-1008
INTRODUCTION
T he human eye is composed of two aspheric lenses, corneaand crystalline lens, which are the main ocular optical
elements accounting for the final quality of the retinal image.The cornea is comprised of two prolate surfaces that inducepositive spherical aberration that increases with age[1] . Thecrystalline lens is comprised of two aspheric surfaces thatinduce negative spherical aberration[2] . With age, thebalance between the spherical aberration of the cornea andcrystalline lens is progressively lost, leading to a reduction inthe level of quality of the retinal image[3-6] . Asphericintraocular lenses ( IOLs) were developed with the aim ofproviding a compensation for the corneal positive sphericalaberration and therefore to maintain the balance in terms ofspherical aberration between cornea and IOL after cataractsurgery[7] . An aspheric IOL may lead then to the achievementof better contrast sensitivity compared to a spherical IOL,especially under dim light conditions[7] .According to some optical simulations, a real benefit can beobtained with aspheric IOLs in corneas of a moderate prolateaspheric shape with a negative asphericity ( Q) value of-0. 22 or below[8] . In spite of the potential benefit of asphericIOLs over conventional spherical IOLs, it should bementioned that the outcomes obtained with aspheric IOLs aremore susceptible to misalignments or decentrations[9] as wellas to residual optical errors[10] . Furthermore, the potentialbenefit of aspheric IOLs has been suggested to be more limitedin longer eyes than in short eyes[8] . This may be due to someinaccuracies in IOL power calculations in such cases.Hoffmann and Lindeman[11] demonstrated that ray tracingbased on biometry data improved IOL prediction accuracy overconventional formulas in normal eyes implanted with asphericIOLs. The aim of the current study was to evaluate thepredictability of the refractive correction achieved with aspecific model of aspheric IOL and to develop a preliminaryalgorithm for IOL power calculation to optimize the refractivepredictability with this IOL by minimizing the error associatedto the keratometric estimation of the corneal power and bydeveloping a predictive formula for the estimation of theeffective lens position. This study was planned as apreliminary evaluation of the possibility of a furtheroptimization of IOL power calculation using paraxial optics.SUBJECTS AND METHODSPatients摇 A total of 65 eyes of 43 patients ranging in agefrom 56 to 92 years old were included retrospectively in thisstudy. All these eyes underwent cataract surgery withimplantation of the aspheric IOL LENTIS L-313 (OculentisGmbH, Berlin, Germany). As will be explained later, twogroups of eyes were differentiated according to the power of the
IOL implanted: group A, including 12 eyes of 8 patientsimplanted with an IOL 逸23. 0 D, and group B, including 53eyes of 35 patients with an IOL < 23. 0 D of power. Theinclusion criteria of this study were patients with visuallysignificant cataract or presbyopic / pre - presbyopic patientssuitable for refractive lens exchange. The exclusion criteriawere patients with active ocular diseases, illiteracy andtopographic astigmatisms > 1. 5 D. All volunteers wereadequately informed and signed a consent form. The studyadhered to the tenets of the Declaration of Helsinki and wasapproved by the ethics committee of the University of Alicante(Alicante, Spain) .Intraocular Lens 摇 The LENTIS L-313 is an acrylic one -piece IOL with a hydrophobic surface and ultraviolet-filteringcomponents. It has biconvex design with a 6. 0-mm optic, anoverall length of 11. 0 mm, and a C-loop haptic design with 0- degree angulation. The posterior surface of the IOL isaspheric and provides some level of negative sphericalaberration aimed at compensating for the positive sphericalaberration of the cornea. It is available in powers from 10 to30 D in 0. 5-D steps and from 0 to 10 D and from 30 to 35 Din 1. 0-D steps.Surgical Technique 摇 All surgeries were performed by oneexperienced surgeon (Ram佼n ML) using a standard techniqueof phacoemulsification. In all cases, topical anesthesia wasadministered and pupillary dilation was induced with acombination of tropicamide and phenylephrine 10% every15min half an hour previous to the procedure. Iodine solution5% was instilled on the eye 10min before the operation. A2郾 75-mm clear incision was made with a diamond knife onthe steepest meridian to minimize post-surgical astigmatism.A paracentesis was made 60毅 -90毅 clockwise from the mainincision and the anterior chamber was filled with viscoelasticmaterial. After the crystalline lens removal, the IOL wasimplanted through the incision into the capsular bag using aspecific injector developed by the manufacturer for suchpurpose. Finally, the surgeon proceeded to retrieve theviscoelastic material using the irrigation-aspiration system. Acombination of topical steroid and antibiotic ( Tobradex,Alcon, Fort Worth, TX, USA) as well as a non - steroidalanti - inflammatory drops ( Dicloabak, Laboratorios Thea,Barcelona, Spain) were prescribed to be applied 4 times dailyfor 1wk after the surgery and 3 times daily the secondpostoperative week. In addition, the non - steroidal anti -inflammatory drops were also prescribed to be applied 3 timesdaily during 2wk more after surgery.Preoperative and Postoperative Examinations 摇Preoperatively, all patients had a full ophthalmologicexamination including the evaluation of the refractive status,distance and near visual acuities, slit lamp examination,optical biometry ( IOL -Master, Carl Zeiss Meditec, Jena,Germany ), tonometry and funduscopy. Postoperatively,patients were evaluated at 1d, 1wk, 1 and 3mo after surgery.In all visits, visual acuity, refraction and the integrity of theanterior segment were evaluated. Funduscopy was alsoperformed in the postoperative revision at 3mo.
