Effects of collagen microstructure and material properties on the deformation of the neural tissues of the lamina cribrosa

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.

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.

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.

Computational study of the mechanical behavior of the astrocyte network and axonal compartments in the mouse optic nerve head

Glaucoma is a blinding disease characterized by the degeneration of the retinal ganglion cell (RGC) axons at the optic nerve head (ONH). A major risk factor for glaucoma is the intraocular pressure (IOP). However, it is currently impossible to measure the IOP-induced mechanical response of the axons of the ONH. The objective of this study was to develop a computational modeling method to estimate the IOP-induced strains and stresses in the axonal compartments in the mouse astrocytic lamina (AL) of the ONH, and to investigate the effect of the structural features on the mechanical behavior. We developed experimentally informed finite element (FE) models of six mouse ALs to investigate the effect of structure on the strain responses of the astrocyte network and axonal compartments to pressure elevation. The specimen-specific geometries of the FE models were reconstructed from confocal fluorescent images of cryosections of the mouse AL acquired in a previous study that measured the structural features of the astrocytic processes and axonal compartments. The displacement fields obtained from digital volume correlation in prior inflation tests of the mouse AL were used to determine the displacement boundary conditions of the FE models. We then applied Gaussian process regression to analyze the effects of the structural features on the strain outcomes simulated for the axonal compartments. The axonal compartments experienced, on average, 6 times higher maximum principal strain but 1800 times lower maximum principal stress compared to those experienced by the astrocyte processes. The strains experienced by the axonal compartments were most sensitive to variations in the area of the axonal compartments. Larger axonal compartments that were more vertically aligned, closer to the AL center, and with lower local actin area fraction had higher strains. Understanding the factors affecting the deformation in the axonal compartments will provide insights into mechanisms of glaucomatous axonal damage.

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.

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 for the development of constitutive models associating micro and macro scales. 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: 0.9° vs. 0.6° and 3.1° vs. 2.7°. 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.

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.

The impact of horizontal eye movements versus intraocular pressure on optic nerve head biomechanics: A tridimensional finite element analysis study

It has been proposed that eye movements could be related to glaucoma development. This research aimed to compare the impact of intraocular pressure (IOP) versus horizontal duction on optic nerve head (ONH) strains. Thus, a tridimensional finite element model of the eye including the three tunics of the eye, all of the meninges, and the subarachnoid space (SAS) was developed using a series of medical tests and anatomical data. The ONH was divided into 22 subregions, and the model was subjected to 21 different eye pressures, as well as 24 different degrees of adduction and abduction ranging from 0.5° to 12°. Mean deformations were documented along anatomical axes and in principal directions. Additionally, the impact of tissue stiffness was assessed. The results show no statistically significant differences between the lamina cribrosa (LC) strains due to eye rotation and IOP variation. However, when assessing LC regions some experienced a reduction in principal strains following a 12° duction, while after the IOP reached 12 mmHg, all LC subzones showed an increase in strains. From an anatomical perspective, the effect on the ONH following 12° duction was opposite to that observed after a rise in IOP. Moreover, high strain dispersion inside the ONH subregions was obtained with lateral eye movements, which was not observed with increased IOP and variation. Finally, SAS and orbital fat stiffness strongly influenced ONH strains during eye movements, while SAS stiffness was also influential under ocular hypertension. Even if horizontal eye movements cause large ONH deformations, their biomechanical effect would be markedly distinct from that induced by IOP. It could be predicted that, at least in physiological conditions, their potential to cause axonal injury would not be so relevant. Thus, a causative role in glaucoma does not appear likely. By contrast, an important role of SAS would be expectable.

Biomechanical analysis of ocular diseases and its in vitro study methods

Ocular diseases are closely related to the physiological changes in the eye sphere and its contents. Using biomechanical methods to explore the relationship between the structure and function of ocular tissue is beneficial to reveal the pathological processes. Studying the pathogenesis of various ocular diseases will be helpful for the diagnosis and treatment of ocular diseases. We provide a critical review of recent biomechanical analysis of ocular diseases including glaucoma, high myopia, and diabetes. And try to summarize the research about the biomechanical changes in ocular tissues (e.g., optic nerve head, sclera, cornea, etc.) associated with those diseases. The methods of ocular biomechanics research in vitro in recent years are also reviewed, including the measurement of biomechanics by ophthalmic equipment, finite element modeling, and biomechanical analysis methods. And the preparation and application of microfluidic eye chips that emerged in recent years were summarized. It provides new inspiration and opportunity for the pathogenesis of eye diseases and personalized and precise treatment.

Quantitative Microstructural Analysis of Cellular and Tissue Remodeling in Human Glaucoma Optic Nerve Head

Purpose

To measure quantitatively changes in lamina cribrosa (LC) cell and connective tissue structure in human glaucoma eyes.

Methods

We studied 27 glaucoma and 19 age-matched non-glaucoma postmortem eyes. In 25 eyes, LC cross-sections were examined by confocal and multiphoton microscopy to quantify structures identified by anti-glial fibrillary acidic protein (GFAP), phalloidin-labeled F-actin, nuclear 4',6-diamidino-2-phenylindole (DAPI), and by second harmonic generation imaging of LC beams. Additional light and transmission electron microscopy were performed in 21 eyes to confirm features of LC remodeling, including immunolabeling by anti-SOX9 and anti-collagen IV. All glaucoma eyes had detailed clinical histories of open-angle glaucoma status, and degree of axon loss was quantified in retrolaminar optic nerve cross-sections.

