Difficult lens power calculations

Theoretical Accuracy of the Raytracing Method for Intraocular Calculation of Lens Power in Myopic Eyes after Small Incision Extraction of the Lenticule

AIM

To evaluate the accuracy of the raytracing method for the calculation of intraocular lens (IOL) power in myopic eyes after small incision extraction of the lenticule (SMILE).

METHODS

Retrospective study. All patients undergoing surgery for myopic SMILE between May 1, 2020, and December 31, 2020, with Scheimpflug tomography optical biometry were eligible for inclusion. Manifest refraction was performed before and 6 months after refractive surgery. One eye from each patient was included in the final analysis. A theoretical model was invited to predict the accuracy of multiple methods of lens power calculation by comparing the IOL-induced refractive error at the corneal plane (IOL-Dif) and the SMILE-induced change of spherical equivalent (SMILE-Dif) before and after SMILE surgery. The prediction error (PE) was calculated as the difference between SMILE-Dif-IOL-Dif. IOL power calculations were performed using raytracing (Olsen Raytracing, Pentacam AXL, software version 1.22r05, Wetzlar, Germany) and other formulae with historical data (Barrett True-K, Double-K SRK/T, Masket, Modified Masket) and without historical data (Barrett True-K no history, Haigis-L, Hill Potvin Shammas PM, Shammas-PL) for the same IOL power and model. In addition, subgroup analysis was performed in different anterior chamber depths, axial lengths, back-to-front corneal radius ratio, keratometry, lens thickness, and preoperative spherical equivalents.

RESULTS

A total of 70 eyes of 70 patients were analyzed. The raytracing method had the smallest mean absolute PE (0.26 ± 0.24 D) and median absolute PE (0.16 D), and also had the largest percentage of eyes within a PE of ± 0.25 D (64.3%), ± 0.50 D (81.4%), ± 0.75 D (95.7%), and ± 1.00 D (100.0%). The raytracing method was significantly better than Double-K SRK/T, Haigis, Haigis-L, and Shammas-PL formulae in postoperative refraction prediction (all p < 0.001), but not better than the following formulae: Barrett True-K (p = 0.314), Barrett True-K no history (p = 0.163), Masket (p = 1.0), Modified Masket (p = 0.806), and Hill Potvin Shammas PM (p = 0.286). Subgroup analysis showed that refractive outcomes exhibited no statistically significant differences in the raytracing method (all p < 0.05).

CONCLUSION

Raytracing was the most accurate method in predicting target refraction and had a good consistency in calculating IOL power for myopic eyes after SMILE.

Influence of miosis and laser peripheral iridotomy on intraocular lens power calculation in patients with primary angle closure disease

OBJECTIVES

To evaluate the effect of miosis and laser peripheral iridotomy (LPI) on intraocular lens (IOL) power prediction and ocular biometry in eyes with primary angle closure disease (PACD).

METHODS

In this prospective observational study, primary angle closure suspects (PACS), and subjects classified with primary angle closure (PAC)/primary angle-closure glaucoma (PACG) undergoing LPI were enrolled. Ocular biometric parameters were measured with IOLMaster700 at baseline (T0), one week after pilocarpine instillation (T1), and another week post LPI (T2). Biometric changes and the IOL power predicted for emmetropia using Barrett Universal II, Haigis, Holladay2, Hoffer Q and SRK/T formulae were analysed and compared among different time points.

RESULTS

100 eyes of 50 PACS and 50 PAC/PACG patients were enrolled. Following pilocarpine-induced miosis, lens thickness (LT) increased and anterior chamber depth (ACD) decreased (all groups p < 0.01), while white-to-white diameter decreased and central corneal thickness increased significantly only in the PACS cohort (both p < 0.01). Compared to baseline, LPI induced an increase of ACD and a slight decrease of LT in PACS (both p < 0.01), whereas only axial length changed significantly (p = 0.012) in the PAC/PACG cohort. Regardless of the formula used, no significant difference to the predicted IOL power for emmetropia existed among the three time points in each group (all p > 0.1).

CONCLUSION

We report the changes of anterior segment parameters induced by miosis and LPI in PACD. These interventions do not significantly affect the IOL power calculation predicted for emmetropia in Chinese eyes when common third-, fourth-and new generation IOL formulae are used.

Efficacy of keratometric values obtained from Sirius topographer® in nidek axial length-scan® for intraocular lens calculation after penetrating keratoplasty

BACKGROUND

To evaluate the accuracy of keratometric values obtained from Scheimpflug (Sirius) topography using Nidek AL-Scan optical biometry (OB) for intraocular lens (IOL) power calculating after penetrating keratoplasty (PK).

METHODS

Thirty eyes of 26 patients were included in this study. The demographic information, complete ophthalmic examination, IOL calculation technique, and its effect on final refractive results were evaluated.

RESULTS

The mean age of the patients was 52.76 ± 16.20 years. The mean K readings using Nidek AL-Scan OB, mean simulated K (SimK) (3mm), and mean pupillary power (MPP) (4.5mm) K readings using Sirius were 41.92 ± 5.05 D, 42.99 ± 5.78 D, and 43.30±6.23 D (p= 0.515).

CONCLUSIONS

Both devices correctly calculated IOL power after PK; however, Sirius SimK (3mm) gave the lowest mean absolute error (MAE) results and can be safely used for IOL power calculation.

A systemic review and network meta-analysis of accuracy of intraocular lens power calculation formulas in primary angle-closure conditions

BACKGROUND

For primary angle-closure and angle-closure glaucoma, the fact that refractive error sometimes deviates from predictions after intraocular lens (IOL) implantation is familiar to cataract surgeons. Since controversy remains in the accuracy of IOL power calculation formulas, both traditional and network meta-analysis on formula accuracy were conducted in patients with primary angle-closure conditions.

METHODS

A comprehensive literature search was conducted through Aug 2022, focusing on studies on intraocular lens power calculation in primary angle-closure (PAC) and primary angle-closure glaucoma (PACG). A systemic review and network meta-analysis was performed. Quality of studies were assessed. Primary outcomes were the mean absolute errors (MAE) and the percentages of eyes with a prediction error within ±0.50 diopiters (D) or ±1.00 D (% ±0.50/1.00 D) by different formulas.

RESULTS

Six retrospective studies involving 419 eyes and 8 formulas (Barrett Universal II, Kane, SRK/T, Hoffer Q, Haigis, Holladay I, RBF 3.0 and LSF) were included. SRK/T was used as a reference as it had been investigated in all the studies included. Direct comparison showed that none of the involved formula outperformed or was defeated by SRK/T significantly in terms of either MAE or % ±0.50/1.00 D (all P>0.05). Network comparison and ranking possibilities disclosed BUII, Kane, RBF 3.0 with statistically insignificant advantage. No significant publication bias was detected by network funnel plot.

