Comparison of ray-tracing method and thin-lens formula in intraocular lens power calculations

Association of refractive outcome with postoperative anterior chamber depth measured with 3 optical biometers

PURPOSE

This study evaluated the relationship between refractive outcomes and postoperative anterior chamber depth (ACD, measured from corneal epithelium to lens) measured by swept-source optical coherence tomography (SS-OCT), optical low-coherence reflectometry (OLCR), and Scheimpflug devices under the undilated pupil.

METHODS

Patients undergoing cataract phacoemulsification with intraocular lens (IOL) implantation in a hospital setting were enrolled. Postoperative ACD (postACD) was performed with an SS-OCT device, an OLCR device, and a Scheimpflug device at least 1 month after cataract surgery. After adjusting the mean predicted error to 0, differences in refractive outcomes were calculated with the Olsen formula using actual postACD measured from 3 devices and predicted value.

RESULTS

Overall, this comparative case study included 69 eyes of 69 patients, and postACD measurements were successfully taken using all 3 devices. The postACD measured with the SS-OCT, OLCR, and Scheimpflug devices was 4.59 ± 0.30, 4.50 ± 0.30, and 4.54 ± 0.32 mm, respectively. Statistically significant differences in postACD were found among 3 devices (P < 0.001), with intraclass correlation coefficients (ICCs) and Bland-Altman showing good agreement. No significant difference in median absolute error was found with the Olsen formula using actual postACD obtained with 3 devices. Percentage prediction errors were within ± 0.50 D in 65% (OLCR), 70% (Scheimpflug), and 67% (SS-OCT) calculated by actual postACD versus 64% by predicted value.

CONCLUSION

Substantial agreement was found in postACD measurements obtained from the SS-OCT, OLCR, and Scheimpflug devices, with a trend toward comparable refractive outcomes in the Olsen formula. Meanwhile, postACD measurements may be potentially superior for the additional enhancement of refractive outcomes.

Comparison of lens refractive parameters in myopic and hyperopic eyes of 6-12-year-old children

Background/aims

To evaluate the influence of cycloplegia on lens refractive parameters in 6-12-year-old children with myopia and hyperopia for exploring the pathogenesis of myopia.

Methods

One hundred eyes of 100 patients (50 boys) were included. In the myopic group, 50 subjects (25 boys and 25 right eyes) were enrolled with a mean age of 9.20 ± 1.69 years. IOLMaster 700 measurements were performed pre- and post-cycloplegia. The pictures were marked using semi-automatic software. The lens curvature and power were obtained using MATLAB image processing software. Paired and independent sample t-tests were used for data analysis. Statistical significance was set at P < 0.05.

Results

Anterior and posterior lens curvature radius in myopic eyes were larger than those in hyperopic eyes, both pre- and post-cycloplegia (both P < 0.001). The refractive power in myopic eyes was lower than that in hyperopic eyes without cycloplegia, both pre- and post-cycloplegia (both P < 0.001). The changes in anterior lens curvature and refractive power between pre- and post-cycloplegia in hyperopic eyes were larger than those in myopic eyes (both P < 0.05). No significant difference was found in the change in posterior lens curvature and refractive power after cycloplegia in hyperopic and myopic eyes (P > 0.05).

Conclusion

Anterior and posterior surfaces of the lens were flatter, and the refractive power was lower in the myopia group than in the hyperopia group. Myopic and hyperopic patients showed a tendency for lens flattening and refractive power decrease after cycloplegia. Hyperopic patients had more changes in anterior lens curvature and refractive power after cycloplegia.

Comparison of two one-piece acrylic foldable intraocular lenses: Short-term change in axial movement after cataract surgery and its effect on refraction

Purpose

To compare the change in intraocular lens (IOL) axial movement, corneal power, and postoperative refraction of eyes implanted with two different single-piece, open loop, acrylic foldable IOLs with planar-haptic design: one IOL with hinges vs. one IOL without hinges. The role of IOL axial movement on short-term refractive shift after cataract surgery was also evaluated.

Methods

This retrospective comparative study enrolled consecutive patients who had phacoemulsification with aspheric IOL implantation. The IOL depth (the distance from corneal endothelium to IOL surface) and corneal power were measured via anterior-segment optical coherence tomography at 4 days and 1 month postoperatively. The changes in axial movement of the IOL, corneal power, and manifest refractive spherical equivalent (MRSE) were compared among groups, and the correlations between each lens were evaluated.

Results

IOL with hinges was implanted in 42 eyes of 42 patients and IOL without hinges was implanted in 42 eyes of 42 patients. The change in axial movement between 4 days and 1 month was significantly smaller in the IOL with hinges group than in the IOL without hinges group (p < 0.001). The axial movement of IOL with hinges did not correlate with the MRSE change; however, the forward shift of IOL without hinges correlated with the myopic refractive change (Pearson r = 0.62, p < 0.001).

