**4. Discussion**

In this first study of its kind, ray tracing was compared to six established IOL power calculation formulae available in the ASCRS online calculator in post-SMILE eyes undergoing cataract surgery. In our analysis, the ray tracing method showed the most accurate IOL power calculation with a ME of 0.18 ± 0.48 D and 82% of eyes being within ±0.50 D and 91% of eyes within ±1.00 D.

Our findings endorse previous, purely theoretical studies (with no actually performed cataract surgery) in eyes after SMILE. Lazaridis et al. [31] used a theoretical model including virtual IOL implantation to evaluate prediction errors between ray tracing and four conventional IOL power calculation formulae. In their analysis, ray tracing yielded

the smallest ME of −0.06 ± 0.40 D and a PE of ±0.5 D in 81.9% of eyes, which is highly coherent with our findings after actual cataract surgery. Moreover, the lowest ME variance (as an indicator of the consistency of an IOL power calculation method), was achieved by ray tracing in both studies. Interestingly, Lazaridis et al. [31] reported better results for the Haigis-L formula (ME of −0.39 ± 0.62 D and 53.4% of eyes with PEs within ± 0.5 D) as compared to our "real world" analysis, where Haigis-L yielded the worst ±0.50 D accuracy of only 9% of all investigated formulae and a ME of −0.81 ± 1.28 D.

In the second previous theoretical study, our group [32] compared the predicted postoperative residual refractive error of the IOL determined by ray tracing with the residual refraction of the same IOL as predicted by a range of conventional IOL power calculation formulae available in the ASCRS post-keratorefractive surgery IOL power calculator. The Masket formula showed the smallest ME (−0.36 ± 0.32 D) and yielded the largest percentage of eyes within ±0.50 D (70%) in reference to the prediction of ray tracing, which was defined as the gold standard method for the purpose of that study. Non-inferior MEs and ±0.50 D accuracies were achieved by the Barrett True K, Barrett True K no history and the Potvin–Hill formula [32].

In the third purely theoretical study, Zhu et al. [33] used the concept of equivalent IOL power differences (EILD) as an indicator for the "stability" of four conventional IOL calculation formulae in post-SMILE eyes. The Barrett True-K and Haigis formulae showed similar stability in eyes with axial lengths between 24 and 26 mm (85.19 vs. 88.89% for a margin of error within 0.5 D; 100 vs. 100% for a margin of error within 1.0 D). In eyes with an axial length of >26 mm, the Barrett True-K formula was the most "stable" formula with respective percentages of 81.49 and 92.59% for margin errors within 0.5 and 1.0 D, respectively.

These compiled theoretical data are confirmed by the present "real world" study, in which the Potvin–Hill and Masket formula showed the best PEs of all conventional formulae. The Potvin–Hill formula yielded the best ME in the present study (ME −0.06 ± 0.86 D and 45% of eyes within ±0.50 D) closely followed by ray tracing (ME 0.18 ± 0.48 D and 82% of eyes within ±0.50 D) and the Masket formula (ME −0.25 ± 0.98 D and 36% of eyes within ±0.50 D). Moreover, the accuracy of the Barrett True K formula was non-inferior when preoperative refractive data were not entered but estimated with the Barrett True K no history formula. By using adjusted keratometry readings, the Shammas formula showed the greatest overestimation of IOL power of all the investigated formulae. Highly congruen<sup>t</sup> findings were also made in the previous theoretical study of our group [32].

As a purely physical approach based on Snell's law, ray tracing offers many advantages over conventional IOL power calculation formulae in post-keratorefractive surgery eyes. Unlike empirically optimized regression formulae, ray tracing does not rely on any fictional keratometric index or "fudge factors" but utilizes measurements of both the anterior and posterior corneal radii to determine total corneal power. Hence, the need for any empirical optimization, clinical history or preoperative refractive data is obsolete. The latter can be a pivotal advantage in eyes with index myopia due to cataract formation and unknown post-keratorefractive surgery refraction.

These theoretical methodological advantages of the ray tracing principle have been previously proven in different samples of post-Excimer ablation eyes undergoing cataract surgery with IOL implantation [15,16,18]. For instance, Savini et al. [16] yielded 71.4% of 21 post myopic Excimer ablation eyes within ± 0.50 D and 85.7% within ± 1.00 D of the predicted refraction utilizing ray tracing. These results seem comparable to our findings in post-SMILE eyes. Saiki et al. [18] reported slightly subpar outcomes for ray tracing in their sample of 24 post myopic LASIK eyes with ±0.50 D and ±1.00 accuracies of 42 and 75%, respectively. Furthermore, the arithmetic prediction error of ray tracing of 0.63 ± 0.85 D indicated an underestimation of IOL power entailing unpleasant hyperopic residual refractive errors after cataract surgery. In our study, we also observed a minimal hyperopic ME for ray tracing after SMILE, even though it was more than three times smaller (0.18 ± 0.48 D).

First recommendations for clinicians encountering post myopic SMILE patients requiring cataract surgery can be formulated based on the findings of the present study. Physical ray tracing should be employed for IOL power calculation and surgeons should be aware of a slight hyperopic ME of less than +0.25 D when selecting the appropriate IOL power, which is only available in 0.50 D steps for most contemporary IOL models. Ray tracing calculations should ideally be interpreted in conjunction with the Potvin-Hill and Masket formula, which should provide comparable results.

Limitations to this study might be found. First and foremost, the study is limited by its relatively small sample size. Nevertheless, the present work represents the first cohort of post-SMILE patients undergoing cataract surgery and may provide clinicians important guidance for IOL power selection. The paucity of post-SMILE cataract cases in Austria and Germany, where the SMILE technique was developed and first introduced more than a decade ago, also prompted us to include both eyes of some patients into the analysis. For the same reason and due to the multicenter approach, the authors felt inclined to accept multiple IOL types, surgeons and surgical protocols. A further limitation of the present study is that not all formulae currently available in the ASCRS calculator could be included as no Atlas-, Galilei- or OCT-based corneal measurements were available.

In summary, this study comprises the first cohort of post myopic SMILE eyes undergoing cataract surgery and IOL implantation. In post-SMILE eyes, ray tracing facilitated IOL power calculations with a superior accuracy and should be the first choice over conventional IOL power calculation formulae that are empirically optimized for post-Excimer ablation eyes.

**Author Contributions:** Conceptualization, R.L. and N.L.; methodology, R.L. and N.L.; validation, R.L., W.S., R.W., M.B., T.C.K., S.G.P., M.D. and N.L.; formal analysis, R.L., W.S., R.W., M.B., T.C.K., S.G.P., M.D. and N.L.; investigation, R.L., W.S., R.W., M.B., T.C.K., S.G.P., M.D. and N.L.; resources, R.L., W.S., R.W., M.B., T.C.K., S.G.P., M.D. and N.L.; data curation, R.L., W.S., R.W., M.B., T.C.K., S.G.P., M.D. and N.L.; writing—original draft preparation, R.L.; writing—review and editing, R.L. and N.L.; visualization, R.L.; supervision, N.L.; project administration, N.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** The study was conducted in accordance with the Declaration of Helsinki and approved by the local institutional review board of the Ludwig Maximilian University for studies involving humans.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.