Results

Within LC pores, the proportionate area of both GFAP and F-actin processes was significantly lower in glaucoma eyes than in controls (P = 0.01). Nuclei were rounder (lower median aspect ratio) in glaucoma specimens (P = 0.02). In models assessing degree of glaucoma damage, F-actin process width was significantly wider in glaucoma eyes with more damage (P = 0.024), average LC beam width decreased with worse glaucoma damage (P = 0.042), and nuclear count per square millimeter rose with worse damage (P = 0.019). The greater cell count in LC pores represented 92.3% astrocytes by SOX9 labeling. The results are consistent with replacement of axons in LC pores by basement membrane labeled by anti-collagen IV and in-migrating astrocytes.

Conclusions

Alteration in LC structure in glaucoma involves migration of astrocytes into axonal bundles, change in astrocyte orientation and processes, production of basement membrane material, and thinning of connective tissue beams.

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.

Analysis of Variation in Incidence of Optic Disc Hemorrhage According to Seasonal and Temperature Changes

PURPOSE

To investigate seasonal variation in optic disc hemorrhage (DH) by review of fundus photographs representative of 2 calendar years (2019 and 2020).

DESIGN

Retrospective, observational trend study.

METHODS

Patients who visited the Glaucoma Clinic of Seoul National University Hospital and underwent fundus photography were included. All available stereo disc photographs and red-free retinal nerve fiber layer photographs taken between January 1, 2019 and December 31, 2020 were retrospectively reviewed. The monthly incidence rate of DH was determined by reference to the photographs. Seasonal temperature information and patients' intraocular pressure (IOP) information were obtained, organized, and analyzed.

RESULTS

Fundus images of 13,514 eyes were reviewed, and 454 eyes were confirmed to have DH. Poisson regression analyses revealed that as the temperature (T) increased by 1 °C, the DH risk ratio was reduced to 0.979 (95% confidence interval [CI] 0.969-0.989, P < .01). The DH incidence ratio was 1.53 (95% CI 1.23-1.91, P < .01) for the T <10 °C group relative to the T ≥20 °C group. The IOP of the patients with DH in winter was significantly higher than that measured in summer.

CONCLUSION

DH is affected by temperature, and as such, shows seasonal variability. This variability is believed to be caused by temperature-related factors such as IOP or hematological factors. © 2022 Elsevier Inc. All rights reserved.

Finite element modeling of the complex anisotropic mechanical behavior of the human sclera and pia mater

BACKGROUND AND OBJECTIVE

Accurate finite element (FE) simulation of the optic nerve head (ONH) depends on accurate mechanical properties of the load-bearing tissues. The peripapillary sclera in the ONH exhibits a depth-dependent, anisotropic, heterogeneous collagen fiber distribution. This study proposes a novel cable-in-solid modeling approach that mimics heterogeneous anisotropic collagen fiber distribution, validates the approach against published experimental biaxial tensile tests of scleral patches, and demonstrates its effectiveness in a complex model of the posterior human eye and ONH.

METHODS

A computational pipeline was developed that defines control points in the sclera and pia mater, distributes the depth-dependent circumferential, radial, and isotropic cable elements in the sclera and pia in a pattern that mimics collagen fiber orientation, and couples the cable elements and solid matrix using a mesh-free penalty-based cable-in-solid algorithm. A parameter study was performed on a model of a human scleral patch subjected to biaxial deformation, and computational results were matched to published experimental data. The new approach was incorporated into a previously published eye-specific model to test the method; results were then interpreted in relation to the collagen fibers' (cable elements) role in the resultant ONH deformations, stresses, and strains.

RESULTS

Results show that the cable-in-solid approach can mimic the full range of scleral mechanical behavior measured experimentally. Disregarding the collagen fibers/cable elements in the posterior eye model resulted in ∼20-60% greater tensile and shear stresses and strains, and ∼30% larger posterior deformations in the lamina cribrosa and peripapillary sclera.

CONCLUSIONS

The cable-in-solid approach can easily be implemented into commercial FE packages to simulate the heterogeneous and anisotropic mechanical properties of collagenous biological tissues.

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.

A feasible method for independently evaluating the mechanical properties of glial LC and RGC axons by combining atomic force microscopy measurement with image segmentation

PURPOSE

The deformation of lamina cribrosa (LC) under the elevated intraocular pressure (IOP) might squeeze the retinal ganglion cell (RGC) axons and impair the visual function. Mechanical behaviors of LC and RGC axons are supposed to be related to the optic nerve damage of glaucoma patients. However, they cannot be independently studied with the existing methods because the LC and RGC axons intertwine in the LC area. This study proposed a feasible method to evaluate the respective mechanical properties of glial LC and RGC axons of rats.

METHODS

The atomic force microscope (AFM) nano-indentation experiment was performed on unfixed cryosection samples acquired from the glial LC tissues of eight eyes from four rats. For each sample, three regions of interests (ROIs) with sizes of 20 × 20 μm² were selected from the ventral, central and dorsal regions of the sample, respectively, and the nano-indentation was performed on 128 × 128 points within each ROI to obtain a Young's modulus image. The glial LC and RGC axons were segmented on each modulus images using Otsu thresholding segmentation method, and their respective Young's modulus was further extracted for statistical analysis.

