Who bears the load? IOP-induced collagen fiber recruitment over the corneoscleral shell.

Collagen is the main load-bearing component of cornea and sclera. When stretched, both of these tissues exhibit a behavior known as collagen fiber recruitment. In recruitment, as the tissues stretch the constitutive collagen fibers lose their natural waviness, progressively straightening. Recruited, straight, fibers bear substantially more mechanical load than non-recruited, wavy, fibers. As such, the process of recruitment underlies the well-established nonlinear macroscopic behavior of the corneoscleral shell. Recruitment has an interesting implication: when recruitment is incomplete, only a fraction of the collagen fibers is actually contributing to bear the loads, with the rest remaining "in reserve". In other words, at a given intraocular pressure (IOP), it is possible that not all the collagen fibers of the cornea and sclera are actually contributing to bear the loads. To the best of our knowledge, the fraction of corneoscleral shell fibers recruited and contributing to bear the load of IOP has not been reported. Our goal was to obtain regionally-resolved estimates of the fraction of corneoscleral collagen fibers recruited and in reserve. We developed a fiber-based microstructural constitutive model that could account for collagen fiber undulations or crimp via their tortuosity. We used experimentally-measured collagen fiber crimp tortuosity distributions in human eyes to derive region-specific nonlinear hyperelastic mechanical properties. We then built a three-dimensional axisymmetric model of the globe, assigning region-specific mechanical properties and regional anisotropy. The model was used to simulate the IOP-induced shell deformation. The model-predicted tissue stretch was then used to quantify collagen recruitment within each shell region. The calculations showed that, at low IOPs, collagen fibers in the posterior equator were recruited the fastest, such that at a physiologic IOP of 15 mmHg, over 90% of fibers were recruited, compared with only a third in the cornea and the peripapillary sclera. The differences in recruitment between regions, in turn, mean that at a physiologic IOP the posterior equator had a fiber reserve of only 10%, whereas the cornea and peripapillary sclera had two thirds. At an elevated IOP of 50 mmHg, collagen fibers in the limbus and the anterior/posterior equator were almost fully recruited, compared with 90% in the cornea and the posterior sclera, and 70% in the peripapillary sclera and the equator. That even at such an elevated IOP not all the fibers were recruited suggests that there are likely other conditions that challenge the corneoscleral tissues even more than IOP. The fraction of fibers recruited may have other potential implications. For example, fibers that are not bearing loads may be more susceptible to enzymatic digestion or remodeling. Similarly, it may be possible to control tissue stiffness through the fraction of recruited fibers without the need to add or remove collagen.

2D or not 2D? Mapping the in-depth inclination of the collagen fibers of the corneoscleral shell.

The collagen fibers of the corneoscleral shell play a central role in the eye mechanical behavior. Although it is well-known that these fibers form a complex three-dimensional interwoven structure, biomechanical and microstructural studies often assume that the fibers are aligned in-plane with the tissues. This is convenient as it removes the out-of-plane components and allows focusing on the 2D maps of in-plane fiber organization that are often quite complex. The simplification, however, risks missing potentially important aspects of the tissue architecture and mechanics. In the cornea, for instance, fibers with high in-depth inclination have been shown to be mechanically important. Outside the cornea, the in-depth fiber orientations have not been characterized, preventing a deeper understanding of their potential roles. Our goal was to characterize in-depth collagen fiber organization over the whole corneoscleral shell. Seven sheep whole-globe axial sections from eyes fixed at an IOP of 50 mmHg were imaged using polarized light microscopy to measure collagen fiber orientations and density. In-depth fiber orientation distributions and anisotropy (degree of fiber alignment) accounting for fiber density were quantified over the whole sclera and in 15 regions: central cornea, peripheral cornea, limbus, anterior equator, equator, posterior equator, posterior sclera and peripapillary sclera on both nasal and temporal sides. Orientation distributions were fitted using a combination of a uniform distribution and a sum of π-periodic von Mises distributions, each with three parameters: primary orientation µ, fiber concentration factor k, and weighting factor a. To study the features of fibers that are not in-plane, i.e., fiber inclination, we quantified the percentage of inclined fibers and the range of inclination angles (half width at half maximum of inclination angle distribution). Our measurements showed that the fibers were not uniformly in-plane but exhibited instead a wide range of in-depth orientations, with fibers significantly more aligned in-plane in the anterior parts of the globe. We found that fitting the orientation distributions required between one and three π-periodic von Mises distributions with different primary orientations and fiber concentration factors. Regions of the posterior globe, particularly on the temporal side, had a larger percentage of inclined fibers and a larger range of inclination angles than anterior and equatorial regions. Variations of orientation distributions and anisotropies may imply varying out-of-plane tissue mechanical properties around the eye globe. Out-of-plane fibers could indicate fiber interweaving, not necessarily long, inclined fibers. Effects of small-scale fiber undulations, or crimp, were minimized by using tissues from eyes at high IOPs. These fiber features also play a role in tissue stiffness and stability and are therefore also important experimental information.