CONCLUSIONS

No absolute advantage was disclosed among the formulas involved in this study for PAC/PACG eyes. Further carefully designed studies are warranted to evaluate IOL calculation formulae in this target population.

TRAIL REGISTRATION

Registration: PROSEPRO ID: CRD42022326541.

Ratio of torus and equivalent power to refractive cylinder and spherical equivalent in phakic lenses - a Monte-Carlo simulation study

BACKGROUND

Spherical and astigmatic powers for phakic intraocular lenses are frequently calculated using fixed ratios of phakic lens refractive power to refractive spherical equivalent, and of phakic lens astigmatism to refractive cylinder. In this study, a Monte-Carlo simulation based on biometric data was used to investigate how variations in biometrics affect these ratios, in order to improve the calculation of implantable lens parameters.

METHODS

A data set of over sixteen thousand biometric measurements including axial length, phakic anterior chamber depth, and corneal equivalent and astigmatic power was used to construct a multidimensional probability density distribution. From this, we determined the axial position of the implanted lens and estimated the refractive spherical equivalent and refractive cylinder. A generic data model resampled the density distributions and interactions between variables, and the implantable lens power was determined using vergence propagation.

RESULTS

50 000 artificial data sets were used to calculate the phakic lens spherical equivalent and astigmatism required for emmetropization, and to determine the corresponding ratios for these two values. The spherical ratio ranged from 1.0640 to 1.3723 and the astigmatic ratio from 1.0501 to 1.4340. Both ratios are unaffected by the corneal spherical / astigmatic powers, or the refractive cylinder, but show strong correlation with the refractive spherical equivalent, mild correlation with the lens axial position, and moderate negative correlation with axial length. As a simplification, these ratios could be modelled using a bi-variable linear regression based on the first two of these factors.

CONCLUSION

Fixed spherical and astigmatic ratios should not be used when selecting high refractive power phakic IOLs as their variation can result in refractive errors of up to ±0.3 D for a 8 D lens. Both ratios can be estimated with clinically acceptable precision using a linear regression based on the refractive spherical equivalent and the axial position.

Back-calculation of keratometer index based on OCT data and raytracing - a Monte Carlo simulation

PURPOSE

This study aims to develop a raytracing-based strategy for calculating corneal power from anterior segment optical coherence tomography data and extracting the individual keratometer index, which converts the corneal front surface radius to corneal power.

METHODS

A large OCT dataset (10,218 eyes of 8,430 patients) from the Casia 2 (Tomey, Japan) was post-processed in MATLAB (MathWorks, USA). Radius of curvature, asphericity of the corneal front and back surface, central corneal thickness and pupil size (aperture) were used to trace a bundle of rays through the cornea and derive the best focus plane. Corneal power was calculated with respect to the corneal front vertex plane, and the keratometer index was back-calculated using corneal power and front surface radius. Keratometer index was analysed in a multivariate linear model.

RESULTS

The averaged resulting keratometer index was 1.3317 ± 0.0017 with a median of 1.3317 and range from 1.3233 to 1.3390. In a univariate model, only the front surface asphericity affected the keratometer index. The multivariate model for modelling the keratometer index using all 6 input parameters performed very well (RMS error: 5.54e-4, R² : 0.90, significance vs. constant model: <0.0001).

CONCLUSIONS

In the classical calculation, the keratometer index used for converting corneal radius to dioptric power uses several model assumptions. As these assumptions are not generally satisfied, corneal power cannot be calculated from corneal front surface radius alone. Considering all 6 input variables, the linear prediction model performs well and can be used if all input parameters are measured with a tomographer.

Predictability of intraocular lens power calculation after small-incision lenticule extraction for myopia

PURPOSE

To evaluate and compare the predictability of intraocular lens (IOL) power calculation after small-incision lenticule extraction (SMILE) for myopia and myopic astigmatism.

SETTING

Department of Ophthalmology, Philipps University of Marburg, Marburg, Germany.

DESIGN

Retrospective comparative case series.

METHODS

Preoperative evaluation included optical biometry using IOLMaster 500 and corneal tomography using Pentacam HR. The corneal tomography measurements were repeated at 3 months postoperatively. The change of spherical equivalent due to SMILE was calculated by the manifest refraction at corneal plane (SMILE-Dif). A theoretical model, involving the virtual implantation of the same IOL before and after SMILE, was used, and the IOL power calculations were performed using ray tracing (OKULIX, version 9.06) and third- (Hoffer Q, Holladay 1, and SRK/T) and fourth-generation (Haigis-L and Haigis) formulas. The difference between the IOL-induced refractive error at corneal plane before and after SMILE (IOL-Dif) was compared with SMILE-Dif. The prediction error (PE) was calculated as the difference between SMILE-Dif-IOL-Dif.

RESULTS

The study included 204 eyes that underwent SMILE. The PE with ray tracing was -0.06 ± 0.40 diopter (D); Haigis-L, -0.39 ± 0.62 D; Haigis, 0.70 ± 0.48 D; Hoffer Q, 0.84 ± 0.47 D; Holladay 1, 1.21 ± 0.51 D; and SRK/T, 1.46 ± 0.54 D. The PE with ray tracing was significantly smaller compared with that of all formulas (P ≤ .001). The PE variance with ray tracing was σ2 = 0.159, being significantly more homogenous compared with that of all formulas (P ≤ .011, F ≥ 6.549). Ray tracing resulted in an absolute PE of 0.5 D or lesser in 81.9% of the cases, followed by Haigis-L (53.4%), Haigis (35.3%), Hoffer Q (25.5%), Holladay 1 (6.4%), and SRK/T (2.9%) formulas.

CONCLUSIONS

Ray tracing was the most accurate approach for IOL power calculation after myopic SMILE.

Comparative clinical accuracy analysis of the newly developed ZZ IOL and four existing IOL formulas for post-corneal refractive surgery eyes

BACKGROUND

Intraocular lens (IOL) calculation using traditional formulas for post-corneal refractive surgery eyes can yield inaccurate results. This study aimed to compare the clinical accuracy of the newly developed Zhang & Zheng (ZZ) formula with previously reported IOL formulas.

STUDY DESIGN

Retrospective study.