RESULTS

Young's modulus of glial LC and RGC axons are 297 ± 98 kPa and 76 ± 36 kPa in ventral regions, 342 ± 84 kPa and 84 ± 32 kPa in central regions, 280 ± 104 kPa and 75 ± 30 kPa in dorsal regions, respectively. No significant differences are found among the Young's modulus of different regions, both for glial LC and RGC axons.

CONCLUSIONS

This study takes the nature property of the LC area as a composite material into consideration, and proposes a feasible method to distinguish between the glial LC and RGC axons and measure their respective Young's modulus. These findings may provide useful information for establishing finite element models of the optic nerve head and promote the study on the deformation of the optic nerve under high intraocular pressure, and finally contribute to the early diagnosis of glaucoma.

Modeling the biomechanics of the lamina cribrosa microstructure in the human eye

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.

So-Called Lamina Cribrosa Defects May Mitigate IOP-Induced Neural Tissue Insult

Purpose

The prevailing theory about the function of lamina cribrosa (LC) connective tissues is that they provide structural support to adjacent neural tissues. Missing connective tissues would compromise this support and therefore are regarded as “LC defects”, despite scarce actual evidence of their role. We examined how so-called LC defects alter IOP-related mechanical insult to the LC neural tissues.

Methods

We built numerical models incorporating LC microstructure from polarized light microscopy images. To simulate LC defects of varying sizes, individual beams were progressively removed. We then compared intraocular pressure (IOP)-induced neural tissue deformations between models with and without defects. To better understand the consequences of defect development, we also compared neural tissue deformations between models with partial and complete loss of a beam.

Results

The maximum stretch of neural tissues decreased non-monotonically with defect size. Maximum stretch in the model with the largest defect decreased by 40% in comparison to the model with no defects. Partial loss of a beam increased the maximum stretch of neural tissues in its adjacent pores by 162%, compared with 63% in the model with complete loss of a beam.

Conclusions

Missing LC connective tissues can mitigate IOP-induced neural tissue insult, suggesting that the role of the LC connective tissues is more complex than simply fortifying against IOP. The numerical models further predict that partial loss of a beam is biomechanically considerably worse than complete loss of a beam, perhaps explaining why defects have been reported clinically but partial beams have not.

Pressure-Induced Changes in Astrocyte GFAP, Actin, and Nuclear Morphology in Mouse Optic Nerve

Purpose

To conduct quantitative analysis of astrocytic glial fibrillary acidic protein (GFAP), actin and nuclei distribution in mouse optic nerve (ON) and investigate changes in the measured features after 3 days of ocular hypertension (OHT).

Method

Serial cross-sections of 3-day microbead-induced OHT and control ONs were fluorescently labelled and imaged using confocal microscope. Eighteen structural features were measured from the acquired images, including GFAP coverage, actin area fraction, process thickness, and aspect ratio of cell nucleus. The measured features were analyzed for variations with axial locations along ON and radial zones transverse to ON, as well as for the correlations with degree of intraocular pressure (IOP) change.

Results

The most significant changes in structural features after 3-day OHT occurred in the unmyelinated ON region (R1), and the changes were greater with greater IOP elevation. Although the GFAP, actin, axonal, and ON areas all increased in 3-day OHT ONs in R1 (P ≤ 0.004 for all), the area fraction of GFAP actually decreased (P = 0.02), the actin area fraction was stable and individual axon compartments were unchanged in size. Within R1, the number of nuclear clusters increased (P < 0.001), but the mean size of nuclear clusters was smaller (P = 0.02) and the clusters became rounder (P < 0.001). In all cross-sections of control ONs, astrocytic processes were thickest in the rim zone compared with the central and peripheral zones (P ≤ 0.002 for both), whereas the overall process width in R1 decreased after 3 days of OHT (P < 0.001).

Conclusions

The changes in structure elucidated IOP-generated alterations that underlie astrocyte mechanotranslational responses relevant to glaucoma.

Collagen fiber interweaving is central to sclera stiffness

The mechanical properties of the microstructural components of sclera are central to eye physiology and pathology. Because these parameters are extremely difficult to measure directly, they are often estimated using inverse-modeling matching deformations of macroscopic samples measured experimentally. Although studies of sclera microstructure show collagen fiber interweaving, current models do not account for this interweaving or the resulting fiber-fiber interactions, which might affect parameter estimates. Our goal was to test the hypothesis that constitutive parameters estimated using inverse modeling differ if models account for fiber interweaving and interactions. We developed models with non-interweaving or interweaving fibers over a wide range of volume fractions (36-91%). For each model, we estimated fiber stiffness using inverse modeling matching biaxial experimental data of human sclera. We found that interweaving increased the estimated fiber stiffness. When the collagen volume fraction was 64% or less, the stiffness of interweaving fibers was about 1.25 times that of non-interweaving fibers. For higher volume fractions, the ratio increased substantially, reaching 1.88 for a collagen volume fraction of 91%. Simulating a model (interweaving/non-interweaving) using the fiber stiffness estimated from the other model produced substantially different behavior, far from that observed experimentally. These results show that estimating microstructural component mechanical properties is highly sensitive to the assumed interwoven/non-interwoven architecture. Moreover, the results suggest that interweaving plays an important role in determining the structural stiffness of sclera, and potentially of other soft tissues in which the collagen fibers interweave. STATEMENT OF SIGNIFICANCE: The collagen fibers of sclera are interwoven, but numerical models do not account for this interweaving or the resulting fiber-fiber interactions. To determine if interweaving matters, we examined the differences in the constitutive model parameters estimated using inverse modeling between models with interweaving and non-interweaving fibers. We found that the estimated stiffness of the interweaving fibers was up to 1.88 times that of non-interweaving fibers, and that the estimate increased with collagen volume fraction. Our results suggest that fiber interweaving is a fundamental characteristic of connective tissues, additional to anisotropy, density and orientation. Better characterization of interweaving, and of its mechanical effects is likely central to understanding microstructure and biomechanics of sclera and other soft tissues.

