Prediction of ocular magnification and aniseikonia after cataract surgery

Abstract

Background: Ocular magnification and aniseikonia after cataract surgery has been widely ignored in modern cataract surgery. The purpose of this study was to analyse ocular magnification and inter-individual differences in a normal cataract population with a focus on monovision. Methods: From a large dataset containing biometric measurements (IOLMaster 700)ofbotheyesof9734patientspriortocataractsurgery,eyeswereindexedrandomly as primary (P) and secondary (S). Intraocular lens power (IOLP) was derived for the HofferQ, Haigis and Castrop formulae for emmetropia for P and emmetropia or myopia (−0.5 to −2 dpt) for S to simulate monovision. Based on the pseudophakic eye model in addition to these formulae, ocular magnification was extracted using matrix algebra(refractionandtranslationmatrices anda system matrix describingtheoptical property of the entire spectacle corrected or uncorrected eye). Results: With emmetropia for P and S the IOLP differences (S-P) showed a standard deviation of 0.162/0.156/0.157 dpt and ocular magnification differences yielded a standard deviation of 0.0414/0.0405/0.0408 mm/mrad for the HofferQ/ Haigis/Castrop setting. Simulating monovision, the myopic eye (S) showed a systematically smaller mean absolute spectacle corrected ocular magnification than the emmetropic eye (−0.0351/−0.0340/−0.0336, respectively, relative magnification around 2%). If myopia in the S eye remains uncorrected, the reduction of ocular magnification is much smaller (around 0.2-0.3%). Conclusion: Vergence formulae for IOLP calculation sometimes implicitly define a pseudophakic eye model which can be directly used to predict ocular magnification after cataract surgery. Despite a strong similarity of both eyes, ocular magnification does not fully match between eyes and the prediction of ocular magnification and aniseikonia might be relevant to avoid eikonic problems in the pseudophakic eye.

Monte‐Carlo simulation of a thick lens IOL power calculation

“…The target refraction at the spectacle plane was assumed to be uniformly distributed between plano and minus ¼ dpt. With the refractive indices of the cornea, aqueous humour and vitreous derived from a schematic model eye (Liou & Brennan, 1997), we calculated the respective IOL lens power PL and the ocular magnification OM thin of the spectacle‐corrected eye as the ratio of retinal image size to incident ray angle in radians (Harris, 2000; Langenbucher, Szentmáry, et al, 2022b). Then we replaced this thin lens model IOL by a thick lens model IOL defined by the same power (equivalent power PL), a refractive index nL, and either a preset IOL thickness LT (situation 1) or a preset optic edge thickness ET (situation 2).…”

“…The Coddington factor CL for the thick lens IOL model was assumed to be randomly distributed in an interval from CL = −1 (plano‐convex) to CL = 1 (convex‐plano). The refractive power of a thin lens IOL (PL) located at an axial position EP behind the corneal front apex was derived to correct the eye for the intended spectacle correction SEQ thin = TR. From the product of all vergences before all refractive surfaces and the product of all vergences behind all refractive surfaces the ocular magnification for the spectacle‐corrected pseudophakic eye (Langenbucher, Szentmáry, et al, 2022b) with the thin lens IOL (OM thin ) was predicted. From the equivalent power of the thin lens IOL derived in the previous step (PL), the Coddington factor CL, and the refractive index nL (preset to nL = 1.52 without loss of generality), the shape of the thick lens IOL was calculated and the haptic plane EP (EP‐ACD behind the IOL front apex) and the image‐side principal plane (HL, HL‐ACD behind the IOL front apex) was derived. Two different situations were considered: situation 1 refers to a predefined lens thickness LT (with variation of edge thickness ET), and situation 2 to a predefined optic edge thickness ET (calculated from both the curvatures of the IOL and the optical diameter LD, with variation of lens thickness LT). The volume of the lens optic part (LVOL) was considered as the sum of the volumes of the anterior part of the lens (positive value for CL > −1 and 0 for a convex‐plano lens with CL = −1), of the posterior part of the lens (positive value for CL < 1 and 0 for a convex‐plano lens with CL = 1) and the cylindric part with thickness ET and diameter LD. The thick lens model IOL (with an equivalent power PL derived from the thin lens model in the previous step) was placed with its haptic plane EP at the equatorial plane of the crystalline lens, and the spherical equivalent refraction at the spectacle plane (SEQ thick ) was extracted.…”

“…Two different situations were considered: situation 1 refers to a predefined lens thickness LT (with variation of edge thickness ET), and situation 2 to a predefined optic edge thickness ET (calculated from both the curvatures of the IOL and the optical diameter LD, with variation of lens thickness LT). The volume of the lens optic part (LVOL) was considered as the sum of the volumes of the anterior part of the lens (positive value for CL > −1 and 0 for a convex‐plano lens with CL = −1), of the posterior part of the lens (positive value for CL < 1 and 0 for a convex‐plano lens with CL = 1) and the cylindric part with thickness ET and diameter LD. The thick lens model IOL (with an equivalent power PL derived from the thin lens model in the previous step) was placed with its haptic plane EP at the equatorial plane of the crystalline lens, and the spherical equivalent refraction at the spectacle plane (SEQ thick ) was extracted. In addition, from the product of all vergences before all refractive surfaces and the product of all vergences behind all refractive surfaces the ocular magnification for the spectacle‐corrected pseudophakic eye (Langenbucher, Szentmáry, et al, 2022b) with the thick lens IOL (OM thick ) was predicted.…”

“…• The refractive power of a thin lens IOL (PL) located at an axial position EP behind the corneal front apex was derived to correct the eye for the intended spectacle correction SEQ thin = TR. From the product of all vergences before all refractive surfaces and the product of all vergences behind all refractive surfaces the ocular magnification for the spectacle-corrected pseudophakic eye (Langenbucher, Szentmáry, et al, 2022b) with the thin lens IOL (OM thin ) was predicted. (with variation of edge thickness ET), and situation 2 to a predefined optic edge thickness ET (calculated from both the curvatures of the IOL and the optical diameter LD, with variation of lens thickness LT).…”

Considerations on the Calculation of Multifocal Duet Implantation in a Monovision Scenario for the Correction of Presbyopia – A Case Example

“…Thus, especially for (toric) IOLs with higher refractive power, the prediction of postoperative pseudophakic ACD may make sense 26 . Theoretically, a paraxial vergence calculation can additionally address total and meridional ocular image magnification in addition to just calculating the required lens power to incorporate aniseikonia into the selection of the appropriate IOL combination 27 , 28 . In our case, the cornea was calculated as a thick lens.…”