Conclusion

The postoperative axial movement of IOL was more stable in the IOL with hinges group than the IOL without hinges group between 4 days and 1 month after cataract surgery. Even though the two study IOLs with planar-haptic design are made of similar acrylic materials, other characteristics such as hinge structure may affect IOL stability in the bag.

IOL Power Calculations and Cataract Surgery in Eyes with Previous Small Incision Lenticule Extraction

Small incision lenticule extraction (SMILE), with over 5 million procedures globally performed, will challenge ophthalmologists in the foreseeable future with accurate intraocular lens power calculations in an ageing population. After more than one decade since the introduction of SMILE, only one case report of cataract surgery with IOL implantation after SMILE is present in the peer-reviewed literature. Hence, the scope of the present multicenter study was to compare the IOL power calculation accuracy in post-SMILE eyes between ray tracing and a range of empirically optimized formulae available in the ASCRS post-keratorefractive surgery IOL power online calculator. In our study of 11 post-SMILE eyes undergoing cataract surgery, ray tracing showed the smallest mean absolute error (0.40 D) and yielded the largest percentage of eyes within ±0.50/±1.00 D (82/91%). The next best conventional formula was the Potvin–Hill formula with a mean absolute error of 0.66 D and an ±0.50/±1.00 D accuracy of 45 and 73%, respectively. Analyzing this first cohort of post-SMILE eyes undergoing cataract surgery and IOL implantation, ray tracing showed superior predictability in IOL power calculation over empirically optimized IOL power calculation formulae that were originally intended for use after Excimer-based keratorefractive procedures.

Three-dimensional topographic changes of anterior chamber depth following phacoemulsification with intraocular lens implantation in cataract patients

PURPOSE

To investigate the three-dimensional topographic changes of anterior chamber depth (ACD) following cataract surgery.

METHODS

Seventy-eight eyes with age-related cataract undergoing phacoemulsification and intraocular lens (IOL) implantation were retrospectively enrolled. Participants were evaluated with Pentacam for ACD topography before and approximately four weeks after the surgery. The absolute changes of ACD (AACD) and the relative changes of ACD (RACD) topography were calculated, and three-dimensional topographic contours were plotted. The influence of age, gender, distance to corneal apex (DCA), temporal-nasal and superior-inferior on AACD and RACD was analyzed.

RESULTS

Both AACD and RACD were negatively correlated with the DCA (p < 0.001; p < 0.001) and positively correlated with the age at all DCA (p < 0.05 for all the analyses). Significantly greater AACD and RACD were observed in female subjects (p < 0.05, respectively, at all DCA). AACD was significantly larger in the temporal compared with the nasal region (p < 0.001) and at the superior compared with the inferior region (p < 0.001), but not RACD. Subgroup analysis indicated that the significant difference of the AACD between the temporal and nasal regions was manifested at the DCA of more than 6 mm (p < 0.001), and the difference between the superior and inferior regions was observed at 2 mm DCA for both AACD (p < 0.001) and RACD (p = 0.001).

CONCLUSIONS

We depicted the topographic changes of ACD following cataract surgery and found that it was significantly influenced by age, gender, DCA and quadrant location. The research provided the basis for including postoperative ACD topography prediction before cataract surgery in the future.

Intraocular lens power calculation in virgin eyes: Accuracy of the Barrett Universal II formula and a Ray tracing software

PURPOSE

To compare the accuracy of Sirius ray tracing software with the Barrett Universal II formula for intraocular lens power prediction in virgin eyes.

METHODS

Retrospective case series including 86 eyes that have undergone uneventful cataract surgery with SN60WF implantation. The median absolute error, mean prediction error, variance, and the percentage of eyes within ± 0.25 D, ± 0.50 D, ± 0.75 D, and ± 1.00 D of the prediction error in refraction were calculated. The correlation of prediction error with different baseline parameters was investigated.

RESULTS

No differences were found between the median absolute error of the Barrett Universal II formula (0.226 D) and the ray tracing software with different intraocular lens centerings; apex (0.331 D), limbus (0.345 D), and pupil (0.342 D) (p = 0.084). The variance, from lowest to highest, was the Barrett Universal II (0.144 D²), ray tracing-limbus (0.285 D²), ray tracing-pupil (0.285 D²), and ray tracing-apex (0.287 D²) (p = 0.027). The Barrett Universal II formula showed a higher percentage of eyes within ± 0.25 D (56.98%), ± 0.50 D (82.56%), and ± 0.75 D (93.02%) compared to ray tracing software (p < 0.01). A significant correlation between the prediction error of the Barrett Universal II formula and corneal diameter (r = 0.322, p = 0.002) and pupil diameter (r = 0.230, p = 0.033) was found. Also, a positive correlation between the prediction error of Sirius ray tracing and axial length (p < 0.001) and pupil diameter (p = 0.01) was found.