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.

Biomechanical research into lamina cribrosa in glaucoma

Glaucoma, a leading cause of irreversible blindness, poses a considerable public health challenge and burden. Mechanical models of the lamina cribrosa under elevated intraocular pressure at different scales, contributing significantly to uncovering the glaucomatous pathogenesis, are discussed. Meanwhile, the open issues and avenues for further development are highlighted.

The Effects of Glaucoma on the Pressure-Induced Strain Response of the Human Lamina Cribrosa

Purpose

To measure the ex vivo pressure-induced strain response of the human optic nerve head and analyze for variations with glaucoma diagnosis and optic nerve axon damage.

Methods

The posterior sclera of 16 eyes from 8 diagnosed glaucoma donors and 10 eyes from 6 donors with no history of glaucoma were inflation tested between 5 and 45 mm Hg. The optic nerve from each donor was examined for degree of axon loss. The posterior volume of the lamina cribrosa (LC) was imaged with second harmonic generation and analyzed using volume correlation to calculate LC strains between 5 and 10 and 5 and 45 mm Hg.

Results

Eye length and LC area were larger in eyes diagnosed with glaucoma (P ≤ 0.03). Nasal-temporal EXX and circumferential Eθθ strains were lower in the LC of diagnosed glaucoma eyes at 10 mm Hg (P ≤ 0.05) and 45 mm Hg (P ≤ 0.07). EXX was smaller in the LC of glaucoma eyes with <25% axon loss compared with undamaged normal eyes (P = 0.01, 45 mm Hg). In general, the strains were larger in the peripheral than central LC. The ratio of the maximum principal strain Emax in the peripheral to central LC was larger in glaucoma eyes with >25% axon loss than in glaucoma eyes with milder damage (P = 0.004, 10 mm Hg).

Conclusions

The stiffness of the LC pressure-strain response was greater in diagnosed glaucoma eyes and varied with glaucomatous axon damage. Lower LC strains in glaucoma eyes with milder damage may represent baseline biomechanical behavior that contributes to axon loss, whereas greater LC strain and altered radial LC strain variation in glaucoma eyes with more severe damage may be caused by glaucoma-related remodeling.

The inflation response of the human lamina cribrosa and sclera: Analysis of deformation and interaction

This study investigated the inflation response of the lamina cribrosa (LC) and adjacent peripapillary sclera (PPS) in post-mortem human eyes with no history of glaucoma. The posterior sclera of 13 human eyes from 7 donors was subjected to controlled pressurization between 5-45 mmHg. A laser-scanning microscope (LSM) was used to image the second harmonic generation (SHG) response of collagen and the two-photon fluorescent (TPF) response of elastin within the volume of the LC and PPS at each pressure. Image volumes were analyzed using digital volume correlation (DVC) to calculate the three-dimensional (3D) deformation field between pressures. The LC exhibited larger radial strain, Err, and maximum principal strain, Emax, (p < 0.0001) and greater posterior displacement (p=0.0007) compared to the PPS between 5-45 mmHg, but had similar average circumferential strain, Eθθ, and maximum shear strain, Γmax. The Emax and Γmax were highest near the LC-PPS interface and lowest in the nasal quadrant of both tissues. Larger LC area was associated with smaller Emax in the peripheral LC and larger Emax in the central LC (p ≤ 0.01). The Emax, Γmax, and Eθθ in the inner PPS increased with increasing strain in adjacent LC regions (p ≤ 0.001). Smaller strains in the PPS were associated with a larger difference in the posterior displacement between the PPS and central LC (p < 0.0001 for Emax and Err), indicating that a stiffer pressure-strain response of the PPS is associated with greater posterior bowing of the LC. STATEMENT OF SIGNIFICANCE: Glaucoma causes vision loss through progressive damage of the retinal ganglion axons at the lamina cribrosa (LC), a connective tissue structure that supports the axons as they pass through the eye wall. It is hypothesized that strains caused by intraocular pressure may initiate this damage and that these strains are modulated by the combined deformation of the LC and adjacent peripapillary sclera (PPS). In this study we present a method to measure the pressure-induced 3D displacement and strain field in the LC and PPS simultaneously. Regional strain variation in the LC and PPS was investigated and compared and strains were analyzed for associations with age, LC area, LC strain magnitude, and LC posterior motion relative to the PPS.