Individual astrocyte morphology in the collagenous lamina cribrosa revealed by multicolor DiOlistic labeling.

Astrocytes in the lamina region of the optic nerve head play vital roles in supporting retinal ganglion cell axon health. In glaucoma, these astrocytes are implicated as early responders to stressors, undergoing characteristic changes in cell function as well as cell morphology. Much of what is currently known about individual lamina astrocyte morphology has been learned from rodent models which lack a defining feature of the human optic nerve head, the collagenous lamina cribrosa (LC). Current methods available for evaluation of collagenous LC astrocyte morphology have significant shortcomings. We aimed to evaluate Multicolor DiOlistic labeling (MuDi) as an approach to reveal individual astrocyte morphologies across the collagenous LC. Gold microcarriers were coated with all combinations of three fluorescent cell membrane dyes, DiI, DiD, and DiO, for a total of seven dye combinations. Microcarriers were delivered to 150 µm-thick coronal vibratome slices through the LC of pig, sheep, goat, and monkey eyes via MuDi. Labeled tissues were imaged with confocal and second harmonic generation microscopy to visualize dyed cells and LC collagenous beams, respectively. GFAP labeling of DiOlistically-labeled cells with astrocyte morphologies was used to investigate cell identity. 3D models of astrocytes were created from confocal image stacks for quantification of morphological features. DiOlistic labeling revealed fine details of LC astrocyte morphologies including somas, primary branches, higher-order branches, and end-feet. Labeled cells with astrocyte morphologies were GFAP+. Astrocytes were visible across seven distinct color channels, allowing high labeling density while still distinguishing individual cells from their neighbors. MuDi was capable of revealing tens to hundreds of collagenous LC astrocytes, in situ, with a single application. 3D astrocyte models allowed automated quantification of morphological features including branch number, length, thickness, hierarchy, and straightness as well as Sholl analysis. MuDi labeling provides an opportunity to investigate morphologies of collagenous LC astrocytes, providing both qualitative and quantitative detail, in healthy tissues. This approach may open doors for research of glaucoma, where astrocyte morphological alterations are thought to coincide with key functional changes related to disease progression.

A direct fiber approach to model sclera collagen architecture and biomechanics.

Sclera collagen fiber microstructure and mechanical behavior are central to eye physiology and pathology. They are also complex, and are therefore often studied using modeling. Most models of sclera, however, have been built within a conventional continuum framework. In this framework, collagen fibers are incorporated as statistical distributions of fiber characteristics such as the orientation of a family of fibers. The conventional continuum approach, while proven successful for describing the macroscale behavior of the sclera, does not account for the sclera fibers are long, interwoven and interact with one another. Hence, by not considering these potentially crucial characteristics, the conventional approach has only a limited ability to capture and describe sclera structure and mechanics at smaller, fiber-level, scales. Recent advances in the tools for characterizing sclera microarchitecture and mechanics bring to the forefront the need to develop more advanced modeling techniques that can incorporate and take advantage of the newly available highly detailed information. Our goal was to create a new computational modeling approach that can represent the sclera fibrous microstructure more accurately than with the conventional continuum approach, while still capturing its macroscale behavior. In this manuscript we introduce the new modeling approach, that we call direct fiber modeling, in which the collagen architecture is built explicitly by long, continuous, interwoven fibers. The fibers are embedded in a continuum matrix representing the non-fibrous tissue components. We demonstrate the approach by doing direct fiber modeling of a rectangular patch of posterior sclera. The model integrated fiber orientations obtained by polarized light microscopy from coronal and sagittal cryosections of pig and sheep. The fibers were modeled using a Mooney-Rivlin model, and the matrix using a Neo-Hookean model. The fiber parameters were determined by inversely matching experimental equi-biaxial tensile data from the literature. After reconstruction, the direct fiber model orientations agreed well with the microscopy data both in the coronal plane (adjusted R2 = 0.8234) and in the sagittal plane (adjusted R2 = 0.8495) of the sclera. With the estimated fiber properties (C10 = 5746.9 MPa; C01 = -5002.6 MPa, matrix shear modulus 200 kPa), the model's stress-strain curves simultaneously fit the experimental data in radial and circumferential directions (adjusted R2's 0.9971 and 0.9508, respectively). The estimated fiber elastic modulus at 2.16% strain was 5.45 GPa, in reasonable agreement with the literature. During stretch, the model exhibited stresses and strains at sub-fiber level, with interactions among individual fibers which are not accounted for by the conventional continuum methods. Our results demonstrate that direct fiber models can simultaneously describe the macroscale mechanics and microarchitecture of the sclera, and therefore that the approach can provide unique insight into tissue behavior questions inaccessible with continuum approaches.