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Calculation of the Adjusted IOL Power 摇 Almost alltheoretical formulas for IOL power calculation are based on theuse of a simplified eye model, with thin cornea and lensmodels[12] . According to such approach, the power of the IOL(PIOL) can be easily calculated using the Gauss equations inparaxial optics[13]:
where Pc is the total corneal power, ELP is the effective lensplane, AL is the axial length of the eye, nha is the aqueoushumour refractive index, nhv is the vitreous humour refractiveindex and Rdes represents the postoperative desired refractioncalculated at corneal vertex.Our research group proposed in 2012 the use of a variablekeratometric index ( nkadj ) depending on the radius of theanterior corneal surface ( r1c ) expressed in millimetres forminimizing the error associated to the keratometric approachfor corneal power calculation[14] . Specifically, the followingexpression was defined according to the Gullstrand eye model:
nkadj = -0. 0064286r1c+ 1. 37688摇 摇 摇 摇 摇 摇 摇 摇 摇 (2)
Using this algorithm, a new keratometric corneal power,named adjusted keratometric corneal power ( Pkadj ), can becalculated using the classical keratometric approach forcorneal power estimation without clinically relevant error[15] .In the current study, an adjusted IOL power ( PIOLadj ) wascalculated, which was defined as the IOL power calculatedfrom the equation 1 using the nkadj value for the estimation ofthe corneal power ( Pkadj), as well as the nha and nhv valuescorresponding to the Gullstrand eye model (1. 336). In suchcalculation, the postoperative spherical equivalent at cornealvertex was considered as the desired refraction (Rdes =SEpost).This adjusted IOL power (PIOLadj) was compared with the realpower of the IOL implanted (PIOLReal). The PIOLadj calculationwas performed after estimating the ELP(effective lens plane)using two different approaches: ELP calculation following theSRK / T formula guidelines ( named PIOLadjSRK / T ) and ELPcalculation using a mathematical expression obtained bymultiple regression analysis ( named ELPadj ), as explainedcarefully in the next section.Furthermore, the PIOL was also calculated using threeconventional formulas ( Haigis, Hoffer Q and Holladay I )considering the ELP defined by each formula and that Rdes =SEpost . A comparative analysis was done between these valuesof PIOL and PIOLadj and PIOLReal . All the formulas wereimplemented in Excel version 14. 0. 0 for Mac ( Microsoft,Irvine, CA, USA).Estimation of Adjusted ELP by Multiple RegressionAnalysis 摇 Considering in each case the equation 1, thevalues of PIOLreal and Pkadj , and that Rdes = SEpost, the real ELP
was obtained. A multiple regression analysis was thenperformed to obtain a mathematical expression predicting thebest as possible the real ELP corresponding to each case. ThisELP was named adjusted effective lens position (ELPadj). Aninitial estimation of ELPadj was obtained considering the wholesample of 65 eyes, but the results were inconsistent leading toclinically relevant errors in the calculation of the PIOL adj . Aswe realized that the calculation of ELPadj was dependent on theIOL power implanted and consequently of the IOL geometry,two groups were differentiated according to this parameter,groups A and B, as previously mentioned. In group A, thiseffective lens position was named ELPadj 逸23, whereas in groupB it was named ELPadj<23 .Statistical Analysis 摇 The statistical analysis was performedusing the SPSS statistics software package version 21. 0 forMac (IBM, Armonk, NY, USA). Normality of data sampleswas evaluated by means of the Kolmogorov - Smirnov test.When parametric analysis was possible, the Student蒺s t- testfor paired data was used for comparing the differentapproaches for PIOL calculation. When parametric analysis wasnot possible, the Wilcoxon rank sum test was applied to assessthe significance of such comparisons. Differences wereconsidered to be statistically significant when the associated P-value was less than 0. 