Dasatinib inhibits peripapillary scleral myofibroblast differentiation

Scleral fibroblast activation occurs in glaucomatous and myopic eyes. Here we perform an unbiased screen to identify kinase inhibitors that reduce fibroblast activation to diverse stimuli in vitro and to in vivo intraocular pressure (IOP) elevation. Primary cultures of peripapillary scleral (PPS) fibroblasts from two human donors were screened using a library of 80 kinase inhibitors to identify compounds that inhibit TGFβ-induced extracellular matrix (ECM) synthesis. Inhibition of myofibroblast differentiation was verified by alpha smooth muscle actin (αSMA) immunoblot and collagen contraction assay. Inhibition of IOP-induced scleral fibroblast proliferation was assessed by ELISA assay for proliferating cell nuclear antigen (PCNA). The initial screen identified 7 inhibitors as showing>80% reduction in ECM binding. Three kinase inhibitors were verified to reduce TGFβ-induced αSMA expression and cellular contractility (rottlerin, PP2, tyrphostin 9). The effect of three Src inhibitors, bosutinib, dasatinib, and SU-6656, on myofibroblast differentiation was evaluated, with only dasatinib significantly inhibiting TGFβ-induced ECM synthesis, αSMA expression, and cellular contractility at nanomolar dosages. Subconjunctival injection of dasatinib reduced IOP-induced scleral fibroblast proliferation compared to control (4.9 ± 11.1 ng/sclera with 0.1 μM versus 88.7 ± 38.6 ng/sclera in control, P < 0.0001). Dasatinib inhibits scleral myofibroblast differentiation and there is pharmacologic evidence that this inhibition is not solely due to Src-kinase inhibition.

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.

A computational multi-scale approach to investigate mechanically-induced changes in tricuspid valve anterior leaflet microstructure

The tricuspid valve is an atrioventricular valve that prevents blood backflow from the right ventricle into the right atrium during ventricular contractions. It is important to study mechanically induced microstructural alterations in the tricuspid valve leaflets, as this aids both in understanding valvular diseases and in the development of new engineered tissue replacements. The structure and composition of the extracellular matrix (ECM) fiber networks are closely tied to an overall biomechanical function of the tricuspid valve. In this study, we conducted experiments and implemented a multiscale modeling approach to predict ECM microstructural changes to tissue-level mechanical responses in a controlled loading environment. In particular, we characterized a sample of a porcine anterior leaflet at a macroscale using a biaxial mechanical testing method. We then generated a three-dimensional finite element model, to which computational representations of corresponding fiber networks were incorporated based on properties of the microstructural architecture obtained from small angle light scattering. Using five different biaxial boundary conditions, we performed iterative simulations to obtain model parameters with an overall R² value of 0.93. We observed that mechanical loading could markedly alter the underlying ECM architecture. For example, a relatively isotropic fiber network (with an anisotropy index value α of 28%) became noticeably more anisotropic (with an α of 40%) when it underwent mechanical loading. We also observed that the mechanical strain was distributed in a different manner at the ECM/fiber level as compared to the tissue level. The approach presented in this study has the potential to be implemented in pathophysiologically altered biomechanical and structural conditions and to bring insights into the mechanobiology of the tricuspid valve. STATEMENT OF SIGNIFICANCE: Quantifying abnormal cellar/ECM-level deformation of tricuspid valve leaflets subjected to a modified loading environment is of great importance, as it is believed to be linked to valvular remodeling responses. For example, developing surgical procedures or engineered tissue replacements that maintain/mimic ECM-level mechanical homeostasis could lead to more durable outcomes. To quantify leaflet deformation, we built a multiscale framework encompassing the contributions of disorganized ECM components and organized fibers, which can predict the behavior of the tricuspid valve leaflets under physiological loading conditions both at the tissue level and at the ECM level. In addition to future in-depth studies of tricuspid valve pathologies, our model can be used to characterize tissues in other valves of the heart.

Comparison of Diagnostic Power of Optic Nerve Head and Posterior Sclera Configuration Parameters on Myopic Normal Tension Glaucoma

PURPOSE

The aim of this study was to compare the diagnostic power of optic nerve head and posterior scleral configuration parameters obtained with the swept-source optical coherence tomography (SSOCT) on myopic normal-tension glaucoma (NTG).

MATERIALS AND METHODS

A total of 203 eyes of 203 participants with myopia diagnosed at Seoul Saint Mary's Hospital between September 2016 and February 2018 were divided into myopic NTG group (n=113) and nonglaucomatous myopia group (n=90). Established optic nerve head (ONH) parameters such as disc torsion, horizontal tilt, and vertical tilt, and novel parameters representing posterior sclera, were quantified using SSOCT. The posterior sclera was presented with the relative position of the deepest point of the eye (DPE) from the optic disc by measuring the distance, depth, and angle. The mean and the statistical distribution of each index were calculated. Differences in distribution led to another novel marker, absolute misaligned angle, which represents the displaced direction of the ONH from the sclera. The ONH was classified as misaligned when the degree of misalignment was >15 degrees in either direction. The area under the receiver operating characteristic curves and multivariate logistic regression analysis were used to test the diagnostic power in the presence of myopic NTG.

RESULTS

No significant difference was observed with respect to age, sex, refractive error, axial length, and central corneal thickness between the 2 groups. However, 20 (22.22%) of 90 eyes in the nonglaucomatous group showed misalignment, whereas 60 (53.09%) of 113 eyes in the NTG group had misalignment (odds ratio: 3.962, P<0.001). The absolute misaligned angle (0.696) and the horizontal tilt (0.682) were significantly associated with myopic NTG, which significantly exceeded other parameters in area under the receiver operating characteristic curves (both P<0.001). The multivariate logistic regression also showed that the absolute misaligned angle (hazard ratio=1.045, 95% confidence interval=1.023-1.068, P<0.001) and the horizontal tilt (hazard ratio=1.061, 95% confidence interval=1.015-1.109, P=0.009) were associated significantly with the presence of NTG.

