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Glaucoma is among the leading causes of blindness worldwide that is characterized by irreversible damage to the retinal ganglion cell axons in the lamina cribrosa (LC) region of the optic nerve head (ONH), most often associated with elevated intraocular pressure (IOP). The LC is a porous, connective tissue structure that provides mechanical support to the axons as they exit the eye and the biomechanics of the LC microstructure likely play a crucial role in protecting the axons passing through it. There is a limited knowledge of the IOP-driven biomechanics of the LC microstructure, primarily due to its small size and the difficulty with imaging the LC both in vitro and in vivo. We present finite element (FE) models of three human eye posterior poles that include the LC microstructure and interspersed neural tissues (NT) composed of retinal axons that are constructed directly from segmented, binary images of the LC. These models were used to estimate the stresses and strains in the LC and NT for an acute IOP elevation from 0 to 45 mmHg and compared with identical models except that the LC was represented as a homogenized continuum material with either homogeneous isotropic neo-Hookean properties or heterogeneous properties derived from local connective tissue volume fraction (CTVF) and predominant LC beam orientation. Stresses and strains in the LC and NT microstructure were investigated, and results were compared against those from the models wherein the LC was represented as a homogenized continuum. The regionalized volumetric average stresses and strains showed that the microstructural model yielded similar patterns to our prior approach using an LC continuum representation with mapped LC CTVF/anisotropy, but the microstructural modeling approach allows analysis of the stresses and strains in the LC and NT separately. As expected, the LC beams carried most of the IOP load in the microstructural models but exhibited less strain, while the encapsulated NT exhibited lower stresses and much higher strains. Results also revealed that the continuum models underestimate the maximum strains in the LC beams and NT by a factor of 2-3. Microstructural modeling should provide greater insight into the biomechanical factors driving damage to the axons (NT) and LC connective tissue remodeling that occur in glaucoma. The methods presented are ideal for modeling any structure with a complex microstructure composed of different materials, such as trabecular bone, lung, and tissue engineering scaffolds such as decellularized LC. Matlab code for mesh generation from a segmented image stack of the microstructure is included as Supplemental Material. STATEMENT OF SIGNIFICANCE: Glaucoma is among the leading causes of blindness worldwide that is characterized by axon damage in the lamina cribrosa (LC) region of the eye. We present a new approach for finite element modeling the entire eye-specific 3D LC microstructure and the interspersed neural tissues, incorporated into an eye-specific posterior eye model that provides appropriate boundary and loading conditions. Results are presented for three human donor eyes, showing that prior modeling approaches underestimate the stresses and strains in the laminar microstructure. We constructed models from image stacks of the segmented microstructure (Matlab code included) using an approach that is ideal for modeling any structure with a complex microstructure composed of different materials, such as trabecular bone, lung, and tissue engineering scaffolds.

Preconditioning by repeated cyclic loads is routinely used in ex vivo mechanical testing of soft biological tissues. The goal of preconditioning is to achieve a steady and repeatable mechanical response and to measure material properties that are representative of the in vivo condition. Preconditioning protocols vary across studies, and their effect on the viscoelastic response of tested soft tissue is typically not reported or analyzed. We propose a methodology to systematically analyze the preconditioning process with application to inflation testing. We investigated the effect of preconditioning on the viscoelastic inflation response of tree shrew posterior sclera using two preconditioning protocols: (i) continuous cyclic loading-unloading without rest and (ii) cyclic loading-unloading with 15-min rest between cycles. Posterior scleral surface strain was measured using three-dimensional Digital Image Correlation (3D-DIC). We used five variables of characterizing features of the stress-strain loop curve to compare the two preconditioning protocols. Our results showed protocol-dependent differences in the tissue response during preconditioning and at the preconditioned state. Incorporating a resting time between preconditioning cycles significantly decreased the number of cycles (10.5 ± 2.9 cycles vs. 3.1 ± 0.5 cycles, p Statement of significance Although applying a preconditioning protocol by repeated cyclic loads is common practice in ex vivo mechanical characterization of soft tissues, the tissue response is typically not reported or analyzed, and the protocol’s potential effect on the response remains unclear. This is partially caused by lack of a standardized methodology to precondition soft tissues. We present the first systematic analysis of two representative preconditioning protocols used during inflation testing in ocular biomechanics. Our results show protocol-dependent differences in the viscoelastic response during the preconditioning process and at the preconditioned state. Consequently, the analysis of the preconditioning response represents an essential part of mechanical testing and a prerequisite to properly characterize the tissue viscoelastic response. The effect of preconditioning on the preconditioned state response must be considered when comparing results across studies with different preconditioning protocols.

Idiopathic pulmonary fibrosis (IPF) is a progressive fibrotic lung disease without effective therapy. Animal models effectively reproducing IPF disease features are needed to study the underlying molecular mechanisms. Tree shrews are genetically, anatomically, and metabolically closer to humans than rodents or dogs; therefore, the tree shrew model presents a unique opportunity for translational research in lung fibrosis. Here we demonstrate that tree shrews have in vivo and in vitro fibrotic responses induced by bleomycin and pro-fibrotic mediators. Bleomycin exposure induced lung fibrosis evidenced by histological and biochemical fibrotic changes. In primary tree shrew lung fibroblasts, transforming growth factor beta-1 (TGF-β1) induced myofibroblast differentiation, increased extracellular matrix (ECM) protein production, and focal adhesion kinase (FAK) activation. Tree shrew lung fibroblasts showed enhanced migration and increased matrix invasion in response to platelet derived growth factor BB (PDGF-BB). Inhibition of FAK significantly attenuated pro-fibrotic responses in lung fibroblasts. The data demonstrate that tree shrews have in vivo and in vitro fibrotic responses similar to that observed in IPF. The data, for the first time, support that the tree shrew model of lung fibrosis is a new and promising experimental animal model for studying the pathophysiology and therapeutics of lung fibrosis.