Stretch-Induced Uncrimping of Equatorial Sclera Collagen Bundles.

Stretch-induced collagen uncrimping underlies the nonlinear mechanical behavior of the sclera according to what is often called the process of recruitment. We recently reported experimental measurements of sclera collagen crimp and pressure-induced uncrimping. Our studies, however, were cross-sectional, providing statistical descriptions of crimp with no information on the effects of stretch on specific collagen bundles. Data on bundle-specific uncrimping is necessary to better understand the effects of macroscale input on the collagen microscale and tissue failure. Our goal in this project was to measure bundle-specific stretch-induced collagen uncrimping of sclera. Three goat eyes were cryosectioned sagittally (30 µm). Samples of equatorial sclera were isolated, mounted to a custom uni-axial stretcher and imaged with polarized light microscopy at various levels of clamp-to-clamp stretch until failure. At each stretch level, local strain was measured using image tracking techniques. The level of collagen crimping was determined from the bundle waviness, defined as the circular standard deviation of fiber orientation along a bundle. Eye-specific recruitment curves were then computed using eye-specific waviness at maximum stretch before sample failure to define fibers as recruited. Nonlinear mixed effect models were used to determine the associations of waviness to local strain and recruitment to clamp-to-clamp stretch. Waviness decreased exponentially with local strain (p < 0.001), whereas bundle recruitment followed a sigmoidal curve with clamp-to-clamp stretch (p < 0.001). Individual bundle responses to stretch varied substantially, but recruitment curves were similar across sections and eyes. In conclusion, uni-axial stretch caused measurable bundle-specific uncrimping, with the sigmoidal recruitment pattern characteristic of fiber-reinforced soft tissues.

Instant polarized light microscopy pi (IPOLπ) for quantitative imaging of collagen architecture and dynamics in ocular tissues.

Collagen architecture determines the biomechanical environment in the eye, and thus characterizing collagen fiber organization and biomechanics is essential to fully understand eye physiology and pathology. We recently introduced instant polarized light microscopy (IPOL) that encodes optically information about fiber orientation and retardance through a color snapshot. Although IPOL allows imaging collagen at the full acquisition speed of the camera, with excellent spatial and angular resolutions, a limitation is that the orientation-encoding color is cyclic every 90 degrees (π/2 radians). In consequence, two orthogonal fibers have the same color and therefore the same orientation when quantified by color-angle mapping. In this study, we demonstrate IPOLπ, a new variation of IPOL, in which the orientation-encoding color is cyclic every 180 degrees (π radians). Herein we present the fundamentals of IPOLπ, including a framework based on a Mueller-matrix formalism to characterize how fiber orientation and retardance determine the color. The improved quantitative capability of IPOLπ enables further study of essential biomechanical properties of collagen in ocular tissues, such as fiber anisotropy and crimp. We present a series of experimental calibrations and quantitative procedures to visualize and quantify ocular collagen orientation and microstructure in the optic nerve head, a region in the back of the eye. There are four important strengths of IPOLπ compared to IPOL. First, IPOLπ can distinguish the orientations of orthogonal collagen fibers via colors, whereas IPOL cannot. Second, IPOLπ requires a lower exposure time than IPOL, thus allowing faster imaging speed. Third, IPOLπ allows visualizing non-birefringent tissues and backgrounds from tissue absorption, whereas both appear dark in IPOL images. Fourth, IPOLπ is cheaper and less sensitive to imperfectly collimated light than IPOL. Altogether, the high spatial, angular, and temporal resolutions of IPOLπ enable a deeper insight into ocular biomechanics and eye physiology and pathology.

Evidence of an Annexin A4 mediated plasma membrane repair response to biomechanical strain associated with glaucoma pathogenesis.

Glaucoma is a common neurodegenerative blinding disease that is closely associated with chronic biomechanical strain at the optic nerve head (ONH). Yet, the cellular injury and mechanosensing mechanisms underlying the resulting damage have remained critically unclear. We previously identified Annexin A4 (ANXA4) from a proteomic analyses of human ONH astrocytes undergoing pathological biomechanical strain that mimics glaucomatous conditions. Annexins are a family of calcium-dependent phospholipid binding proteins with key functions in plasma membrane repair (PMR); an active mechanism to limit and mend cellular injury that involves membrane and cytoskeletal reorganizations. However, a role for direct membrane damage and PMR has not been well studied in the context of biomechanical strain, such as that associated with glaucoma. Here we report that this moderate strain surprisingly damages cell membranes to increase permeability in a calcium-dependent manner, and induces rapid aggregation of ANXA4 at injury sites. ANXA4 loss-of-function increases permeability, while exogenous ANXA4 reduces it. Furthermore, ANXA4 aggregation is associated with F-actin dynamics in vitro, and remarkably this interaction and aggregation signature is also observed in the glaucomatous ONH in patient samples. Together these studies link moderate biomechanical strain with direct membrane damage and actin dynamics, and identify an active PMR role for ANXA4 in new model of cell injury associated with glaucoma pathogenesis.