CONCLUSIONS

The diagnostic power of absolute misaligned angle and the horizontal tilt angle significantly exceeded other parameters on myopic NTG. These parameters may be associated with a displaced direction of the ONH to the posterior sclera, which can be linked to the altered sclera configuration of myopic NTG subjects.

Thin Lamina Cribrosa Beams Have Different Collagen Microstructure Than Thick Beams

Purpose

To compare the collagen microstructural crimp characteristics between thin and thick lamina cribrosa (LC) beams.

Methods

Seven eyes from four sheep were fixed at 5 mm Hg IOP in 10% formalin. For each eye, one to three coronal cryosections through the LC were imaged with polarized light microscopy and analyzed to visualize the LC and determine collagen fiber microstructure. For every beam, we measured its width and three characteristics of the crimp of its collagen fibers: waviness, tortuosity, and amplitude. Linear mixed effects models were used to test whether crimp characteristics were associated with the LC beam width.

Results

For each eye and over all the eyes, LC beam width was positively associated with crimp waviness and tortuosity, and negatively associated with crimp amplitude (P's < 0.0001). Thin beams, average width 13.11 μm, had average (SD) waviness, tortuosity, and amplitude of 0.27 (0.17) radians, 1.017 (0.028) and 1.88 (1.41) μm, respectively. For thick beams, average width 26.10 μm, these characteristics were 0.33 (0.18) radians, 1.025 (0.037) and 1.58 (1.36) μm, respectively.

Conclusions

Our results suggest heterogeneity in LC beam mechanical properties. Thin beams were less wavy than their thicker counterparts, suggesting that thin beams may stiffen at lower IOP than thick beams. This difference may allow thin beams to support similar amounts of IOP-induced force as thicker beams, thus providing a similar level of structural support to the axons at physiologic IOP, despite the differences in width. Measurements of beam-level mechanical properties are needed to confirm these predictions.

Racioethnic differences in the biomechanical response of the lamina cribrosa

Glaucoma is the second leading cause of irreversible blindness in the world with a higher prevalence in those of African Descent (AD) and Hispanic Ethnicity (HE) than in those of European Descent (ED). The objective of this study was to investigate the pressure dependent biomechanical response of the lamina cribrosa (LC) in normal human donor tissues from these racioethnic backgrounds. Pressure inflation tests were performed on 24 human LCs (n = 9 AD, n = 6 ED, and n = 9 HE) capturing the second harmonic generation (SHG) signal of collagen at 5, 15, 30, and 45 mmHg from an anterior view. A non-rigid image registration technique was utilized to determine the 3D displacement field in each LC from which 3D Green strains were calculated. The peak shear strain in the superior quadrant of the LC in those of ED was significantly higher than in those of AD and HE (p-value = 0.005 & 0.034, respectively) where ED = 0.017 [IQR = 0.012-0.027], AD = 0.0002 [IQR = -0.001-0.007], HE = 0.0016 [IQR = -0.002-0.012]). There were also significant differences in the regional strain heterogeneity in those of AD and HE that were absent in those of ED. This work represents, to our knowledge, the first ex-vivo study identifying significant differences in the biomechanical response of the LC in populations at increased risk of glaucoma. Future work will be necessary to assess if and how these differences play a role in predisposing those of Hispanic Ethnicity and African Descent to the onset and/or progression of primary open angle glaucoma. STATEMENT OF SIGNIFICANCE: Glaucoma is the second leading cause of irreversible blindness in the world and occurs more frequently in those of African Descent and Hispanic Ethnicity than in those of European Descent. To date, there has been no ex-vivo study quantifying differences in the biomechanical response of the non-glaucomatous lamina cribrosa (LC) across these racioethnic backgrounds. In this work we report, for the first time, differences in the pressure dependent biomechanical response of LC across different racioethnic groups as quantified using nonlinear optical microscopy. This study lays the foundation for future work investigating if and how these differences may play a role in predisposing those at increased risk to the onset and/or progression of primary open angle glaucoma.

Peripapillary sclera architecture revisited: A tangential fiber model and its biomechanical implications

The collagen fiber architecture of the peripapillary sclera (PPS), which surrounds the scleral canal, is a critical factor in determining the mechanical response of the optic nerve head (ONH) to variations in intraocular pressure (IOP). Experimental and clinical evidence point to IOP-induced deformations within the scleral canal as important contributing factors of glaucomatous neural tissue damage and consequent vision loss. Hence, it is imperative to understand PPS architecture and biomechanics. Current consensus is that the fibers of the PPS form a closed ring around the canal to support the delicate neural tissues within. We propose an alternative fiber architecture for the PPS, in which the scleral canal is supported primarily by long-running fibers oriented tangentially to the canal. We present evidence that this tangential model is consistent with histological observations in multiple species, and with quantitative measurements of fiber orientation obtained from small angle light scattering and wide-angle X-ray scattering. Using finite element models, we investigated the biomechanical implications of a tangential fiber PPS architecture. We found that the tangential arrangement of fibers afforded better mechanical support to the tissues within the scleral canal as compared to a simple circumferential ring of fibers or a combination of fibers oriented radially and circumferentially. We also found that subtle variations from a tangential orientation could reproduce clinically observed ONH behavior which has yet to be explained using current theories of PPS architecture and simulation, namely, the contraction of the scleral canal under elevated IOP.