CONCLUSION

There is a trend of the Barrett Universal II formula to be more accurate than Sirius ray tracing software for intraocular lens power calculation in virgin eyes. This should be confirmed in future prospective comparative studies.

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.

Predictability of Refractive Outcome of a Small-Aperture Intraocular Lens in Eyes With Irregular Corneal Astigmatism

PURPOSE

To compare different new-generation biometric formulas and ray-tracing for small-aperture intraocular lens (IOL) (IC-8; Acufocus, Inc) implantation in patients undergoing cataract and refractive lens exchange surgery with highly irregular corneas.

METHODS

This monocenter study included 17 eyes of 17 patients with highly irregular corneas of different genesis. Biometric and topographic corneal data were assessed using the IOLMaster 700 (Carl Zeiss Meditec) and Pentacam (Oculus Optkigeräte GmbH). Prediction and absolute error were compared after 3 months based on manifest refraction. Furthermore, change of total corneal refractive power in different corneal pathologies was also evaluated. For IOL power calculation, three fourth-generation IOL formulas were compared (Haigis, SRK-T, and Barrett Universal II). The dataset was then checked against ray-tracing and analyzed to improve prediction error in these highly irregular corneas.

RESULTS

All patients showed an improvement in visual acuity postoperatively with a mean spherical equivalent of -1.22 ± 0.49 diopters (D). Overall comparison of the three formulas showed the Haigis formula to be superior in terms of the smallest deviation of predictive and absolute error. IOL calculations with ray-tracing were possible in all eyes, but showed inaccurate results with keratometric values of 48.00 D and greater.

CONCLUSIONS

The IC-8 IOL is well suited for patients with lens exchange in highly irregular corneas. The Haigis formula seemed to be the most accurate in the patient group. Ray-tracing confirmed the results of biometric formulas up to a keratometric value of 48.00 D and should be compared with standard biometric formulas to address corneal irregularities and to minimize refractive surprises after surgery. A comparison with ray-tracing in eyes with a keratometric value of greater than 48.00 D should not be considered due to the inaccurate results. [J Refract Surg. 2021;37(5):312-317.].

Evaluation and comparison of a novel Scheimpflug-based optical biometer with standard partial coherence interferometry for biometry and intraocular lens power calculation

In the present study, the axial length (AL), corneal curvature, anterior chamber depth (ACD) and white-to-white (WTW) distance were assessed using the Pentacam AXL (Oculus Optikgeraete GmbH), a novel Scheimpflug-based optical biometer with standard partial coherence interferometry (PCI). The Pentacam AXL and PCI biometer (IOLMaster 500; Carl Zeiss AG) were compared in terms of their intraocular lens (IOL) power calculations. The medical records of patients (eyes, n=190) who underwent cataract surgery were retrospectively reviewed. Biometry measurements involved the eyes of patients with cataract and were performed by the same examiner with the Pentacam AXL biometer and the IOLMaster 500 device. Following determination of the AL, mean keratometry (Km), ACD and WTW distance, the IOL power calculation was compared between the two devices using the Sanders, Retzlaff and Kraff theoretical (SRK/T) and Haigis formulas. The AL, Km and WTW values for the Pentacam AXL group were significantly lower compared with those of the IOLMaster 500 group. The difference was -0.02±0.04 mm, -0.20±0.28 D and -0.10±0.20 mm, respectively (P<0.001). The ACD for the Pentacam AXL group was higher compared with that of the IOLMaster 500 group with a difference of 0.02±0.13 mm (P=0.13). The IOL power calculated using the SRK/T and Haigis formulas exhibited significant differences between the two devices (t=11.48 and 10.97, respectively; P<0.001). In conclusion, the AL, ACD, WTW measurement and IOL power indicated optimal agreement and strong correlations between the two devices. However, constant optimization may be necessary for the novel biometer Pentacam AXL.

A Comparative Study of Total Corneal Power Using a Ray Tracing Method Obtained from 3 Different Scheimpflug Camera Devices

PURPOSE

We sought to assess the agreement of ray-traced corneal power values by 3 Scheimpflug tomographers tp construct the corresponding arithmetic adjustment factor in comparison with an automated keratometer (IOLMaster) and a conventional Placido-based topographer (Allegro Topolyzer).

DESIGN

Prospective reliability analysis.

