Journal of Ophthalmology

Volume 2019, Article ID 2796126, 9 pages

https://doi.org/10.1155/2019/2796126

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

^{1}Department of Ophthalmology (Qvision), Vithas Virgen Del Mar Hospital, 04120 Almería, Spain^{2}Department of Ophthalmology, Torrecardenas Hospital Complex, 04009 Almería, Spain^{3}Department of Optics, Pharmacology and Anatomy, University of Alicante, Alicante, Spain^{4}Department of Ophthalmology, Vithas Medimar International Hospital, Alicante, Spain

Correspondence should be addressed to David P. Piñero; se.au@oreynip.divad

Received 8 February 2019; Revised 4 April 2019; Accepted 28 April 2019; Published 14 May 2019

Guest Editor: Damian Siedlecki

Copyright © 2019 Joaquín Fernández et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

*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, ), 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.

#### 1. Introduction

Intraocular lens (IOL) power calculation formulas have evolved since the publication of the Fyodorov formula in 1967 [1, 2]. Nowadays, there are several methods for calculating the IOL power that can be classified in one of the following groups: (1) historical/refraction based, (2) regression, (3) vergence, (4) artificial intelligence, and (5) ray tracing [3]. The first two approaches are considered out of date, the artificial intelligence is growing in popularity but not in predictability [4], and the ray tracing [5, 6] is the promising option that has not still replaced the most used methods based on the vergence formula. An important reason for the absence of a clear evidence of differences between these previous three approaches is the inclusion of some regression components in all of them, including ray tracing [3]. In fact, the main difference between vergence formulas is the number of variables used for estimating the effective-thin lens position (ELP_{o}), [7] ranging from two in SRK/T, Hoffer Q, and Holladay I formulas to five or seven in the Barrett Universal II or Holladay II formulas, respectively [3].

There are several studies that report the predictability of vergence formulas for eyes with different axial lengths, but high discrepancies are found in the percentage of eyes within ±0.50 D between studies [4, 8–13]. For instance, Shrivastava et al. [14] reported no differences between SRK/T and the newer formulas in short eyes, but a meta-analysis reported superiority of the Haigis formula [15]. The reality is that there are no clinically relevant differences in the statistics of centrality for the postoperative spherical equivalent (SE) between equations, and special attention should be taken in dispersion [10]. This dispersion of the data has been reported to be lower for the Barrett Universal II, which results in a higher percentage of eyes within ±0.50 D in medium to long eyes [4, 8–13]. The Barrett Universal II was born from the theoretical universal formula which considers the thick lens formula [16] and after an estimation of the lens factor, which is the distance from the iris to the second principal plane of the IOL [17]. Therefore, the thin lens formula can be used considering the ELP_{o} as the anterior chamber depth (ACD) plus the lens factor which can be derived from the A-constant [17]. Other authors have used the terms surgeon factor [18] or offset [19] instead of lens factor but the aim of these constants was the same: to estimate the location of the second principle plane of the IOL optic from a relatively fixed anatomical reference plane and to compute the ELP_{o} by means of this factor [16].

If the intended preoperative spherical equivalent (SE) and the postoperative SE are not equal, the constants implemented by different formulas can be optimized for improving refractive results in eyes with different axial lengths [20, 21], but this may contribute to an error in the ELP_{o} if the lens position is not measured during the postoperative follow-up. The aim of this study was to evaluate if the postoperative SE after implantation of a trifocal IOL was due to an error in the ELP_{o} estimated with the SRK/T formula and, if this was not the reason, to identify the possible sources of error. For this purpose, the actual lens position (ALP) of each eye was measured after surgery, and the thick lens formula [22] was used to avoid the optical approximations required by the vergence formula [2].

#### 2. Materials and Methods

##### 2.1. Subjects and Procedures

The study was approved by the local Ethics Committee and was performed in adherence to the tenets of the Declaration of Helsinki. Data from 43 subjects measured at the 3-month follow-up visit were retrospectively retrieved from our historical database, including only one eye randomly in the analysis. The tomography obtained at this visit with the Pentacam HR (Oculus, Wetzlar, Germany) was used for collecting data including anterior (*r*_{1c}) and posterior corneal radii (*r*_{2c}), corneal thickness (*e*_{c}), and ALP measured from corneal vertex (anterior corneal surface) to the anterior IOL surface. The axial length (AXL), the preoperative ACD, and the anterior corneal radius (*r*_{k}) were retrieved from the measurements obtained with the IOLMaster 500 system (Carl Zeiss Meditec AG, Germany). The postoperative best spectacle refraction was also obtained for each eye computing the SE. The pupil diameter for the conditions for which the refraction was performed (around 90 lux) was estimated as the mean between photopic and mesopic pupils measured with the Keratograph 5M system (Oculus, Wetzlar, Germany).

##### 2.2. Surgery Procedure

All surgeries were conducted by the same surgeon (X) by means of phacoemulsification or femtosecond laser-assisted cataract surgery (Victus, Bausch & Lomb Inc, Dornach, Germany) through clear corneal incisions of 2.2 mm for manual incisions or 2.5 mm for laser incisions, both at temporal location. The implanted IOL at capsular bag was the Liberty Trifocal (Medicontur Medical Engineering Ltd. Inc., Zsámbék, Hungary) based on the elevated phase shift (EPS) technology, which is an aspheric hydrophilic IOL with +3.50 D of addition for near and +1.75 D for intermediate at the IOL plane. The preoperative calculation of the IOL power was conducted with the SRK/T [19] formula considering the manufacturer recommended constant of 118.9.

##### 2.3. Thick Lens Formula

All the calculations were conducted by means of paraxial optics and coupling the measured optical structures with the thick lens formula [22]. Some approaches were conducted depending on the system used to measure the cornea. For the anterior corneal radius (*r*_{k}) obtained with IOLMaster, the corneal power in equation (1) (*P*_{k}) should be estimated with a fictitious index (*n*_{k}), and the cornea was considered as a single dioptric surface; therefore, corneal principal planes were approximated to the anterior corneal surface (Figure 1(a)). For the measurement of both corneal radii (*r*_{1c} and *r*_{2c}) and corneal thickness (*e*_{c}) with the Pentacam (Figure 1(b)), the total corneal power was computed with equation (2), and corneal principal planes were calculated since the cornea was considered as a thick lens (Figure 1(b)) [22]: