Model of accommodation: contributions of lens geometry and mechanical properties to the development of presbyopia

A Review of Lens Biomechanical Contributions to Presbyopia

Purpose: Presbyopia-the progressive loss of near focus with age-is primarily a result of changes in lens biomechanics. In particular, the shape of the ocular lens in the absence of zonular tension changes significantly throughout adulthood. Contributors to this change in shape are changes in lens biomechanical properties, continuous volumetric growth lens, and possibly remodeling of the lens capsule. Knowledge in this area is growing rapidly, so the purpose of this mini-review was to summarize and synthesize these gains.Methods: We review the recent literature in this field.Results: The mechanisms governing age-related changes in biomechanical properties remains unknown. We have recently shown that lens growth may be driven by zonular tension. The same mechanobiological mechanism driving lens growth may also lead to remodeling of the capsule, though this remains to be demonstrated.Conclusions: This mini-review focuses on identifying mechanisms which cause these age-related changes, suggesting future work which may elucidate these mechanisms, and briefly discusses ongoing efforts to develop a non-surgical approach for therapeutic management of presbyopia. We also propose a simple model linking lens growth and biomechanical properties.

Membrane elasticity modulated by cholesterol in model of porcine eye lens-lipid membrane

Experimental evidence shows that the eye lens loses its elasticity dramatically with age. It has also been reported that the cholesterol (Chol) content in the eye lens fiber cell plasma membrane increases significantly with age. High Chol content leads to the formation of cholesterol bilayer domains (CBDs) in the lens membrane. The role of high Chol associated with lens elasticity is unclear. The purpose of this research is to investigate the membrane elasticity of the model of porcine lens-lipid (MPLL) membrane with increasing Chol content to elucidate the role of high Chol in lens membrane elasticity. In this study, we used atomic force microscopy (AFM) to study the mechanical properties (breakthrough force and area compressibility modulus (K_A)) of the MPLL membrane with increasing Chol content where K_A is the measure of membrane elasticity. We varied Chol concentration in Chol/MPLL membrane from 0 to ∼71 mol%. Supported Chol/MPLL membranes were prepared by fusion of small unilamellar vesicles (SUVs) on top of a flat mica surface. SUVs of the Chol/MPLL lipid mixture were prepared with the rapid solvent exchange method followed by probe-tip sonication. For the Chol/MPLL mixing ratio of 0, AFM image showed the formation of two distinct phases of the membrane, i.e., liquid-disordered phase (l_d) and solid-ordered phase (s_o) membrane. However, with Chol/MPLL mixing ratio of 0.5 and above, only liquid-ordered phase (l_o) membrane was formed. Also, two distinct breakthrough forces corresponding to l_d and s_o were observed for Chol/MPLL mixing ratio of 0, whereas only one breakthrough force was observed for membranes with Chol/MPLL mixing ratio of 0.5 and above. No significant difference in the membrane surface roughness was measured with increasing Chol content for these membranes; however, breakthrough force and K_A for l_o membrane increased when Chol/MPLL mixing ratio was increased from 0.5 to 1. Interestingly above the Chol/MPLL mixing ratio of 1, both breakthrough force and K_A decreased, indicating the formation of CBDs. Furthermore, these results showed that membrane elasticity increases at high Chol content, suggesting that high Chol content in lens membrane might be responsible for maintaining lens membrane elasticity.

Physiological Mechanisms Regulating Lens Transport

The transparency and refractive properties of the lens are maintained by the cellular physiology provided by an internal microcirculation system that utilizes spatial differences in ion channels, transporters and gap junctions to establish standing electrochemical and hydrostatic pressure gradients that drive the transport of ions, water and nutrients through this avascular tissue. Aging has negative effects on lens transport, degrading ion and water homeostasis, and producing changes in lens water content. This alters the properties of the lens, causing changes in optical quality and accommodative amplitude that initially result in presbyopia in middle age and ultimately manifest as cataract in the elderly. Recent advances have highlighted that the lens hydrostatic pressure gradient responds to tension transmitted to the lens through the Zonules of Zinn through a mechanism utilizing mechanosensitive channels, multiple sodium transporters respond to changes in hydrostatic pressure to restore equilibrium, and that connexin hemichannels and diverse intracellular signaling cascades play a critical role in these responses. The mechanistic insight gained from these studies has advanced our understanding of lens transport and how it responds and adapts to different inputs both from within the lens, and from surrounding ocular structures.

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.