Myopia and glaucoma are both increasing in prevalence and are linked by an unknown mechanism as many epidemiologic studies have identified moderate to high myopia as an independent risk factor for glaucoma. Myopia and glaucoma are both chronic conditions that lead to connective tissue remodeling within the sclera and optic nerve head. The mechanobiology underlying connective tissue remodeling differs substantially between both diseases, with different homeostatic control mechanisms. In this article, we discuss similarities and differences between connective tissue remodeling in myopia and glaucoma; selected multi-scale mechanisms that are thought to underlie connective tissue remodeling in both conditions; how asymmetric remodeling of the optic nerve head may predispose a myopic eye for pathological remodeling and glaucoma; and how neural tissue deformations may accumulate throughout both pathologies and increase the risk for mechanical insult of retinal ganglion cell axons.

Scleral crosslinking using genipin has been identified as a promising treatment approach for myopia control. The efficacy of genipin to alter biomechanical properties of the sclera has been shown in several animal models of myopia but its safety profile remains unclear. In this safety study, we aim to investigate the effect of scleral crosslinking using retrobulbar injections of genipin on retinal structure and function at genipin doses that were shown to be effective in slowing myopia progression in juvenile tree shrews. To this end, three or five retrobulbar injections of genipin at 0 mM (sham), 10 mM, or 20 mM were performed in one eye every other day. Form deprivation myopia was induced in the injected eye. We evaluated retinal function using full-field electroretinography and retinal structure using in vivo optical coherence tomography imaging and ex vivo histology. The optical coherence tomography results revealed significant thinning of the peripapillary retinal nerve fiber layer in all genipin treated groups including the lowest dose group, which showed no significant treatment effect in slowing myopia progression. In contrast, inducing form deprivation myopia alone and in combination with sham injections caused no obvious thinning of the retinal nerve fiber layer. Electroretinography results showed a significant desensitizing shift of the b-wave semi-saturation constant in the sham group and the second highest genipin dose group, and a significant reduction in b-wave maxima in the two highest genipin dose groups. The ex vivo histology revealed noticeable degeneration of photoreceptors and retinal pigment epithelium in one of two investigated eyes of the highest genipin dose group. While scleral crosslinking using genipin may still be a feasible treatment option for myopia control, our results suggest that repeated retrobulbar injections of genipin at 10 mM or higher are not safe in tree shrews. An adequate and sustained delivery strategy of genipin at lower concentrations will be needed to achieve a safe and effective scleral crosslinking treatment for myopia control in tree shrews. Caution should be taken if the proposed treatment approach is translated to humans.

We describe an analysis strategy to obtain ultrasonography-matched axial dimensions of small animal eyes using the LenStar biometer. The LenStar optical low-coherence reflectometer is an attractive device for animal research due to its high precision, non-invasiveness, and the ability to measure the axial dimensions of cornea, anterior chamber, lens, vitreous chamber, and axial length. However, this optical biometer was designed for clinical applications in human eyes and its internal analysis provides inaccurate values when used on small eyes due to species-dependent differences in refractive indices and relative axial dimensions. The LenStar uses a near infrared light source to measure optical path lengths (OPLs) that are converted by the LenStar’s EyeSuite software into geometrical lengths (GLs) based on the refractive indices and axial dimensions of the human eye. We present a strategy that extracts the OPLs, determines refractive indices specific for the small animal eye of interest and then calculates corrected GLs. The refractive indices are obtained by matching the LenStar values to ultrasonography values to ultrasonography values in the same eyes. As compared to ultrasounography, we found that the internal calculations of the LenStar underestimate the axial dimensions of all ocular compartments of the tree shrew eye: anterior segment depth by 6.17 ± 4.50%, lens thickness by 1.37 ± 3.06%, vitreous chamber depth by 29.23 ± 2.35%, and axial length by 10.62 ± 1.75%. Using tree shrew-specific refractive indices, the axial dimensions closely matched those measured by ultrasonography for each compartment. Our analysis strategy can be easily translated to other species by obtaining a similar paired data set using ultrasonography and LenStar, and applying our step by step procedures.

The postnatal growing eye uses visual cues to actively control its own axial elongation to achieve and maintain sharp focus, a process termed emmetropization. The primary visual cue may be the difference in image sharpness as sensed by the arrays of short- and long-wavelength sensitive cone photoreceptors caused by longitudinal chromatic aberration: Shorter wavelengths focus in front of longer wavelengths. However, the sparse distribution of short-wavelength sensitive cones across the retina suggests that they do not have sufficient spatial sampling resolution for this task. Here, we show that the spacing of the short-wavelength sensitive cones in humans is sufficient for them, in conjunction with the longer wavelength cones, to use chromatic signals to detect defocus and guide emmetropization. We hypothesize that the retinal spacing of the short-wavelength sensitive cones in many mammalian species is an evolutionarily ancient adaption that allows the efficient use of chromatic cues in emmetropization.

Commercial finite element modeling packages do not have the tools necessary to effectively incorporate the complex anisotropic and heterogeneous material properties typical of the biological tissues of the eye. We propose a mesh-free approach to incorporate realistic material properties into finite element models of individual human eyes. The method is based on the idea that material parameters can be estimated or measured at so called control points, which are arbitrary and independent of the finite element mesh. The mesh-free approach approximates the heterogeneous material parameters at the Gauss points of each finite element while the boundary value problem is solved using the standard finite element method. The proposed method was applied to an eye-specific model a human posterior pole and optic nerve head. We demonstrate that the method can be used to effectively incorporate experimental measurements of the lamina cribrosa micro-structure into the eye-specific model. It was convenient to define characteristic material orientations at the anterior and posterior scleral surface based on the eye-specific geometry of each sclera. The mesh-free approach was effective in approximating these characteristic material directions with smooth transitions across the sclera. For the first time, the method enabled the incorporation of the complex collagen architecture of the peripapillary sclera into an eye-specific model including the recently discovered meridional fibers at the anterior surface and the depth dependent width of circumferential fibers around the scleral canal. The model results suggest that disregarding the meridional fiber region may lead to an underestimation of local strain concentrations in the retina. The proposed approach should simplify future studies that aim to investigate collagen remodeling in the sclera and optic nerve head or in other biological tissues with similar challenges.

