Stretch-dependent changes in surface profiles of the human crystalline lens during accommodation: a finite element study

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.

A method for generating zonular tension in the murine eye by embedding and compressing the globe in a hydrogel

The ocular lens is the primary organ within the eye responsible for accommodation. During accommodation, the lens is subject to biomechanical forces. We previously demonstrated that stretching the porcine lens can increase lens epithelial cell proliferation. Although murine lenses are commonly employed in lens research, murine lens stretching has remained unexplored. Murine lens stretching thus represents a novel source of potential discovery in lens research. In the present study, we describe a method for stretching the murine lens by compressing the murine globe embedded in a hydrogel. We hypothesized that, as the eye is compressed along the optic axis, the lens would stretch through zonular tension due to the equatorial region of the eye bulging outward. Our results showed that this led to a compression-dependent increase in murine lens epithelial cell proliferation, suggesting that compression of the embedded murine globe is a viable technique for studying the mechanobiology of the lens epithelium.

The major influence of anterior and equatorial zonular fibres on the far-to-near accommodation revealed by a 3D pre-stressed model of the anterior eye

PURPOSE

To explore the synergistic function of the ligaments in eye, the zonular fibres, that mediate change in eye lens shape to allow for focussing over different distances.

METHODS

A set of 3D Finite Element models of the anterior eye together with a custom developed pre-stress modelling approach was proposed to simulate vision for distant objects (the unaccommodated state) to vision for near objects (accommodation). One of the five zonular groups was cut off in sequence creating five models with different zonular arrangements, the contribution of each zonular group was analysed by comparing results of each specific zonular-cut model with those from the all-zonules model in terms of lens shape and zonular tensions.

RESULTS

In the all-zonular model, the anterior and equatorial zonules carry the highest tensions. In the anterior zonular-cut model, the equatorial zonular tension increases while the posterior zonular tension decreases, resulting in an increase in the change in Central Optical Power (COP). In the equatorial zonular-cut model, both the anterior and posterior zonular tensions increase, causing a decreasing change in COP. The change in COP decreases only slightly in the other models. For vitreous zonular-cut models, little change was seen in either the zonular tension or the change in COP.

CONCLUSIONS

The anterior and the equatorial zonular fibres have the major influence on the change in lens optical power, with the anterior zonules having a negative effect and the equatorial zonules contributing a positive effect. The contribution to variations in optical power by the equatorial zonules is much larger than by the posterior zonules.

Characterisation and Modelling of an Artificial Lens Capsule Mimicking Accommodation of Human Eyes

A synthetic material of silicone rubber was used to construct an artificial lens capsule (ALC) in order to replicate the biomechanical behaviour of human lens capsule. The silicone rubber was characterised by monotonic and cyclic mechanical tests to reveal its hyper-elastic behaviour under uniaxial tension and simple shear as well as the rate independence. A hyper-elastic constitutive model was calibrated by the testing data and incorporated into finite element analysis (FEA). An experimental setup to simulate eye focusing (accommodation) of ALC was performed to validate the FEA model by evaluating the shape change and reaction force. The characterisation and modelling approach provided an insight into the intrinsic behaviour of materials, addressing the inflating pressure and effective stretch of ALC under the focusing process. The proposed methodology offers a virtual testing environment mimicking human capsules for the variability of dimension and stiffness, which will facilitate the verification of new ophthalmic prototype such as accommodating intraocular lenses (AIOLs).

Image registration of the human accommodating eye demonstrates equivalent increases in lens equatorial radius and central thickness

AIM

To compare the results of in vivo human high resolution image registration studies of the eye during accommodation to the predictions of mathematical and finite element models of accommodation.

METHODS

Data from published high quality image registration studies of pilocarpine induced accommodative changes of equatorial lens radius (ELR) and central lens thickness (CLT) were statistically analyzed.

RESULTS

The mean changes in ELR and CLT were 6.76 µm/diopter and 6.51 µm/diopter, respectively. The linear regressions, reflecting the association between ELR and accommodative amplitude (AAELR) was: slope=6.58 µm/diopter, r2 =0.98, P<0.0001 and between CLT and AACLT was: slope=6.75 µm/diopter, r2 =0.83, P<0.001. On the basis of these relationships, the CLT slope and the AAELR were used to predict the measured change in ELR (ELRpredicted). There was no statistical difference between ELRpredicted and the measured ELR as demonstrated by a Student's paired t-test: P=0.96 and linear regression analysis: slope=0.97, r2 =0.98, P<0.00001.

CONCLUSION

Image registration with invariant positional references demonstrates that ELR and CLT equivalently minimally increase ∼7.0 µm/diopter during accommodation. The small equivalent increases in ELR and CLT are associated with a large accommodative amplitude. These findings are consistent with the predictions of mathematical and finite element models that specified the stiffness of the lens nucleus is the same or greater than the lens cortex and that accommodation involves a small force (<5 g).