Real-time imaging of optic nerve head collagen microstructure and biomechanics using instant polarized light microscopy.

Current tools lack the temporal or spatial resolution necessary to image many important aspects of the architecture and dynamics of the optic nerve head (ONH). We evaluated the potential of instant polarized light microscopy (IPOL) to overcome these limitations by leveraging the ability to capture collagen fiber orientation and density in a single image. Coronal sections through the ONH of fresh normal sheep eyes were imaged using IPOL while they were stretched using custom uniaxial or biaxial micro-stretch devices. IPOL allows identifying ONH collagen architectural details, such as fiber interweaving and crimp, and has high temporal resolution, limited only by the frame rate of the camera. Local collagen fiber orientations and deformations were quantified using color analysis and image tracking techniques. We quantified stretch-induced collagen uncrimping of lamina cribrosa (LC) and peripapillary sclera (PPS), and changes in LC pore size (area) and shape (convexity and aspect ratio). The simultaneous high spatial and temporal resolutions of IPOL revealed complex ONH biomechanics: i) stretch-induced local deformation of the PPS was nonlinear and nonaffine. ii) under load the crimped collagen fibers in the PPS and LC straightened, without torsion and with only small rotations. iii) stretch-induced LC pore deformation was anisotropic and heterogeneous among pores. Overall, with stretch the pores were became larger, more convex, and more circular. We have demonstrated that IPOL reveals details of collagen morphology and mechanics under dynamic loading previously out of reach. IPOL can detect stretch-induced collagen uncrimping and other elements of the tissue nonlinear mechanical behavior. IPOL showed changes in pore morphology and collagen architecture that will help improve understanding of how LC tissue responds to load.

Eye-specific 3D modeling of factors influencing oxygen concentration in the lamina cribrosa.

Our goal was to identify the factors with the strongest influence on the minimum lamina cribrosa (LC) oxygen concentration as potentially indicative of conditions increasing hypoxia risk. Because direct measurement of LC hemodynamics and oxygenation is not yet possible, we developed 3D eye-specific LC vasculature models. The vasculature of a normal monkey eye was perfusion-labeled post-mortem. Serial cryosections through the optic nerve head were imaged using fluorescence and polarized light microscopy to visualize the vasculature and collagen, respectively. The vasculature within a 450 µm-thick region containing the LC - identified from the collagen, was segmented, skeletonized, and meshed for simulations. Using Monte Carlo sampling, 200 vascular network models were generated with varying vessel diameter, neural tissue oxygen consumption rate, inflow hematocrit, and blood pressures (arteriole, venule, anterior boundary, and posterior boundary). Factors were varied over ranges of baseline ±20% with uniform probability. For each model we first obtained the blood flow, and from this the neural tissue oxygen concentration. ANOVA was used to identify the factors with the strongest influence on the minimum (10th percentile) oxygen concentration in the LC. The three most influential factors were, in ranked order, vessel diameter, neural tissue oxygen consumption rate, and arteriole pressure. There was a strong interaction between vessel diameter and arteriole pressure whereby the impact of one factor was larger when the other factor was small. Our results show that, for the eye analyzed, conditions that reduce vessel diameter, such as vessel compression due to elevated intraocular pressure or gaze-induced tissue deformation, may particularly contribute to decreased LC oxygen concentration. More eyes must be analyzed before generalizing.

Lamina cribrosa vessel and collagen beam networks are distinct.