METHODS

Post-corneal refractive surgery eyes were assessed for IOL power using the ZZ, Haigis-L, Shammas, Barrett True-K (no history), and ray tracing (C.S.O Sirius) IOL formulas, and their accuracy was compared. No pre-refractive surgery information was used in the calculations.

RESULTS

This study included 38 eyes in 26 patients. ZZ IOL yielded a lower arithmetic IOL prediction error (PE) compared with ray tracing (P = 0.04), whereas the other formulas had values like that of ZZ IOL (P > 0.05). The arithmetic IOL PE for the ZZ IOL formula was not significantly different from zero (P = 0.96). ZZ IOL yielded a lower absolute IOL PE compared with Shammas (P < 0.01), Haigis-L (P = 0.02), Barrett true K (P = 0.03), and ray tracing (P < 0.01). The variance of the mean arithmetic IOL PE for ZZ IOL was significantly smaller than those of Shammas (P < 0.01), Haigis-L (P = 0.03), Barrett True K (P = 0.02), and ray tracing (P < 0.01). The percentages of eyes within ± 0.5 D of the target refraction with the ZZ IOL, Shammas, Haigis-L, Barrett True-K, and ray-tracing formulas were 86.8 %, 45.5 %, 66.7 %, 73.7 %, and 50.0 %, respectively (P < 0.05 for Shammas and ray tracing vs. ZZ IOL).

CONCLUSIONS

The ZZ IOL formula might offer superior outcomes for IOL power calculation for post-corneal refractive surgery eyes without prior refractive data.

[Back-calculation of the keratometer index-Which value would have been correct in cataract surgery?]

BACKGROUND AND PURPOSE

In the clinical routine the conversion of corneal radii into corneal refractive power using a keratometer index is rarely discussed. The purpose of this study was to back-calculate the keratometer index in pseudophakic eyes based on the refractive power of the lens, biometric measurements and refraction, and to compare it to clinically established values.

PATIENTS AND METHODS

In this retrospective case series 99 eyes of 99 patients without pathological alterations, previous diseases, comorbidities or history of ocular surgery apart from the uneventful cataract surgery were enrolled. In all eyes a CT Asphina 409M(P) (Carl-Zeiss Meditec, Berlin, Germany) had been implanted by two surgeons (EF and PE). For calculation we used shape and power data of the intraocular lens and data from optical biometry (axial length, pseudophakic anterior chamber depth, lens thickness, corneal radius; IOLMaster 700, Carl-Zeiss Meditec, Jena, Germany). The refraction was derived manually with a trial frame (measurement distance 5 m) and autorefractometry (iProfiler, Carl-Zeiss, Jena, Germany). For this three model eyes were used: a thin lens with the nominal refractive power positioned in the equatorial plane (model A) or in the secondary principal plane of the thick lens (model B) as well as a model considering the intraocular lens as a thick lens located at its measured position (model C).

RESULTS

Back-calculation of the keratometer index using vergence formulas resulted in a keratometer index based on subjective refraction measurements considering lane distance correction of 1.3307 ± 0.0026/1.3312 ± 0.0026/1.332 ± 0.0027 for model A/model B/model C, respectively. Based on objective refraction measurements (autorefraction calibrated to infinity object distances) resulted in a keratometer index of 1.3301 ± 0.0021/1.3306 ± 0.0021/1.3315 ± 0.0021, for model A/model B/model C, respectively. The keratometer index did not show any trend in linear regression for axial length or corneal radius for any of the three models or for any refraction method.

CONCLUSION

The keratometer index derived from back-calculation matched with the Zeiss index (1.332) but was much lower compared to other established indexes, e.g. the Javal index (1.3375). The missing trend for axial length or corneal radius implies that simple vergence formulas for intraocular lens refractive power calculation without correction terms or fudge factors perform best with a keratometer index slightly below 1.332, if the biometrically measured position of the intraocular lens is used as the effective lens position.

Prediction model for best focus, power, and spherical aberration of the cornea: Raytracing on a large dataset of OCT data

Purpose

To analyse corneal power based on a large optical coherence tomography dataset using raytracing, and to evaluate corneal power with respect to the corneal front apex plane for different definitions of best focus.

Methods

A large OCT dataset (10,218 eyes of 8,430 patients) from the Casia 2 (Tomey, Japan) was post-processed in MATLAB (MathWorks, USA). Using radius of curvature, corneal front and back surface asphericity, central corneal thickness, and pupil size (aperture) a bundle of rays was traced through the cornea. Various best focus definitions were tested: a) minimum wavefront error, b) root mean squared ray scatter, c) mean absolute ray scatter, and d) total spot diameter. All 4 target optimisation criteria were tested with each best focus plane. With the best-fit keratometer index the difference of corneal power and keratometric power was evaluated using a multivariate linear model.

Results

The mean corneal powers for a/b/c/d were 43.02±1.61/42.92±1.58/42.91±1.58/42.94±1.59 dpt respectively. The root mean squared deviations of corneal power from keratometric power (n_K = 1.3317/1.3309/1.3308/1.3311 for a/b/c/d) were 0.308/0.185/0.171/0.209 dpt. With the multivariate linear model the respective RMS error was reduced to 0.110/0.052/0.043/0.065 dpt (R² = 0.872/0.921/0.935/0.904).

Conclusions

Raytracing improves on linear Gaussian optics by considering the asphericity of both refracting surfaces and using Snell’s law of refraction in preference to paraxial simplifications. However, there is no unique definition of best focus, and therefore the calculated corneal power varies depending on the definition of best focus. The multivariate linear model enabled more precise estimation of corneal power compared to the simple keratometer equation.

Analysis of Optical Properties of Posterior Surface of Cornea in Patients after Anterior Radial Keratotomy

Taking into account the constant increase in patients with age-related cataracts after radial keratotomy, a careful analysis of both the optical and anatomical properties of the cornea with the examination of the posterior surface is of particular importance.

Aim. To analyze the optical properties of the posterior surface of the cornea in patients after anterior radial keratotomy. 

Materials and methods. An examination of 24 patients (48 eyes) with age-related cataracts of varying degrees of density, myopia and the presence of a previous anterior radial keratotomy or radial-tangential keratotomy in history. The average age of patients was 59.5 years (from 47 to 68), there were 19 women and 5 men.

Results. The radius of curvature of the anterior surface in patients after anterior radial keratotomy was 9.45 ± 0.91 mm on average along the meridians, which is significantly more in comparison with these indices in control patients – 7.70 ± 0.19 mm (p = 0.0001). The ratio of the radii of the posterior cornea curvature to the anterior radius on average along the meridians in patients after anterior radial keratotomy was 1.07 ± 0.70, and in control patients – 1.20 ± 0.02 (p = 0.0001). The keratometric index in patients after anterior radial keratotomy was 1.3538 ± 0.0239, and in the control group – 1.3372 ± 0.0003 (p = 0.23).

