Biomechanical analysis of the accommodative apparatus in primates

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.

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).

An Artificial Lens Capsule with a Lens Radial Stretching System Mimicking Dynamic Eye Focusing

Presbyopia is a common eye disorder among aged people which is attributed to the loss of accommodation of the crystalline lens due to the increasing stiffness. One of the potential techniques to correct presbyopia involves removing the lens substance inside the capsule and replacing it with an artificial lens. The development of such devices, e.g., accommodating intraocular lenses (AIOLs), relies on the understanding of the biomechanical behaviour of the lens capsule and the essential design verification ex vivo. To mimic the eye’s dynamic focusing ability (accommodation), an artificial lens capsule (ALC), from silicone rubber accompanied by a lens radial stretching system (LRSS) was developed. The ALC was manufactured to offer a dimension and deforming behaviour replicating the human lens capsule. The LRSS was calibrated to provide a radial stretch simulating the change of diameter of capsules during accommodating process. The biomechanical function of the ALC was addressed by studying its evolution behaviour and reaction force under multiaxial stretch from the LRSS. The study highlighted the convenience of this application by performing preliminary tests on prototypes of ophthalmic devices (e.g., AIOLs) to restore accommodation.

Deformations and Ruptures in Human Lenses With Cortical Cataract Subjected to Ex Vivo Simulated Accommodation

Purpose

Human cortical opacities are most commonly accompanied by changes in lens fiber structure in the equatorial region at the lens nucleus–cortex interface. Cortex and nucleus have different elastic properties, which change with age. We therefore subjected ex vivo lenses to simulated accommodation and studied the internal deformations to better understand the mechanism of cortical cataract formation.

Methods

Nine human donor lenses (33–88 years old) were tested using a bespoke radial stretching device for anterior eye segments. Seven of the lenses exhibited cortical cataracts. The other two lenses, without cataract, were used as controls. Frontal and cross-sectional images of the lens obtained during stretching facilitated measurements on equatorial lens diameter and central lens thickness in the stretched and unstretched states.

Results

Stretching caused the lens equatorial diameter to increase in all cases. Conversely, the lens central thickness showed no systematic variation during stretching. For four of the lenses with cortical cataract, ruptures were observed during stretching at the nucleus–cortex boundary adjacent to the cortical cataracts. Ruptures were not observed in the control lenses or in the three other lenses with cortical cataract.

Conclusions

Internal ruptures can occur in aged ex vivo lenses subjected to simulated disaccommodation. These ruptures occur at the nucleus–cortex interface; at this location, a significant stiffness discontinuity is expected to develop with age. It is hypothesized that ruptures occur in in vivo lenses during accommodation—or attempted accommodation.

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).

Lens Stretching Modulates Lens Epithelial Cell Proliferation via YAP Regulation

Purpose

The continuous growth of the lens throughout life may contribute to the onset of age-related conditions in the lens (i.e., presbyopia and cataract). Volumetric growth is the result of continuous proliferation of lens epithelial cells (LECs). The driving factors controlling LEC proliferation are not well understood. This study tested the hypothesis that mechanical stretching modulates LEC proliferation.

Methods

Biomechanical regulation of LEC proliferation was investigated by culturing whole porcine lenses and connective tissues ex vivo under varying physiologically relevant stretching conditions using a bespoke lens stretching device. Additionally, some lenses were treated with a YAP function inhibitor to determine the Hippo signaling pathway's role in regulating lens growth. Resulting changes in LEC labeling index were analyzed using EdU incorporation and flow cytometry for each lens.

Results

LEC proliferation was found to be modulated by mechanical strain. Increasing both the magnitude of static stretching and the stretching frequency in cyclic stretching resulted in a proportional increase in the labeling indices of the LECs. Additionally, treatment with the YAP function inhibitor effectively eliminated this relationship.

Conclusions

These data demonstrate that LEC proliferation is regulated in part, by the mechanotransduction of stresses induced in the lens capsule and that YAP plays an important role in mechanosensing. These results have important implications for understanding lens growth and morphogenesis. The model may also be used to identify and evaluate targets for modulating lens growth.

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.

Simulating the Mechanics of Lens Accommodation via a Manual Lens Stretcher

The goal of this protocol is to mimic the biomechanics of physiological accommodation in a cost-efficient, practical manner. Accommodation is achieved through the contraction of the ciliary body and relaxation of zonule fibers, which results in the thickening of the lens necessary for near vision. Here, we present a novel, simple method in which accommodation is replicated by tensing the zonules connected to the lens capsule via a manual lens stretcher (MLS). This method monitors the radial stretching achieved by a lens when subjected to a consistent force and allows for a comparison of accommodating lenses, which can be stretched, to non-accommodating lenses, which cannot be stretched. Importantly, the stretcher couples to the zonules directly, and not to the sclera of the eye, thus only requiring the lens, zonules, and ciliary body rather than the entire globe sample. This difference can significantly decrease the cost of acquiring donor cadaver lenses by about 62% compared to acquiring an entire globe.

