IOL Power Calculation by Ray Tracing in Eyes with Previous Radial Keratotomy

1. Introduction

Intraocular lens (IOL) power calculation in eyes with previous radial keratotomy (RK) is still a major challenge for cataract surgeons. In addition to the well-known sources of errors typical of eyes that have undergone excimer laser refractive surgery (i.e., the instrument error, the index of refraction error and the formula error) [1], other important factors reduce the accuracy of IOL power calculation after RK. First, the optical zone is often small, irregular and decentered; this makes it difficult to accurately measure the anterior corneal radius, due to the fact that keratometry (K) mires are projected onto the area representing the inflection point between the incised cornea and the flattened central region. Second, the irregularity of the optical zone can generate higher-order aberrations (HOAs) of the cornea, whose effect can hardly be taken into account by paraxial IOL formulas. Third, corneal flattening of both corneal surfaces can be much higher [2], so that some formulas cannot be used (the Barrett True-K, EVO and PEARL-DGS, for example, do not allow users to enter keratometry (K) values lower than 30 diopters (D)). Fourth, RK encompasses cases with different numbers of incisions leading to different degrees of flattening, which makes it hard to develop predictive models. Finally, eyes with prior RK are relatively rare compared to those that have undergone myopic LASIK or PRK and are prone to early hyperopic shift and diurnal variations [3].

For these reasons, the results of IOL power calculation after RK are poor compared to both calculations in virgin eyes and in eyes with previous excimer laser refractive surgery. Most studies have reported that, even with the best formulas, only about 50% of eyes show a prediction error (PE) within ±0.50 D [4,5,6,7,8,9], a percentage remarkably lower than those observed in unoperated as well as in post-LASIK eyes. The only exception is a paper by Turnbull et al., who found that more than 70% of eyes could achieve a PE within ±0.50 D with the Barrett True-K [10].

Exact ray tracing offers a potentially useful solution to calculate the IOL power in post-RK eyes, because it considers both corneal surfaces (and, therefore, is not affected by the keratometric index error), takes HOAs into account, can be adjusted according to the pupil size and does not need historical data. We previously found that the ray-tracing software available on the anterior segment optical coherence tomographer (AS-OCT) MS-39 (CSO) leads to accurate refractive outcomes after myopic LASIK [11]. In this study we aimed to assess its performance in eyes with previous RK.

2. Materials and Methods

This was a retrospective analysis of consecutive patients that underwent phacoemulsification and IOL implantation after previous RK at two institutions, Studio Oculistico d’Azeglio (Bologna, Italy) and Centro Oculistico Bresciano (Brescia, Italy), between 2019 and 2024. Deidentified data were transferred to and analyzed at IRCCS Bietti Foundation (Rome, Italy). The study was conducted in accordance with the Declaration of Helsinki and approved by the Comitato Etico Centrale IRCCS Lazio (protocol code CEC/157/15, date of approval March 31st, 2015). Informed consent was obtained from all subjects involved in the study. Exclusion criteria were any intraoperative or postoperative complication, postoperative corrected distance visual acuity equal to or lower than 20/40 and implantation of a pinhole IOL (as this may mask postoperative refractive errors). Subjective refraction was performed at 4 to 6 weeks postoperatively, as previously done by other authors in post-RK eyes [10], at a distance of 4 m.

2.1. Preoperative Measurements and Surgery

The same procedure as previously described in our study on post-LASIK eyes was followed [11]. Briefly, patients underwent anterior segment imaging by the AS-OCT combined with the MS-39 (software version 4.1.4), whose high repeatability of measurements has been previously demonstrated [12]. Only measurements with a good quality, as assessed by the instrument, were used. Optical biometry was performed with the IOLMaster 700 (software version 1.90.38.02, Zeiss). Cataract surgery was performed by 3 experienced surgeons using a temporal clear corneal incision, phacoemulsification and IOL implantation in the bag. In no case was a scleral approach deemed necessary in our series to reduce the risk of RK incisions opening. No intraoperative or postoperative complications occurred.