METHODS

A total of 74 eyes from 74 healthy subjects who underwent corneal power measurements using Pentacam, Sirius, Galilei, IOLMaster, and Allegro Topolyzer were included. Ray-traced corneal power values, such as total corneal refractive power (TCRP), mean pupil power (MPP), total corneal power (TCP), mean keratometry (Km), and simulated keratometry (SimK) were recorded respectively and analyzed using one-way analysis of variance (ANOVA) and Bland-Altman plots.

RESULTS

Among the 3 ray-traced corneal power values, TCRP and MPP did not differ significantly (P = 0.81), whereas TCP presented a slightly significant larger value (P < 0.001). Compared to Km or SimK, corneal power measurements by the ray tracing method exhibited significantly lower values (P < 0.001). Bland-Altman plots disclosed that the 3 Scheimpflug tomographers showed similar 95% limits of agreement after arithmetic adjustment compared with Km (-0.40 to 0.40 D, -0.39 to 0.39 D, and -0.35 to 0.34 D) or SimK (-0.50 to 0.51 D, -0.43 to 0.42 D, and -0.46 to 0.46 D).

CONCLUSIONS

Ray-traced corneal power values obtained using 3 Scheimpflug tomographers with default diameter settings were similar, indicating that they could be used interchangeably in daily clinical practice. The 3 Scheimpflug tomographers were satisfactory in agreement after arithmetical adjustment compared with conventional automated keratometer or Placido-based topographer.

Update on Intraocular Lens Formulas and Calculations

Investigators, scientists, and physicians continue to develop new methods of intraocular lens (IOL) calculation to improve the refractive accuracy after cataract surgery. To gain more accurate prediction of IOL power, vergence lens formulas have incorporated additional biometric variables, such as anterior chamber depth, lens thickness, white-to-white measurement, and even age in some algorithms. Newer formulas diverge from their classic regression and vergence-based predecessors and increasingly utilize techniques such as exact ray-tracing data, more modern regression models, and artificial intelligence. This review provides an update on recent literature comparing the commonly used third- and fourth-generation IOL formulas with newer generation formulas. Refractive outcomes with newer formulas are increasingly more and more accurate, so it is important for ophthalmologists to be aware of the various options for choosing IOL power. Historically, refractive outcomes have been especially unpredictable in patients with unusual biometry, corneal ectasia, a history of refractive surgery, and in pediatric patients. Refractive outcomes in these patient populations are improving. Improved biometry technology is also allowing for improved refractive outcomes and surgery planning convenience with the availability of newer formulas on various biometry platforms. It is crucial for surgeons to understand and utilize the most accurate formulas for their patients to provide the highest quality of care.

Accuracy of Constant C for Ray Tracing: Assisted Intraocular Lens Power Calculation in Normal Ocular Axial Eyes

OBJECTIVE

To evaluate the effect of constant C for ray tracing-assisted intraocular lens (IOL) power calculation in patients with different refractive power, we compared the refractive outcome of the ray tracing method based on constant C and conventional IOL calculation.

METHODS

215 eyes which underwent phacoemulsification and IOL implantation were enrolled in the study. According to the average corneal power, patients were divided into 3 groups: high corneal power (K >45 D) group, medium corneal power (43 ≤ K ≤ 45 D) group, and low corneal power (K <43 D) group. The predicted sphero-equivalent refractive outcome for the IOL power implanted at surgery was calculated using the ray tracing method, SRK/T, and Haigis formulas.

RESULTS

On the basis of the corneal refractive power, there were 65 eyes of K >45 D (30.23%), 96 eyes of 43 ≤ K ≤ 45 D (44.65%), and 54 eyes of K <43 D (25.12%). In general, the ray tracing group had the smallest value of mean absolute error (MAE) and mean error, and the proportions of eyes with absolute error (AE) <0.50 and <0.75 D were significantly higher than those of the other 2 formulas (p = 0.010). In each group, the value of MAE was smallest in the ray tracing group; for the proportions of AEs <0.50 and <0.75 D, the values in the ray tracing group were higher than those in the SRK/T and Haigis groups. Especially in the high and low corneal refractive groups, the proportion of AE <0.25 D was also obviously higher, but only in the low corneal refractive power group, and the difference was statistically significant (p = 0.006).

CONCLUSIONS

Compared with the conventional formulas, C constant of the ray tracing-assisted IOL power calculation has more accuracy for the patients with different corneal refractive powers. Ray tracing could provide better guidance for IOL selection clinically.