STATEMENT OF SIGNIFICANCE

It is hypothesized that vision loss in glaucoma is due to excessive mechanical deformation within the neural tissue inside the scleral canal. This study proposes a new model for how the collagen of the peripapillary sclera surrounding the canal is organized to support the delicate neural tissue inside. Previous low-resolution studies of the peripapillary sclera suggested that the collagen fibers are arranged in a ring around the canal. Instead, we provide microscopic evidence suggesting that the canal is also supported by long-running interwoven fibers oriented tangentially to the canal. We demonstrate that this arrangement has multiple biomechanical advantages over a circular collagen arrangement and can explain previously unexplained experimental findings including contraction of the scleral canal under elevated intraocular pressure.

Polarized light microscopy for 3-dimensional mapping of collagen fiber architecture in ocular tissues

Collagen fibers play a central role in normal eye mechanics and pathology. In ocular tissues, collagen fibers exhibit a complex 3-dimensional (3D) fiber orientation, with both in-plane (IP) and out-of-plane (OP) orientations. Imaging techniques traditionally applied to the study of ocular tissues only quantify IP fiber orientation, providing little information on OP fiber orientation. Accurate description of the complex 3D fiber microstructures of the eye requires quantifying full 3D fiber orientation. Herein, we present 3dPLM, a technique based on polarized light microscopy developed to quantify both IP and OP collagen fiber orientations of ocular tissues. The performance of 3dPLM was examined by simulation and experimental verification and validation. The experiments demonstrated an excellent agreement between extracted and true 3D fiber orientation. Both IP and OP fiber orientations can be extracted from the sclera and the cornea, providing previously unavailable quantitative 3D measures and insight into the tissue microarchitecture. Together, the results demonstrate that 3dPLM is a powerful imaging technique for the analysis of ocular tissues.

Cerebrospinal Fluid Pressure: Revisiting Factors Influencing Optic Nerve Head Biomechanics

Purpose

To model the sensitivity of the optic nerve head (ONH) biomechanical environment to acute variations in IOP, cerebrospinal fluid pressure (CSFP), and central retinal artery blood pressure (BP).

Methods

We extended a previously published numerical model of the ONH to include 24 factors representing tissue anatomy and mechanical properties, all three pressures, and constraints on the optic nerve (CON). A total of 8340 models were studied to predict factor influences on 98 responses in a two-step process: a fractional factorial screening analysis to identify the 16 most influential factors, followed by a response surface methodology to predict factor effects in detail.

Results

The six most influential factors were, in order: IOP, CON, moduli of the sclera, lamina cribrosa (LC) and dura, and CSFP. IOP and CSFP affected different aspects of ONH biomechanics. The strongest influence of CSFP, more than twice that of IOP, was on the rotation of the peripapillary sclera. CSFP had similar influence on LC stretch and compression to moduli of sclera and LC. On some ONHs, CSFP caused large retrolamina deformations and subarachnoid expansion. CON had a strong influence on LC displacement. BP overall influence was 633 times smaller than that of IOP.

Conclusions

Models predict that IOP and CSFP are the top and sixth most influential factors on ONH biomechanics. Different IOP and CSFP effects suggest that translaminar pressure difference may not be a good parameter to predict biomechanics-related glaucomatous neuropathy. CON may drastically affect the responses relating to gross ONH geometry and should be determined experimentally.

Machine-learning based segmentation of the optic nerve head using multi-contrast Jones matrix optical coherence tomography with semi-automatic training dataset generation

A pixel-by-pixel tissue classification framework using multiple contrasts obtained by Jones matrix optical coherence tomography (JM-OCT) is demonstrated. The JM-OCT is an extension of OCT that provides OCT, OCT angiography, birefringence tomography, degree-of-polarization uniformity tomography, and attenuation coefficient tomography, simultaneously. The classification framework consists of feature engineering, k-means clustering that generates a training dataset, training of a tissue classifier using the generated training dataset, and tissue classification by the trained classifier. The feature engineering process generates synthetic features from the primary optical contrasts obtained by JM-OCT. The tissue classification is performed in the feature space of the engineered features. We applied this framework to the in vivo analysis of optic nerve heads of posterior eyes. This classified each JM-OCT pixel into prelamina, lamina cribrosa (lamina beam), and retrolamina tissues. The lamina beam segmentation results were further utilized for birefringence and attenuation coefficient analysis of lamina beam.

Tortuous Pore Path Through the Glaucomatous Lamina Cribrosa

The lamina cribrosa is a primary site of damage in glaucoma. While mechanical distortion is hypothesized to cause reduction of axoplasmic flow, little is known about how the pores, which contains the retinal ganglion cell axons, traverse the lamina cribrosa. We investigated lamina cribrosa pore paths in vivo to quantify differences in tortuosity of pore paths between healthy and glaucomatous eyes. We imaged 16 healthy, 23 glaucoma suspect and 48 glaucomatous eyes from 70 subjects using a swept source optical coherence tomography system. The lamina cribrosa pores were automatically segmented using a previously described segmentation algorithm. Individual pore paths were automatically tracked through the depth of the lamina cribrosa using custom software. Pore path convergence to the optic nerve center and tortuosity was quantified for each eye. We found that lamina cribrosa pore pathways traverse the lamina cribrosa closer to the optic nerve center along the depth of the lamina cribrosa regardless of disease severity or diagnostic category. In addition, pores of glaucoma eyes take a more tortuous path through the lamina cribrosa compared to those of healthy eyes, suggesting a potential mechanism for reduction of axoplasmic flow in glaucoma.