A numerical investigation of changes in lens shape during accommodation

The purpose of this study was to investigate how the mechanical properties and geometry of the lens influence the changes in lens shape during accommodation. To do so, ex vivo stretching tests of the isolated lens were simulated via finite element analysis. In these tests, the lens is stretched from the accommodated state to the non-accommodated state. Several key characteristics of the lens were studied: the stiffness gradient of the lens material, the distribution of the capsule thickness, the mechanical properties of the capsule and the material comprising the lens, nucleus and cortex, and the influence of two different age-related lens geometries (17 and 29 y/o subjects). To determine the effects on the changes in lens shape during accommodation, changes in the anterior and posterior radius, the lens and nucleus thicknesses and the equatorial lens diameter were analysed. The results suggest that multiple factors exert statistically significant influences on how the lens changes its shape, but two factors predominate over the rest: the stiffness ratio between the nucleus and cortex and the stiffness of the capsule, specifically the posterior surface.

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.

Mechanism of accommodation assessed by change in precisely registered ocular images associated with concurrent change in auto-refraction

PURPOSE

Our purpose was to determine the changes in anterior chamber depth (ACD) and central lens thickness (CLT) during pharmacologically induced accommodation.

METHODS

Following pupillary dilation with phenylephrine 10%, baseline auto-refractions and swept-source optical coherence tomographic biometric images (Zeiss IOLMaster 700) were obtained from the right eyes of 25 subjects aged 19 to 24 years. Pilocarpine 4% and phenylephrine 10% were then instilled into these right eyes. One hour later, auto-refractions and biometric imaging were repeated. Only data from eight of 25 subjects met the following stringent criteria to be included in the study analysis: pre and post-pilocarpine biometric foveal images were registerable, the images of the corneal centers were shifted by ≤100 μm, pupils >5 mm and the pharmacologically induced refractive change was ≥ -7 diopters.

RESULTS

The mean auto-refractive accommodative change for the eight included subjects was -12.45 diopters (± 3.45 diopters). The mean change in CLT was 81 μm (± 54 μm) and the mean change in ACD was -145 μm (± 86 μm). Superimposition of the registered pre and post-pilocarpine biometric images of the sagittal sections of the whole eye from each subject demonstrated that the position of the whole lens did not shift either anteriorly, posteriorly or vertically during pharmacologically induced accommodation.

CONCLUSIONS

A small increase in lens thickness was associated with a large change in accommodative amplitude and no significant change in lens position as predicted by the Schachar theory.

In Vivo Brillouin Analysis of the Aging Crystalline Lens

Purpose

To analyze the age dependence of the longitudinal modulus of the crystalline lens in vivo using Brillouin scattering data in healthy subjects.

Methods

Brillouin scans were performed along the crystalline lens in 56 eyes from 30 healthy subjects aged from 19 to 63 years. Longitudinal elastic modulus was acquired along the sagittal axis of the lens with a transverse and axial resolution of 4 and 60 μm, respectively. The relative lens stiffness was computed, and correlations with age were analyzed.

Results

Brillouin axial profiles revealed nonuniform longitudinal modulus within the lens, increasing from a softer periphery toward a stiffer central plateau at all ages. The longitudinal modulus at the central plateau showed no age dependence in a range of 19 to 45 years and a slight decrease with age from 45 to 63 years. A significant intersubject variability was observed in an age-matched analysis. Importantly, the extent of the central stiff plateau region increased steadily over age from 19 to 63 years. The slope of change in Brillouin modulus in the peripheral regions were nearly age-invariant.

Conclusions

The adult human lens showed no measurable age-related increase in the peak longitudinal modulus. The expansion of the stiff central region of the lens is likely to be the major contributing factor to age-related lens stiffening. Brillouin microscopy may be useful in characterizing the crystalline lens for the optimization of surgical or pharmacological treatments aimed at restoring accommodative power.

Accommodation in human eye models: a comparison between the optical designs of Navarro, Arizona and Liou-Brennan

AIM

To simulate and compare accommodation in accommodative and non-accommodative human eye models.

METHODS

Ray tracing and optical design program was used. Three eye models were designed and studied: the Navarro, the Arizona and the Liou-Brennan. In order to make the Navarro and Liou-Brennan models to accommodate, specific geometric parameters of the models were altered with values that were chosen from the literature. For the Arizona model, its' mathematical functions for accommodation were used for the same accommodative demands. The simulation included four distances of accommodation for each model: at infinity, 3, 1 and 0.5 m.The results were diffraction images of a "letter F" for graphical comparison, spot diagrams on the retinal field and Modulation Transfer Function (MTF) graphs.

RESULTS

Zernike coefficients for the aberrations, Airy disk diameter, root mean square (RMS) error diameter and total axial length of the model were provided from the program. These were compared between them in all distances. The Navarro model had the smallest axial length change as a simple model. The Arizona did not change its axial length because it is designed to be accommodative. The Liou-Brennan model had different results concerning the aberrations because of the decentration of the pupil. The MTF graphs showed small differences between the models because of the differences in their designs.