Our goal was to analyze the spatial interrelation between vascular and collagen networks in the lamina cribrosa (LC). Specifically, we quantified the percentages of collagen beams with/without vessels and of vessels inside/outside of collagen beams. To do this, the vasculature of six normal monkey eyes was labeled by perfusion post-mortem. After enucleation, coronal cryosections through the LC were imaged using fluorescence and polarized light microscopy to visualize the blood vessels and collagen beams, respectively. The images were registered to form 3D volumes. Beams and vessels were segmented, and their spatial interrelationship was quantified in 3D. We found that 22% of the beams contained a vessel (range 14%-32%), and 21% of vessels were outside beams (13%-36%). Stated differently, 78% of beams did not contain a vessel (68%-86%), and 79% of vessels were inside a beam (64%-87%). Individual monkeys differed significantly in the fraction of vessels outside beams (p < 0.01 by linear mixed effect analysis), but not in the fraction of beams with vessels (p > 0.05). There were no significant differences between contralateral eyes in the percent of beams with vessels and of vessels outside beams (p > 0.05). Our results show that the vascular and collagenous networks of the LC in monkey are clearly distinct, and the historical notions that each LC beam contains a vessel and all vessels are within beams are inaccurate. We postulate that vessels outside beams may be relatively more vulnerable to mechanical compression by elevated IOP than are vessels shielded inside of beams.

A Workflow for Three-Dimensional Reconstruction and Quantification of the Monkey Optic Nerve Head Vascular Network.

A comprehensive characterization of the three-dimensional (3D) vascular network of the optic nerve head (ONH) is critical to understanding eye physiology and pathology. Current in vivo imaging technologies, however, do not have simultaneous high spatial resolution and imaging depth to resolve the small vessels deep within the ONH. We describe a workflow for the 3D reconstruction and quantitative morphological analysis of the ONH vasculature. The vessels of a normal monkey ONH were perfusion labeled. Serial cryosections of the ONH were imaged using fluorescence microscopy (FM) and instant polarized light microscopy (IPOL) to visualize the labeled vessels and label-free collagen, respectively. The IPOL images were registered and used to form a stack of FM images from which the vessels were segmented and skeletonized to reconstruct the 3D vascular network. The network consisted of 12,966 vessel segments, 7989 branching points, and 1100 terminal points at the boundaries. For each vessel segment, we measured its length, tortuosity, inclination (θ), and polar orientation (φ). The length followed a lognormal distribution, whereas the distribution of the tortuosity followed an exponential decay. The vessels were mainly oriented toward the coronal plane (θ = 90 deg). For orientation, there were nearly as many vessels aligned circumferentially (φ = 90 deg) and radially (φ = 0 deg). Our results demonstrate the workflow for 3D eye-specific reconstruction and quantification of the monkey ONH vascular network. This is a critical first step to analyze the blood flow and oxygenation within the ONH, which will help understand the role of vascular dysfunction in glaucoma.

Interplay between intraocular and intracranial pressure effects on the optic nerve head in vivo.

Intracranial pressure (ICP) has been proposed to play an important role in the sensitivity to intraocular pressure (IOP) and susceptibility to glaucoma. However, the in vivo effects of simultaneous, controlled, acute variations in ICP and IOP have not been directly measured. We quantified the deformations of the anterior lamina cribrosa (ALC) and scleral canal at Bruch's membrane opening (BMO) under acute elevation of IOP and/or ICP. Four eyes of three adult monkeys were imaged in vivo with OCT under four pressure conditions: IOP and ICP either at baseline or elevated. The BMO and ALC were reconstructed from manual delineations. From these, we determined canal area at the BMO (BMO area), BMO aspect ratio and planarity, and ALC median depth relative to the BMO plane. To better account for the pressure effects on the imaging, we also measured ALC visibility as a percent of the BMO area. Further, ALC depths were analyzed only in regions where the ALC was visible in all pressure conditions. Bootstrap sampling was used to obtain mean estimates and confidence intervals, which were then used to test for significant effects of IOP and ICP, independently and in interaction. Response to pressure manipulation was highly individualized between eyes, with significant changes detected in a majority of the parameters. Significant interactions between ICP and IOP occurred in all measures, except ALC visibility. On average, ICP elevation expanded BMO area by 0.17 mm2 at baseline IOP, and contracted BMO area by 0.02 mm2 at high IOP. ICP elevation decreased ALC depth by 10 µm at baseline IOP, but increased depth by 7 µm at high IOP. ALC visibility decreased as ICP increased, both at baseline (-10%) and high IOP (-17%). IOP elevation expanded BMO area by 0.04 mm2 at baseline ICP, and contracted BMO area by 0.09 mm2 at high ICP. On average, IOP elevation caused the ALC to displace 3.3 µm anteriorly at baseline ICP, and 22 µm posteriorly at high ICP. ALC visibility improved as IOP increased, both at baseline (5%) and high ICP (8%). In summary, changing IOP or ICP significantly deformed both the scleral canal and the lamina of the monkey ONH, regardless of the other pressure level. There were significant interactions between the effects of IOP and those of ICP on LC depth, BMO area, aspect ratio and planarity. On most eyes, elevating both pressures by the same amount did not cancel out the effects. Altogether our results show that ICP affects sensitivity to IOP, and thus that it can potentially also affect susceptibility to glaucoma.