Intrasession Repeatability of Biometric Measurements Obtained with a Low-Coherence Interferometry System in Pseudophakic Eyes

Purpose: To evaluate the intrasession repeatability of the biometric measurements obtained with a low-coherence reflectometry optical biometer in pseudophakic eyes implanted with two different types of intraocular lens (IOL).Methods: Prospective, single-center, comparative study including 69 eyes of 69 patients with ages ranging from 51 to 92 years. Previous uncomplicated cataract surgery had been performed in all patients 1 to 2 months before measurements, with implantation of the Acrysof SN60WF IOL in 35 eyes (35 patients, group 1) and the IOL Akreos MI60 in 34 eyes (34 patients, group 2). A complete postoperative ophthalmological examination was performed including three consecutive measurements with the "Aladdin" system from (Topcon, Japan). Intrasession repeatability of axial length (AXL), anterior chamber depth (ACD) and IOL thickness (IOLT) were assessed with the within-subject standard deviation (S_w), intraobserver precision (1.96 × S_w), coefficient of variation (CV) and intraclass correlation coefficient (ICC). Results: The S_w for AXL measurements was 0.03 and 0.05 mm in groups 1 and 2, respectively, with ICC of 1.000 and 0.999 (CV: 0.14% and 0.22%) (p ≤ 0.031). Concerning pseudophakic ACD, the S_w was 0.03 and 0.09 mm in groups 1 and 2, respectively, with ICC of 0.992 and 0.956 (CV: 0.55% and 1.75%) (p ≤ 0.021). The variability of IOLT measurements was high in both groups, with S_w of 0.12 and 0.29 mm for groups 1 and 2 (p = .008), respectively, and ICC of 0.065 and 0.770 (CV: 20.84% and 62.39%).Conclusions: The optical biometer "Aladdin" (Topcon, Japan) provides consistent measurements of AXL and ACD in pseudophakic eyes. However, there is a limitation in the consistency of IOLT measurements that should be investigated further.

New Approach for the Calculation of the Intraocular Lens Power Based on the Fictitious Corneal Refractive Index Estimation

Purpose

To identify the sources of error in predictability beyond the effective lens position and to develop two new thick lens equations.

Methods

Retrospective observational case series with 43 eyes. Information related to the actual lens position, corneal radii measured with specular reflection and Scheimpflug-based technologies, and the characteristics of the implanted lenses (radii and thickness) were used for obtaining the fictitious indexes that better predicted the postoperative spherical equivalent (SE) when the real effective lens position (ELP) was known. These fictitious indexes were used to develop two thick lens equations that were compared with the predictability of SRK/T and Barrett Universal II.

Results

The SE relative to the intended target was correlated to the difference between real ELP and the value estimated by SRK/T (ΔELP) (r = -0.47, p=0.002), but this only predicted 22% of variability in a linear regression model. The fictitious index for the specular reflection (n _k) and Scheimpflug-based devices (n _c) were significantly correlated with axial length. Including both indexes fitted to axial length in the prediction model with the ΔELP increased the r-square of the model up to 83% and 39%, respectively. Equations derived from these fictitious indexes reduced the mean SE in comparison to SRK/T and Barrett Universal II.

Conclusions

The predictability with the trifocal IOL evaluated is not explained by an error in the ELP. An adjustment fitting the fictitious index with the axial length improves the predictability without false estimations of the ELP.

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.

Comparison of OKULIX ray-tracing software with SRK-T and Hoffer-Q formula in intraocular lens power calculation

Purpose

To compare the performance of OKULIX ray-tracing software with SRK-T and Hoffer Q formula in intraocular lens (IOL) power calculation in patients presenting with cataract.

Methods

In this prospective study, 104 eyes of 104 patients with cataract who underwent phacoemulsification and IOL implantation were recruited. Three IOL brands were used and for all eyes, IOL power calculation was performed using SRK-T, Hoffer Q formula and also OKULIX ray-tracing software. For all patients, axial length and keratometry data was obtained with IOLMaster 500 device and IOL power was determined using Hoffer Q and SRK-T formula. The IOL powers were also calculated using the OKULIX ray-tracing software combined with CASIA AS-OCT and IOLMaster 500 device. Optically measured axial length of eyes were inserted to OKULIX software from IOLMaster 500 device, and anterior and posterior tomographic and corneal pachymetry data was imported from CASIA AS-OCT into the OKULIX.

The performance of each calculation methods was measured by subtracting the predicted postoperative refraction from the postoperative manifest refraction spherical equivalent (MRSE). For each of the 3 methods, the mean absolute prediction error was determined, too.

Results

The mean value absolute prediction error by OKULIX, SRK-T and Hoffer Q formulas, respectively, were 0.42 (±0.03), 0.36 (±0.02) and 0.37 (±0.02). The mean absolute prediction error by OKULIX had no significant difference between three IOL groups (P = 0.96), and it was confirmed that there was no meaningful statistically difference in mean absolute prediction error between the OKULIX, SRK-T and Hoffer Q formula. (P = 0.25). Also in each group of implanted IOLs, all three formulas worked with the same accuracy. The prediction error using OKULIX were within ±0.50 diopter in 63.5% of eyes and within ±1.00 diopter in 94.2% of eyes.