05. Regarding the interchangeabilitybetween pairs of methods used for obtaining PIOL, the Bland-Altman analysis was used[16] .A multiple regression analysis was used for predicting the realELP from different preoperative anatomical and clinicalparameters ( ELPadj ). Model assumptions were evaluated byanalysing residuals, the normality of non - standardizedresiduals ( homoscedasticity ), and the Cook蒺s distance todetect influential points or outliers. In addition, the lack ofcorrelation between errors and multicolinearity was assessedusing the Durbin - Watson test, the calculation of thecolinearity tolerance, and the variance inflation factor.RESULTSGroup A included 12 eyes of 8 patients [11 eyes in males(91. 7% )], with a mean age of 68. 2依9. 4y (range: 56. 0 to80. 0y ) . In this group, mean preoperative keratometry( Pk1. 3375 ), axial length ( AL) and anterior chamber depth(ACD) were 44. 79依1. 44 D ( range: 42. 92 to 47. 34 D),22. 33依0. 55 mm (range: 21. 30 to 23. 09 mm), and 2. 95依0. 33 mm ( range: 2. 41 to 3. 35 mm ), respectively.According to all these data and using the SRK-T formula,mean IOL power implanted ( PIOLReal ) was 23. 75 依 0. 69 D( range: 23. 00 to 25. 00 D). Group B included 53 eyes of 35patients [24 eyes in males (45郾 3% )], with a mean age of72. 2依7郾 1y (range: 57. 0 to 92. 0y) . Mean Pk1. 3375, AL andACD were 44. 37依1. 35 D (range: 41. 09 to 47. 28 D), 23.70依1. 13 mm (range: 22郾 20 to 28. 33 mm), and 3. 32依0. 34mm (range: 2. 48 to 4. 15 mm), respectively. According toall these data and using the SRK-T formula, mean IOL powerimplanted was 19. 72依3. 10 D ( range: 7. 50 to 22. 50 D).All these data are summarized in Table 1.
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Table 1摇 Mean visual, refractive, biometric and IOL power calculation data
ParameterPIOLReal逸23. 0D
Mean依SD RangePIOLReal<23. 0D
Mean依SD RangeSEpre(D) 1. 04依1. 64 -2. 38 to 2. 75 -0. 84依3. 05 -12. 38 to 3. 38SEpost(D) -0. 20依0. 40 -0. 75 to 0. 75 -0. 25依0. 44 -1. 38 to 0. 75r1c(mm) 7. 54依0. 24 7. 13 to 7. 86 7. 61依1. 13 7. 14 to 8. 21ACD (mm) 2. 95依0. 33 2. 41 to 3. 35 3. 32依0. 34 2. 48 to 4. 15AL (mm) 22. 33依0. 55 21. 30 to 23. 09 23. 70依1. 13 22. 20 to 28. 33ELPadjSRK / T(mm) 4. 60依0. 13 4. 37 to 4. 86 5. 17依0. 78 4. 65 to 9. 24ELPadj(mm) 4. 44依0. 31 3. 93 to 5. 01 4. 59依0. 50 3. 90 to 6. 16ELPHaigis(mm) 4. 75依0. 14 4. 54 to 4. 90 5. 04依0. 21 4. 66 to 5. 65ELPHofferQ(mm) 4. 68依0. 08 4. 59 to 4. 88 5. 06依0. 33 4. 74 to 6. 42ELPHolladay(mm) 3. 77依0. 42 3. 08 to 4. 29 4. 24依0. 43 3. 17 to 5. 31nkadj 1. 328依0. 002 1. 326 to 1. 331 1. 328依0. 002 1. 324 to 1. 331Pk 1. 3375(D) 44. 79依1. 44 42. 92 to 47. 34 44. 37依1. 35 41. 09 to 47. 28PcHaigis(D) 43. 99依1. 41 42. 16 to 46. 50 43. 58依1. 33 40. 35 to 46. 43Pkadj(D) 43. 58依1. 61 41. 50 to 46. 44 43. 11依1. 51 39. 45 to 46. 36PIOLReal(D) 23. 75依0. 69 23. 00 to 25. 00 19. 72依3. 10 7. 50 to 22. 50PIOLadjSRK / T(D) 24. 18依0. 99 21. 85 to 25. 87 20. 69依3. 00 9. 81 to 24. 31PIOLadj(D) 23. 82依1. 02 22. 16 to 25. 76 19. 70依3. 13 7. 41 to 23. 08PIOLHaigis(D) 23. 95依1. 16 21. 25 to 26. 14 19. 95依3. 58 6. 35 to 24. 05PIOLHofferQ(D) 22. 68依1. 47 20. 24 to 25. 07 17. 93依4. 15 4. 55 to 22. 47PIOLHolladay(D) 22. 90依1. 00 20. 51 to 24. 61 19. 19依3. 37 5. 58 to 23. 01
SEpre: Preoperative spherical equivalent; SEpost: Postoperative spherical equivalent; r1c: Radius of curvature of the anterior corneal surface;ACD: Anterior chamber depth; AL: Axial length; ELPSRK / T: Effective lens position for the SRK / T formula; ELPadj: Effective lens position forthe adjusted formula; ELPHaigis: Effective lens position for the Haigis formula; ELPHofferQ: Effective lens position for the Hoffer Q formula;ELPHolladay: Effective lens position for the Holladay formula; nkadj: Adjusted keratometric index; Pk1. 3375: Corneal power obtained using IOL-Master or keratometric power; PcHaigis: Corneal power obtained for the Haigis formula; Pkadj: Corneal power obtained using the adjustedkeratometric index; PIOLReal: Power of the intraocular lens implanted which was calculated using the SRK / T formula; PIOladj-SRK / T: Power of theintraocular lens obtained using adjusted formula and ELP calculated with the SRK / T formula; PIOLadj: Intraocular lens power obtained using theadjusted formula and ELPadj; PIOLHaigis: Intraocular lens power obtained using the Haigis formula; PIOLHofferQ: Intraocular lens power obtainedusing the Hoffer Q formula; PIOLHolladay: Intraocular lens power obtained using the Holladay formula.