2.2. Intraocular Lens Power Calculation

The IOL power was calculated using the MS-39 software, which requires a few manual inputs: the AL, the target refraction, the pupil diameter and the IOL A-constant. As regards the pupil diameter, since 3 diameters are available (2.0, 2.5 and 3.0 mm) the value closest to the one measured by the MS-39 was selected. The A-constant was retrieved from the User Group for Laser Interferometry Biometry (ULIB, www.ocusoft.de), or IOLCon websites (https://iolcon.org, both accessed on November 14th, 2025). The A-constant is needed to refine the prediction of the IOL position through a proprietary method. Based on our previous study [11], AL was adjusted according to the polynomial equation described by Holladay for the Holladay 2 formula in the errata accompanying the letter by Wang et al. [13]. This adjustment was carried out using Holladay IOL Consultant Software & Surgical Outcomes Assessment (version 2022.0910, Bellaire, TX). The ray tracing software is based on Snell’s law and specific refractive indices for each optical element. The method used to calculate the IOL power has been previously described in detail [11].

For comparative purposes, the IOL power was also calculated with the post-RK version of the Barrett True-K formula (www.apacrs.org), the EVO (www.evoiolcalculator.com) and PEARL-DGS (www.iolsolver.com, all accessed on November 15th, 2025) [14]. Other new generation formulas, like the Cooke K6, Hoffer QST and Kane could not be evaluated, as they do not offer a post-RK version. The Barrett True-K and EVO were used with both predicted and measured posterior corneal astigmatism (i.e., posterior keratometry (PK)). The IOLMaster 700 measurements, including posterior keratometry, were used in this case and the constants available on the formula websites were adopted. In addition, Total Keratometry values from the IOLMaster 700 were entered into the standard Haigis formula [15], since this combination has been previously found to be accurate in post-myopic LASIK eyes [5].

The PE was calculated as the difference between the measured and the predicted postoperative refractive spherical equivalent for the power of the implanted IOL, so that a negative PE was correlated to a more myopic result than planned and a positive PE to a more hyperopic result. The mean PE, its standard deviation (SD), the median absolute error (MedAE), the mean absolute error (MAE) and the percentage of eyes with a PE within ±0.25 diopters (D), ±0.50 D, ±0.75 and ±1.00 were calculated.

2.3. Statistics

MedCalc (software version 12.3.0.0, Ostend, Belgium) was used for statistical analysis. Correlation was used to evaluate the relationship between the PE and the preoperatively measured variables. While the primary aim of this study was to evaluate the accuracy of ray tracing for IOL power calculation after RK, a paired comparison was performed with the Barrett-True K, EVO, PEARL-DGS and Haigis-TK for the subset of eyes whose IOL power could be calculated with these methods (i.e., those with an average K > 30 D). For this purpose, Eyetemis was used (www.eyetemis.com, accessed on November 14th, 2025) [16].

Given a type I error of 0.05 and a power of 0.80, a mean difference of the PE of 0.50 D and a mean standard deviation of the difference of 0.70 D, PS Power and Sample Size (https://cqsclinical.app.vumc.org/ps/, accessed on November 14th, 2025) calculated a minimum sample size for paired comparisons of 18 eyes. A p-value <0.05 was considered statistically significant.

3. Results

Twenty-eight eyes of 27 patients with previous RK were identified. Four eyes of 3 patients with a pinhole IOL were excluded, thus leaving a dataset of 24 eyes of 24 patients (13 males (54%), mean age: 61.2 ±8.2 years, mean number of RK incisions: 10.4 ±3.1). Eight different IOL models were implanted and the most commonly used were the Tecnis Ehyance (Johnson & Johnson, n = 9), the toric AcrySof SN6ATx (Alcon, n = 5) and the non-toric AcrySof SN60WF (n = 4). The mean biometric measurements are reported in Table 1. On average, standard keratometry underestimated Total Keratometry by 0.16 ±0.20 D. In no case was the difference higher than 0.50 D and in 16 eyes (64%) the difference was lower than 0.25 D.

Based on ray tracing, the mean PE was -0.03 ±0.65 D (range: -1.30 to +1.64 D). The MedAE was 0.48 D and the MAE was 0.52 D. The percentage of eyes with a PE within ±0.25, ±0.50, ±0.75 and ±1.00 D was 29.17%, 62.50%, 87.50% and 91.67%, respectively. All cases had a PE within ±2.00 D. When AL was <26 mm (n = 12), the percentage of eyes with a PE within ±0.50 D was 75%, compared to 50% when it was >26 mm (n = 12). The PE was not correlated to AL, K, ACD, LT or scotopic pupil diameter.