Conclusion

OKULIX ray-tracing IOL power measurements provides reliable and satisfactory postoperative results, which are comparable to other 3rd generation formulas of SRK-T and Hoffer Q.

Myopic Laser Corneal Refractive Surgery Reduces Interdevice Agreement in the Measurement of Anterior Corneal Curvature

OBJECTIVES

To investigate interdevice differences and agreement in the measurement of anterior corneal curvature obtained by different technologies after laser corneal refractive surgery.

METHODS

The prospective study comprised 109 eyes of 109 consecutive patients who had undergone laser-assisted in situ keratomileusis (LASIK). Preoperative and postoperative corneal parameters were measured by Scheimpflug imaging (Pentacam), Placido-slit-scanning (Orbscan) and auto-keratometry (IOLMaster). Preoperative and postoperative anterior corneal curvatures (K readings) were compared between devices. Interdevice agreement was evaluated by Bland-Altman analysis.

RESULTS

Preoperatively, the difference of K reading for Pentacam-IOLMaster (0.04±0.20 D) was not statistically significant (P=0.059). The differences between Pentacam-Orbscan and Orbscan-IOLMaster were 0.20±0.34 D (P<0.001) and -0.17±0.29 D (P<0.001), respectively. After surgery, no difference was found for Pentacam-Orbscan (-0.05±0.38, P=0.136). The differences between Pentacam-IOLMaster and Orbscan-IOLMaster were 0.13±0.29 D (P<0.001) and 0.19±0.34 D (P<0.001). Preoperative interdevice agreement (95% limit of agreement [LOA]) between Pentacam and Orbscan, Pentacam and IOLMaster, and Orbscan and IOLMaster were 1.31 D, 0.79 D and 1.14 D, respectively. The 95% LOAs decreased to 1.47 D, 1.14 D, and 1.34 D after refractive surgery.

CONCLUSION

Corneal refractive surgery changed the preoperative and postoperative interdevice differences in corneal curvature measurements and reduced interdevice agreement, indicating that the devices are not interchangeable.

Prediction of Postoperative Intraocular Lens Position with Angle-to-Angle Depth Using Anterior Segment Optical Coherence Tomography

PURPOSE

To evaluate the accuracy of a new formula for predicting postoperative anterior chamber depth (ACD) with preoperative angle-to-angle (ATA) depth using anterior segment (AS) optical coherence tomography (OCT) and to compare it with established methods.

DESIGN

Retrospective consecutive case series.

PARTICIPANTS

Three hundred four eyes (276 patients) implanted with acrylic intraocular lenses (IOLs) were divided randomly into a training set (152 eyes) and a validation set (152 eyes).

METHODS

Based on the training set data, the postoperative ACD measured 1 month after surgery was analyzed via multiple linear regression analysis with 5 preoperatively measured variables: ATA depth, ATA width, preoperative ACD measured with AS OCT, axial length (AL), and corneal power. A new regression formula for predicting postoperative ACD was developed using the results of the stepwise analysis. In the validation set data, the coefficients of determination (R²) between the measured postoperative ACD and the predicted postoperative ACD obtained using the new formula were compared with those obtained using the Sanders-Retzlaff-Kraff theoretic (SRK/T) and Haigis formulas. The absolute prediction errors were compared with each formula.

MAIN OUTCOME MEASURES

Postoperative ACD, median absolute prediction error of postoperative ACD, and ocular biometric parameters.

RESULTS

In the training set, ATA depth yielded the highest standard partial regression coefficient value, indicating that ATA depth is the most effective parameter for predicting postoperative ACD. The new regression formula was developed with 3 variables; ATA depth, preoperative ACD, and AL. In the validation set, the postoperative ACDs of the new formula, the SRK/T formula, and Haigis formula were predicted with R² of 0.71, 0.36, and 0.55, respectively, and the medians of the absolute prediction errors were 0.10 mm, 0.65 mm, and 0.30 mm, respectively. The absolute prediction error with the new formula was significantly smaller than those obtained with the SRK/T and Haigis formulas (P < 0.0001).

CONCLUSIONS

The new formula with 3 preoperative parameters-ATA depth, preoperative ACD, and AL-predicted postoperative ACD more accurately than the SRK/T and Haigis formulas. It may be possible to improve the accuracy of IOL power calculation using an improved postoperative ACD prediction with the ATA depth measured by AS OCT.

Mathematical Method for Analysis of the Refractive Outcome after Toric Intraocular Lens Implantation

PURPOSE

We aimed to develop a self-designed software programmed with a mathematical method that analyzes the refractive outcome after toric intraocular lens (IOL) implantation, taking the axis misalignment of the toric IOL into consideration.