Strain-Dependent Differences in Sensitivity to Myopia-Inducing Stimuli in Guinea Pigs and Role of Choroid

Purpose

To investigate differences in sensitivity to myopia-inducing stimuli of two strains of pigmented guinea pigs.

Methods

Eleven-day-old animals (New Zealand [NZ], n = 24 and Elm Hill strains [EH], n = 26) wore either a +2 or -2 diopter (D) lens over one eye and a plano lens over the fellow eye for 5 days; other 10-day-old EH (n = 9) and 7-day-old NZ (n = 9) animals were monocularly form-deprived (FD) for 28 days. Choroidal thickness and axial length were measured using A-scan ultrasonography at baseline and after 1 and 5 days for optical defocus treatments, and at baseline and after 28 days for the FD treatment. Refractive errors were measured by retinoscopy. Choroids of untreated animals were also evaluated using spectral-domain optical coherence tomography.

Results

One day of optical defocus induced bidirectional (optical sign-dependent) choroidal responses in EH animals only (P < 0.01). Similar responses were detected in NZ animals after 5 days (P < 0.01), with concordant spherical equivalent refraction changes (P < 0.01). Compared with NZ animals, EH animals developed minimal myopia with FD after 28 days (-4.58 ± 0.97 vs. -0.69 ± 0.75 D for NZ versus EH, P < 0.001). Yet, EH animals showed paradoxical choroidal thickening, 20 ± 9 vs. -8 ± 8 μm for EH versus NZ, P < 0.001. Untreated EH animals also had significantly thicker choroids than NZ animals (147 ± 19 vs. 132 ± 16 μm, P < 0.05), with well-defined layering.

Conclusions

As previously reported in chicks, guinea pigs show strain-related differences in response to myopia-inducing stimuli. The finding of a thicker, multilayered choroid in the strain showing decreased sensitivity to FD is provocative, suggesting a possible protective role of the choroid.

A Modeling Approach for Investigating Opto-Mechanical Relationships in the Human Eye Lens

OBJECTIVE

The human visual system alters its focus by a shape change of the eye lens. The extent to which the lens can adjust ocular refractive power is dependent to a significant extent on its material properties. Yet, this fundamental link between the optics and mechanics of the lens has been relatively under-investigated. This study aims to investigate this opto-mechanical link within the eye lens to gain insight into the processes of shape alteration and their respective decline with age.

METHODS

Finite Element models based on biological lenses were developed for five ages: 16, 35, 40, 57, and 62 years by correlating in vivo measurements of the longitudinal modulus using Brillouin scattering with in vitro X-ray interferometric measurements of refractive index and taking into account various directions of zonular force.

RESULTS

A model with radial cortical Young's moduli provides the same amount of refractive power with less change in thickness than a model with uniform cortical Young's modulus with a uniform stress distribution and no discontinuities along the cortico-nuclear boundary. The direction of zonular angles can significantly influence curvature change regardless of the modulus distribution.

CONCLUSIONS

The present paper proposes a modelling approach for the human lens, coupling optical and mechanical properties, which shows the effect of parameter choice on model response.

SIGNIFICANCE

This advanced modelling approach, considering the important interplay between optical and mechanical properties, has potential for use in design of accommodating implant lenses and for investigating non-biological causes of pathological processes in the lens (e.g., cataract).

Contributions of shape and stiffness to accommodative loss in the ageing human lens: a finite element model assessment

Ageing changes to the various components of the accommodative system of the eye lens contribute to the loss of focusing power. The relative contributions of each ageing component, however, are not well defined. This study investigates the contribution of geometric parameters and material properties on accommodation, simulated using models based on human lenses aged 16, 35, and 48 years. Each model was tested using two different sets of material properties and a range of zonular fiber angles and was compared to results from in vivo measurements. The geometries and material parameters of older and younger lens models were interchanged to investigate the role of shape and material on accommodative capacity. Results indicate that geometry has the greater role in accommodation.

The importance of parameter choice in modelling dynamics of the eye lens

The lens provides refractive power to the eye and is capable of altering ocular focus in response to visual demand. This capacity diminishes with age. Current biomedical technologies, which seek to design an implant lens capable of replicating the function of the biological lens, are unable as yet to provide such an implant with the requisite optical quality or ability to change the focussing power of the eye. This is because the mechanism of altering focus, termed accommodation, is not fully understood and seemingly conflicting theories require experimental support which is difficult to obtain from the living eye. This investigation presents finite element models of the eye lens based on data from human lenses aged 16 and 35 years that consider the influence of various modelling parameters, including material properties, a wide range of angles of force application and capsular thickness. Results from axisymmetric models show that the anterior and posterior zonules may have a greater impact on shape change than the equatorial zonule and that choice of capsular thickness values can influence the results from modelled simulations.