Contribution of the crystalline lens gradient refractive index to the accommodation amplitude in non-human primates: in vitro studies

Optical coherence tomography quantifies gradient refractive index and mechanical stiffness gradient across the human lens

BACKGROUND

As a key element of ocular accommodation, the inherent mechanical stiffness gradient and the gradient refractive index (GRIN) of the crystalline lens determine its deformability and optical functionality. Quantifying the GRIN profile and deformation characteristics in the lens has the potential to improve the diagnosis and follow-up of lenticular disorders and guide refractive interventions in the future.

METHODS

Here, we present a type of optical coherence elastography able to examine the mechanical characteristics of the human crystalline lens and the GRIN distribution in vivo. The concept is demonstrated in a case series of 12 persons through lens displacement and strain measurements in an age-mixed group of human subjects in response to an external (ambient pressure modulation) and an intrinsic (micro-fluctuations of accommodation) mechanical deformation stimulus.

RESULTS

Here we show an excellent agreement between the high-resolution strain map retrieved during steady-state micro-fluctuations and earlier reports on lens stiffness in the cortex and nucleus suggesting a 2.0 to 2.3 times stiffer cortex than the nucleus in young lenses and a 1.0 to 7.0 times stiffer nucleus than the cortex in the old lenses.

CONCLUSIONS

Optical coherence tomography is suitable to quantify the internal stiffness and refractive index distribution of the crystalline lens in vivo and thus might contribute to reveal its inner working mechanism. Our methodology provides new routes for ophthalmic pre-surgical examinations and basic research.

BCLA CLEAR presbyopia: Mechanism and optics

With over a billion adults worldwide currently affected, presbyopia remains a ubiquitous, global problem. Despite over a century of study, the precise mechanism of ocular accommodation and presbyopia progression remains a topic of debate. Accordingly, this narrative review outlines the lenticular and extralenticular components of accommodation together with the impact of age on the accommodative apparatus, neural control of accommodation, models of accommodation, the impact of presbyopia on retinal image quality, and both historic and contemporary theories of presbyopia.

Intracapsular accommodation mechanism in terms of lens curvature gradient

The intracapsular accommodation mechanism (IAM) may be understood as an increase in the lens equivalent refractive index as the eye accommodates. Our goal was to evaluate the existence of an IAM by analysing observed changes in the inner curvature gradient of the lens. To this end, we fitted a gradient index and curvature lens model to published experimental data on external and nucleus geometry changes during accommodation. For each case analysed, we computed the refractive power and equivalent index for each accommodative state using a ray transfer matrix. All data sets showed an increase in the effective refractive index, indicating a positive IAM, which was stronger for older lenses. These results suggest a strong dependence of the lens equivalent refractive index on the inner curvature gradient.

Paraxial equivalent of the gradient-index lens of the human eye

The lens of the eye has a refractive index gradient that changes as the lens grows throughout life. These changes play a key role in the optics of the eye. Yet, the lens is generally simulated using a homogeneous model with an equivalent index that does not accurately represent the gradient. We present an analytical paraxial model of the gradient lens of the eye that gives the direct relation between refractive index distribution and paraxial characteristics. The model accurately simulates the changes in lens power with age and accommodation. It predicts that a decrease in equivalent index with age is associated with a flattening of the axial refractive index profile and that changes in lens power with accommodation are due primarily to changes in the axial variation of the iso-indicial curvature, consistent with Gullstrand's intracapsular theory of accommodation. The iso-indicial curvature gradient causes a shift of the principal planes compared to the homogeneous equivalent model. This shift introduces a clinically significant error in eye models that implement a homogenous lens. Our gradient lens model can be used in eye models to better predict the optics of the eye and the changes with age and accommodation.