METHODS

A mathematical method that can analyze the refractive outcome after toric IOL implantation was devised. Compared with the conventional method, which performs the analysis based on precise alignment of the IOL, optional meridian orientations of the toric IOL were taken into account in this method. Self-designed computer software was developed using the mathematical method.

RESULTS

Relatively high accordance was achieved between the mathematical analysis and the actual postoperative outcome. The mean predicted spherical power was 0.37 ± 0.74 dpt, and the mean measured spherical power was 0.37 ± 0.71 dpt (paired t test, p = 0.98). The mean predicted cylindrical power was -1.35 ± 0.86 dpt, and the mean measured cylindrical power was -1.42 ± 0.85 dpt (p = 0.27). The mean predicted change in the astigmatic axis was 33.7 ± 11.8°, and the mean measured parameter was 32.5 ± 15.4° (p = 0.49).

CONCLUSIONS

The advantage of the present mathematical method is that the postoperative refractive outcome can be analyzed under IOL misalignment.

Intraocular lens power calculation by ray-tracing after myopic excimer laser surgery

PURPOSE

To investigate the refractive outcomes of intraocular lens (IOL) power calculation by ray-tracing after myopic excimer laser surgery.

DESIGN

Prospective, interventional case series.

METHODS

setting: Multicenter study. participants: Twenty-one eyes of 21 patients undergoing phacoemulsification and IOL implantation after myopic laser in situ keratomileusis or photorefractive keratectomy were enrolled. intervention: IOL power calculation was performed using internal software of a Scheimpflug camera combined with a Placido disc corneal topographer (Sirius; CSO). Exact ray-tracing was carried out after the axial length (measured either by immersion ultrasound biometry or partial coherence interferometry), target refraction, and pupil size had been entered. main outcome measures: Median absolute error, mean absolute error, and mean arithmetic error in refraction prediction, that is, the difference between the expected refraction (as calculated by the software) and the actual refraction 1 month after surgery.

RESULTS

The mean postoperative refraction was -0.43 ± 1.08 diopters (D), with a range between -1.28 and 0.85 D. The mean arithmetic error was -0.13 ± 0.49 D. The median and mean absolute errors were +0.25 D and 0.36 D, respectively. Also, 71.4% of the eyes were within ± 0.50 D of the predicted refraction, 85.7% were within ± 1.00 D, and 100% within ± 1.50 D.

CONCLUSIONS

Ray-tracing can calculate IOL power accurately in eyes with prior myopic laser in situ keratomileusis and photorefractive keratectomy, with no need for preoperative data.

Challenges and approaches in modern biometry and IOL calculation

The introduction of new intraocular lenses (IOLs), industry marketing to the public and patient expectations has warranted increased accuracy of IOL power calculations. Toric IOLs, multifocal IOLs, aspheric IOLs, phakic lenses, accommodative lenses, cases of refractive lens exchange and eyes that have undergone previous refractive surgery all require improved clinical measurements and IOL prediction formulas. Hence, measurement techniques and IOL calculation formulas are essential factors that affect the refractive outcome. Measurement with ultrasound has been the historic standard for measurement of ocular parameters for IOL calculation. However the introduction of optical biometry using partial coherence interferometry (PCI) has steadily established itself as the new standard. Additionally, modern optical instruments such as Scheimpflug cameras and optical coherence tomographers are being used to determine corneal power that was normally the purview of manual keratometry and topography. A number of methods are available to determine the IOL power including the empirical, analytical, numerical or combined methods. Ray tracing techniques or paraxial approximation by matrix methods or classical analytical 'IOL formulas' are actively used in for the prediction of IOL power. There is no universal formula for all cases - phakic and pseudophakic cases require different approaches, as do short eyes, long eyes, astigmatic eyes or post-refractive surgery eyes. Invariably, IOLs are characterized by different methods and lens constants, which require individual optimization. This review describes the current methods for biometry and IOL calculation.

Minimizing the IOL power error induced by keratometric power

PURPOSE

To evaluate theoretically in normal eyes the influence on IOL power (PIOL) calculation of the use of a keratometric index (nk) and to analyze and validate preliminarily the use of an adjusted keratometric index (nkadj) in the IOL power calculation (PIOLadj).

METHODS

A model of variable keratometric index (nkadj) for corneal power calculation (Pc) was used for IOL power calculation (named PIOLadj). Theoretical differences (ΔPIOL) between the new proposed formula (PIOLadj) and which is obtained through Gaussian optics ((Equation is included in full-text article.)) were determined using Gullstrand and Le Grand eye models. The proposed new formula for IOL power calculation (PIOLadj) was prevalidated clinically in 81 eyes of 81 candidates for corneal refractive surgery and compared with Haigis, 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 was used. If nkadj was used for Pc calculation, a maximal calculated error in ΔPIOL of ±0.5 diopters at corneal vertex in most cases was observed independently from the eye model, r1c, and the desired postoperative refraction. The use of nkadj in IOL power calculation (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 may explain some IOL power overestimations with conventional formulas. These inaccuracies can be minimized by using the new PIOLadj based on the algorithm of nkadj.