Role of radially aligned scleral collagen fibers in optic nerve head biomechanics.

Collagen fibers organized circumferentially around the canal in the peripapillary sclera are thought to provide biomechanical support to the sensitive tissues within the optic nerve head (ONH). Recent studies have demonstrated the existence of a family of fibers in the innermost sclera organized radially from the scleral canal. Our goal was to determine the role of these radial fibers in the sensitivity of scleral canal biomechanics to acute increases in intraocular pressure (IOP). Following the same general approach of previous parametric sensitivity studies, we created nonlinear generic finite element models of a posterior pole with various combinations of radial and circumferential fibers at an IOP of 0 mmHg. We then simulated the effects of normal and elevated IOP levels (15 and 30 mmHg). We monitored four IOP-induced geometric changes: peripapillary sclera stretch, scleral canal displacement, lamina cribrosa displacement, and scleral canal expansion. In addition, we examined the radial (maximum tension) and through-thickness (maximum compression) strains within the ONH tissues. Our models predicted that: 1) radial fibers reduced the posterior displacement of the lamina, especially at elevated IOP; 2) radial fibers reduced IOP-induced radial strain within the peripapillary sclera and retinal tissue; and 3) a combination of radial and circumferential fibers maintained strains within the ONH at a level similar to those conferred by circumferential fibers alone. In conclusion, radial fibers provide support for the posterior globe, additional to that provided by circumferential fibers. Most importantly, a combination of both fiber families can better protect ONH tissues from excessive IOP-induced deformation than either alone.

A Mesh-Free Approach to Incorporate Complex Anisotropic and Heterogeneous Material Properties into Eye-Specific Finite Element Models.

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.

Gaze-Evoked Deformations in Optic Nerve Head Drusen: Repetitive Shearing as a Potential Factor in the Visual and Vascular Complications.

PURPOSE: To determine if ocular ductions deform intrapapillary and peripapillary tissues in optic nerve head drusen (ONHD) and to compare these deformations with healthy eyes and eyes with other optic neuropathies. DESIGN: Observational case series. PARTICIPANTS: Twenty patients with ONHD. METHODS: Axial rasters of the optic nerve from a spectral-domain OCT device (Cirrus 5000; Carl Zeiss Meditec, Inc, Dublin, CA) were used to analyze the shape of the peripapillary basement membrane (ppBM) layer in 20 confirmed cases of ONHD. We compared registered images obtained from 2 eye positions: 10° to 15° in adduction and 30° to 40° in abduction. Geometric morphometrics was used to analyze the shape of the ppBM layer defined by placing 10 equidistant landmarks extending 2500 µm on both sides of the basement membrane opening. We also adapted an image strain tracking technique to measure regional intrapapillary strains in 6 patients. Using manually placed nodes on the reference image (in adduction), an iterative, block-matching algorithm is used to determine local displacements between the reference and its paired image in abduction. Displacement vectors were used to calculate the mean shear and effective strain (percent change). MAIN OUTCOME MEASURES: Peripapillary shape deformations, intrapapillary shear strains, and effective strains. RESULTS: We found a statistically significant difference in the shape of the ppBM layer between abduction and adduction (P < 0.01). The deformation was characterized by a relative posterior displacement temporally in adduction that reversed in abduction. Strain tracking in all 6 patients showed substantial gaze-induced shearing and effective strains. Mean effective strains were 7.5% outside the drusen. Shear and effective strains were significantly larger outside versus within the drusen (P < 0.003 and P < 0.01, respectively). CONCLUSIONS: This study demonstrates that horizontal ocular ductions induce significant shearing deformations of the peripapillary retina and prelaminar intrapapillary tissues. We also found that the deformations in healthy persons are similar in magnitude to ONHD. Based on these findings, we speculate that patients with intrapapillary calcifications exposed to the long-term effects of repetitive shearing (induced by ocular ductions) may contribute to the progressive axonal loss and vascular complications associated with ONHD.

Crimp around the globe; patterns of collagen crimp across the corneoscleral shell.

