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.
Intraocular lens (IOL) power calculation after corneal refractive surgery continues to be challenging. More than 30 methods have been proposed as possible solutions to this problem. Some of them have been shown to lead to good refractive outcomes, similar to those achieved in unoperated eyes. However, such calculations require much more time than those carried out in virgin eyes and still depend on the expertise of the ophthalmologist who has to choose the IOL power. The difficulties derive from several factors, such as the necessity of selecting the result from one of the several formulas presently available, which often produce a wide range of IOL powers; the need to enter all the formulae in calculation spreadsheets, which may be subject to errors; the risk of measuring a wrong corneal radius if the optical zone is small, because the instrument readings may be taken outside the treated area (so-called radius error ); the lack of methods to calculate corneal power reliably when the optic zone is decentered or when multiple treatments have been carried out (eg, excimer laser surgery after radial keratotomy). Two solutions have been offered to help surgeons make accurate calculations and correct decisions. The first consists of an Excel spreadsheet (Hoffer-Savini LASIK IOL Power Tool) released by Hoffer and Savini in 2007. The second is an Internet-based IOL power calculator developed by the American Society of Cataract and Refractive Surgery. With both tools, however, surgeons still have to decide which formula should be used. Moreover, they cannot be used for cases with decentered optical zones or multiple treatments. Lastly, the American Society of Cataract and Refractive Surgery calculator does not allow the operator to enter manual or simulated keratometry values and does not include several excellent published formulas.
Theoretically, a better solution is represented by optical ray-tracing based on the Snell law. This method is not subject to the 3 problems that make IOL power calculation inaccurate after corneal refractive surgery : the keratometric index problem, because ray-tracing does not rely on any fictitious index to calculate the corneal power; the radius problem or instrument error, because ray-tracing can be performed over any corneal diameter; and the formula error, because the IOL position can be calculated without relying on the anterior corneal curvature (unlike in the case of third-generation theoretical formulas, such as the Hoffer Q, Holladay 1, and SRK/T). In addition, ray-tracing does not require any historical data and can incorporate corneal aberrations in IOL power calculation. Previous studies have shown encouraging results with this approach. The purpose of this study was to evaluate the preliminary results of ray-tracing, as performed by a rotating Scheimpflug camera combined with a Placido disc corneal topographer, in a series of eyes undergoing phacoemulsification and IOL implantation after previous excimer laser surgery.
Methods
This was a prospective, interventional case series carried out between December 2010 and December 2012. Before being included in the study, the subjects were informed of the study’s purpose and they gave their written informed consent. The study methods adhered to the tenets of the Declaration of Helsinki for the use of human participants in biomedical research. The study was approved by the Giovanni Battista Bietti Foundation Institutional Review Board. All patients undergoing phacoemulsification and IOL implantation after myopic laser in situ keratomileusis (LASIK) or photorefractive keratectomy (PRK) were enrolled. If both eyes underwent surgery, only the first eye was evaluated.
Before surgery, all patients underwent anterior segment imaging by a Scheimpflug camera combined with a Placido disc corneal topographer (Sirius, software version 2.5; CSO, Florence, Italy), which provides repeatable measurements of corneal power, corneal thickness, and aqueous depth. Axial length was measured either by immersion ultrasound biometry (Ocuscan; Alcon Laboratories, Fort Worth, Texas, USA) or partial coherence interferometry (IOLMaster; Carl Zeiss, Jena, Germany).
Ray-Tracing Procedure
After the anterior segment of the eye was imaged and the scan was processed, the Sirius internal software calculated the IOL power. Four parameters had to be entered manually: the axial length, the target refraction, the pupil diameter (which was set to 3 mm in all patients), and the labeled A-constant of the IOL. The latter was required because most IOL manufacturers do not provide the curvature and thickness values of their IOLs, which are required for exact ray-tracing. The actual position of the IOL was predicted using a proprietary algorithm, which is based on several measured parameters of the anterior segment of the eye and the A-constant of the IOL.
For ray-tracing to be performed, a bundle of rays parallel to the instrument axis and passing within the entrance pupil of the eye was traced through the anterior and posterior corneal surfaces (as measured by the Scheimpflug and Placido technologies) using the Snell law. For each incoming ray, its intersection with the anterior corneal surface and its angle of incidence relative to the anterior surface normal were calculated. The ray refracted by the anterior surface was obtained using the Snell law, with n air = 1.0 and n stroma = 1.376. This ray then was considered as an incoming ray for the posterior corneal surface and the same procedure as above was applied to calculate the ray refracted by this surface using the Snell law, with n stroma = 1.376 and n aqueous = 1.336. The ray coming from the aqueous humor then was traced through the IOL surface and the vitreous (n vitreous = 1.336) until the retina. The intersections of rays with the retina created the retinal spot, whose shape and density depended on the aberrations of the optical system. All rays traced until the retina were used to calculate the wavefront error, that is, the difference between the measured wavefront and an ideal spherical wavefront. From this calculation, the refractive outcome associated with a given IOL was estimated by means of the proprietary algorithm.
A final evaluation was performed by assessing the subjective manifest refractive outcomes at 1 month after surgery, which is when refractive stability can be expected with small-incision clear cornea surgery. To calculate the mean arithmetic error in the prediction of refractive outcome, the measured manifest refractive spherical equivalent was subtracted from the predicted refraction (based on the IOL actually implanted) provided by the IOL power software of Sirius. The median and mean absolute errors also were calculated.
Results
Twenty-one eyes of 21 patients (12 women; mean age, 62.4 ± 8.6 years), operated on by 11 different surgeons, were enrolled and completed the follow-up. Ten had undergone myopic LASIK and 11 had undergone myopic PRK. The mean axial length was 27.35 ± 2.16 mm (range, 23.2 to 32.6 mm); the mean power of the implanted IOL was 17.81 ± 3.69 diopters (D; range, 6.0 to 22.5 D), and the mean expected refraction was −0.61 ± 1.38 D. A decentered optical zone was detected in 3 eyes, and central corneal haze was detected in 1 eye.
The following models of IOL were implanted: the AcrySof SA60AT (Alcon Laboratories; n = 9), the AcrySof MA60AC (Alcon Laboratories; n = 5), the AcrySof SN60WF (Alcon Laboratories; n = 4), the MI60 (Bausch & Lomb; n = 1), the Envista (Bausch & Lomb, Rochester, New York, USA; n = 1), and the LS-313 (Oculentis, Eerbek, the Netherlands; n = 1).
The mean postoperative refraction was −0.43 ± 1.08 D (range, −1.28 to 0.85 D). The median absolute error was +0.25 D and the mean absolute error was 0.36 D, whereas 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. The mean arithmetic error was −0.13 ± 0.49 D (constant optimization could not be carried out because different IOLs were used in this study). Regarding the 3 eyes with a decentered optical zone, the median and mean absolute errors were 0.33 and 0.32 D, respectively.
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