Collagen fiber recruitment: A microstructural basis for the nonlinear response of the posterior pole of the eye to increases in intraocular pressure

Our goal was to quantify and characterize how the collagen fiber crimp waviness of the lamina cribrosa (LC) and peripapillary sclera (PPS) changes with intraocular pressure (IOP). Thirteen sheep (ovine) eyes were immersion and perfusion fixed while maintaining IOP at 0, 10, 15, 20, or 50 mmHg. Coronal optic nerve head (ONH) sections (30 µm) were imaged with polarized light microscopy (PLM) and analyzed for collagen fiber orientation and waviness (SD of fiber orientation). In the LC, the waviness of every LC beam was measured. In the PPS, at least 900 collagen bundles were measured per eye. Using the waviness at 50 mmHg IOP, we defined tissue-specific thresholds to determine the fraction of loaded or recruited fibers. We found that fiber waviness decreased with IOP (P < 0.001). At every IOP, the waviness of the collagen fibers, and the fraction of fibers recruited in the LC were smaller or equal than those of the PPS (P < 0.001). At 15 mmHg IOP, both LC and PPS had ¾ recruited fibers and ¼ left in reserve. The decreased waviness with IOP and associated fiber recruitment is experimental evidence of fiber-based nonlinear biomechanical behavior of the ONH. At all IOPs the PPS had an equal or larger fraction of fibers recruited than the LC. That both LC and PPS had the same fraction of recruited and reserve fibers at normal IOP suggests that this may be an optimal fraction of recruitment for healthy eyes. Whether this extends to human eyes remains unknown.

STATEMENT OF SIGNIFICANCE

Collagen fibers exhibit a natural waviness or crimp that largely determine the nonlinear biomechanics of soft tissue. Experimental measurements of crimp morphology in the sheep eye, and how it changes with intraocular pressure (IOP), however, are exceedingly sparse. We quantified how posterior eye crimp changes with increasing IOP. We found that the lamina cribrosa and peripapillary sclera have fundamentally different crimp, and with increasing IOP, have different proportions of fibers that straighten, or get recruited, versus remaining wavy, or in reserve. Interestingly, at physiologic IOP of 15 mmHg, both tissues had about ¾ fibers recruited and ¼ fibers in reserve, indicating there may be an optimal fraction of fibers.

Lamina Cribrosa Pore Shape and Size as Predictors of Neural Tissue Mechanical Insult

Purpose

The purpose of this study was to determine how the architecture of the lamina cribrosa (LC) microstructure, including the shape and size of the lamina pores, influences the IOP-induced deformation of the neural tissues within the LC pores using computational modeling.

Methods

We built seven specimen-specific finite element models of LC microstructure with distinct nonlinear anisotropic properties for LC beams and neural tissues based on histological sections from three sheep eyes. Changes in shape (aspect ratio and convexity) and size (area and perimeter length) due to IOP-induced hoop stress were calculated for 128 LC pores. Multivariate linear regression was used to determine if pore shape and size were correlated with the strain in the pores. We also compared the microstructure models to a homogenized model built following previous approaches.

Results

The LC microstructure resulted in focal tensile, compressive, and shear strains in the neural tissues of the LC that were not predicted by homogenized models. IOP-induced hoop stress caused pores to become larger and more convex; however, pore aspect ratio did not change consistently. Peak tensile strains within the pores were well predicted by a linear regression model considering the initial convexity (negative correlation, P < 0.001), aspect ratio (positive correlation, P < 0.01), and area (negative correlation, P < 0.01). Significant correlations were also found when considering the deformed shape and size of the LC pores.

Conclusions

The deformation of the LC neural tissues was largely dependent on the collagenous LC beams. Simple measures of LC pore shape and area provided good estimates of neural tissue biomechanical insult.

Microstructural Crimp of the Lamina Cribrosa and Peripapillary Sclera Collagen Fibers

Purpose

Although collagen microstructural crimp is a major determinant of ocular biomechanics, no direct measurements of optic nerve head (ONH) crimp have been reported. Our goal was to characterize the crimp period of the lamina cribrosa (LC) and peripapillary sclera (PPS) at low and normal IOPs.

Methods

ONHs from 11 sheep eyes were fixed at 10-, 5-, or 0-mm Hg IOP and crimp periods measured manually from coronal cryosections imaged with polarized light microscopy (PLM). Using linear mixed-effect models, we characterized the LC and PPS periods, and how they varied with distance from the scleral canal edge.

Results

A total of 17,374 manual collagen crimp period measurements were obtained with high repeatability (1.9 μm) and reproducibility (4.7 μm). The periods were smaller (P < 0.001) and less variable in the LC than in the PPS: average (SD) of 13.8 (3.1) μm in the LC, and 31.0 (10.4) μm in the PPS. LC crimp period did not vary with distance from the scleral canal wall (P > 0.1). PPS period increased with the square root of the distance to the canal (P < 0.0001).

Conclusions

Small, uniform crimp periods within the sheep LC and immediately adjacent PPS may indicate that these tissues are setup to prevent large or heterogeneous deformations that insult the neural tissues within the canal. An increasing more variable period with distance from the canal provides a smooth transition of mechanical properties that minimizes stress and strain concentrations.