Agreement of PIOLReal and PIOLadj-SRK / T 摇 In group A, nostatistically significant differences were found betweenPIOLadj-SRK / T and PIOLReal when ELP was calculated with the SRK /T formula guidelines and Rdes = SEpost ( P = 0. 06, pairedStudent蒺s t - test ) . The correlation between PIOLadj-SRK / T andPIOLReal was statistically significant ( r = 0. 680, P < 0. 01 )(Figure 1A). According to the Bland and Altman analysis,mean difference between PIOLadj-SRK / T and PIOLReal was 0. 43 D,with limits of agreement of +1. 84 and - 0. 98 D. Figure 2Ashows the Bland and Altman plot corresponding to thisagreement analysis.In group B, statistically significant differences were foundbetween PIOLadj-SRK / T and PIOLReal when ELP was calculated withthe SRK / T formula guidelines and Rdes = SEpost ( P < 0. 01,Wilcoxon test ) . A very strong and statistically significantcorrelation was found between PIOLadj-SRK / T and PIOLReal ( r =0郾 898, P < 0. 01 ) ( Figure 1B). The Bland and Altmananalysis showed a mean difference between PIOLadj-SRK / T andP IOLReal of 0 . 97 D, with limits of agreement of +2 . 24 and-0. 30 D (Figure 2B).Estimation of ELPadj 摇 The multiple regression analysisrevealed that the ELPadj was significantly correlated with age
and corneal astigmatism (CA) (P<0. 01) in group A:
ELPadj 逸23 =5. 983-0. 015Age-0. 460CA摇 摇 摇 摇 摇 摇 (3)
The homoscedasticity of the model was confirmed by thenormality of the non-standardized residuals distribution (P =0. 20) and the absence of influential points or outliers (meanCook蒺s distance: 0. 146依0. 259). With this model, 58. 33%of non-standardized residuals were 0. 20 or lower. The poorcorrelation between residuals (Durbin-Watson test: 2. 320)and the lack of multicolinearity ( tolerance 0. 971 to 0. 971;variance inflation factors 1. 029 to 1. 029 ) was alsoconfirmed.No statistically significant differences were found between ELPcalculated with the SRK / T formula guidelines and theELPadj 逸23(P=0. 07, Student蒺s t-test) .In group B, the ELPadj <23 was found to be significantlycorrelated with age, ACD, AL and r1c(P<0. 01):
ELPadj<23 =5. 327+0. 015Age+0. 346ACD+0. 334AL-1. 430r1c摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 摇 (4)
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Figure 1 摇 Scattergram showing the relation between theadjusted IOL power using the ELP estimated using the SRK-Tformula guidelines (PIOLadj-SRK/ T) and the real power of the IOLimplanted (PIOLReal)摇 A: Results in group A; B: Results in group B.
Figure 2摇 Bland-Altman plots for the comparison between theadjusted IOL power using the ELP estimated using the SRK-Tformula guidelines (PIOLadj-SRK/ T) and the real power of the IOLimplanted ( PIOLReal ) 摇 The dotted lines show the limits ofagreement ( 依 1. 96SD). A: Results in group A; B: Results ingroup B.