We propose an empirical distortion correction approach for optical coherence tomography (OCT) devices that use a fan-scanning pattern to image the posterior eye segment. Two types of reference markers were used to empirically estimate the distortion correction approach in tree shrew eyes: retinal curvature from MRI images and implanted glass beads of known diameter. Performance was tested by correcting distorted images of the optic nerve head. In small animal eyes, our purposed method effectively reduced nonlinear distortions compared to a linear scaling method. No commercial posterior segment OCT provides anatomically correct images, which may bias the 3D interpretation of these scans. Our method can effectively reduce such bias.

Purpose To evaluate the effect of scleral crosslinking (SXL) on slowing experimental progressive myopia in tree shrew eyes using sub-Tenon's injections of genipin (GEN) at different concentrations and number of injections. Methods Three or five sub-Tenon's injections of GEN at 0 mM (sham), 10 mM, or 20 mM were performed in one eye every other day starting at 18 days of visual experience. Form deprivation (FD) myopia was induced in the injected eye between 24 and 35 days of visual experience; the fellow eye served as control. Tree shrews were randomly assigned to five experimental groups: FD (n = 8); FD + 5 × sham injections (n = 6); FD + 3 × GEN injections at 10 mM (n = 6) and 20 mM (n = 6); and FD + 5 × GEN injections at 20 mM (n = 6). Refractive state and ocular dimensions were measured daily. Results Compared with the FD group, the sham-injected group showed a transient effect on slowing vitreous chamber elongation. With increasing GEN dose, SXL had an increasing treatment effect on slowing vitreous chamber elongation and myopia progression. In addition, SXL led to a dose-dependent shortening of the aqueous chamber depth and corneal thickening. Lens thickening was observed in the group with the highest concentration. Conclusions We have shown that SXL using GEN can slow axial elongation and myopia progression in tree shrews. The extent of this treatment effect was dose dependent. Several unexpected effects were observed (corneal thickening, decrease of the anterior chamber depth, and lens thickening), which require further optimization of the GEN delivery approach before clinical consideration. Translational relevance The results of this preclinical study suggest that scleral crosslinking using genipin can slow myopia progression.

PURPOSE: To compare the three-dimensional (3D) morphology of the deep load-bearing structures of the human optic nerve head (ONH) as revealed in vivo by spectral domain optical coherence tomography (SDOCT) with ex vivo quantitative 3D histology. METHODS: SDOCT imaging of the ONH was performed in six eyes from three brain-dead organ donors on life-support equipment awaiting organ procurement (in vivo conditions). Following organ procurement (ex vivo conditions), the eyes were enucleated and underwent a pars plana vitrectomy followed by pressurization to physiologic IOP and immersion fixation. Ex vivo ONH morphology was obtained from high-fidelity episcopic fluorescent 3D reconstruction. Morphologic parameters of the observed ONH canal geometry and peripapillary choroid, as well as the shape, visibility and depth of the lamina cribrosa were compared between ex vivo and in vivo measurements using custom software to align, scale, and manually delineate the different regions of the ONH. RESULTS: There was significant correspondence between in vivo and ex vivo measurements of the depth and shape of the lamina cribrosa, along with the size and shape of Bruch’s membrane opening (BMO) and anterior scleral canal opening (ASCO). Weaker correspondence was observed for choroidal thickness; as expected, a thinner choroid was seen ex vivo due to loss of blood volume upon enucleation (−79.9 %, p

Background and objective Biomechanical stresses and strains can be simulated in the optic nerve head (ONH) using the finite element (FE) method, and various element types have been used. This study aims to investigate the effects of element type on the resulting ONH stresses and strains. Methods A single eye-specific model was constructed using 3D delineations of anatomic surfaces in a high-resolution, fluorescent, 3D reconstruction of a human posterior eye, then meshed using our simple meshing algorithm at various densities using 4- and 10-noded tetrahedral elements, as well as 8- and 20-noded hexahedral elements. A mesh-free approach was used to assign heterogeneous, anisotropic, hyperelastic material properties to the lamina cribrosa, sclera and pia. The models were subjected to elevated IOP of 45 mmHg after pre-stressing from 0 to 10 mmHg, and solved in the open-source FE package Calculix; results were then interpreted in relation to computational time and simulation accuracy, using the quadratic hexahedral model as the reference standard. Results The 10-noded tetrahedral and 20R-noded hexahedral elements exhibited similar scleral canal and laminar deformations, as well as laminar and scleral stress and strain distributions; the quadratic tetrahedral models ran significantly faster than the quadratic hexahedral models. The linear tetrahedral and hexahedral elements were stiffer compared to the quadratic element types, yielding much lower stresses and strains in the lamina cribrosa. Conclusions Prior studies have shown that 20-noded hexahedral elements yield the most accurate results in complex models. Results show that 10-noded tetrahedral elements yield very similar results to 20-noded hexahedral elements and so they can be used interchangeably, with significantly lower computational time. Linear element types did not yield acceptable results.

The sclera uses unknown mechanisms to match the eye’s axial length to its optics during development, producing eyes with good focus (emmetropia). A myopic eye is too long for its own optics. We propose a multi-scale computational model to simulate eye development based on the assumption that scleral growth is controlled by genetic factors while scleral remodeling is driven by genetic factors and the eye’s refractive error. We define growth as a mechanism that changes the tissue volume and mass while remodeling involves internal micro-deformations that are volume-preserving at the macro-scale. The model was fitted against longitudinal refractive measurements in tree shrews of different ages and exposed to three different visual conditions: (i) normal development; (ii) negative lens wear to induce myopia; and (iii) recovery from myopia by removing the negative lens. The model was able to replicate the age- and vision-dependent response of the tree shrew experiments. Scleral growth ceased at younger age than scleral remodeling. The remodeling rate decreased as the eye emmetropized but increased at any age when a negative lens was put on. The predictive power of the model was investigated by calculating the susceptibility to scleral remodeling and the response to form deprivation myopia in tree shrews. Both predictions were in good agreement with experimental data that were not used to fit the model. We propose the first model that distinguishes scleral growth from remodeling. The good agreement of our results with experimental data supports the notion that scleral growth and scleral remodeling are two independently controlled mechanisms during eye development.