Ultrasound biomicroscopy value in evaluation of restoration of ciliary muscles contractility after cataract extraction

Purpose

To assess the changes in the contractility of the ciliary muscle in eyes with presbyopia before and after phacoemulsification and intracapsular lens implantation using ultrasound biomicroscopy (UBM).

Patients and methods

This prospective study included 50 eyes of 30 consecutive subjects operated at the Department of Ophthalmology. Patients with any ocular disorder affecting visual acuity, corneal surface irregularities, had posterior capsular perforation or intensive postoperative corneal edema, or were <35 years of age, were excluded. A clear corneal phacoemulsification and posterior chamber intraocular lens were implanted. UBM was performed with and without instilling 2% pilocarpine. Ciliary body axial length (CBAXL), anterior chamber depth, and angle were measured before and 1 month after surgery.

Results

The CBAXL showed a greater contractile shortening (P<0.5), with centripetal, contractile shift of ciliary muscle mass.

Conclusion

After phacoemulsification and intracapsular lens implantation, ultrasonic biomicroscopy showed significant centripetal movement of the ciliary body compared with that before surgery. This shows that a lenticular sclerotic component may influence both lens movement and the contractility of the ciliary muscle and is believed to be related to the presbyopia.

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 lens stiffness due to capsular opacification in accommodative lens refilling

Accommodation may be restored to presbyopic lenses by refilling the lens capsular bag with a soft polymer. After this accommodative lens refilling prevention of capsular opacification is a requirement, since capsular opacification leads to a decreased clarity of the refilled lens. It has been hypothesized that capsular fibrosis causing the capsular opacification results in increased stiffness of the lens capsular bag, therewith contributing to a decrease in accommodative amplitude of the lens. However, the change in viscoelastic properties of refilled lenses due to capsular fibrosis has never been measured directly. In this study we examined natural lenses from enucleated porcine eyes and refilled lenses directly after refilling and after three months of culturing, when capsular fibrosis had developed, and determined their viscoelastic properties with a low load compression tester. Control refilled lenses were included in which capsular opacification was prevented by treatment with actinomycin D. We related lens stiffening to the degree of capsular opacification, as derived from the microscopic images taken with a confocal laser scanning microscope. Overall, the refilled lenses directly after refilling were softer than refilled lenses after three months of culturing, and refilled lenses treated with actinomycin D were softer compared with untreated refilled lenses. The degree of capsular opacification as assessed by microscopy corresponds to an increase in lens stiffness. This indicates that the viscoelastic properties of the refilled lens are influenced by capsular fibrosis and modulated by treatment of the lens epithelium. In conclusion, this study shows that the development of capsular fibrosis negatively affects the viscoelastic properties of isolated, cultured refilled lenses.

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.

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.

Pig lenses in a lens stretcher: implications for presbyopia treatment

PURPOSE

To investigate porcine lenses in a lens stretcher with regard to presbyopia corrective procedures.

METHODS

A lens stretching device was designed, which allows to simultaneously determine all relevant geometrical and optical parameters at each stretch position. The setup was used to compare the optical and geometrical lens properties of young slaughter pigs (n = 5) with older sows (n = 7).

RESULTS

The change of optical power with stretching is about five times larger for young porcine lenses than for sows. For young pigs, the gradient index profile of the crystalline lens significantly contributes to the induced accommodation amplitude.

CONCLUSIONS

We have shown that sow lenses are a suitable model for in vitro experiments on possible treatments for presbyopia. The rapid decrease in the induced accommodation amplitude with age may be explained by a reduced change of all geometrical lens parameters, which in turn leads to a smaller contribution of the gradient index profile to accommodation.

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

The purpose of this study was to determine the contribution of the gradient refractive index to the change in lens power in hamadryas baboon and cynomolgus monkey lenses during simulated accommodation in a lens stretcher. Thirty-six monkey lenses (1.4-14.1 years) and twenty-five baboon lenses (1.8-28.0 years) were stretched in discrete steps. At each stretching step, the lens back vertex power was measured and the lens cross-section was imaged with optical coherence tomography. The radii of curvature for the lens anterior and posterior surfaces were calculated for each step. The power of each lens surface was determined using refractive indices of 1.365 for the outer cortex and 1.336 for the aqueous. The gradient contribution was calculated by subtracting the power of the surfaces from the measured lens power. In all lenses, the contribution of the surfaces and gradient increased linearly with the amplitude of accommodation. The gradient contributes on average 65 ± 3% for monkeys and 66 ± 3% for baboons to the total power change during accommodation. When expressed in percent of the total power change, the relative contribution of the gradient remains constant with accommodation and age in both species. These findings are consistent with Gullstrand's intracapsular theory of accommodation.

