Numerical Analysis Enhances Postoperative Visual Assessment and Optimization for Multifocal Intraocular Lenses (IOLs)

Introduction and Research Background

One of the main goals of cataract surgery is to achieve spectacle-free vision for patients. However, this goal is limited by two major challenges: loss of accommodative function and postoperative corneal astigmatism. To address these issues, toric intraocular lenses (toric IOLs) were introduced to correct corneal astigmatism. Concurrently, the development of multifocal intraocular lenses (multifocal IOLs) aimed to meet the demands of multifocal vision. Based on clinical observations, though, eyes implanted with multifocal IOLs often exhibit more significant visual performance decline under the same amount of astigmatism compared to monofocal IOLs, especially in the case of trifocal IOLs. This phenomenon has introduced new challenges to the selection of multifocal IOLs and expectations for postoperative visual quality.

Therefore, this study aims to conduct a numerical analysis of the astigmatism tolerance of multifocal IOLs under polychromatic conditions using a customized finite eye model. It evaluates energy efficiency and visual performance under varying degrees of astigmatism, providing a theoretical basis for predicting postoperative visual function.

Source and Author Information

This research was conducted by Jongin You and Mooseok Jang from the Korea Advanced Institute of Science and Technology (KAIST) and was published in Biomedical Optics Express (Vol. 16, No. 2) on February 1, 2025. By combining numerical models and customized algorithms, the study offers a novel theoretical approach and tool for evaluating postoperative visual function in multifocal IOL implantation.

Research Process and Experimental Design

1. Construction of a Customized Finite Eye Model

The researchers employed a customized finite eye model based on full-wave analysis, which accurately simulates the entire eye structure, including thin refracting surfaces of the cornea and crystalline lens, propagation media (e.g., aqueous humor and vitreous body), and light propagation conditions under polychromatic light. The eye model’s benchmark wavelength was set to 550 nm, emulating the optical system of a normal eye with an effective system power of 60 diopters.

Corneal and Lens Parameter Design

• The anterior and posterior surface radii of the cornea were set to 7.77 mm and 6.40 mm, respectively, yielding a total corneal power of 42.17 D.
• The effective single-point lens power was 21.37 D, achieving an overall effective optical power of 60 D in the eye model.
• The model also incorporated a generalized Cauchy equation to characterize chromatic aberration properties of the eye’s components under varying wavelengths.

Multifocal IOL Parameter Definitions

To simulate three types of commercially available multifocal IOLs (ReSTOR, Symfony, and POD-F), the study adopted the following configurations: - ReSTOR: A bifocal IOL with a refractive power of 21.37 D and an additional diffractive power of +3.0 D. - Symfony: An extended depth-of-focus (EDOF) IOL with a diffractive power of +1.75 D, optimized for chromatic aberration correction. - POD-F: A trifocal IOL combining two diffractive components for intermediate focus (+1.75 D) and near focus (+3.5 D).

The design parameters of each IOL were sourced from existing literature and information provided by manufacturers.

2. Wave Propagation and Retinal Light Field Simulation

Through the customized model, the researchers introduced a full-wave propagation approach to describe light propagation in the cornea, lens, aqueous humor, and vitreous body: - Light propagation through distances within the media was computed using the angular spectrum method, decomposing wave components into angular domains and transforming them back into spatial domains for phase modulation. - The “light-in-the-bucket” (LIB) metric quantified the light intensity within the diffraction-limited region of the retina at 550 nm.

Additionally, the Seidel representation of astigmatism was integrated into the analysis to study the critical effects of corneal astigmatism on image formation.

3. Data Analysis and Simulation

The researchers simulated various scenarios to evaluate the effect of astigmatism on visual imaging, as well as the light energy distribution and diffraction efficiencies at distant, intermediate, and near foci for multifocal IOLs. Modulation transfer function (MTF) analysis was performed under different astigmatic conditions to assess changes in imaging quality.

Results and Key Findings

1. Impact of Chromatic Aberration on IOL Performance

The analysis showed that Symfony, due to its chromatic aberration compensation design, exhibited the best chromatic correction capability at the far focus, outperforming POD-F and ReSTOR. Although POD-F showed lower material dispersion (Abbe number = 56), it presented better balance in imaging capabilities at intermediate distances, albeit with increased chromatic aberration for distant focus.

2. Energy Efficiency Under Astigmatism

Under corneal astigmatism, different IOLs displayed varying levels of astigmatism tolerance: - Symfony: Showed the highest tolerance to astigmatism, with a normalized energy efficiency of 12% at the far focus under +1.5 D astigmatism. - ReSTOR: Achieved 10% efficiency under the same conditions, demonstrating lower tolerance compared to Symfony. - POD-F: While the intermediate focus remained relatively stable, the far and near foci showed the lowest tolerance among the three IOLs.

3. Imaging Quality and Simulated Vision

The visual quality at the far focus also varied—Symfony demonstrated clearer imaging due to its diffractive design minimizing high-order harmonic interference. In comparison, POD-F exhibited uneven light distribution in multifocal imaging due to its trifocal design.

The study simulated vision under astigmatic conditions using a model of the letter “E,” validating the accuracy of the numerical predictions.

Conclusions and Significance

This study reveals the intrinsic optical mechanisms affecting chromatic aberration, astigmatism tolerance, and visual quality in multifocal IOLs through a combination of full-wave analysis and polychromatic retinal field modeling. Key findings include: 1. EDOF IOLs (e.g., Symfony) provide superior chromatic aberration compensation, making them suitable for patients with moderate or higher levels of astigmatism. 2. For patients with astigmatism greater than +1.0 D, the use of multifocal toric IOLs is recommended to optimize postoperative visual function. 3. The proposed model serves as an important tool for predicting postoperative visual function and can contribute to customized IOL design.

Highlights of the Study

1. The study innovatively integrates full-wave analysis and the angular spectrum method to offer a highly precise whole-eye model.
2. Polychromatic simulations across the E-band (400–700 nm) provide valuable data supporting chromatic compensation principles for IOLs.
3. Predictions align with existing clinical research, offering theoretical guidance for multifocal IOL selection.
4. High expandability of the model allows it to incorporate individualized biometric data, facilitating precise and personalized medical applications.

This study not only provides a theoretical framework for evaluating multifocal IOLs postoperatively but also holds potential for the design of novel IOLs and the development of tailored treatment strategies for patients. This work represents significant scientific and clinical advancement.