Our goal was to systematically quantify the collagen crimp morphology around the corneoscleral shell, and test the hypothesis that collagen crimp is not uniform over the globe. Axial longitudinal cryosections (30 µm) of three sheep eyes, fixed at 0 mmHg IOP, were imaged using polarized light microscopy to quantify the local collagen in 8 regions: two corneal (central and peripheral) and six scleral (limbus, anterior-equatorial, equatorial, posterior-equatorial, posterior and peripapillary). Collagen crimp period (length of one wave), tortuosity (path length divided by end-to-end length), waviness (SD of orientation), amplitude (half the peak to trough distance), and conformity (width of contiguous similarly oriented bundles) were measured in each region. Measurements were obtained on 8216 collagen fiber bundles. When pooling measurements across the whole eye globe, the median crimp values were: 23.9 µm period, 13.2 µm conformity, 0.63 µm amplitude, 1.006 tortuosity, and 12.7° waviness. However, all parameters varied significantly across the globe. Median bundle periods in the central cornea, limbus, and peripapillary sclera (PPS) were 14.1 µm, 29.5 µm, and 22.9 µm, respectively. Median conformities were 20.8 µm, 14.5 µm, and 15.1 µm, respectively. Median tortuosities were 1.005, 1.007, and 1.007, respectively. Median waviness' were 11.4°, 13.2°, and 13.2°, respectively. Median amplitudes were 0.35 µm, 0.87 µm, and 0.65 µm, respectively. All parameters varied significantly across the globe. All regions differed significantly from one another on at least one parameter. Regions with small periods had large conformities, and bundles with high tortuosity had high waviness and amplitude. Waviness, tortuosity, and amplitude, associated with nonlinear biomechanical behavior, exhibited "double hump" distributions, whereas period and conformity, representing tissue organization, were substantially different between sclera and cornea. Though the biomechanical implications and origin of the patterns observed remain unclear, our findings of well-defined patterns of collagen crimp across the corneoscleral shell, consistent between eyes, support the existence of mechanisms that regulate collagen characteristics at the regional or smaller levels. These results are experimental data necessary for more realistic models of ocular biomechanics and remodeling.

Whole-globe biomechanics using high-field MRI.

The eye is a complex structure composed of several interconnected tissues acting together, across the whole globe, to resist deformation due to intraocular pressure (IOP). However, most work in the ocular biomechanics field only examines the response to IOP over smaller regions of the eye. We used high-field MRI to measure IOP induced ocular displacements and deformations over the whole globe. Seven sheep eyes were obtained from a local abattoir and imaged within 48 h using MRI at multiple levels of IOP. IOP was controlled with a gravity perfusion system and a cannula inserted into the anterior chamber. T2-weighted imaging was performed to the eyes serially at 0 mmHg, 10 mmHg, 20 mmHg and 40 mmHg of IOP using a 9.4 T MRI scanner. Manual morphometry was conducted using 3D visualization software to quantify IOP-induced effects at the globe scale (e.g. axial length and equatorial diameters) or optic nerve head scale (e.g. canal diameter, peripapillary sclera bowing). Measurement sensitivity analysis was conducted to determine measurement precision. High-field MRI revealed an outward bowing of the posterior sclera and anterior bulging of the cornea due to IOP elevation. Increments in IOP from 10 to 40 mmHg caused measurable increases in axial length in 6 of 7 eyes of 7.9 ± 5.7% (mean ± SD). Changes in equatorial diameter were minimal, 0.4 ± 1.2% between 10 and 40 mmHg, and in all cases less than the measurement sensitivity. The effects were nonlinear, with larger deformations at normal IOPs (10-20 mmHg) than at elevated IOPs (20-40 mmHg). IOP also caused measurable increases in the nasal-temporal scleral canal diameter of 13.4 ± 9.7% between 0 and 20 mmHg, but not in the superior-inferior diameter. This study demonstrates that high-field MRI can be used to visualize and measure simultaneously the effects of IOP over the whole globe, including the effects on axial length and equatorial diameter, posterior sclera displacement and bowing, and even changes in scleral canal diameter. The fact that the equatorial diameter did not change with IOP, in agreement with previous studies, indicates that a fixed boundary condition is a reasonable assumption for half globe inflation tests and computational models. Our results demonstrate the potential of high-field MRI to contribute to understanding ocular biomechanics, and specifically of the effects of IOP in large animal models.

Fibrous finite element modeling of the optic nerve head region.