Conclusion. In patients after anterior radial keratotomy, keratometry of the posterior surface of the cornea is significantly higher than in the control. The ratio of the radius of curvature of the posterior cornea to the radius of curvature of the anterior cornea varies significantly after anterior radial keratotomy, which is due to a more pronounced flattening of the posterior cornea. The standard keratometric index (1.3375) is invalid for patients after anterior radial keratotomy and must be calculated individually for each patient when deciding on the operative treatment of cataracts.

Impact of ultrasound and optical biometry on refractive outcomes of cataract surgery after penetrating keratoplasty in keratoconus

AIM

To analyse the impact of ultrasound and optical intraocular lens (IOL) calculation methods on refractive outcomes of cataract phacoemulsification performed after penetrating keratoplasty (PK) in keratoconus.

METHODS

Phacoemulsification cataract surgery was performed on 42 eyes of 34 patients with keratoconus who had previously undergone PK. The IOL power was determined by using both standard and corneal topography-derived keratometry using the SRK/T formula. We used two independent methods-ultrasound biometry (UB) and interferometry [optical biometry (OB)] for IOL calculation. The analysed data from medical records included demographics, medical history, best corrected visual acuity (BCVA) on Snellen charts, technique of IOL calculation and calculation formula and its impact on final refractive result.

RESULTS

BCVA ranged from 0.01 to 0.4 (mean 0.09±0.19) before surgery and ranged from 0.2 to 0.7 (mean 0.38±0.14) at 1mo and from 0.2 to 1.0 (mean 0.56±0.16) (P<0.05) at 3mo, postoperatively. The refractive aim differed significantly from the refractive outcome in both the UB and OB groups (P<0.05). There was no statistically significant difference in the accuracy of the two biometry methods.

CONCLUSION

The refractive aim in keratoconus eyes post-PK is not achieved with either ultrasound or OB.

Intraocular lens power calculation in eyes with previous corneal refractive surgery

Background

This review aims to explain the reasons why intraocular lens (IOL) power calculation is challenging in eyes with previous corneal refractive surgery and what solutions are currently available to obtain more accurate results.

Review

After IOL implantation in eyes with previous LASIK, PRK or RK, a refractive surprise can occur because i) the altered ratio between the anterior and posterior corneal surface makes the keratometric index invalid; ii) the corneal curvature radius is measured out of the optical zone; and iii) the effective lens position is erroneously predicted if such a prediction is based on the post-refractive surgery corneal curvature. Different methods are currently available to obtain the best refractive outcomes in these eyes, even when the perioperative data (i.e. preoperative corneal power and surgically induced refractive change) are not known. In this review, we describe the most accurate methods based on our clinical studies.

Conclusions

IOL power calculation after myopic corneal refractive surgery can be calculated with a variety of methods that lead to relatively accurate outcomes, with 60 to 70% of eyes showing a prediction error within 0.50 diopters.

[Predictability of residual astigmatism after implantation of posterior chamber toric lenses]

BACKGROUND

The objective of the study was to examine the predictability of residual astigmatism after cataract surgery and implantation of the posterior chamber aspheric toric lens TECNIS® ZCT, Abott Medical Optic (Ettlingen, Deutschland).

MATERIAL AND METHODS

The retrospective study included a total of 88 patient eyes undergoing a cataract operation with a toric lens implantation between March 2014 and October 2015. The inclusion criteria were a regular astigmatism of at least 0.75 dpt. Posterior chamber toric lenses (model Tecnis ZCT) were exclusively implanted. Post-surgery check-ups were performed after 1 day, 1 month and 2 months. Main study outcome was best-corrected visual acuity (BCVA), spherical and astigmatic aberration and the difference between expected and actual residual astigmatism after cataract surgery.

RESULTS

The median reduction of corneal astigmatism was from -2.50 dpt (±1.06 dpt) to -0.75 dpt (±0.51 dpt) (p ≤ 0.05). The median BCVA increased from 0.37 logMAR (±0.25 logMAR) before surgery to 0.09 logMAR (±0.10 logMAR) after surgery. The spherical equivalent was reduced from +3.50 dpt (±1.11 dpt) (presurgery) to -0.56 dpt (±0.51 dpt) (postsurgery) in hyperopic patients and from -2.44 dpt (±3.03 dpt) to -0.69 dpt (±0.81 dpt) in myopic patients. By using the power vector analysis no significant deviation from the expected target values was observed; however, the median discrepancy between the expected and actual residual astigmatism was -0.50 dpt despite a surgical orientation of the intraocular lens (IOL) within 5° of the desired axis. The IOL showed a median rotation of 3.00° (±4.46°).

CONCLUSION

Implantation of the aspheric toric intraocular lens Tecnis ZCT is a predictable, effective and reproducible tool in cataract surgery to account for regular corneal astigmatis; however, despite an optimal surgical orientation of the toric IOL, a small and rarely a large discrepancy might occur between expected and actual residual astigmatism.

Bilateral cataract surgery in a 56-year-old man following presbyopia laser in situ keratomileusis: A case report

We describe a case of bilateral cataract surgery in a 56-year-old man following presbyopia laser in situ keratomileusis. The preoperative refraction was −2.00 in the right eye and −0.75 × 105 in the left eye. On the last examination, the uncorrected distance visual acuity was 20/80 that can be corrected to 20/20 in the right eye with a refraction of −2.25 and 20/20 in the left eye, whereas the visual acuity for reading was 20/40 in the right eye and 20/80 in the left eye with a refraction of +2.25. His monovision surgery design of previous cornea surgery was also taken into consideration for the phacoemulsification and posterior chamber intraocular lens (IOL) implantation. Two-step surgery is helpful for predicting an accurate IOL degree.

Intraocular lens power calculation following laser refractive surgery

Refractive outcomes following cataract surgery in patients that have previously undergone laser refractive surgery have traditionally been underwhelming. This is related to several key issues including the preoperative assessment (keratometry) and intraocular lens power calculations. Peer-reviewed literature is overwhelmed by the influx of methodology to manipulate the corneal or intraocular lens (IOL) powers following refractive surgery. This would suggest that the optimal derivative formula has yet been introduced. This review discusses the problems facing surgeons approaching IOL calculations in these post-refractive laser patients, the existing formulae and programs to address these concerns. Prior published outcomes will be reviewed.