Gullstrand Intracapsular Accommodation Mechanism Revised

More than a century has passed since Allvar Gullstrand proposed his so called “mechanism of intracapsular accommodation” based on the concept that the change in lens power during accommodation can be larger if the lens is modeled by two different refractive indexes (cortex and nucleus) than if it is homogenous. Intracapsular accommodation of the original eye model proposed by Gullstrand is compared with that of a six-surfaces model eye built based on actual experimental data obtained with precise imaging techniques of the lens change during accommodation. The results show that nearly half (42%) of the accommodation of the Gullstrand model eye is produced by said mechanism, while a model eye based on actual data produces a small intracapsular dis-accommodation. The main reason for the discrepancy is the larger change in the radii of curvature of the lens nucleus during accommodation proposed by Gullstrand, which is necessary because his model likely did not take into account the reduction in the change in lens power produced by depth-of-focus.

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.

The Structure of the Lens and Its Associations with the Visual Quality

In humans, the lens is the organ with the ability to change morphology and refractive power, designated as accommodation, to focus light from various distances and obtain clear retinal image. The accommodative ability of the lens depends on its structure and biological parameters. The lens grows throughout the life, forming specific lens sutures and a unique gradient refractive index, and possesses regenerative ability under certain circumstances. Minimally invasive lens surgery that preserves endogenous lens epithelial stem/progenitor cells (LECs) can achieve functional lens regeneration in humans. The lens is the main source of intraocular aberration, especially intraocular higher-order aberrations (IHOAs) which is found to be binocularly symmetrical in phakic eyes. There is a compensation mechanism between corneal aberrations and lens aberrations. Therefore, the structure and the biological parameters of the lens, the binocular relationship of the lens and the correlation between the lens and cornea affect visual quality. This paper summarises the above findings and their current and potential applications in refractive surgeries, providing a comprehensive understanding of the lens as a strong determinant of visual quality in the optical system.

Peripheral Defocus of the Monkey Crystalline Lens With Accommodation in a Lens Stretcher

Purpose

To characterize the peripheral defocus of the monkey crystalline lens and its changes with accommodation.

Methods

Experiments were performed on 15 lenses from 11 cynomolgus monkey eyes (age: 3.8–12.4 years, postmortem time: 33.5 ± 15.3 hours). The tissue was mounted in a motorized lens stretcher to allow for measurements of the lens in the accommodated (unstretched) and unaccommodated (stretched) states. A custom-built combined laser ray tracing and optical coherence tomography system was used to measure the paraxial on-axis and off-axis lens power for delivery angles ranging from −20° to +20° (in air). For each delivery angle, peripheral defocus was quantified as the difference between paraxial off-axis and on-axis power. The peripheral defocus of the lens was compared in the unstretched and stretched states.

Results

On average, the paraxial on-axis lens power was 52.0 ± 3.4 D in the unstretched state and 32.5 ± 5.1 D in the stretched state. In both states, the lens power increased with increasing delivery angle. From 0° to +20°, the relative peripheral lens power increased by 10.7 ± 1.4 D in the unstretched state and 7.5 ± 1.6 D in the stretched state. The change in field curvature with accommodation was statistically significant (P < 0.001), indicating that the unstretched (accommodated) lens has greater curvature or relative peripheral power.

Conclusions

The cynomolgus monkey lens has significant accommodation-dependent curvature of field, which suggests that the lens asserts a significant contribution to the peripheral optical performance of the eye that also varies with the state of accommodation.

System for on- and off-axis volumetric OCT imaging and ray tracing aberrometry of the crystalline lens

We present a new in vitro instrument for measuring shape and wavefront aberrations of the primate crystalline lens, both on- and off-axis, while simulating accommodation with a motorized lens stretching system. The instrument merges spectral domain optical coherence tomography (SD-OCT) imaging and ray tracing aberrometry using an approach that senses wavefront aberrations of the lens with the OCT probing beam. Accuracy and repeatability of aberration measurements were quantified. Preliminary experiments on two human and four cynomolgus monkey lenses demonstrate the ability of the system to measure the lens shape, spherical aberration and peripheral defocus, and their changes during simulated accommodation.

Nonhuman Primate Ocular Biometry

PURPOSE

To examine ocular growth in nonhuman primates (NHPs) from measurements on ex vivo eyes.