Age-dependence of the optomechanical responses of ex vivo human lenses from India and the USA, and the force required to produce these in a lens stretcher: the similarity to in vivo disaccommodation

The purpose of this study was to study the age-dependence of the optomechanical properties of human lenses during simulated disaccommodation in a mechanical lens stretcher, designed to determine accommodative forces as a function of stretch distance, to compare the results with in vivo disaccommodation and to examine whether differences exist between eyes harvested in the USA and India. Postmortem human eyes obtained in the USA (n=46, age=6-83 years) and India (n=91, age=1 day-85 years) were mounted in an optomechanical lens stretching system and dissected to expose the lens complete with its accommodating framework, including zonules, ciliary body, anterior vitreous and a segmented rim of sclera. Disaccommodation was simulated through radial stretching of the sectioned globe by 2mm in increments of 0.25 mm. The load, inner ciliary ring diameter, lens equatorial diameter, central thickness and power were measured at each step. Changes in these parameters were examined as a function of age, as were the dimension/load and power/load responses. Unstretched lens diameter and thickness increased over the whole age range examined and were indistinguishable from those of in vivo lenses as well as those of in vitro lenses freed from zonular attachments. Stretching increased the diameter and decreased the thickness in all lenses examined but the amount of change decreased with age. Unstretched lens power decreased with age and the accommodative amplitude decreased to zero by age 45-50. The load required to produce maximum stretch was independent of age (median 80 mN) whereas the change in lens diameter and power per unit load decreased significantly with age. The age related changes in the properties of human lenses, as observed in the lens stretching device, are similar to those observed in vivo and are consistent with the classical Helmholtz theory of accommodation. The response of lens diameter and power to disaccommodative (stretching) forces decreases with age, consistent with lens nuclear stiffening.

Semiautomated analysis of optical coherence tomography crystalline lens images under simulated accommodation

Presbyopia is an age related, gradual loss of accommodation, mainly due to changes in the crystalline lens. As part of research efforts to understand and cure this condition, ex vivo, cross-sectional optical coherence tomography images of crystalline lenses were obtained by using the Ex-Vivo Accommodation Simulator (EVAS II) instrument and analyzed to extract their physical and optical properties. Various filters and edge detection methods were applied to isolate the edge contour. An ellipse is fitted to the lens outline to obtain central reference point for transforming the pixel data into the analysis coordinate system. This allows for the fitting of a high order equation to obtain a mathematical description of the edge contour, which obeys constraints of continuity as well as zero to infinite surface slopes from apex to equator. Geometrical parameters of the lens were determined for the lens images captured at different accommodative states. Various curve fitting functions were developed to mathematically describe the anterior and posterior surfaces of the lens. Their differences were evaluated and their suitability for extracting optical performance of the lens was assessed. The robustness of these algorithms was tested by analyzing the same images repeated times.

Functionalised polysiloxanes as injectable, in situ curable accommodating intraocular lenses

The aged eye's ability to change focus (accommodation) may be restored by replacing the hardened natural lens with a soft gel. Functionalised polysiloxane macromonomers, designed for application as an injectable, in situ curable accommodating intraocular lens (A-IOL), were prepared via a two-step synthesis. Prepolymers were synthesised via ring opening polymerisation (ROP) of octamethylcyclotetrasiloxane (D(4)) and 2,4,6,8-tetramethylcyclotetrasiloxane (D(4)(H)) in toluene using trifluoromethanesulfonic acid (TfOH) as catalyst. Hexaethyldisiloxane (HEDS) was used as the end group to control the molecular weight of the prepolymers, which were then converted to macromonomers by hydrosilylation of the SiH groups with allyl methacrylate (AM) to introduce polymerisable groups. The resulting macromonomers had an injectable consistency and thus, were able to be injected into and refill the empty lens capsular bag. The macromonomers also contained a low ratio of polymerisable groups so that they may be cured on demand, in situ, under irradiation of blue light, in the presence of a photo-initiator, to form a soft polysiloxane gel (an intraocular lens) in the eye. The pre-cure viscosity and post-cure modulus of the polysiloxanes, which are crucial factors for an injectable, in situ curable A-IOL application, were controlled by adjusting the end group and D(4)(H) concentrations, respectively, in the ROP. The macromonomers were fully cured within 5 min under light irradiation, as shown by the rapid change in modulus monitored by photo-rheology. Ex vivo primate lens stretching experiments on an Ex Vivo Accommodation Simulator (EVAS) showed that the polysiloxane gel refilled lenses achieved over 60% of the accommodation amplitude of the natural lens. An in vivo biocompatibility study in rabbits using the lens refilling (Phaco-Ersatz) procedure demonstrated that the soft gels had good biocompatibility with the ocular tissue. The polysiloxane macromonomers meet the targeted optical and mechanical properties of a young natural crystalline lens and show promise as candidate materials for use as injectable, in situ curable A-IOLs for lens refilling procedures.