A numerical investigation of changes in lens shape during accommodation

The Effect of Lens Shape, Zonular Insertion and Finite Element Model on Simulated Shape Change of the Eye Lens

The process of lens shape change in the eye to alter focussing (accommodation) is still not fully understood. Modelling approaches have been used to complement experimental findings in order to determine how constituents in the accommodative process influence the shape change of the lens. An unexplored factor in modelling is the role of the modelling software on the results of simulated shape change. Finite element models were constructed in both Abaqus and Ansys software using biological parameters from measurements of shape and refractive index of two 35-year-old lenses. The effect of zonular insertion on simulated shape change was tested on both 35-year-old lens models and with both types of software. Comparative analysis of shape change, optical power, and stress distributions showed that lens shape and zonular insertion positions affect the results of simulated shape change and that Abaqus and Ansys show differences in their respective models. The effect of the software package used needs to be taken into account when constructing finite element models and deriving conclusions.

Investigation of crystalline lens overshooting: ex vivo experiment and optomechanical simulation results

Introduction: Crystalline lens overshooting refers to a situation in which the lens momentarily shifts too much from its typical location immediately after stopping the rotational movement of the eye globe. This movement can be observed using an optical technique called Purkinje imaging. Methods: In this work, an experimental setup was designed to reproduce this effect ex vivo using a fresh porcine eye. The sample was rotated 90° around its centroid using a high-velocity rotation stage, and the Purkinje image sequences were recorded, allowing us to quantify the overshooting effect. The numerical part of the study consisted of developing a computational model of the eye, based on the finite element method, that allowed us to understand the biomechanical behavior of the different tissues in this dynamic scenario. A 2D fluid-structure interaction model of the porcine eye globe, considering both the solid parts and humors, was created to reproduce the experimental outcomes. Results: Outputs of the simulation were analyzed using an optical simulation software package to assess whether the mechanical model behaves optically like the real ex vivo eye. The simulation predicted the experimental results by carefully adjusting the mechanical properties of the zonular fibers and the damping factor. Conclusion: This study effectively demonstrates the importance of characterizing the dynamic mechanical properties of the eye tissues to properly comprehend and predict the overshooting effect.

The potential influence of the ligament of Wieger on the crystalline lens shape

This research uses mathematical modelling to evaluate the influence of the ligament of Wieger on the crystalline lens shape at rest, and during accommodation. An axisymmetric model of the anterior segment, including the ligament of Wieger, was created using the finite element method. Different conditions including variations of stiffness and positions of the ligament, with and without the ligament, were tested to see how they affected lens curvature and optical power. Adding the ligament of Wieger to the simulation had a noticeable impact on the optical power of the lens, particularly on the posterior surface power and total power. Ligament stiffness and width significant influenced the accommodative range of the eye by - 0.95D and - 2.39D for ligaments with the same and 3× the stiffness of the capsular bag, respectively. Ligament width and inner diameter had negligible effects on lens thickness but did have significant effects on posterior surface power and accommodation. In this simulation, we found that the ligament of Wieger can significantly affect the lens shape, both at rest and during accommodation, and may need to be considered in lens models.

Implantation of a capsular tension ring during cataract surgery attenuates predicted remodeling of the post-surgical lens capsule along the visual axis

Introduction: Cataract surgery permanently alters the mechanical environment of the lens capsule by placing a hole in the anterior portion and implanting an intraocular lens (IOL) that has a very different geometry from the native lens. We hypothesized that implant configuration and mechanical interactions with the post-surgical lens capsule play a key role in determining long-term fibrotic remodeling. Methods: We developed the first finite element-growth and remodeling (FE-G&R) model of the post-surgical lens capsule to evaluate how implantation of an IOL with and without a capsular tension ring (CTR) impacted evolving lens capsule mechanics and associated fibrosis over time after cataract surgery. Results: Our models predicted that implantation of a CTR with the IOL into the post-surgical lens capsule reduced the mechanical perturbation, thickening, and stiffening along the visual axis in both the remnant anterior and posterior portions compared to implantation of the IOL alone. Discussion: These findings align with patient studies and suggest that implantation of a CTR with the IOL during routine cataract surgery would attenuate the incidence of visually-debilitating capsule fibrosis. Our work demonstrates that use of such modeling techniques has substantial potential to aid in the design of better surgical strategies and implants.