Commercial finite element modeling packages do not have the tools necessary to effectively incorporate the complex anisotropic and heterogeneous material properties typical of the biological tissues of the eye. We propose a mesh-free approach to incorporate realistic material properties into finite element models of individual human eyes. The method is based on the idea that material parameters can be estimated or measured at so called control points, which are arbitrary and independent of the finite element mesh. The mesh-free approach approximates the heterogeneous material parameters at the Gauss points of each finite element while the boundary value problem is solved using the standard finite element method. The proposed method was applied to an eye-specific model a human posterior pole and optic nerve head. We demonstrate that the method can be used to effectively incorporate experimental measurements of the lamina cribrosa micro-structure into the eye-specific model. It was convenient to define characteristic material orientations at the anterior and posterior scleral surface based on the eye-specific geometry of each sclera. The mesh-free approach was effective in approximating these characteristic material directions with smooth transitions across the sclera. For the first time, the method enabled the incorporation of the complex collagen architecture of the peripapillary sclera into an eye-specific model including the recently discovered meridional fibers at the anterior surface and the depth dependent width of circumferential fibers around the scleral canal. The model results suggest that disregarding the meridional fiber region may lead to an underestimation of local strain concentrations in the retina. The proposed approach should simplify future studies that aim to investigate collagen remodeling in the sclera and optic nerve head or in other biological tissues with similar challenges.

As the eye's main load-bearing connective tissue, the sclera is centrally important to vision. In addition to cooperatively maintaining refractive status with the cornea, the sclera must also provide stable mechanical support to vulnerable internal ocular structures such as the retina and optic nerve head. Moreover, it must achieve this under complex, dynamic loading conditions imposed by eye movements and fluid pressures. Recent years have seen significant advances in our knowledge of scleral biomechanics, its modulation with ageing and disease, and their relationship to the hierarchical structure of the collagen-rich scleral extracellular matrix (ECM) and its resident cells. This review focuses on notable recent structural and biomechanical studies, setting their findings in the context of the wider scleral literature. It reviews recent progress in the development of scattering and bioimaging methods to resolve scleral ECM structure at multiple scales. In vivo and ex vivo experimental methods to characterise scleral biomechanics are explored, along with computational techniques that combine structural and biomechanical data to simulate ocular behaviour and extract tissue material properties. Studies into alterations of scleral structure and biomechanics in myopia and glaucoma are presented, and their results reconciled with associated findings on changes in the ageing eye. Finally, new developments in scleral surgery and emerging minimally invasive therapies are highlighted that could offer new hope in the fight against escalating scleral-related vision disorder worldwide.

Purpose Myopia progression is thought to involve biomechanical weakening of the sclera, which leads to irreversible deformations and axial elongation of the eye. Scleral crosslinking has been proposed as a potential treatment option for myopia control by strengthening the mechanically weakened sclera. The biomechanical mechanism by which the sclera weakens during myopia and strengthens after crosslinking is not fully understood. Here, we assess the effect of lens-induced myopia and exogenous crosslinking using genipin on the inelastic mechanical properties of the tree shrew sclera measured by cyclic tensile tests. Methods Cyclic tensile tests were performed on 2-mm wide scleral strips at physiological loading conditions (50 cycles, 0-3.3 g, 30 s cycle-1 ). Two scleral strips were obtained from each eye of juvenile tree shrews exposed to two different visual conditions: normal and 4 days of monocular -5 D lens wear to accelerate scleral remodelling and induce myopia. Scleral strips were mechanically tested at three alternative conditions: immediately after enucleation; after incubation in phosphate buffered saline (PBS) for 24 h at 37°C; and after incubation for 24 h in PBS supplemented with genipin at a low cytotoxicity concentration (0.25 mm). Cyclic softening was defined as the incremental strain increase from one cycle to the next. Results -5D lens treatment significantly increased the cyclic softening response of the sclera when compared to contralateral control eyes (0.10% ± 0.029%, mean ± standard error, P = 0.037). Exogenous crosslinking of the lens treated sclera significantly decreased the cyclic softening response (-0.12% ± 0.014%, P = 2.2 × 10-5 ). Contrary to all other groups, the genipin-cross-linked tissue did not exhibit cyclic softening significantly different from zero within the 50-cycle test. Conclusions Results indicated that cyclic tensile loading leads to an inelastic, cyclic softening of the juvenile tree shrew sclera. The softening rate increased during lens-induced myopia and was diminished after genipin crosslinking. This finding suggests that axial elongation in myopia may involve a biomechanical weakening mechanism that increased the cyclic softening response of the sclera, which was inhibited by scleral crosslinking using genipin.

PURPOSE We tested the hypothesis that there are age- and race-related differences in posterior scleral material properties, using eyes from human donors of European (20-90 years old, n = 40 eyes) and African (23-74 years old, n = 22 eyes) descent. METHODS Inflation tests on posterior scleral shells were performed while full-field, three-dimensional displacements were recorded using laser speckle interferometry. Scleral material properties were fit to each eye using a microstructure-based constitutive formulation that incorporates the collagen fibril crimp and the local anisotropic collagen architecture. The effects of age and race were estimated using Generalized Estimating Equations, while accounting for intradonor correlations. RESULTS The shear modulus significantly increased (P = 0.038) and collagen fibril crimp angle significantly decreased with age (P = 0.002). Donors of African descent exhibited a significantly higher shear modulus (P = 0.019) and showed evidence of a smaller collagen fibril crimp angle (P = 0.057) compared to donors of European descent. The in-plane strains in the peripapillary sclera were significantly lower with age (P < 0.015) and African ancestry (P < 0.015). CONCLUSIONS The age- and race-related differences in scleral material properties result in a loss of scleral compliance due to a higher shear stiffness and a lower level of stretch at which the collagen fibrils uncrimp. The loss of compliance should lead to larger high frequency IOP fluctuations and changes in the optic nerve head (ONH) biomechanical response in the elderly and in persons of African ancestry, and may contribute to the higher susceptibility to glaucoma in these at-risk populations.