METHODS

We obtained NHP eyes from animals that had been killed as part of other studies or because of health-related issues. Digital calipers were used to measure the horizontal, vertical, and anteroposterior globe diameters as well as corneal horizontal and vertical diameters of excised globes from 98 hamadryas baboons, 551 cynomolgus monkeys, and 112 rhesus monkeys, at ages ranging from 23 to 360 months. Isolated lens sagittal thickness and equatorial diameter were measured by shadowphotogrammetry. Wet and fixed dry weights were obtained for lenses.

RESULTS

Nonhuman primate globe growth continues throughout life, slowing toward an asymptotic maximum. The final globe size scales with negative allometry to adult body size. Corneal growth ceases at around 20 months. Lens diameter increases but thickness decreases with increasing age. Nonhuman primate lens wet and dry weight accumulation is monophasic, continuing throughout life toward asymptotic maxima. The dry/wet weight ratio reaches a maximum of 0.33.

CONCLUSIONS

Nonhuman primate ocular globe and lens growth differ in several respects from those in humans. Although age-related losses of lens power and accommodative amplitude are similar, lens growth and properties are different indicating care should be taken in extrapolating NHP observations to the study of human accommodation.

Toxicity evaluation of high-fluorescent rare-earth metal nanoparticles for bioimaging applications

Research on nanometer-sized luminescent semiconductors and their biological applications in detectors and contrasting agents is an emergent field in nanotechnology. When new nanosize technologies are developed for human health applications, their interaction with biological systems should be studied in depth. Rare-earth elements are used in medical and industrial applications, but their toxic effects are not known. In this work, the biological interaction between terbium-doped gadolinium oxysulfide nanoparticles (GOSNPs) with human peripheral blood mononuclear cells (PBMC), human-derived macrophages (THP-1), and human cervical carcinoma cell (HeLa) were evaluated. The GOSNPs were synthetized using a hydrothermal method to obtain monodisperse nanoparticles with an average size of 91 ± 9 nm. Characterization techniques showed the hexagonal phase of the Gd₂ O₂ S:Tb³⁺ free of impurities, and a strong green emission at λ_emi  = 544 nm produced by Tb³⁺ was observed. Toxic effects of GOSNPs were evaluated using cell viability, apoptosis, cell-cycle progression, and immunological response techniques. In addition, an Artemia model was used to assess the toxicity in vivo. Results indicated cell apoptosis in both types of cells with less sensitivity for PBMC cells compared to HeLa cells. In addition, no toxic effects were observed in the in vivo model of Artemia. Moreover, GOSNPs significantly reduced the activation and cell-cycle progression of PBMC and HeLa cells, respectively. Interestingly, an increase in proinflammatory cytokines was not observed. Our data suggest that fluorescence applications of GOSNPs for biolabeling are not toxic in primary immune cells and they may have an immunomodulatory effect. © 2015 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 105B: 605-615, 2017.

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.

Objective measurement of accommodative biometric changes using ultrasound biomicroscopy

PURPOSE

To demonstrate that ultrasound biomicroscopy (UBM) can be used for objective quantitative measurements of anterior segment accommodative changes.

SETTING

College of Optometry, University of Houston, Houston, Texas, USA.

DESIGN

Prospective cross-sectional study.

METHODS

Anterior segment biometric changes in response to 0 to 6.0 diopters (D) of accommodative stimuli in 1.0 D steps were measured in eyes of human subjects aged 21 to 36 years. Imaging was performed in the left eye using a 35 MHz UBM (Vumax) and an A-scan ultrasound (A-5500) while the right eye viewed the accommodative stimuli. An automated Matlab image-analysis program was developed to measure the biometry parameters from the UBM images.

RESULTS

The UBM-measured accommodative changes in anterior chamber depth (ACD), lens thickness, anterior lens radius of curvature, posterior lens radius of curvature, and anterior segment length were statistically significantly linearly correlated with accommodative stimulus demands. Standard deviations of the UBM-measured parameters were independent of the accommodative stimulus demands (ACD: 0.0176 mm; lens thickness: 0.0294 mm; anterior lens radius of curvature: 0.3350 mm; posterior lens radius of curvature: 0.1580 mm; and anterior segment length: 0.0340 mm). The mean difference between the A-scan and UBM measurements was -0.070 mm for ACD and 0.166 mm for lens thickness.