Postoperative refractive error after phacovitrectomy for epiretinal membrane with and without macular oedema

PURPOSE

This study was initiated to investigate whether the presence of macular oedema influenced intraocular lens (IOL) power calculation in eyes with epiretinal membrane.

METHODS

The files of patients undergoing combined phacoemulsification were retrospectively reviewed. Two groups were defined according to presence of macular oedema. The main outcome measure was the IOL power prediction error (PE). Secondary outcome measures were the correlation between preoperative macular thickness, absolute change of macular thickness and dioptric shift. The mean postoperative PE achieved with the Haigis formula was compared with the PE that would have been obtained had the SRKII and HofferQ formulas been used.

RESULTS

We investigated 47 eyes of 47 consecutive patients. Regardless of the IOL formula used, the PE was on average higher in eyes without macula oedema (group 1). The myopic dioptric shift was dependent on preoperative macular thickness and absolute change of macular thickness. This association was more markedly pronounced in group 1.

CONCLUSIONS

Increased retinal thickness is the main cause for underestimation of the cornea-photoreceptor layer distance, and therefore could contribute to inaccuracy in IOL power calculations. The current results show that a myopic shift tends to be less pronounced in cases where a macula oedema is present. Eyes with pure traction have less predictable refractive results in terms of higher PE and dioptric shift.

The accuracy of the double-K adjustment for third-generation intraocular lens calculation formulas in previous keratorefractive surgery eyes

PURPOSE

To evaluate the effect of the double-K (DK) modification on third-generation formulas.

METHODS

Thirty-eight previously myopic and 24 previously hyperopic eyes that underwent phacoemulsification with intraocular lens (IOL) insertion after Laser in situ keratomileusis (LASIK) were evaluated. Pre-LASIK refraction and keratometry, post-LASIK topography, axial length (AL), IOL type and power, and 1-month postphacoemulsification refraction were recorded spherical equivalent after phacoemulsification (SE(postphaco)). Measured corneal power was adjusted using published and validated methods for postmyopic and posthyperopic LASIK. For each eye, and using SE(postphaco), different DK-IOL formulas were used to calculate the corresponding IOL power, the outcome measure, which was compared with the implanted IOL.

RESULTS

DK-Holladay 1 yielded the highest Pearson correlation coefficient (PCC), 0.955 for myopes and 0.943 for high myopes (AL>26 mm). Mean error (ME) and mean absolute error (MAE) for myopes for DK Sanders-Retzlaff-Kraff theoretical formula [DK-SRK/T] were 0.44±0.84 D and 0.75±0.61 D for DK-SRK/T compared with -0.04±0.67 D and 0.52±0.40 D for DK-Holladay 1 (P<0.001 and P=0.016, respectively), and 0.03±0.88 and 0.64±0.58 for DK-Hoffer Q. For high myopes, ME and MAE were 0.75±0.81 D and 0.84±0.69 D for DK-SRK/T, and -0.05±0.74 D (P<0.0001) and 0.57±0.45 D (P=0.019) for DK-Holladay 1. About 29% of DK-SRK/T eyes with large AL had MAE>1.5 D, compared with 0% for DK-Holladay 1 and 14% for DK-Hoffer-Q. Eyes with previous hyperopic LASIK faired similarly for all formulas, with similar PCCs, and only 8% in each category with MAE>1.5 D.

CONCLUSIONS

DK-SRK/T overestimates IOL power in eyes with large AL, especially with concomitant steep pre-lasik keratometry. Among third-generation formulas, DK-Holladay 1 seems more accurate to use in postmyopic LASIK eyes.

Intraocular lens power calculations after myopic laser refractive surgery: a comparison of methods in 173 eyes

PURPOSE

To evaluate and compare published methods of intraocular lens (IOL) power calculation after myopic laser refractive surgery in a large, multi-surgeon study.

DESIGN

Retrospective case series.

PARTICIPANTS

A total of 173 eyes of 117 patients who had uneventful LASIK (89) or photorefractive keratectomy (84) for myopia and subsequent cataract surgery.

METHODS

Data were collected from primary sources in patient charts. The Clinical History Method (vertex corrected to the corneal plane), the Aramberri Double-K, the Latkany Flat-K, the Feiz and Mannis, the R-Factor, the Corneal Bypass, the Masket (2006), the Haigis-L, and the Shammas.cd postrefractive adjustment methods were evaluated in conjunction with third- and fourth-generation optical vergence formulas, as appropriate. Intraocular lens power required for emmetropia was back-calculated using stable post-cataract surgery manifest refraction and implanted IOL power, and then formula accuracy was compared.

MAIN OUTCOME MEASURES

Prediction error arithmetic mean ± standard deviation (SD), range (minimum and maximum), and percent within 0 to -1.0 diopters (D), ±0.5 D, ±1.0 D, and ±2.0 D relative to target refraction.

RESULTS

The top 5 corneal power adjustment techniques and formula combinations in terms of mean prediction errors, standard deviations, and minimizing hyperopic "refractive surprises" were the Masket with the Hoffer Q formula, the Shammas.cd with the Shammas-PL formula, the Haigis-L, the Clinical History Method with the Hoffer Q, and the Latkany Flat-K with the SRK/T with mean arithmetic prediction errors and standard deviations of -0.18±0.87 D, -0.10±1.02 D, -0.26±1.13 D, -0.27±1.04 D, and -0.37±0.91 D, respectively.

CONCLUSIONS

By using these methods, 70% to 85% of eyes could achieve visual outcomes within 1.0 D of target refraction. The Shammas and the Haigis-L methods have the advantage of not requiring potentially inaccurate historical information.

Origins of the keratometer and its evolving role in ophthalmology

The keratometer, or ophthalmometer as it was originally known, had its origins in the attempt to discover the seat of accommodation in the eye. Since that early beginning, it has been re-invented a number of times, with improvements and modifications made in the original principles of its design for new applications that arose as ophthalmology advanced. The cornea is not only responsible for the majority of the refraction in the eye, but is also readily accessible for measurement and modification. The keratometer's ability to measure the cornea has allowed it to play a central role in critical advances in ophthalmic history. This review describes the origins and principles of this instrument, the novel applications that led to the keratometer's continued resurgences over its nearly 250-year history, and the modern devices that have borrowed its basic principles and are beginning to replace it in common clinical practice.

Intraocular lens power calculation after laser refractive surgery: corrective algorithm for corneal power estimation

PURPOSE

To evaluate an algorithm for corneal power estimation in intraocular lens (IOL) power calculation after myopic laser refractive surgery using direct corneal measurements.