To test the hypothesis that mechanical strain in the posterior human sclera is altered with age, 20 pairs of normal eyes from human donors aged 20 to 90 years old were inflation tested within 48-h postmortem. The intact posterior scleral shells were pressurized from 5 to 45 mmHg, while the full-field three-dimensional displacements of the scleral surface were measured using laser speckle interferometry. The full strain tensor of the outer scleral surface was calculated directly from the displacement field. Mean maximum principal (tensile) strain was computed for eight circumferential sectors (45° wide) within the peripapillary and mid-peripheral regions surrounding the optic nerve head (ONH). To estimate the age-related changes in scleral strain, results were fit using a functional mixed effects model that accounts for intradonor variability and spatial autocorrelation. Mechanical tensile strain in the peripapillary sclera is significantly higher than the strain in the sclera farther away from the ONH. Overall, strains in the peripapillary sclera decrease significantly with age. Sectorially, peripapillary scleral tensile strains in the nasal sectors are significantly higher than the temporal sectors at younger ages, but the sectorial strain pattern reverses with age, and the temporal sectors exhibited the highest tensile strains in the elderly. Overall, peripapillary scleral structural stiffness increases significantly with age. The sectorial pattern of peripapillary scleral strain reverses with age, which may predispose adjacent regions of the lamina cribrosa to biomechanical insult. The pattern and age-related changes in sectorial peripapillary scleral strain closely match those seen in disk hemorrhages and neuroretinal rim area measurement change rates reported in previous studies of normal human subjects.

Glaucoma is among the leading causes of blindness worldwide. The disease involves damage to the retinal ganglion cell axons that transmit visual information from the eye to the brain. Experimental evidence indicates that biomechanical mechanisms at different length scales are involved in pathophysiology of glaucoma, where chronic intraocular pressure (IOP) elevation at the organ level initiates axonal insult at the level of the lamina cribrosa. The lamina cribrosa consists of a porous collagen structure through which the axons of retinal ganglion cells (RGCs) pass on their path from the retina to the brain. The extent to which the structural mechanics of the lamina cribrosa contribute to the axonal insult remains unclear. In this book chapter, we give a short review of the present understanding of the structural mechanics of the lamina cribrosa and its role in glaucoma. The main aim is to present a first computationally coupled two-scale analysis of the lamina cribrosa that translates the IOP load at the macroscale to the mechanical insult of the axons within the mesostructure of the lamina cribrosa. The numerical results of two-scale analysis suggest that the collagen structures of the lamina cribrosa and its surrounding peripapillary sclera effectively provide mechanical support to the axons by protecting them from high tensile stresses even at elevated IOP levels. However, in-plane shear stresses in the axonal tissue may increase with increasing IOP at the posterior lamina insertion region and contribute to a mechanical insult of the RGC axons in glaucoma.

Increasing evidence suggests that unknown collagen remodeling mechanisms in the sclera underlie myopia development. We are proposing a novel organ culture system in combination with two-photon fluorescence imaging to quantify collagen remodeling at the tissue- and lamella-level. Tree shrew scleral shells were cultured up to 7 days in serum-free media and cellular viability was investigated under: (i) minimal tissue manipulations; (ii) removal of intraocular tissues; gluing the eye to a washer using (iii) 50 μL and (iv) 200 μL of cyanoacrylate adhesive; (v) supplementing media with Ham's F-12 Nutrient Mixture; and (vi) culturing eyes subjected to 15 mmHg intraocular pressure in our new bioreactor. Two scleral shells of normal juvenile tree shrews were fluorescently labeled using a collagen specific protein and cultured in our bioreactor. Using two-photon microscopy, grid patterns were photobleached into and across multiple scleral lamellae. These patterns were imaged daily for 3 days, and tissue-/lamella-level strains were calculated from the deformed patterns. No significant reduction in cell viability was observed under conditions (i) and (v). Compared to condition (i), cell viability was significantly reduced starting at day 0 (condition (ii)) and day 3 (conditions (iii, iv, vi)). Tissue-level strain and intralamellar shear angel increased significantly during the culture period. Some scleral lamellae elongated while others shortened. Findings suggest that tree shrew sclera can be cultured in serum-free media for 7 days with no significant reduction in cell viability. Scleral fibroblasts are sensitive to tissue manipulations and tissue gluing. However, Ham's F-12 Nutrient Mixture has a protective effect on cell viability and can offset the cytotoxic effect of cyanoacrylate adhesive. This is the first study to quantify collagen micro-deformations over a prolonged period in organ culture providing a new methodology to study scleral remodeling in myopia.

The biomechanics of the optic nerve head is assumed to play an important role in ganglion cell loss in glaucoma. Organized collagen fibrils form complex networks that introduce strong anisotropic and nonlinear attributes into the constitutive response of the peripapillary sclera (PPS) and lamina cribrosa (LC) dominating the biomechanics of the optic nerve head. The recently presented computational remodeling approach (Grytz and Meschke in Biomech Model Mechanobiol 9:225-235, 2010) was used to predict the micro-architecture in the LC and PPS, and to investigate its impact on intraocular pressure-related deformations. The mechanical properties of the LC and PPS were derived from a microstructure-oriented constitutive model that included the stretch-dependent stiffening and the statistically distributed orientations of the collagen fibrils. Biomechanically induced adaptation of the local micro-architecture was captured by allowing collagen fibrils to be reoriented in response to the intraocular pressure-related loading conditions. In agreement with experimental observations, the remodeling algorithm predicted the existence of an annulus of fibrils around the scleral canal in the PPS, and a predominant radial orientation of fibrils in the periphery of the LC. The peripapillary annulus significantly reduced the intraocular pressure-related expansion of the scleral canal and shielded the LC from high tensile stresses. The radial oriented fibrils in the LC periphery reinforced the LC against transversal shear stresses and reduced LC bending deformations. The numerical approach presents a novel and reasonable biomechanical explanation of the spatial orientation of fibrillar collagen in the optic nerve head.