CONCLUSIONS

Accommodating phakic eyes imaged using UBM allowed visualization of the accommodative response, and automated image analysis of the UBM images allowed reliable, objective, quantitative measurements of the accommodative intraocular biometric changes.

FINANCIAL DISCLOSURE

Neither author has a financial or proprietary interest in any material or method mentioned.

Measurement of Crystalline Lens Volume During Accommodation in a Lens Stretcher

PURPOSE

To determine if the lens volume changes during accommodation.

METHODS

The study used data acquired on 36 cynomolgus monkey lenses that were stretched in a stepwise fashion to simulate disaccommodation. At each step, stretching force and dioptric power were measured and a cross-sectional image of the lens was acquired using an optical coherence tomography system. Images were corrected for refractive distortions and lens volume was calculated assuming rotational symmetry. The average change in lens volume was calculated and the relation between volume change and power change, and between volume change and stretching force, were quantified. Linear regressions of volume-power and volume-force plots were calculated.

RESULTS

The mean (± SD) volume in the unstretched (accommodated) state was 97 ± 8 mm3. On average, there was a small but statistically significant (P = 0.002) increase in measured lens volume with stretching. The mean change in lens volume was +0.8 ± 1.3 mm3. The mean volume-power and volume-load slopes were -0.018 ± 0.058 mm3/D and +0.16 ± 0.40 mm3/g.

CONCLUSIONS

Lens volume remains effectively constant during accommodation, with changes that are less than 1% on average. This result supports a hypothesis that the change in lens shape with accommodation is accompanied by a redistribution of tissue within the capsular bag without significant compression of the lens contents or fluid exchange through the capsule.

The zonules selectively alter the shape of the lens during accommodation based on the location of their anchorage points

PURPOSE

To determine the role of anterior and posterior zonular tension on the optomechanical lens response during accommodation simulation.

METHODS

Ten eyes from nine hamadryas baboons (4.9 ± 0.7 years) and 20 eyes from 18 cynomolgus monkeys (5.4 ± 0.3 years) were dissected, leaving the lens, zonules, ciliary body, hyaloid membrane, anterior vitreous, and a segmented scleral rim intact. The lens preparation was mounted in a lens stretcher, and the outer scleral shell was displaced radially in a stepwise fashion. The load, lens, and ciliary body diameters, lens power, lens thickness, and the anterior and posterior radius of curvature were measured during stretching. The zonular fibers attached to either the posterior or anterior lens surface were then carefully transected and the experiment was repeated. Zonular transection was confirmed in four eyes via laser scanning confocal microscopy after immunostaining. The effect of zonular transection on the tissue response to stretching was quantified.

RESULTS

Without anterior zonules, 48% and 97% of the changes in anterior and posterior radii are retained. Without posterior zonules, 81% and 67% of the changes in anterior and posterior radii are retained. The changes in lens shape were reduced after transecting either the anterior or posterior zonules; however, both surfaces still changed shape.

CONCLUSIONS

While either the anterior or posterior zonules alone are capable of changing the shape of both lens surfaces, the anterior zonules have a greater effect on the anterior lens surface, and the posterior zonules have a greater effect on the posterior lens surface.

Changes in monkey crystalline lens spherical aberration during simulated accommodation in a lens stretcher

PURPOSE

The purpose of this study was to quantify accommodation-induced changes in the spherical aberration of cynomolgus monkey lenses.

METHODS

Twenty-four lenses from 20 cynomolgus monkeys (Macaca fascicularis; 4.4-16.0 years of age; postmortem time 13.5 ± 13.0 hours) were mounted in a lens stretcher. Lens spherical aberration was measured in the unstretched (accommodated) and stretched (relaxed) states with a laser ray tracing system that delivered 51 equally spaced parallel rays along 1 meridian of the lens over the central 6-mm optical zone. A camera mounted below the lens was used to measure the ray height at multiple positions along the optical axis. For each entrance ray, the change in ray height with axial position was fitted with a third-order polynomial. The effective paraxial focal length and Zernike spherical aberration coefficients corresponding to a 6-mm pupil diameter were extracted from the fitted values.