Viscoelastic properties of porcine lenses using optical coherence elastography and inverse finite element analysis

The mechanical properties of the crystalline lens are crucial in determining the changes in lens shape that occur during the accommodation process and are also a major factor in the development of the two most prevalent age-related diseases of the lens, presbyopia and cataracts. However, a comprehensive understanding of these properties is currently lacking. Previous methods for characterizing the mechanical properties of the lens have been limited by the amount of data that could be collected during each test and the lack of complex material modeling. These limitations were mainly caused by the lack of imaging techniques that can provide data for the entire crystalline lens and the need for more complex models to describe the non-linear behavior of the lens. To address these issues, we characterized the mechanical properties of 13 porcine lenses during an ex vivo micro-controlled-displacement compression experiment using optical coherence elastography (OCE) and inverse finite element analysis (iFEA). OCE allowed us to quantify the internal strain distribution of the lens and differentiate between the different parts of the lens, while iFEA enabled us to implement an advanced material model to characterize the viscoelasticity of the lens nucleus and the relative stiffness gradient in the lens. Our findings revealed a pronounced and rapid viscoelastic behavior in the lens nucleus (g₁ = 0.39 ± 0.13, τ₁ = 5.01 ± 2.31 s) and identified the lens nucleus as the stiffest region, with a stiffness 4.42 ± 1.20 times greater than the anterior cortex and 3.47 ± 0.82 times greater than the posterior cortex. However, due to the complex nature of lens properties, it may be necessary to employ multiple tests simultaneously for a more comprehensive understanding of the crystalline lens.

Automated segmentation of the ciliary muscle in OCT images using fully convolutional networks

Quantifying shape changes in the ciliary muscle during accommodation is essential in understanding the potential role of the ciliary muscle in presbyopia. The ciliary muscle can be imaged in-vivo using OCT but quantifying the ciliary muscle shape from these images has been challenging both due to the low contrast of the images at the apex of the ciliary muscle and the tedious work of segmenting the ciliary muscle shape. We present an automatic-segmentation tool for OCT images of the ciliary muscle using fully convolutional networks. A study using a dataset of 1,039 images shows that the trained fully convolutional network can successfully segment ciliary muscle images and quantify ciliary muscle thickness changes during accommodation. The study also shows that EfficientNet outperforms other current backbones of the literature.

Regulation of the Membrane Trafficking of the Mechanosensitive Ion Channels TRPV1 and TRPV4 by Zonular Tension, Osmotic Stress and Activators in the Mouse Lens

Lens water transport generates a hydrostatic pressure gradient that is regulated by a dual-feedback system that utilizes the mechanosensitive transient receptor potential vanilloid (TRPV) channels, TRPV1 and TRPV4, to sense changes in mechanical tension and extracellular osmolarity. Here, we investigate whether the modulation of TRPV1 or TRPV4 activity dynamically affects their membrane trafficking. Mouse lenses were incubated in either pilocarpine or tropicamide to alter zonular tension, exposed to osmotic stress, or the TRPV1 and TRPV4 activators capsaicin andGSK1016790A (GSK101), and the effect on the TRPV1 and TRPV4 membrane trafficking in peripheral fiber cells visualized using confocal microscopy. Decreases in zonular tension caused the removal of TRPV4 from the membrane of peripheral fiber cells. Hypotonic challenge had no effect on TRPV1, but increased the membrane localization of TRPV4. Hypertonic challenge caused the insertion of TRPV1 and the removal of TRPV4 from the membranes of peripheral fiber cells. Capsaicin caused an increase in TRPV4 membrane localization, but had no effect on TRPV1; while GSK101 decreased the membrane localization of TRPV4 and increased the membrane localization of TRPV1. These reciprocal changes in TRPV1/4 membrane localization are consistent with the channels acting as mechanosensitive transducers of a dual-feedback pathway that regulates lens water transport.

A validated finite element model to reproduce Helmholtz's theory of accommodation: a powerful tool to investigate presbyopia

PURPOSE

To reproduce human in vivo accommodation numerically. For that purpose, a finite element model specific for a 29-year-old subject was designed. Once the proposed numerical model was validated, the decrease in accommodative amplitude with age was simulated according to data available in the literature.

METHODS

In contrast with previous studies, the non-accommodated eye condition was the reference configuration. Consequently, two aspects were specifically highlighted: contraction of the ciliary muscle, which was simulated by a continuum electro-mechanical model and incorporation of initial lens capsule stresses, which allowed the lens to become accommodated after releasing the resting zonular tension.

RESULTS

The morphological changes and contraction of the ciliary muscle were calibrated accurately according to the experimental data from the literature. All dynamic optical and biometric lens measurements validated the model. With the proposed numerical model, presbyopia was successfully simulated.

CONCLUSIONS

The most widespread theory of accommodation, proposed by Helmholtz, was simulated accurately. Assuming the same initial stresses in the lens capsule over time, stiffening of the lens nucleus is the main cause of presbyopia.