This paper presents a computational homogenization scheme that is of particular interest for problems formulated in curvilinear coordinates. The main goal of this contribution is to generalize the computational homogenization scheme to a formulation of micro–macro transitions in curvilinear convective coordinates, where different physical spaces are considered at the homogenized macro-continuum and at the locally attached representative micro-structures. The deformation and the coordinate system of the micro-structure are assumed to be coupled with the local deformation and the local coordinate system at a corresponding point of the macro-continuum. For the consistent formulation of micro–macro transitions, the operations scale-up and scale-down are introduced, considering the rotated representation of tensor variables at the different physical reference frames of micro- and macro-structure. The second goal of this paper is to use objective strain measures like the Green–Lagrange strain tensor for the solution of boundary value problems on the micro- and macro-scale by providing the required transformations for the work-conjugate stress, strain and tangent tensors into variables admissible for the considered micro–macro transitions and satisfying the averaging theorem. Copyright © 2007 John Wiley & Sons, Ltd.

PURPOSE To estimate two collagen-specific material properties (crimp angle and elastic modulus of collagen fibrils) of the remodeling tree shrew sclera during monocular -5 diopter (D) lens wear and recovery. METHODS Tensile tests were performed on scleral strips obtained from juvenile tree shrews exposed to three different visual conditions: normal, monocular -5 D lens wear to induce myopia, and recovery. Collagen fibrils are crimped in the unloaded sclera and uncrimp as the tissue stiffens under load. Inverse numerical analyses were performed to estimate the (unloaded) crimp angle and elastic modulus of collagen fibrils using a microstructure-based constitutive model. RESULTS Compared with the control eye, the crimp angle was significantly higher in the treated eye after 2 days and remained significantly higher until 21 days of lens wear (P < 0.05). The difference between the crimp angle of the treated and control eye rapidly vanished during recovery in concert with the changes in axial elongation rate. A rapid and extensive increase in the elastic modulus was seen in both eyes after starting and stopping the lens wear. CONCLUSIONS The estimated change in the crimp of scleral collagen fibrils is temporally associated with the change in axial elongation rate during myopia development and recovery. This finding suggests that axial elongation may be controlled by a remodeling mechanism that modulates the collagen fibril crimp. The observed binocular changes in scleral stiffness are not temporally associated with the axial elongation rate, indicating that scleral stiffening may not be causally related to myopia.

This contribution is concerned with the consideration of material incompressibility at large strains and proposes various methods for the enforcement of the corresponding constraint into finite-rotation shell models. The incompressibility condition can be expressed in terms of displacement as well as strain variables and is considered by means of three different procedures in the numerical implementation. As kinematic hypothesis a quadratic assumption with respect to the thickness coordinate is used in which the corresponding directors are decomposed into two stretch parameters and a common inextensible unit vector. Various constitutive laws holding for incompressible isotropic hyperelasticity are considered and directly coupled with shell equations through a numerical thickness integration. A 4-node isoparametric shell element is developed parameterizing the inextensible shell director in terms of rotation variables in the framework of an up-dated rotation formulation. Finally, several examples are analysed to identify the most effective procedure for modelling isochoric deformations in thin-walled structures.

Glaucoma is a leading cause of blindness in the world and is due to the damage of retinal ganglion cell axons. While an abnormally high intraocular pressure (IOP) is the most relevant risk factor for glaucomatous damage, the elderly and persons of African ancestry have a significantly greater tendency for developing glaucoma than younger people and those of European ancestry.Copyright © 2013 by ASME

In glaucoma, the optic nerve head (ONH) is the site of damage to the retinal ganglion cell axons that transmit the visual information from the eye to the brain. Results of several randomized prospective trials showed that intraocular pressure (IOP), age1, increased optic disc cupping, corneal thickness, and African ancestry2 are independently associated with glaucomatous progression. All of these risk factors have a biologically plausible association with either the level of IOP, the severity of disease, or biomechanical properties of the ONH. Importantly, age is the only risk factor other than IOP that is independently associated with the onset and progression of glaucoma across all of the major prospective clinical trials conducted over the past twenty years. In addition, every population-based survey conducted to date has demonstrated a strong relationship between the prevalence of glaucoma with advancing age, despite almost no studies showing IOP changes with age. These findings indicate that the aging ONH becomes increasingly vulnerable to glaucomatous injury at similar levels of IOP.Copyright © 2013 by ASME

To characterize the material properties of posterior and peripapillary sclera from human donors, and to investigate the macro- and micro-scale strains as potential control mechanisms governing mechanical homeostasis. Posterior scleral shells from 9 human donors aged 57–90 years were subjected to IOP elevations from 5 to 45 mmHg and the resulting full-field displacements were recorded using laser speckle interferometry. Eye-specific finite element models were generated based on experimentally measured scleral shell surface geometry and thickness. Inverse numerical analyses were performed to identify material parameters for each eye by matching experimental deformation measurements to model predictions using a microstructure-based constitutive formulation that incorporates the crimp response and anisotropic architecture of scleral collagen fibrils. The material property fitting produced models that fit both the overall and local deformation responses of posterior scleral shells very well. The nonlinear stiffening of the sclera with increasing IOP was well reproduced by the uncrimping of scleral collagen fibrils, and a circumferentially aligned ring of collagen fibrils around the scleral canal was predicted in all eyes. Macroscopic in-plane strains were significantly higher in peripapillary region then in the mid-periphery. In contrast, the meso- and micro-scale strains at the collagen network and collagen fibril level were not significantly different between regions. The elastic response of the posterior human sclera can be characterized by the anisotropic architecture and crimp response of scleral collagen fibrils. The similar collagen fibril strains in the peripapillary and mid-peripheral regions support the notion that the scleral collagen architecture including the circumpapillary ring of collagen fibrils evolved to establish optimal load bearing conditions at the collagen fibril level.

Glaucoma is a blinding diseases in which damage to the axons results in loss of retinal ganglion cells. Experimental evidence indicates that chronic intraocular pressure elevation initiates axonal insult at the level of the lamina cribrosa. The lamina cribrosa is a porous collagen structure through which the axons pass on their path from the retina to the brain. Recent experimental studies revealed the extensive structural changes of the lamina cribrosa and its surrounding tissues during the development and progression of glaucoma. In this perspective paper we review the experimental evidence for growth and remodeling mechanisms in glaucoma including adaptation of tissue anisotropy, tissue thickening/thinning, tissue elongation/shortening and tissue migration. We discuss the existing predictive computational approaches that try to elucidate the potential biomechanical basis of theses growth and remodeling mechanisms and highlight open questions, challenges, and avenues for further development.