The homoscedasticity of the model was also confirmed by thenormality of the non-standardized residuals distribution (P =0. 20) and the absence of influential points or outliers (meanCook蒺s distance: 0. 04依0. 13). With this model, 84. 91% ofnon-standardized residuals were 0. 50. The poor correlationbetween residuals (Durbin-Watson test: 2. 208) and the lack
Figure 3 摇 Scattergram showing the relation between theadjusted IOL power using the regression analysis adjusted ELP(PIOLadj) and the real power of the IOL implanted (PIOLReal) 摇A: Results in group A; B: Results in group B.
of multicolinearity ( tolerance 0. 733 to 0. 926; varianceinflation factors 1. 080 to 1. 364) was also confirmed.A statistically significant difference was found between ELPcalculated with the SRK / T formula guidelines and theELPadj <23(P<0. 01, Wilcoxon test), with a lower value withour adjustment (Table 1) .Agreement between PIOLReal and PIOLadj 摇 No statisticallysignificant differences were found in any group between PIOLadj
and PIOLReal when ELPadj and Rdes = SEpost were considered forPIOLadj calculation (Group A: P=0. 64, unpaired Student蒺s t-test; Group B: P = 0. 82, Wilcoxon test ) . A strong andstatistically significant correlation was found between PIOLadj
and PIOLReal in both groups ( Group A: r = 0. 88, P <0. 01;Group B: r= 0. 91, P<0. 01) (Figure 3) . In group A, theBland and Altman analysis showed a mean difference betweenPIOLadj and PIOLReal of 0. 08 D, with limits of agreement of +1郾 11 and - 0. 96 D ( Figure 4A). In group B, the meandifference between PIOLadj and PIOLReal was -0. 02 D, with limitsof agreement of +1. 14 and -1. 18 D (Figure 4B).Agreement of PIOLadj and PIOL with Other Formulas 摇 TheELP values corresponding to different available IOL powerformulas were calculated and afterwards an estimation of PIOL
was performed with each of these formulas ( Table 1 ) . Ingroup A, statistically significant differences were found in allcomparisons (P<0. 01, paired Student蒺s t-test) except for the
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摇 摇 Table 2摇 Bland & Altman analysis outcomes of the comparison between PIOLadj and the IOL power obtained with other摇 摇 commonly used formulas
FormulasGroup A
DPIOL依SD (D) LoA (D) PGroup B
DPIOL依SD (D) LoA (D) PHaigis 0. 13依0. 69 1. 47 to -1. 22 =0. 53 0. 25依0. 50 1. 24 to -0. 73 <0. 01Hoffer Q -1. 14依1. 15 1. 11 to -3. 40 <0. 01 -1. 76依1. 84 1. 84 to -5. 36 <0. 01Holladay 1 -0. 93依0. 61 0. 26 to -2. 12 <0. 01 -0. 50依0. 36 0. 20 to -1. 20 <0. 01
摇 摇 DPIOL: Difference in intraocular lens power; LoA: Limits of agreement; SD: Standard deviation.
Figure 4摇 Bland-Altman plots for the comparison between theadjusted IOL power using the regression analysis adjusted ELP(PIOLadj) and the real power of the IOL implanted (PIOLReal) 摇The dotted lines show the limits of agreement ( 依 1. 96SD); A:Results in group A; B: Results in group B.
comparison of PIOLadj and PIOLHaigi s(P=0. 53 paired Student蒺s t-test) . A strong and statistically significant correlation wasfound between PIOLHaigis and PIOLadj( r = 0. 81, P<0. 01), andbetween PIOLHolladay and PIOLadj( r = 0. 82, P <0. 01). Also, astatistically significant correlation but of moderate strength wasfound between PIOLHofferQ and PIOLadj( r = 0. 63, P = 0. 03). Ingroup B, statistically significant differences were foundbetween PIOLadj and all formulas analysed (P<0. 01, Wilcoxontest) . A strong and statistically significant correlation wasfound between PIOLHaigis and PIOLadj ( r = 0. 99, P < 0. 01 ),between PIOLHofferQ and PIOLadj( r=0. 66, P<0. 01) and betweenPIOLHolladay and PIOLadj( r=0. 98, P<0. 01). Table 2 summarizesthe outcomes of the Bland and Altman analysis whencomparing PIOLadj with the rest of formulas.DISCUSSIONThe selection of the IOL power to implant in cataract surgeryis a critical step for obtaining an optimized outcome[17-18] .This power is determined by using mathematical formulasbased most of them on paraxial optics[17-18] . In theseformulas, some ocular parameters are required as well as theintended target refraction[17-18] . The AL and corneal power arealways necessary for IOL power calculation and the accuracyof the measurement of these parameters is considered as thefirst potential source of inaccuracy in the determination of theIOL power to implant. Another source of potential bias is theestimation of the IOL position that is required for the opticalcalculations. Specifically, the “ effective lens position 冶