SETTING

International Vision Correction Research Centre, University of Heidelberg, Heidelberg, Germany.

METHODS

Corneal parameters in normal eyes and eyes of refractive surgery cases were evaluated by rotating Scheimpflug imaging. Corneal optical power (K(optical)) calculated by a Gaussian optics formula was simplified as K(optical) = K(anterior) + K(2) (K(anterior) = anterior corneal power; K(posterior) = posterior corneal power; K(2) = K(posterior)--K(anterior) x K(posterior) x corneal thickness/1.376). The variation and change in K(2) induced by refractive surgery were analyzed. A corrective algorithm to calculate K(optical) using mean K(2) (-6.10 diopters [D]), K(corrective) = 1.114 x measured K - 6.10, was derived based on statistical analysis, which was in accordance with the modified Maloney method. The IOL power after refractive surgery was calculated using K(corrective).

RESULTS

The mean K(2) of normal and post-refractive corneas was -6.10 +/- 0.23 D and -6.16 +/- 0.17 D, respectively (P = .17). The mean refractive surgery-induced change in K(2) was -0.06 +/- 0.10 D. The variations in K(2) were small (95% confident interval, -6.55 to -5.65 [normal cornea]; -6.48 to -5.70 [pre-refractive]; - 6.49 to -5.83 [post-refractive)]. Using K(corrective) for IOL power calculation in post-refractive cases yielded mean absolute prediction errors of 0.58 +/- 0.52 D (Haigis), 0.59 +/- 0.49 D (double-K Hoffer Q), and 0.58 +/- 0.47 D (double-K SRK/T).

CONCLUSION

The algorithm that induced low error in corneal power estimation was relatively reliable in IOL calculation after myopic laser refractive surgery.

FINANCIAL DISCLOSURE

No author has a financial or proprietary interest in any material or method mentioned.

Calculations of Corneal Power After Corneo-Refractive Surgery from Keratometry and Change of Spectacle Refraction: Some Considerations on the “Clinical History Method”

PURPOSE

To derive corneal power after kerato-refractive laser surgery (KRS) to be used for a subsequent intraocular lens (IOL) power calculation.

MODEL

Based on the proportion of curvatures of the corneal front and back surface, the central thickness, and the ablation characteristics, we demonstrate a vergence-based formalism to derive the equivalent and back vertex corneal power before and after KRS from the preoperative measured keratometry. As a second option, we demonstrate in the paper how to derive the respective values from the postoperative (instead of the preoperative) measured keratometry.

EXAMPLE

Initial refraction before/after KRS, -12.0/-2.0 D; corneal thickness, 550/440 microm; front/back surface power 48.20-5.81 D, measured Zeiss keratometry before KRS, 42.5 D. After KRS, we calculate a corneal front surface power of 39.82 D and an equivalent/back vertex power and keratometry of 34.08/34.48/35.11 D (result of the "Clinical History Method" at spectacle/corneal plane 32.50/33.96 D). Calculated corneal power values are around 2-3 D lower than measured Zeiss keratometry (37.0 D), which will lead to an IOL power overestimation of about 3-4 D and subsequent hyperopia.

CONCLUSIONS

This formalism may help to prevent hyperopia after cataract surgery subsequent to refractive surgery for myopia.

Corneal refractive power estimation and intraocular lens calculation after hyperopic LASIK

PURPOSE

To identify key independent variables in estimating corneal refractive power (KBC) after hyperopic LASIK.

DESIGN

Retrospective study.

PARTICIPANTS

We included 24 eyes of 16 hyperopic patients who underwent LASIK with subsequent phacoemulsification and posterior chamber intraocular lens (IOL) implantation in the same eye.

METHODS

Pre-LASIK and post-LASIK spherical equivalent (SE) refractions and topographies, axial length, implant type and power, and 3-month postphacoemulsification SE were recorded. Using the double-K Hoffer Q formula, corneal power was backcalculated for every eye (KBC), regression-based formulas derived, and corresponding IOL powers calculated and compared with published methods.

MAIN OUTCOME MEASURES

The Pearson correlation coefficient (PCC) and arithmetic and absolute corneal and IOL power errors.

RESULTS

Adjusting either the average central corneal power (ACCP(3mm)) or SimK based on the laser-induced spherical equivalent change (DeltaSE) resulted in an estimated corneal power (ACCP(adj) and SimK(adj)) with highest correlation with KBC (PCC=0.940 and 0.956, respectively) and lowest absolute corneal estimation error (0.37+/-0.45 and 0.38+/-0.39 diopter [D], respectively). The ACCP(adj) closely mirrored published DeltaSE-based adjustments of central corneal power on different topographers, whereas DeltaSE-based SimK adjustments varied across platforms. Using ACCP(adj) or SimK(adj) in the double-K Hoffer Q, using ACCP(3mm) or SimK in single-K Hoffer Q and adjusting the resultant IOL power based on DeltaSE, or applying Masket's formula all yielded accurate and similar IOL powers. The Latkany method consistently underestimated IOL power. The Feiz-Mannis and clinical history methods yielded poor IOL correlations and large IOL errors.

CONCLUSION

After hyperopic LASIK, adjusting either corneal power or IOL power based on DeltaSE accurately estimates the appropriate IOL power.

[Determination of toric intraocular lenses]

BACKGROUND

In the last decades, toric posterior chamber lenses (TPCLs) for cataract surgery and phakic toric lenses (PTLs) for refractive surgery have become more and more popular for correcting high or excessive corneal astigmatism. The purpose of this article is to present a vergence-based calculation scheme for TPCLs and PTLs.

METHODS

In Gaussian optics (in the paraxial space), spherocylindrical optical surfaces can be described in a mathematically equivalent formulation as vergences. There are dual notations: The standard notation is used for transforming vergences through a homogeneous optical medium, and the component notation is applied to add up the power of a refractive surface to the vergence. Both notations can be used interchangeably. For calculating TPCLs, the vergences in front of and behind the predicted pseudophakic lens position are determined and subtracted. For calculating PTLs, the anterior vergence at the predicted lens position is estimated for the preoperative and postoperative states, and the difference between the two yields the desired lens power. WORKING EXAMPLES: In the 1(st) example, the power of a thin TPCL is determined step by step by applying the presented calculation scheme, which was designed to be transferred directly to a simple computer program (e.g., Microsoft Excel). In the 2(nd) example, the postoperative refraction is estimated for a simulation in which a TPCL similar to that in example 1 is implanted in a slightly misaligned orientation. In a 3(rd) example, the power of a PTL is determined step by step using the above-mentioned calculation scheme.