CONCLUSION

All the three models are able to simulate accommodation with the expected results. There is no model that can be assumed as the best choice. Accommodation can be simulated in non-accommodativemodels and in customized ones.

Gradient moduli lens models: how material properties and application of forces can affect deformation and distributions of stress

The human lens provides one-third of the ocular focussing power and is responsible for altering focus over a range of distances. This ability, termed accommodation, defines the process by which the lens alters shape to increase or decrease ocular refractive power; this is mediated by the ciliary muscle through the zonule. This ability decreases with age such that around the sixth decade of life it is lost rendering the eye unable to focus on near objects. There are two opponent theories that provide an explanation for the mechanism of accommodation; definitive support for either of these requires investigation. This work aims to elucidate how material properties can affect accommodation using Finite Element models based on interferometric measurements of refractive index. Gradients of moduli are created in three models from representative lenses, aged 16, 35 and 48 years. Different forms of zonular attachments are studied to determine which may most closely mimic the physiological form by comparing stress and displacement fields with simulated shape changes to accommodation in living lenses. The results indicate that for models to mimic accommodation in living eyes, the anterior and posterior parts of the zonule need independent force directions. Choice of material properties affects which theory of accommodation is supported.

Pharmacological Treatment of Presbyopia by Novel Binocularly Instilled Eye Drops: A Pilot Study

PURPOSE

The feasibility, in terms of safety and potential efficacy, of a new drug combination for binocular use as a noninvasive pharmacological solution for treating presbyopia was examined.

METHODS

Fourteen emmetropic presbyopic subjects (28 eyes) were given one drop of the preparation under study in each eye. For each patient, the uncorrected distance visual acuity, uncorrected near visual acuity, near and far refraction, best corrected visual acuity, best corrected far-near visual acuity, photopic and scotopic pupil size, Schirmer's test, endothelial cell count, intraocular pressure, keratometry, pachymetry, and anterior chamber depth were all performed or assessed prior to the administration of the eye drops and then 0.5, 1, 2, 3, 4, and 5 h, 1 week, and 1 month post-administration prospectively in each eye and binocularly.

RESULTS

The results showed that near uncorrected visual acuity improved by about 2-3 lines from baseline in each eye and binocularly. There was no degradation in uncorrected far vision in each eye and binocularly in any patient. Refractive measurements performed in this study showed there was a maximum myopic shift of just 0.5 D that progressively reduced and disappeared at 4 h.

CONCLUSION

The new topical drug treatment analyzed herein significantly improved near vision without affecting far vision. This binocular pharmacologic treatment of presbyopia has the potential to ameliorate the reading vision of presbyopes and possesses the advantages of a nonmonovision therapy. A randomized, controlled, double-masked clinical trial with a twice-a-day treatment schedule is ongoing at our institution.

FUNDING

This study was supported in part by the Spanish Ministry of Health, Instituto Carlos III, Red Temática de Investigación Oftalmológica (OFTALRED), and Fundación Oftalmológica Vejarano (Popayán, Colombia).

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

BACKGROUND

A non-linear isotropic finite element (FE) model of a 29-year-old human crystalline lens was constructed to study the effects of various geometrical parameters on lens accommodation.

METHODS

The model simulates dis-accommodation by stretching of the lens and predicts the change in surface profiles of the lens capsule, cortex and nucleus at select states of stretching/accommodation. Multiple regression analysis (MRA) is used to develop a stretch-dependent mathematical model relating the lens sagittal height to the radial position of the lens surface as a function of dis-accommodative stretch. A load analysis is performed to compare the finite element results to empirical results from lens stretcher studies. Using the predicted geometrical changes, the optical response of the whole eye during accommodation was analysed by ray-tracing.

RESULTS

Aspects of lens shape change relative to stretch were evaluated, including change in diameter, central thickness and accommodation. Maximum accommodation achieved was 10.29 D. From the multiple regression analysis, the stretch-dependent mathematical model of the lens shape related lens curvatures as a function of lens ciliary stretch well (maximum mean-square residual error 2.5 × 10(-3 ) μm, p < 0.001). The results are compared with those from in vitro studies.

CONCLUSIONS

The finite element and ray-tracing predictions are consistent with Ex Vivo Accommodation Simulator (EVAS) studies in terms of load and power change versus change in thickness. The mathematical stretch-dependent model of accommodation presented may have utility in investigating lens behaviour at states other than the relaxed or fully accommodated states.