The Barrett True-K, EVO and PEARL-DGS formulas could not be used in 4 eyes whose average K was <30 D. In the remaining 20 eyes, the results (Table 2) were similar to those obtained with ray tracing and Eyetemis did not detect any statistically significant difference for trueness, precision or accuracy or for the percentage of eyes within each threshold.

4. Discussion

Our study confirms that IOL power calculation after RK is still a challenging task, since the refractive outcomes are usually worse than those achieved not only in virgin eyes, but also in eyes with previous myopic PRK or LASIK. In fact, in the event of previous myopic laser vision correction, most formulas lead to a PE within ±0.50 D in a percentage of eyes that ranges between 60 and 70% [17], but with the best formulas the percentage can be higher than 70% [11,18,19]. In our dataset of post-RK eyes, the highest percentage was obtained with ray tracing, which reached 62.5% across the whole sample (n = 24) and 65% in the subset (n = 20) used for formula comparison (Barrett True-K, EVO, Haigis-TK and PEARL-DGS). With the remaining formulas, only 50-60% of eyes resulted in a PE within ±0.50 D, with the exception of the Haigis-TK (65%). It should be highlighted that in post-myopic LASIK eyes, the same ray tracing technology enabled us to calculate a PE within ±0.50 D in a higher (77%) percentage of eyes [11]. Due to the retrospective nature of the study and the lack of postoperative AS-OCT measurements, we cannot assess whether the lower accuracy in post-RK eyes depends on an incorrect prediction of the postoperative IOL position, a postoperative change of corneal power or other factors.

In addition to the highest percentage of eyes with a PE within ±0.50 D, ray tracing offered a mean PE close to zero, thus showing that the combination of optimized constants derived from ULIB or IOLCon datasets and AL optimization previously adopted by our group in post-LASIK eyes is also a good approach in post-RK eyes [11]. On the other hand, the refractive outcomes of the Barrett True-K, EVO, Haigis-TK and PEARL-DGS did not show any statistically significant differences compared to ray tracing. All formulas had a PE <0.30 D and absolute PEs slightly higher or slightly lower than obtained with ray tracing. As a consequence, none of these methods should be discarded a priori when calculating the IOL power in eyes with previous RK, unless the average K is lower than 30 D. Another interesting observation regards PK: contrary to what has been observed in post-LASIK eyes [11], PK does not seem to significantly improve the accuracy of the Barrett True-K and EVO formulas.

With respect to previously published studies, our data suggest that ray tracing provides us with potentially accurate refractive outcomes. Voytsekhivskyy did not yield percentages of eyes with a PE within ±0.50 D higher than 53% [4]. None of the formulas investigated by other authors reached the value of 50% [6,7,9], except for the Barrett True-K and the ASCRS calculator average power, which obtained a PE within ±0.50 D in 56% of cases in a study by Shetty et al. [8]. However, the real exception is the paper by Turnbull et al., who found that more than 70% had a PE within ±0.50 D with the Barrett True-K [10]. This difference may depend on the lower AL of their sample, whose mean was 24.98 ±0.87 mm as compared to an average of 27.33 ± 2.94 mm in our dataset [10]. Although we did not detect a statistically significant relationship between the PE and AL, our subgroup analysis revealed that eyes with a shorter AL (<26 mm) can reach a higher percentage (75%) than eyes with a longer AL (50%). We can therefore argue that IOL power calculation after RK is more accurate in shorter eyes and that studies with a lower mean AL are likely to display better outcomes.

This study has some limitations. First, the sample size is small and for this reason we aim to collect a larger sample. However, since—apart from a single case report—[20] there are no published papers about IOL power calculation by ray tracing in post-RK eyes, we feel that our results are important for both ophthalmologists and patients, who can at least have preliminary information on the accuracy of this method. Second, no postoperative scans were available for the majority of eyes, so that we could not assess the influence of corneal power changes and error in IOL position predictions.

5. Conclusions

Our data show that ray tracing is a promising option to calculate the IOL power in eyes with previous RK, although the refractive accuracy is still lower than in eyes with previous laser vision correction. Paraxial formulas provide similar outcomes and should be considered in these patients.