CONCLUSIONS

The presented calculation scheme allows determination of"thin" TPCLs or PTLs to achieve spherocylindrical target refraction with a cylinder axis at random or to predict the postoperative refraction for any toric lens implanted in any axis. The concept can be easily generalized to"thick" toric intraocular lenses if the geometric data and refraction index of the material are known.

Calculating the power of toric phakic intraocular lenses

BACKGROUND AND PURPOSE

A toric phakic intraocular lens (IOL) implanted in the anterior or posterior chamber of the eye has the potential to correct high or excessive ametropia and astigmatism with high predictability of the postoperative refraction and preservation of phakic accommodation. The calculation of spherical phakic lenses has been described previously, but a formalism for estimating the power of toric phakic lenses has not yet been published. The purpose of this study is to describe a mathematical strategy for calculating toric phakic IOLs.

METHODS

The method presented in this paper is based on vergence transformation in the paraxial Gaussian space. Parameters used for the calculations are the spherocylindrical spectacle refraction before implantation, corneal power (sphere and astigmatism) and (spherocylindrical) target refraction, together with the vertex distance and the predicted position of the phakic IOL. The lens power is determined as the difference in vergences between the spectacle-corrected eye and the uncorrected eye at the reference plane of the predicted lens position. The axes of the preoperative refraction, the target refraction and the corneal astigmatism are at random (not necessarily aligned).

RESULTS

The method was applied to two clinical examples. In example 1 we calculate the power of a phakic lens for the simple case, when the target refraction is plano and the axis of the preoperative refraction is aligned to the axis of the corneal astigmatism. In example 2, the cylindrical axis of the preoperative refraction is not aligned to the corneal astigmatism and the target refraction is spherocylindrical (and the axis of the target refraction is not aligned to the preoperative refractive cylinder or the corneal astigmatism). The calculations for both examples are described step-by-step and illustrated in a table.

CONCLUSIONS

The calculation scheme can be generalized to an unlimited number of crossed cylinders in the optical pathway. Based on paraxial raytracing, the spherical and cylindrical power as well as the orientation of the cylinder are determined from the preoperative refraction (including vertex distance), the corneal power, the intended target refraction (including vertex distance) and the predicted position of the phakic lens implant provided by the lens manufacturer. This calculation scheme can be easily implemented in a simple computer program (i.e. in Microsoft excel or matlab).

Torische Intraokularlinsen und Astigmatismuskorrektur

Toric intraocular lenses (tIOLs) have the potential to correct corneal astigmatism. The purpose of this review paper is: 1. to describe the biometric, keratometric and topographic conditions for implantion of tIOLs, 2. to highlight the advantages and disadvantages of tIOLs, 3. to define indications for and contraindications to tIOL implantation, 4. to provide clinical recommendations for the implantation of toric lenses, and 5. to report the specifications of all tIOLs that are currently available commercially.

Calculating Intraocular Lens Geometry by Real Ray Tracing

PURPOSE

An implementation of real ray tracing based on Snell's law is tested by predicting the refraction of pseudophakic eyes and calculating the geometry of intraocular lenses (IOLs).

METHODS

The refraction of 30 pseudophakic eyes was predicted with the measured corneal topography, axial length, and the known IOL geometry and compared to the manifest refraction. Intraocular lens calculation was performed for 30 normal eyes and 12 eyes that had previous refractive surgery for myopia correction and compared to state-of-the-art IOL calculation formulae.

RESULTS

Mean difference between predicted and manifest refraction for a 2.5-mm pupil were sphere 0.11 +/- 0.43 diopters (D), cylinder -0.18 +/- 0.52 D, and axis 5.13 degrees +/- 30.19 degrees. Pearson's correlation coefficient was sphere r = 0.92, P < .01; cylinder r = 0.79, P < .01; and axis r = 0.91, P < .01. Intraocular lens calculation for the normal group showed that the mean absolute error regarding refractive outcome is largest for SRK II (0.49 D); all other formulae including ray tracing result in similar values ranging from 0.36 to 0.40 D. Intraocular lens calculation for the refractive group showed that depending on pupil size (3.5 to 2.5 mm), ray tracing delivers values 0.95 to 1.90 D higher compared to the average of Holladay 1, SRK/T, Haigis, and Hoffer Q formulae.

CONCLUSIONS

It has been shown that ray tracing can compete with state-of-the-art IOL calculation formulae for normal eyes. For eyes with previous refractive surgery, IOL powers obtained by ray tracing are significantly higher than those from the other formulae. Thus, a hyperopic shift may be avoided using ray tracing even without clinical history.

The AS biometry technique--a novel technique to aid accurate intraocular lens power calculation after corneal laser refractive surgery

Intraocular lens power (IOL) calculation for cataract surgery has been shown to be inaccurate after photorefractive keratectomy (PRK), laser-assisted subepithelial keratectomy (LASEK) and laser in situ keratomileusis (LASIK). Many techniques exist to calculate corneal power with varying results and require the clinician to be aware of the pitfalls of IOL power calculation in post-refractive eyes. The AS biometry method proposed here is a simple method which does not rely on the calculation of corneal power. This new method is compared to the current gold standard the clinical history method (CHM). Twenty-nine eyes of 15 patients had routine biometry prior to LASIK, LASEK or PRK. The range of pre-operative spherical equivalent refractive error was -5.37 to +4.00 diopters. The post-operative refraction was measured at 3-6 months. The IOL power calculation was calculated using the AS biometry method and the CHM. The two methods were compared using the Student's paired t-test and the Bland Altman technique. There was no statistical difference between the AS biometry method and the CHM. The paired Student's t-test comparing the AS biometry method and the CHM showed no statistical difference, t=0.33 with a p-value of 0.75, at a 95% confidence interval. The authors conclude that the AS biometry technique is as accurate as the CHM. The former is a simpler method which avoids many of the pitfalls and confounding factors involved in IOL power calculation following corneal excimer laser surgery. However, like the CHM it requires measurements prior to laser surgery.

Excimer laser surgery for correction of ametropia after cataract surgery

PURPOSE

To review the cases of patients who had excimer laser refractive surgery to correct unintentional or undesired ametropia after cataract extraction with intraocular lens (IOL) implantation.

SETTING

Wilmer Laser Vision Correction Center, Wilmer Eye Institute, Baltimore, Maryland, USA.

METHODS

In this retrospective noncomparative review of consecutive cases, the Wilmer Laser Vision Correction Center's database was searched for patients who had laser in situ keratomileusis or photorefractive keratectomy to correct ametropia after cataract extraction with IOL implantation.