Glaucoma is among the leading causes of blindness worldwide. The ocular disease is characterized by irreversible damage of the retinal ganglion cell axons at the level of the lamina cribrosa (LC). The LC is a porous, connective tissue structure whose function is believed to provide mechanical support to the axons as they exit the eye on their path from the retina to the brain. Early experimental glaucoma studies have shown that the LC remodels into a thicker, more posterior structure which incorporates more connective tissue after intraocular pressure (IOP) elevation. The process by which this occurs is unknown. Here we present a microstructure motivated growth and remodeling (G&R) formulation to explore a potential mechanism of these structural changes. We hypothesize that the mechanical strain experienced by the collagen fibrils in the LC stimulates the G&R response at the micro-scale. The proposed G&R algorithm controls collagen fibril synthesis/degradation and adapts the residual strains between collagen fibrils and the surrounding tissue to achieve biomechanical homeostasis. The G&R algorithm was applied to a generic finite element model of the human eye subjected to normal and elevated IOP. The G&R simulation underscores the biomechanical need for a LC at normal IOP. The numerical results suggest that IOP elevation leads to LC thickening due to an increase in collagen fibril mass, which is in good agreement with experimental observations in early glaucoma monkey eyes. This is the first study to demonstrate that a biomechanically-driven G&R mechanism can lead to the LC thickening observed in early experimental glaucoma.

Numerical simulations or inverse numerical analyses of individual eyes or eye segments are often based on an eye-specific geometry obtained from in vivo medical images such as computed tomography (CT) scans or from in vitro 3D digitiser scans. These eye-specific geometries are usually measured while the eye is subjected to internal pressure. Due to the nonlinear stiffening of the collagen fibril network in the eye, numerical incorporation of the pre-existing stress/strain state may be essential for realistic eye-specific computational simulations. Existing prestressing methods either compute accurate predictions of the prestressed state or guarantee a unique solution. In this contribution, a forward incremental prestressing method is presented which unifies the advantages of the existing approaches by providing accurate and unique predictions of the pre-existing stress/strain state at the true measured geometry. The impact of prestressing is investigated on (i) the inverse constitutive parameter identification of a synthetic sclera inflation test and (ii) an eye-specific simulation that estimates the realistic mechanical response of a pre-loaded posterior monkey scleral shell. Evaluation of the pre-existing stress/strain state in the inverse analysis had a significant impact on the reproducibility of the constitutive parameters but may be estimated based on an approximative approach. The eye-specific simulation of one monkey eye shows that prestressing is required for accurate displacement and stress/strain predictions. The numerical results revealed an increasing error in displacement, strain and stress predictions with increasing pre-existing pressure load when the pre-stress/strain state is disregarded. Disregarding the prestress may lead to a significant underestimation of the strain/stress environment in the sclera and overestimation in the lamina cribrosa.

The retinal ganglion cell axons carry visual information, and pass through the optic nerve head (ONH) as they traverse from inside the eye to the brain. The ONH is the site of axonal damage in glaucoma, the second leading cause of blindness in the world, and ONH biomechanics is hypothesized to play a crucial role in the development and progression of the disease. The load bearing tissues of the ONH insert into the surrounding sclera, which provides the boundary conditions for this important structure. It is therefore important to develop accurate experimental techniques to measure scleral shell deformations under intraocular pressure (IOP) loading that can be used to drive constitutive and computational models of scleral biomechanics. The overall goal of this project is to better understand the role of ocular biomechanics in the development of glaucoma by constructing eye-specific finite element models of the posterior pole and ONH.

Glaucoma is a leading cause of blindness in the world and is due to the loss of retinal ganglion cell axons. These axons deteriorate in a region in the posterior pole of the eye known as the optic nerve head (ONH). The axons pass through the lamina cribrosa (LC) as they exit the eye at the ONH. The LC is characterized by a porous, connective tissue structure composed of laminar beams. The function of the LC is unclear, but is believed to include providing mechanical support to the axons as they transition from inside the pressurized globe to the lower pressure orbital space. Early experimental glaucoma studies have shown that the LC remodels into a thicker, more posterior structure which incorporates more connective tissue after chronic IOP elevation [1,2]. The process by which this occurs is unknown. These structural changes are assumed to play an important role in the pathophysiology of the ocular disease glaucoma, where elevated IOP is known to be the most relevant risk factor.Copyright © 2011 by ASME

Tissue adaptation and the mechanical condition within biological tissues are complex and mutually dependent phenomena. In this contribution, a computational model is presented to investigate the interaction between collagen fibril architecture and mechanical loading conditions in eye tissues. The biomechanical properties of eye tissues are derived from the single crimped fibril at the micro-scale via the collagen network of distributed fibrils at the meso-scale to the incompressible and anisotropic soft tissue at the macro-scale. Biomechanically induced remodeling of the collagen network is captured on the meso-scale by allowing for a continues reorientation of collagen fibrils. The remodeling process is introduced into an incompressible finite shell formulation. Finally, the presented approach is applied to a numerical human eye model considering the cornea and sclera. The predicted fibril morphology correlates well with experimental observations from x-ray scattering data.

A microstructurally oriented constitutive formulation for the hyperelastic response of crimped collagen fibrils existing in soft connective tissues is proposed. The model is based on observations that collagen fibrils embedded in a soft matrix crimp into a smooth three-dimensional pattern when unloaded. Following ideas presented by Beskos and Jenkins [Beskos, D., Jenkins, J., 1975. A mechanical model for mammalian tendon. ASME Journal of Applied Mechanics 42, 755-758] and Freed and Doehring [Freed, A., Doehring, T., 2005. Elastic model for crimped collagen fibrils. Journal of Biomechanical Engineering 127, 587-593] the collagen fibril crimp is approximated by a cylindrical helix to represent the constitutive behavior of the hierarchical organized substructure of biological tissues at the fibrillar level. The model is derived from the nonlinear axial force-stretch relationship of an extensible helical spring, including the full extension of the spring as a limit case. The geometrically nonlinear solution of the extensible helical spring is carried out by an iterative procedure. The model only requires one material parameter and two geometrical parameters to be determined from experiments. The ability of the proposed model to reproduce the biomechanical response of fibrous tissues is demonstrated for fascicles from rat tail tendons, for porcine cornea strips, and for bovine Achilles tendons.

