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

Lipid mediators in glaucoma: Unraveling their diverse roles and untapped therapeutic potential

Glaucoma is a complex neurodegenerative disease characterized by optic nerve damage and visual field loss, and remains a leading cause of irreversible blindness. Elevated intraocular pressure (IOP) is a critical risk factor that requires effective management. Emerging research underscores dual roles of bioactive lipid mediators in both IOP regulation, and the modulation of neurodegeneration and neuroinflammation in glaucoma. Bioactive lipids, encompassing eicosanoids, specialized pro-resolving mediators (SPMs), sphingolipids, and endocannabinoids, have emerged as crucial players in these processes, orchestrating inflammation and diverse effects on aqueous humor dynamics and tissue remodeling. Perturbations in these lipid mediators contribute to retinal ganglion cell loss, vascular dysfunction, oxidative stress, and neuroinflammation. Glaucoma management primarily targets IOP reduction via pharmacological agents and surgical interventions, with prostaglandin analogues at the forefront. Intriguingly, additional lipid mediators offer promise in attenuating inflammation and providing neuroprotection. Here we explore these pathways to shed light on their intricate roles, and to unveil novel therapeutic avenues for glaucoma management.

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.

Computational study on the effects of central retinal blood vessels with asymmetric geometries on optic nerve head biomechanics

Optic nerve head (ONH) biomechanics are associated with glaucoma progression and have received considerable attention. Central retinal vessels (CRVs) oriented asymmetrically in the ONH are the single blood supply source to the retina and are believed to act as mechanically stable elements in the ONH in response to intraocular pressure (IOP). However, these mechanical effects are considered negligible in ONH biomechanical studies and received less attention. This study investigated the effects of CRVs on ONH biomechanics taking into consideration three-dimensional asymmetric CRV geometries. A CRV geometry was constructed based on CRV centerlines extracted from optical coherence tomography ONH images in eight healthy subjects and superimposed in the idealized ONH geometry established in previous studies. Mechanical analyses of the ONH in response to the IOP were conducted in the cases with and without CRVs for comparison. Obtained results demonstrated that the CRVs induced anisotropic ONH deformation, particularly in the lamina cribrosa and the associated upper neural tissues (prelamina) with wide ranges of spatial strain distributions. These results indicated that the CRVs result in anisotropic deformation with local strain concentration, rather than function to mechanically support in response to the IOP as in the conventional thinking in ophthalmology.

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.

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.

Differing Associations between Optic Nerve Head Strains and Visual Field Loss in Patients with Normal- and High-Tension Glaucoma

PURPOSE

To study the associations between optic nerve head (ONH) strains under intraocular pressure (IOP) elevation with retinal sensitivity in patients with glaucoma.

DESIGN

Clinic-based cross-sectional study.

PARTICIPANTS

Two hundred twenty-nine patients with primary open-angle glaucoma (subdivided into 115 patients with high-tension glaucoma [HTG] and 114 patients with normal-tension glaucoma [NTG]).

METHODS

For 1 eye of each patient, we imaged the ONH using spectral-domain OCT under the following conditions: (1) primary gaze and (2) primary gaze with acute IOP elevation (to approximately 35 mmHg) achieved through ophthalmodynamometry. A 3-dimensional strain-mapping algorithm was applied to quantify IOP-induced ONH tissue strain (i.e., deformation) in each ONH. Strains in the prelaminar tissue (PLT), the retina, the choroid, the sclera, and the lamina cribrosa (LC) were associated (using linear regression) with measures of retinal sensitivity from the 24-2 Humphrey visual field test (Carl Zeiss Meditec). This was performed globally, then locally according to a previously published regionalization scheme.

MAIN OUTCOME MEASURES

Associations between ONH strains and values of retinal sensitivity from visual field testing.

RESULTS

For patients with HTG, we found (1) significant negative linear associations between ONH strains and retinal sensitivity (P < 0.001; on average, a 1% increase in ONH strains corresponded to a decrease in retinal sensitivity of 1.1 decibels [dB]), (2) that high-strain regions colocalized with anatomically mapped regions of high visual field loss, and (3) that the strongest negative associations were observed in the superior region and in the PLT. In contrast, for patients with NTG, no significant associations between strains and retinal sensitivity were observed except in the superotemporal region of the LC.

CONCLUSIONS

We found significant negative associations between IOP-induced ONH strains and retinal sensitivity in a relatively large glaucoma cohort. Specifically, patients with HTG who experienced higher ONH strains were more likely to exhibit lower retinal sensitivities. Interestingly, this trend in general was less pronounced in patients with NTG, which could suggest a distinct pathophysiologic relationship between the two glaucoma subtypes.

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.