RESULTS

Using the Visx Star excimer laser system (Visx, Inc.), 11 procedures were performed in 11 eyes of 10 patients a mean of 47 months (range 2 to 216 months) after cataract extraction with IOL implantation. Except for 1 patient with a silicone plate lens, all patients received 3-piece poly(methyl methacrylate) lenses. The mean age at time of excimer treatment was 75 years (range 70 to 81 years). Before laser surgery, the mean spherical equivalent of patient eyes was -3.76 diopters (D) +/- 2.50 (SD) (range -6.50 to +0.75 D), spherical refraction ranged from -9.00 D to plano, and the highest cylindrical refraction was +5.50 D. At last follow-up (mean 12.2 months; range 1 to 38 months), the mean manifest spherical equivalent was -0.88 +/- 1.43 D (range -2.75 to +2.13 D). Changes in mean manifest spherical equivalent were highly significant (P = .03, Wilcoxon signed rank test for paired values). There was no difference between targeted and achieved postoperative refraction (P = .34, Wilcoxon test). Increasing age was correlated with a hyperopic shift (r = 0.525, P = .05). All patients were satisfied with their final uncorrected visual acuity (UCVA), which improved in every case. Except for 1 patient in whom an epiretinal membrane developed, best spectacle-corrected visual acuity remained unchanged or improved.

CONCLUSIONS

In this series of patients, who were a few decades older than the typical excimer laser candidate, laser refractive surgery was a safe, effective, and predictable method to correct ametropia after cataract extraction with IOL implantation. It may be a viable, noninvasive alternative to intraocular surgery, which has potential complications. Although satisfactory for all patients, final UCVA was not as high as that reported in laser refractive surgery patients in general, and this result may be because of prior cataract extraction with IOL implantation or increased age.

Intraocular lens power calculation using ray tracing following excimer laser surgery

PURPOSE

To evaluate intraocular lens (IOL) power calculation using ray tracing in patients presenting with cataract after excimer laser surgery.

METHODS

Ten eyes of seven consecutive patients who presented for cataract surgery following excimer laser treatment without any pre-refractive biometry data were enrolled in this prospective clinical study. Preoperatively, IOL power calculation was performed using a ray tracing software called OKULIX. Keratometry data (C-Scan) were imported and axial length (IOLMaster) was entered manually. Accuracy of IOL power calculation was investigated by subtracting attempted and achieved spherical equivalent.

RESULTS

Mean spherical equivalent was -3.51+/-2.77 D (range -10.38 to -0.5 D) preoperatively and -1.01+/-1.08 D (range -2.5 to +0.75 D) postoperatively. Mean error was 0.31+/-0.84 D, mean absolute error was 0.74+/-0.46 D, and IOL calculation errors ranged from -1.39 to +1.47 D. A total of 40% of eyes were within +/-0.5 D, 70% within +/-1.0 D, and 100% within +/-1.5 D. Three eyes with corneal radii over 10 mm showed calculation errors exceeding +/-1.0 D. Mean best-corrected visual acuity increased from 20/60 to 20/30 postoperatively.

CONCLUSIONS

IOL power calculation after excimer laser surgery can be difficult, especially when pre-refractive keratometry values are not available. In these cases, ray tracing combined with corneal topography measurements provides reliable and satisfactory postoperative results. However, it is advisable to be careful when calculating IOL power for eyes with corneal radii exceeding 10 mm because of slightly higher prediction errors.

Refractive lens exchange combined with pars plana vitrectomy to correct high myopia

PURPOSE

To describe the results of refractive lens exchange (RLE) combined with simultaneous pars plana vitrectomy (PPV) in the management of severe myopia.

METHODS

This retrospective study comprised 14 eyes of eight patients who had RLE to treat myopia of -19.0+/-5.4 diopters (D). Phacoemulsification, posterior chamber intraocular lens (IOL) implantation, and standard three-port vitrectomy were performed. Mean postoperative follow-up time was 30 months (range 12-49).

RESULTS

The postoperative best-corrected visual acuity (BCVA) was 0.68+/-0.23 compared to 0.37+/-0.24 preoperatively. There was no postoperative decrease in visual acuity in any eye. Mean postoperative spherical equivalent was -0.7 D (+/-1.6). At 30 months mean follow-up time, the spherical equivalents of nine eyes (64.3%) were within +/-1 D of emmetropia. There was no significant change in astigmatism due to operative procedures. During the 30 months follow-up period three eyes (21.4%) required neodymium : yttrium-aluminium-garnet (Nd : YAG) capsulotomy for posterior capsule opacification. No retinal detachments or cases of cystoid macular oedema (CME) were observed during the follow-up.

CONCLUSION

RLE was effective in correcting severe myopia. The simultaneously performed PPV may reduce the risk of postoperative retinal detachment. This was a pilot study, to draw definitive conclusions a prospective study has to be initiated.

Compensation of aniseikonia with toric intraocular lenses and spherocylindrical spectacles

BACKGROUND AND PURPOSE

Magnification disparity between the two eyes (aniseikonia) is one of the major unresolved problems in modern cataract surgery, potentially degrading binocular visual function or causing diplopia. The purpose of this study is to describe a paraxial computing scheme using 4x4 system matrices to simulate a corrected pseudophakic 'optical system eye' with a meridional magnification that matches the magnification of a given contralateral eye.

METHODS

Based on the definition of a centred optical system in the paraxial Gaussian space containing astigmatic surfaces using 4x4 refraction and translation matrices, we derived a methodology for calculating the refractive power and axis of toric intraocular lenses and spherocylindrical spectacle corrections for (i) fully correcting the optical system eye and (ii) realizing an arbitrary meridional magnification by solving a linear equation system.

RESULTS

The capabilities of this computing scheme are demonstrated with two examples. In example 1 we calculate a toric lens and a spherocylindrical spectacle correction for compensation of a corneal astigmatism to realize a predefined iso-meridional magnification. In example 2 we first determine the meridional magnification of the contralateral eye, which has been treated with cataract surgery and toric lens implantation, and then we compute the appropriate combination of a fully correcting toric lens and spherocylindrical spectacle refraction, which exactly matches the meridional magnification of the contralateral eye.

CONCLUSION

We presented an en bloc matrix based strategy for the calculation of an optical system eye containing an astigmatic cornea, a toric lens implant and a spherocylindrical spectacle correction, where the toric lens and the spherocylindrical spectacle correction are determined to fully correct the system and to realize an arbitrary meridional magnification i.e. to eliminate aniseikonia.