Biological tissues such as those existing in the eye, heart, veins or arteries are heterogeneous on one or another spatial scale and can undergo very large strains in the elastic range (hyperelasticity). Frequently, these tissues are characterized by thin-walled, shell-like structures. The use of computational homogenization schemes [1], [2], [3] together with a formulation of the continua in curvilinear coordinates is a prerequisite for realistic biomechanical simulations of thin-walled soft tissues on different scales. The goal of this contribution is the generalization of the computational homogenization scheme for the formulation of micro-macro transitions in curvilinear convective coordinates. We consider a homogenized macro-continuum with a locally attached representative micro-structure. The deformation and the coordinate system of the micro-structure are assumed to be coupled with the local deformation and the local coordinate system at a corresponding point of the macro-continuum. For a consistent formulation of micro-macro transitions principal material directions are defined on both scales. To formulate the generalized micro-macro transitions in absolute tensor notation the new operations scale-up and scale-down are introduced. The multi-scale analysis discussed in this paper considering arbitrary curvilinear coordinates as well as geometrical and material nonlinearities rests upon a finite-element discretization of the macro-continuum by means of a bilinear finite shell element with a quadratic kinematic assumption in thickness direction [4]. A finite-element discretization of the micro-structure is attached to each integration point of these macro-elements and is modeled with trilinear brick elements.

PURPOSE We tested the hypothesis that the variation of peripapillary scleral structural stiffness with age is different in donors of European (ED) and African (AD) descent. METHODS Posterior scleral shells from normal eyes from donors of European (n = 20 pairs; previously reported) and African (n = 9 pairs) descent aged 0 and 90 years old were inflation tested within 48 hours post mortem. Scleral shells were pressurized from 5 to 45 mm Hg and the full-field, 3-dimensional (3D) deformation of the outer surface was recorded at submicrometric accuracy using speckle interferometry (ESPI). Mean maximum principal (tensile) strain of the peripapillary and midperipheral regions surrounding the optic nerve head (ONH) were fit using a functional mixed effects model that accounts for intradonor variability, same-race correlation, and spatial autocorrelation to estimate the effect of race on the age-related changes in mechanical scleral strain. RESULTS Mechanical tensile strain significantly decreased with age in the peripapillary sclera in the African and European descent groups (P < 0.001), but the age-related stiffening was significantly greater in the African descent group (P < 0.05). Maximum principal strain in the peripapillary sclera was significantly higher than in the midperipheral sclera for both ethnic groups. CONCLUSIONS The sclera surrounding the ONH stiffens more rapidly with age in the African descent group compared to the European group. Stiffening of the peripapillary sclera with age may be related to the higher prevalence of glaucoma in the elderly and persons of African descent.

Biological tissues such as those involved in the eye, heart, veins or arteries are heterogeneous on one or another spatial scale and can undergo very large elastic strains. Frequently, the se tissues are characterized by shell-like structures at th e macroscopic scale and the physical material directions follow curvilinear paths. We consider a homogenized macro-continuum formulated in curvilinear convective coordinates with locally attached representative micro-structures. Micro-st ructures attached to different macroscopic points are assumed to be rotated counterparts according to the curvilinear path of the p hysical material directions at the macro-scale. The solution of suc h multi-scale problems according to the computational homogenization scheme [1, 2, 3] would need a different RVE at each macroscopic point. The goal of this paper is to use the same initial RVE at each macroscopic point by generalizing the computational homogenization scheme to a formulation considering different physical spaces at the micro- and macro-scale. The deformation and the reference frame of the micro-structure are assumed to be coupled with the local deformation and the local reference frame at the corresponding point of the macrocontinuum. For a consistent formulation of micro-macro transitions physical reference directionsare defined on both scales, where the macroscopic one follows a curvilinear path. To formulate the generalized micro-macro transitions in absolute tensor notation the operations scale-up and scale-down are introduced. Copyright line will be provided by the publisher

PURPOSE. The goal of this study was to establish sectorial and regional variability in the mechanical strain of peripapillary and mid-peripheral sclera in normal eyes from elderly human donors. METHODS. Ten pairs of normal eyes from human donors aged 57 to 90 years old were mechanically inflation-tested within 48 hours post mortem. The intact posterior scleral shells were pressurized from 5 to 45 mm Hg while the full-field threedimensional displacements of the scleral surface were measured using laser speckle interferometry. The displacement field was fit to continuous and differentiable analytical functions, from which the full strain tensor of the outer scleral surface was calculated. Mean maximum principal (tensile) strain was computed for eight circumferential sectors (458 wide) within the peripapillary and mid-peripheral regions surrounding the optic nerve head (ONH). RESULTS. Overall, the peripapillary sclera exhibited significantly higher tensile strain (1.2%) than mid-peripheral sclera (0.95%) for a 40 mm Hg IOP elevation (P < 0.00001). In the peripapillary region, the inferotemporal sector exhibited the highest tensile strain (1.45%) while the superior sector had the lowest (1.19%; P < 0.00001). Mid-peripheral scleral strains were lower but exhibited a similar sectorial pattern. CONCLUSIONS. Human posterior sclera exhibits complex regional mechanical behavior in response to acute IOP elevations from 5 to 45 mm Hg. Results indicate 1) the peripapillary sclera is subjected to significantly higher tensile strain than the adjacent mid-peripheral sclera, and 2) strains are significantly higher in the temporal and inferior quadrants of the peripapillary sclera, which may contribute to the increased prevalence of glaucomatous damage associated with these regions of the ONH. (Invest Ophthalmol Vis Sci. 2012;53:5326‐5333) DOI