(ELP) is estimated which is defined as the effective distancefrom the anterior surface of the cornea to the lens plane as ifthe lens was of infinite thinness[19] . This parameter is formula-dependent and do not need to reflect the true postoperativeACD in the anatomical sense[19] . Indeed, each formula forIOL power calculation has its own algorithm to estimate theELP that is based on different anatomical parameters, such ascorneal power, preoperative ACD[19] or the horizontal cornealdiameter or white - to - white distance (WTW) [20] . In thecurrent study, a preliminary algorithm based on paraxialoptics was developed to calculate the power to implant of aspecific model of aspheric IOL. This algorithm was optimizedby minimizing the error associated to the keratometricestimation of the corneal power as well as by obtaining aconsistent predictive formula for the estimation of the ELP. Aspreviously commented, the visual outcomes obtained withaspheric IOLs are especially worsened when refractive residualerrors are present due to inaccurate IOL powercalculations[10] .In our series, the refractive outcomes obtained with theaspheric IOL evaluated were less predictable for those eyesimplanted with IOLs of powers of less than 23 D. Specifically,the postoperative SE ranged from -0. 75 to +0. 75 D in eyesimplanted with PIOL逸23 D and from -1. 38 to +0. 75 D ineyes implanted with PIOL<23 D. Therefore, there was a slighttrend to residual myopia in those eyes implanted with lowerIOL power values and consequently longer AL. This isconsistent with the results of previous studies reporting myopicresidual refractive errors in myopic eyes implanted withaspheric IOLs, especially in those with extreme preoperativemyopia[21] . The results of the study of Eldaly and Mansour[22]
suggested that AL -adjusted A-constants might be used forIOL power calculations. Indeed, these authors found differenttrends for a personal A-constant with different aspheric IOLseven for the same range of axial length[22] . In our series, inspite of the acceptable predictability achieved with the specificmodel of aspheric IOL evaluated, an attempt of optimizationhas been done by using an optimized model for corneal powercalculation and an equation to estimate ELP based on aretrospective regression analysis of the postoperative outcomesobtained. As the behaviour of this regression model was verydependent on the IOL power, two groups were differentiated,as previously mentioned.A limitation of the predictability of the refractive correctionwith the evaluated aspheric IOL may be attributable to the bias
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associated to the use of the keratometric approach for thecalculation of the corneal power, errors in the determination ofthe axial length or inaccuracy in the estimation of the ELP forthis specific IOL. However, the errors in the estimation of ALwith optical biometry have been shown to be minimal and witha very limited impact on the refractive predictability[23] . Forthis reason, the current study was aimed at analysing thepotential contribution of the corneal power and ELP factors tothe limitation of the refractive predictability with the asphericIOL evaluated. The potential impact of the keratometric errorwas first evaluated by calculating the corneal power using anadjusted keratometric index aimed at minimizing the clinicalerror in the estimation of the corneal power[13-15] . Thisadjusted corneal power was used to obtain an estimation of theIOL power considering the AL, Rdes = SEpost and an ELPestimated with the algorithm established for the SRK - Tformula (PIOLadj-SRK / T)
[24] . Thus, the ability of this approachto reproduce the real clinical outcome was evaluated. In thetwo groups of our study, eyes implanted with PIOL逸23 D andeyes implanted with PIOL<23 D, clinically relevant differenceswere found between PIOLadjSRK / T and PIOLReal which demonstratedthat the correction of this factor had a minimal effect on theoutcomes achievable with the aspheric IOL evaluated.Likewise, statistically significant differences were foundbetween PIOLadjSRK / T and PIOLReal in those eyes implanted withlower IOL powers. The reason for not finding statisticallysignificant differences in group A may be the smaller numberof patients included in this group.According to these first outcomes, the estimation of ELPseemed to be the most critical factor accounting for thepresence of a relatively limited predictability with the asphericIOL, especially in eyes with shorter AL. In order to confirmthis, an analysis was performed to obtain an expression forestimating an optimized ELP ( ELPadj ). As a result, twodifferent expressions were obtained by means of multiple linearregression analysis according to the power of the IOLimplanted, one expression for PIOL < 23 D ( ELPadj<23 ) andanother for PIOL 逸 23 D ( ELPadj 逸23 ). This confirms therelevance of the geometric factor of the IOL in the estimationof ELP. The adjusted ELP was used to recalculate the IOLpower considering that Rdes = SEpost( PIOLadj ) with the aim ofchecking if this new estimation was able to reproduce the realclinical outcome. An initial expression for ELPadj consideringthe whole sample of 65 eyes was obtained, but the ELPadj
values obtained led to inconsistent values of PIOL adj . However,when the two differentiated groups of eyes were considered,and two different expressions for ELPadj were obtained(ELPadj<23D and ELPadj 逸23D ), no statistically significant andclinically acceptable differences between PIOLadjand PIOLReal werefound. Indeed, mean differences between simulated andclinical outcomes were practically zero in groups A and B,with limits of agreement around 1 D, which is themanufacturer tolerance for extreme IOL powers ( IOLs withpowers from 0 to 10 D and from 30 to 35 D).
