Ray tracing optimization: a new method for intraocular lens power calculation in regular and irregular corneas

Abstract

To develop a novel algorithm based on ray tracing, simulated visual performance and through-focus optimization for an accurate intraocular lens (IOL) power calculation. Custom-developed algorithms for ray tracing optimization (RTO) were used to combine the natural corneal higher-order aberrations (HOAs) with multiple sphero-cylindrical corrections in 210 higher order statistical eye models for developing keratoconus. The magnitude of defocus and astigmatism producing the maximum Visual Strehl was considered as the optimal sphero-cylindrical target for IOL power calculation. Corneal astigmatism and the RMS HOAs ranged from - 0.64 ± 0.35D and 0.10 ± 0.04 μm (0-months) to - 3.15 ± 1.38D and 0.82 ± 0.47 μm (120-months). Defocus and astigmatism target was close to neutral for eyes with low amount of HOAs (0 and 12-months), where 91.66% of eyes agreed within ± 0.50D in IOL power calculation (RTO vs. SRK/T). However, corneas with higher amounts of HOAs presented greater visual improvement with an optimized target. In these eyes (24- to 120-months), only 18.05% of eyes agreed within ± 0.50D (RTO vs. SRK/T). The power difference exceeded 3D in 42.2% while the cylinder required adjustments larger than 3D in 18.4% of the cases. Certain amounts of lower and HOAs may interact favourably to improve visual performance, shifting therefore the refractive target for IOL power calculation.

Figure 1

Illustration of the ray tracing optimization (RTO) method for IOL power calculation. (1) Corneal input data: anterior and posterior three-dimensional corneal elevation maps (SyntEye at 36 months; #145); (2) virtual ray tracing through the anterior and posterior corneal surfaces to determine the corneal wavefront aberrations at the pupil plane and the simulated visual performance (the point spread function, PSF, and the Snellen E-letter of 30 arc-min for 4-mm pupil diameter); (3) through-focus optimization process to calculate the sphero-cylindrical correction producing the highest VSOTF (representation of the Snellen E letter for different astigmatism and defocus magnitudes); and (4) pseudophakic virtual eye.

Figure 2

Through-focus Visual Strehl (VSOTF) for representative examples of each SyntEye group: uncorrected cornea (red), zero-target (grey) and optimized (light blue).

Figure 3

Theoretical simulations of 30 arc-min Snellen E-letters (4-mm pupil) for representative examples of each SyntEye group. Left column: convolved letter with the astigmatism and natural aberrations of the cornea. Middle column: convolved letter after full cancellation of defocus and astigmatism. Right column: convolved letter with the sphero-cylindrical correction that produced the best optical quality (peak Visual Strehl).

Figure 4

VSOTF (zero defocus and astigmatism) vs. Visual benefit, defined as VSOTF (optimized defocus and astigmatism) divided by VSOTF (zero defocus and astigmatism).

Figure 5

VSOTF magnitude for the original data (corneal astigmatism and HOAs, in red), zero target condition (zero defocus and astigmatism, in grey) and optimized calculation (sphero-cylindrical correction combined with the natural amount of HOAs, in light blue) and tolerance to ± 0.5D of defocus (zero target condition and optimized calculation).

Figure 6

Tolerance to toric IOL rotation: VSOTF magnitude for the optimized calculation and zero target condition (zero defocus and astigmatism).

Figure 7

Difference in residual refractive error between RTO and SRK/T expressed as power vectors M, J₀ and J₄₅. (a) Regular astigmatism: Normal—SyntEyes 0 and 12 months; (b) irregular astigmatism and HOAs: SyntEyes with simulated progression of 24 and 36 months (mid-stage KC); (c) irregular astigmatism and higher amount of HOAs: SyntEyes with simulated progression of 48, 60 and 120 months (late-stage keratoconus).