RESULTS

The unstretched lens power decreased with age from 59.3 ± 4.0 diopters (D) for young lenses to 45.7 ± 3.1 D for older lenses. The unstretched lens shifted toward less negative spherical aberration with age, from -6.3 ± 0.7 μm for young lenses to -5.0 ± 0.5 μm for older lenses. The power and spherical aberration of lenses in the stretched state were independent of age, with values of 33.5 ± 3.4 D and -2.6 ± 0.5 μm, respectively.

CONCLUSIONS

Spherical aberration is negative in cynomolgus monkey lenses and becomes more negative with accommodation. These results are in good agreement with the predicted values using computational ray tracing in a lens model with a reconstructed gradient refractive index. The spherical aberration of the unstretched lens becomes less negative with age.

OCT 3-D surface topography of isolated human crystalline lenses

Quantitative 3-D Optical Coherence Tomography was used to measure surface topography of 36 isolated human lenses, and to evaluate the relationship between anterior and posterior lens surface shape and their changes with age. All lens surfaces were fitted to 6th order Zernike polynomials. Astigmatism was the predominant surface aberration in anterior and posterior lens surfaces (accounting for ~55% and ~63% of the variance respectively), followed by spherical terms, coma, trefoil and tetrafoil. The amount of anterior and posterior surface astigmatism did not vary significantly with age. The relative angle between anterior and posterior surface astigmatism axes was on average 36.5 deg, tended to decrease with age, and was >45 deg in 36.1% lenses. The anterior surface RMS spherical term, RMS coma and 3rd order RMS decreased significantly with age. In general, there was a statistically significant correlation between the 3rd and 4th order terms of the anterior and posterior surfaces. Understanding the coordination of anterior and posterior lens surface geometries and their topographical changes with age sheds light into the role of the lens in the optical properties of the eye and the lens aging mechanism.

Influence of shape and gradient refractive index in the accommodative changes of spherical aberration in nonhuman primate crystalline lenses

PURPOSE

To estimate changes in surface shape and gradient refractive index (GRIN) profile in primate lenses as a function of accommodation. To quantify the contribution of surface shape and GRIN to spherical aberration changes with accommodation.

METHODS

Crystalline lenses from 15 cynomolgus monkeys were studied in vitro under different levels of accommodation produced by a stretching system. Lens shape was obtained from optical coherence tomography (OCT) cross-sectional images. The GRIN was reconstructed with a search algorithm using the optical path measured from OCT images and the measured back focal length. The spherical aberration of the lens was estimated as a function of accommodation using the reconstructed GRIN and a homogeneous refractive index.

RESULTS

The lens anterior and posterior radii of curvature decreased with increasing lens power. Both surfaces exhibited negative asphericities in the unaccommodated state. The anterior surface conic constant shifted toward less negative values with accommodation, while the value of the posterior remained constant. GRIN parameters remained constant with accommodation. The lens spherical aberration with GRIN distribution was negative and higher in magnitude than that with a homogeneous equivalent refractive index (by 29% and 53% in the unaccommodated and fully accommodated states, respectively). Spherical aberration with the equivalent refractive index shifted with accommodation toward negative values (-0.070 μm/diopter [D]), but the reconstructed GRIN shifted it farther (-0.124 μm/D).

CONCLUSIONS

When compared with the lens with the homogeneous equivalent refractive index, the reconstructed GRIN lens has more negative spherical aberration and a larger shift toward more negative values with accommodation.