In our linear regression analyses, ELPadj was found to berelated to different factors in groups A and B. Age is the onlyfactor shared by both models. This may be in relation with theage - dependence of the capsular behaviour after cataractsurgery. A retrospective cohort study conducted on 801patients in a Spanish hospital revealed that age could beassociated with capsular bag distension syndrome[25] . Vass etal[26] confirmed that the capsular bag diameter was correlatedwith age, among other factors such as AL, corneal power orlens thickness. In group B that included eyes with longer AL,the anatomical factors were crucial determinants of the ELP ofthe IOL evaluated. Specifically, ELPadj was higher in thoseeyes with longer AL and ACD, which is consistent with thelinear dependence of the final position of the IOL on the ALreported by previous authors[27] . Besides the AL and ACDanatomical factors in group B, a corneal factor was included inthe ELP models obtained in groups A and B in terms ofcorneal astigmatism magnitude and radius of curvature of thefirst corneal surface, respectively. This may be expected assome level of anatomical correlation between the cornealgeometry and intraocular dimensions has been described in thehuman eye[28] .Finally, commonly used IOL power formulas were comparedwith our PIOLadj . In both groups, according to the Bland andAltman analysis, clinically relevant differences were foundbetween PIOLadj and the IOL power values obtained with theHaigis, Hoffer Q, and Holladay I formulas. Likewise, thesedifferences were also statistically significant. Only thedifference between PIOLadj and the IOL power calculated withthe Haigis formula in group A did not reach statisticalsignificance possibly due to the limitation in the sample size ofthis group. These differences between formulas seem to be inrelation with the different estimations of ELP provided by eachof them, with the most accurate outcome for ELPadj . PIOLadj wasable to reproduce more accurately the real value of the powerof the IOL implanted and therefore the refractive outcome.This suggests that our approach may be a useful method forIOL power calculation with the aspheric IOL evaluated. Thisshould be corroborated in future prospective studies.There are several limitations in the currentstudy, such as thelimited sample size, the use in some cases of both eyes of thesame subject or the short follow-up. It should be consideredthat, although rare, changes in IOL position has beendescribed more than 3mo after surgery, especially after Nd:YAG capsulotomy[29] . Another potential limitation is that theHolladay II formula was not used in our comparison as it wasnot available in our clinic. Possibly, our approach may bemore similar to the results of the Holladay II formula as bothtypes of calculation use an optimized algorithm for theestimation of ELP, but this should be confirmed in futurestudies. This study was planned as a preliminary experience toevaluate the possibility of optimizing further the widely usedapproaches for IOL power calculation based on paraxialoptics. For this reason, a retrospective study with a limitedsample size was conducted. According to the positive findings
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obtained, a prospective study with a large sample size is beingconducted currently, including eyes implanted with differenttypes of IOL. Finally, it should be mentioned that only onesurgeon performed all the surgeries and therefore the algorithmdeveloped could be somewhat imprecise for some surgeons. Infuture studies, this algorithm will be validated for differentsurgeons and the clinical relevance of differences will beevaluated. Furthermore, an analysis similar to that performedin the current study could be used to define a personalizedalgorithm for IOL power calculation for each specific surgeon.In conclusion, the refractive outcomes after cataract surgerywith implantation of aspheric IOLs can be optimized byminimizing the keratometric error using a variable keratometricindex for corneal power estimation and by estimating ELPusing a mathematical expression dependent on the geometricfactor of the IOL, age and anatomical factors. Therefore,optimizations of paraxial models for IOL power calculationscan be performed to improve the clinical outcomes obtainedwith currently available IOL models without the need for raytracing simulations. Jin et al[30] confirmed in a simulationstudy that theoretical thin-lens formulas were as accurate asthe ray-tracing method in IOL power calculations in normaleyes and even in eyes after refractive surgery. Futureprospective studies should be performed to validate this modelof IOL power calculation for the evaluated aspheric IOL andother models with larger sample of sizes including moreextreme cases ( long and short AL).REFERENCES1 Ali佼 JL, Schimchak P, Negri HP, Mont佴s-Mic佼 R. Crystalline lensoptical dysfunction through aging. Ophthalmology 2005;112(11):2022-20292 Philip K, Martinez A, Ho A, Conrad F, Ale J, Mitchell P,Sankaridurg P. Total ocular, anterior corneal and lenticular higher orderaberrations in hyperopic, myopic and emmetropic eyes. Vision Res 2012;52(1):31-373 Lyall DA, Srinivasan S, Gray LS. Changes in ocular monochromatichigher-order aberrations in the aging eye. Optom Vis Sci 2013;90(9):996-10034 Fujikado T, Kuroda T, Ninomiya S, Maeda N, Tano Y, Oshika T,Hirohara Y, Mihashi T. Age - related changes in ocular and cornealaberrations. Am J Ophthalmol 2004;138(1):143-1465 Amano S, Amano Y, Yamagami S, Miyai T, Miyata K, Samejima T,Oshika T. Age - related changes in corneal and ocular higher - orderwavefront aberrations. Am J Ophthalmol 2004;137(6):988-9926 Glasser A, Campbell MC. Presbyopia and the optical changes in thehuman crystalline lens with age. Vision Res 1998;38(2):209-2297 Schuster AK, Tesarz J, Vossmerbaeumer U. The impact on vision ofaspheric to spherical monofocal intraocular lenses in cataract surgery: asystematic review with meta - analysis. Ophthalmology 2013;120 (11):2166-21758 Langenbucher A, Janunts E, Seitz B, Kannengie茁er M, Eppig T.Theoretical image performance with customized aspheric and sphericalIOLs - when do we get a benefit from customized aspheric design? Z MedPhys 2014;24(2):94-1039 Guo H, Goncharov A, Dainty C. Intraocular lens implantation positionsensitivity as a function of refractive error. Ophthalmic Physiol Opt 2012;32(2):117-124
10 Dick HB. Recent developments in aspheric intraocular lenses. CurrOpin Ophthalmol 2009;20(1):25-3211 Hoffmann PC, Lindemann CR. Intraocular lens calculation foraspheric intraocular lenses. J Cataract Refract Surg 2013;39(6):867-87212 Olsen T. Calculation of intraocular lens power: a review. ActaOphthalmol Scand 2007;85(5):472-48513 Camps VJ, Pi觡ero DP, de Fez D, Mateo V. Minimizing the IOLpower error induced by keratometric power. Optom Vis Sci 2013;90(7):639-64914 Camps VJ, Pinero-Llorens DP, de Fez D, Coloma P, Caballero MT,Garcia C, Miret JJ. Algorithm for correcting the keratometric estimationerror in normal eyes. Optom Vis Sci 2012;89(2): 221-22815 Camps VJ, Pi觡ero DP, Mateo V, Ribera D, de Fez D, Blanes -Momp佼 FJ, Alzamora - Rodr侏guez A. Algorithm for correcting thekeratometric error in the estimation of the corneal power in eyes withprevious myopic laser refractive surgery. Cornea 2013; 32(11):1454-145916 Bland JM, Altman DG. Statistical methods for assessing agreementbetween two methods of clinical measurement. Lancet 1986;1 (8476):307-31017 Hoffer KJ. IOL power. Thorofare, NJ, USA: Slack Incorporated, 201118 Shammas HJ. Intraocular lens power calculations. Thorofare, NJ,USA: Slack Incorporated, 200419 Olsen T. Prediction of the effective postoperative ( intraocular lens)anterior chamber depth. J Cataract Refract Surg 2006;32(3):419-42420 Fenzl RE, Gills JP, Cherchio M. Refractive and visual outcome ofhyperopic cataract cases operated on before and after implementation ofthe Holladay II formula. Ophthalmology 1998;105(9):1759-176421 Fang Y, Lu Y, Miao A, Luo Y. Aspheric intraocular lensesimplantation for cataract patients with extreme myopia. ISRN Ophthalmol2014;2014:40343222 Eldaly MA, Mansour KA. Personal A-constant in relation to axiallength with various intraocular lenses. Indian J Ophthalmol 2014;62(7):788-79123 Faria-Ribeiro M, Lopes-Ferreira D, L仵pez-Gil N, Jorge J, Gonz仳lez-M伢ijome JM. Errors associated with IOLMaster biometry as a function ofinternal ocular dimensions. J Optom 2014;7(2):75-7824 Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK / Tintraocular lens implant power calculation formula. J Cataract RefractSurg 1990;16(3):333-34025 Gonz仳lez - Mart侏n - Moro J, Gonz仳lez - L仵pez JJ, G仵mez - Sanz F,Zarallo -Gallardo J, Cobo - Soriano R. Posterior capsule opacification,capsular bag distension syndrome, and anterior capsular phimosis: Aretrospective cohort study. Arch Soc Esp Oftalmol 2015;90(2):69-7526 Vass C, Menapace R, Schmetterer K, Findl O, Rainer G, SteineckI. Prediction of pseudophakic capsular bag diameter based on biometricvariables. J Cataract Refract Surg 1999;25(10):1376-138127 Engren AL, Behndig A. Anterior chamber depth, intraocular lensposition, and refractive outcomes after cataract surgery. J CataractRefract Surg 2013;39(4):572-57728 Park SH, Park KH, Kim JM, Choi CY. Relation between axial lengthand ocular parameters. Ophthalmologica 2010;224(3):188-19329 Ale JB. Intraocular lens tilt and decentration: a concern forcontemporary IOL designs. Nepal J Ophthalmol 2011;3(1):68-7730 Jin H, Rabsilber T, Ehmer A, Borkenstein AF, Limberger IJ, GuoH, Auffarth GU. Comparison of ray - tracing method and thin - lensformula in intraocular lens power calculations. J Cataract Refract Surg2009;35(4):650-662
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