Refractive changes after removal of anterior IOLs in temporary piggyback IOL implantation for congenital cataracts

Purpose

To assess the refractive change and prediction error after temporary intraocular lens (IOL) removal in temporary polypseudophakic eyes using IOL power calculation formulas and Gills' formula.

Methods

Four consecutive patients (7 eyes) who underwent temporary IOL explantation were enrolled. Postoperative refractions calculated using IOL power calculation formulas (SRK-II, SRK-T, Hoffer-Q, Holladay, and the modified Gills' formula for residual myopia and residual hyperopia) were compared to the manifest spherical equivalents checked at 1 month postoperatively.

Results

The mean ages of temporary piggyback IOL implantation and IOL removal were 6.71 ± 3.68 months (range, 3 to 12 months) and 51.14 ± 18.38 months (range, 29 to 74 months), respectively. The average refractive error was -13.11 ± 3.10 diopters (D) just before IOL removal, and improved to -1.99 ± 1.04 D after surgery. SRK-T showed the best prediction error of 1.17 ± 1.00 D. The modified Gills' formula for myopia yielded a relatively good result of 1.47 ± 1.27 D, with only the variable being axial length.

Conclusions

Formulas to predict refractive change after temporary IOL removal in pediatric polypseudophakia were not as accurate as those used for single IOL implantation in adult eyes. Nonetheless, this study will be helpful in predicting postoperative refraction after temporary IOL removal.

Clinically relevant biometry

PURPOSE OF REVIEW

Obtaining precise postoperative target refraction is of utmost importance in today's modern cataract and refractive surgery. Given the growing number of patients undergoing premium intraocular lens (IOL) implantations, patient expectation continues to rise. In order to meet heightened patient expectations, it is crucial to pay utmost attention to patient selection, accurate keratometry and biometry readings, as well as to the application of correct IOL power formula with optimized lens constants. This article reviews recent advances in the field of clinical biometry and IOL power calculations.

RECENT FINDINGS

Recently developed low-coherence reflectometry optical biometry is comparable to older ultrasonic biometric and keratometric techniques. In addition, the new IOLMaster software upgrade has improved reproducibility and enhanced signal acquisition. Further, the modern lens power formulas currently determine the effective lens position and the shape of the intraocular lens power prediction curve more accurately.

SUMMARY

In order to reach target refraction, precise biometric measurements are imperative. Understanding the strengths and limitations of the currently available biometry devices allows prevention of high variability and inaccuracy, ultimately determining the refractive outcomes.

Estimation of effective lens position using a method independent of preoperative keratometry readings

PURPOSE

To evaluate the validity of a keratometry (K)-independent method of estimating effective lens position (ELP) before phacoemulsification cataract surgery.

SETTING

Institute of Eye Surgery, Whitfield Clinic, Waterford, Ireland.

DESIGN

Evaluation of diagnostic test or technology.

METHODS

The anterior chamber diameter and corneal height in eyes scheduled for cataract surgery were measured with a rotating Scheimpflug camera. Corneal height and anterior chamber diameter were used to estimate the ELP in a K-independent method (using the SRK/T [ELP(rs)] and Holladay 1 [ELP(rh)] formulas).

RESULTS

The mean ELP was calculated using the traditional (mean ELP(s) 5.59 mm ± 0.52 mm [SD]; mean ELP(h) 5.63 ± 0.42 mm) and K-independent (mean ELP(rs) 5.55 ± 0.42 mm; mean ELP(rh) ± SD 5.60 ± 0.36 mm) methods. Agreement between ELP(s) and ELP(rs) and between ELP(h) and ELP(rh) were represented by Bland-Altman plots, with mean differences (± 1.96 SD) of 0.06 ± 0.65 mm (range -0.59 to +0.71 mm; P=.08) in association with ELP(rs) and -0.04 ± 0.39 mm (range -0.43 to +0.35 mm; P=.08) in association with ELP(rh). The mean absolute error for ELP(s) versus ELP(rs) estimation and for ELP(h) versus ELP(rh) estimation was 0.242 ± 0.222 mm (range 0.001 to 1.272 mm) and 0.152 ± 0.137 mm (range 0.001 to 0.814 mm), respectively.

CONCLUSION

This study confirms that the K-independent ELP estimation method is comparable to traditional K-dependent methods and may be useful in post-refractive surgery patients.

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.