Contribution of the gradient refractive index and shape to the crystalline lens spherical aberration and astigmatism

The optical properties of the crystalline lens are determined by its shape and refractive index distribution. However, to date, those properties have not been measured together in the same lens, and therefore their relative contributions to optical aberrations are not fully understood. The shape, the optical path difference, and the focal length of ten porcine lenses (age around 6 months) were measured in vitro using Optical Coherence Tomography and laser ray tracing. The 3D Gradient Refractive Index distribution (GRIN) was reconstructed by means of an optimization method based on genetic algorithms. The optimization method searched for the parameters of a 4-variable GRIN model that best fits the distorted posterior surface of the lens in 18 different meridians. Spherical aberration and astigmatism of the lenses were estimated using computational ray tracing, with the reconstructed GRIN lens and an equivalent homogeneous refractive index. For all lenses the posterior radius of curvature was systematically steeper than the anterior one, and the conic constant of both the anterior and posterior positive surfaces was positive. In average, the measured focal length increased with increasing pupil diameter, consistent with a crystalline lens negative spherical aberration. The refractive index of nucleus and surface was reconstructed to an average value of 1.427 and 1.364, respectively, for 633 nm. The results of the GRIN reconstruction showed a wide distribution of the index in all lens samples. The GRIN shifted spherical aberration towards negative values when compared to a homogeneous index. A negative spherical aberration with GRIN was found in 8 of the 10 lenses. The presence of GRIN also produced a decrease in the total amount of lens astigmatism in most lenses, while the axis of astigmatism was only little influenced by the presence of GRIN. To our knowledge, this study is the first systematic experimental study of the relative contribution of geometry and GRIN to the aberrations in a mammal lens.

In vivo human crystalline lens topography

Custom high-resolution high-speed anterior segment spectral domain optical coherence tomography (OCT) was used to characterize three-dimensionally (3-D) the human crystalline lens in vivo. The system was provided with custom algorithms for denoising and segmentation of the images, as well as for fan (scanning) and optical (refraction) distortion correction, to provide fully quantitative images of the anterior and posterior crystalline lens surfaces. The method was tested on an artificial eye with known surfaces geometry and on a human lens in vitro, and demonstrated on three human lenses in vivo. Not correcting for distortion overestimated the anterior lens radius by 25% and the posterior lens radius by more than 65%. In vivo lens surfaces were fitted by biconicoids and Zernike polynomials after distortion correction. The anterior lens radii of curvature ranged from 10.27 to 14.14 mm, and the posterior lens radii of curvature ranged from 6.12 to 7.54 mm. Surface asphericities ranged from -0.04 to -1.96. The lens surfaces were well fitted by quadrics (with variation smaller than 2%, for 5-mm pupils), with low amounts of high order terms. Surface lens astigmatism was significant, with the anterior lens typically showing horizontal astigmatism ([Formula: see text] ranging from -11 to -1 µm) and the posterior lens showing vertical astigmatism ([Formula: see text] ranging from 6 to 10 µm).

Hyperelastic modelling of the crystalline lens: Accommodation and presbyopia

Purpose

The modification of the mechanical properties of the human crystalline lens with age can be a major cause of presbyopia. Since these properties cannot be measured in vivo, numerical simulation can be used to estimate them. We propose an inverse method to determine age-dependent change in the material properties of the tissues composing the human crystalline lens.

Methods

A finite element model of a 30-year-old lens in the accommodated state was developed. The force necessary to achieve full accommodation in a 30-year-old lens of known external geometry was computed using this model. Two additional numerical models of the lens corresponding to the ages of 40 and 50 years were then built. Assuming that the accommodative force applied to the lens remains constant with age, the material properties of nucleus and cortex were estimated by inverse analysis.

Results

The zonular force necessary to reshape the model of a 30-year-old lens from the accommodated to the unaccommodated geometry was 0.078 newton (N). Both nucleus and cortex became stiffer with age. The stiffness of the nucleus increased with age at a higher rate than the cortex.

Conclusions

In agreement with the classical theory of Helmholtz, on which we based our model, our results indicate that a major cause of presbyopia is that both nucleus and cortex become stiffer with age; therefore, a constant value of the zonular forces with aging does not achieve full accommodation, that is, the accommodation capability decreases.