The optic nerve head (ONH) region at the posterior pole of the eye is supported by a fibrous structure of collagen fiber bundles. Discerning how the fibrous structure determines the region biomechanics is crucial to understand normal physiology, and the roles of biomechanics on vision loss. The fiber bundles within the ONH structure exhibit complex three-dimensional (3D) organization and continuity across the various tissue components. Computational models of the ONH, however, usually represent collagen fibers in a homogenized fashion without accounting for their continuity across tissues, fibers interacting with each other and other fiber-specific effects in a fibrous structure. We present a fibrous finite element (FFE) model of the ONH that incorporates discrete collagen fiber bundles and their histology-based 3D organization to study ONH biomechanics as a fibrous structure. The FFE model was constructed using polarized light microscopy data of porcine ONH cryosections, representing individual fiber bundles in the sclera, dura and pia maters with beam elements and canal tissues as continuum structures. The FFE model mimics the histological in-plane orientation and width distributions of collagen bundles as well as their continuity across different tissues. Modeling the fiber bundles as linear materials, the FFE model predicts the nonlinear ONH response observed in an inflation experiment from the literature. The model also captures important microstructural mechanisms including fiber interactions and long-range strain transmission among bundles that have not been considered before. The FFE model presented here advances our understanding of the role of fibrous collagen structure in the ONH biomechanics. STATEMENT OF SIGNIFICANCE: The microstructure and mechanics of the optic nerve head (ONH) are central to ocular physiology. Histologically, the ONH region exhibits a complex continuous fibrous structure of collagen bundles. Understanding the role of the fibrous collagen structure on ONH biomechanics requires high-fidelity computational models previously unavailable. We present a computational model of the ONH that incorporates histology-based fibrous collagen structure derived from polarized light microscopy images. The model predictions agree with experiments in the literature, and provide insight into important microstructural mechanisms of fibrous tissue biomechanics, such as long-range strain transmission along fiber bundles. Our model can be used to study the microstructural basis of biomechanical damage and the effects of collagen remodeling in glaucoma.

Lamina Cribrosa Insertions Into the Sclera Are Sparser, Narrower, and More Slanted in the Anterior Lamina.

Purpose: The lamina cribrosa (LC) depends on the sclera for support. The support must be provided through the LC insertions. Although a continuous insertion over the whole LC periphery is often assumed, LC insertions are actually discrete locations where LC collagenous beams meet the sclera. We hypothesized that LC insertions vary in number, size, and shape by quadrant and depth. Methods: Coronal cryosections through the full LCs from six healthy monkey eyes were imaged using instant polarized light microscopy. The images were registered into a stack, on which we manually marked LC insertion outlines, nothing their position in-depth and quadrant (inferior, superior, nasal, or temporal). From the marks, we determined the insertion number, width, angle to the canal wall (90 degrees = perpendicular), and insertion ratio (fraction of LC periphery represented by insertions). Using linear mixed effect models, we determined if the insertion characteristics were associated with depth or quadrant. Results: Insertions in the anterior LC were sparser, narrower, and more slanted than those in deeper LC (P values < 0.001). There were more insertions spanning a larger ratio of the canal wall in the middle LC than in the anterior and posterior (P values < 0.001). In the nasal quadrant, the insertion angles were significantly smaller (P < 0.001). Conclusions: LC insertions vary substantially and significantly over the canal. The sparser, narrower, and more slanted insertions of the anterior-most LC may not provide the robust support afforded by insertions of the middle and posterior LC. These variations may contribute to the progressive deepening of the LC and regional susceptibility to glaucoma.

Direct measurements of collagen fiber recruitment in the posterior pole of the eye.

Collagen is the main load-bearing component of the peripapillary sclera (PPS) and lamina cribrosa (LC) in the eye. Whilst it has been shown that uncrimping and recruitment of the PPS and LC collagen fibers underlies the macro-scale nonlinear stiffening of both tissues with increased intraocular pressure (IOP), the uncrimping and recruitment as a function of local stretch have not been directly measured. This knowledge is crucial to understanding their functions in bearing loads and maintaining tissue integrity. In this project we measured local stretch-induced collagen fiber bundle uncrimping and recruitment curves of the PPS and LC. Thin coronal samples of PPS and LC of sheep eyes were mounted and stretched biaxially quasi-statically using a custom system. At each step, we imaged the PPS and LC with instant polarized light microscopy and quantified pixel-level (1.5 µm/pixel) collagen fiber orientations. We used digital image correlation to measure the local stretch and quantified collagen crimp by the circular standard deviation of fiber orientations, or waviness. Local stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers than the LC at the low levels of stretch. At 10% stretch the curves crossed with 75% bundles recruited. The PPS had higher uncrimping rate and waviness remaining after recruitment than the LC: 0.9º vs. 0.6º and 3.1º vs. 2.7º. Altogether our findings support describing fiber recruitment of both PPS and LC with sigmoid curves, with the PPS recruiting faster and at lower stretch than the LC, consistent with a stiffer tissue. STATEMENT OF SIGNIFICANCE: Peripapillary sclera (PPS) and lamina cribrosa (LC) collagen recruitment behaviors are central to the nonlinear mechanical behavior of the posterior pole of the eye. How PPS and LC collagen fibers recruit under stretch is crucial to develop constitutive models of the tissues but remains unclear. We used image-based stretch testing to characterize PPS and LC collagen fiber bundle recruitment under local stretch. We found that fiber-level stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers at a low stretch, but at 10% bundle stretch the two curves crossed with 75% bundles recruited. We also found that PPS and LC fibers had different uncrimping rates and non-zero waviness's when recruited.