Morphological Changes of Glial Lamina Cribrosa of Rats Suffering from Chronic High Intraocular Pressure

Deformations or remodeling of the lamina cribrosa (LC) induced by elevated intraocular pressure (IOP) are associated with optic nerve injury. The quantitative analysis of the morphology changes of the LC will provide the basis for the study of the pathogenesis of glaucoma. After the chronic high-IOP rat model was induced by cauterizing episcleral veins with 5-Fluorouracil subconjunctival injection, the optic nerve head (ONH) cross sections were immunohistochemically stained at 2 w, 4 w, 8 w, and 12 w. Then the sections were imaged by a confocal microscope, and six morphological parameters of the ONH were calculated after the images were processed using Matlab. The results showed that the morphology of the ONH changed with the duration of chronic high IOP. The glial LC pore area fraction, the ratio of glial LC pore area to the glial LC tissue area, first decreased at 2 w and 4 w and then increased to the same level as the control group at 8 w and continued to increase until 12 w. The number and density of nuclei increased significantly at 8 w in the glial LC region. The results might mean the fraction of glial LC beam increased and astrocytes proliferated at the early stage of high IOP. Combined with the images of the ONH, the results showed the glial LC was damaged with the duration of chronic elevated IOP.

Finite element modeling of effects of tissue property variation on human optic nerve tethering during adduction

Tractional tethering by the optic nerve (ON) on the eye as it rotates towards the midline in adduction is a significant ocular mechanical load and has been suggested as a cause of ON damage induced by repetitive eye movements. We designed an ocular finite element model (FEM) simulating 6° incremental adduction beyond the initial configuration of 26° adduction that is the observed threshold for ON tethering. This FEM permitted sensitivity analysis of ON tethering using observed material property variations in measured hyperelasticity of the anterior, equatorial, posterior, and peripapillary sclera; and the ON and its sheath. The FEM predicted that adduction beyond the initiation of ON tethering concentrates stress and strain on the temporal side of the optic disc and peripapillary sclera, the ON sheath junction with the sclera, and retrolaminar ON neural tissue. However, some unfavorable combinations of tissue properties within the published ranges imposed higher stresses in these regions. With the least favorable combinations of tissue properties, adduction tethering was predicted to stress the ON junction and peripapillary sclera more than extreme conditions of intraocular and intracranial pressure. These simulations support the concept that ON tethering in adduction could induce mechanical stresses that might contribute to ON damage.

Mechanobiological responses of astrocytes in optic nerve head due to biaxial stretch

Background

Elevated intraocular pressure (IOP) is the main risk factor for glaucoma, which might cause the activation of astrocytes in optic nerve head. To determine the effect of mechanical stretch on the astrocytes, we investigated the changes in cell phenotype, proteins of interest and signaling pathways under biaxial stretch.

Method

The cultured astrocytes in rat optic nerve head were stretched biaxially by 10 and 17% for 24 h, respectively. Then, we detected the morphology, proliferation and apoptosis of the stretched cells, and performed proteomics analysis. Protein expression was analyzed by Isobaric tags for relative and absolute quantification (iTRAQ) mass spectrometry. Proteins of interest and signaling pathways were screened using Gene Ontology enrichment analysis and pathway enrichment analysis, and the results were verified by western blot and the gene-chip data from Gene Expression Omnibus (GEO) database.

Result

The results showed that rearrangement of the actin cytoskeleton in response to stimulation by mechanical stress and proliferation rate of astrocytes decreased under 10 and 17% stretch condition, while there was no significant difference on the apoptosis rate of astrocytes in both groups. In the iTRAQ quantitative experiment, there were 141 differential proteins in the 10% stretch group and 140 differential proteins in the 17% stretch group. These proteins include low-density lipoprotein receptor-related protein (LRP6), caspase recruitment domain family, member 10 (CARD10), thrombospondin 1 (THBS1) and tetraspanin (CD81). The western blot results of LRP6, THBS1 and CD81 were consistent with that of iTRAQ experiment. ANTXR2 and CARD10 were both differentially expressed in the mass spectrometry results and GEO database. We also screened out the signaling pathways associated with astrocyte activation, including Wnt/β–catenin pathway, NF-κB signaling pathway, PI3K-Akt signaling pathway, MAPK signaling pathway, Jak-STAT signaling pathway, ECM-receptor interaction, and transforming growth factor-β (TGF-β) signaling pathway.

Conclusion

Mechanical stimulation can induce changes in cell phenotype, some proteins and signaling pathways, which might be associated with astrocyte activation. These proteins and signaling pathways may help us have a better understanding on the activation of astrocytes and the role astrocyte activation played in glaucomatous optic neuropathy.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12886-022-02592-8.

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.

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.

Microstructural Deformations Within the Depth of the Lamina Cribrosa in Response to Acute In Vivo Intraocular Pressure Modulation

Purpose

The lamina cribrosa (LC) is a leading target for initial glaucomatous damage. We investigated the in vivo microstructural deformation within the LC volume in response to acute IOP modulation while maintaining fixed intracranial pressure (ICP).

Methods

In vivo optic nerve head (ONH) spectral-domain optical coherence tomography (OCT) scans (Leica, Chicago, IL, USA) were obtained from eight eyes of healthy adult rhesus macaques (7 animals; ages = 7.9-14.4 years) in different IOP settings and fixed ICP (8-12 mm Hg). IOP and ICP were controlled by cannulation of the anterior chamber and the lateral ventricle of the brain, respectively, connected to a gravity-controlled reservoir. ONH images were acquired at baseline IOP, 30 mm Hg (H1-IOP), and 40 to 50 mm Hg (H2-IOP). Scans were registered in 3D, and LC microstructure measurements were obtained from shared regions and depths.

Results

Only half of the eyes exhibited LC beam-to-pore ratio (BPR) and microstructure deformations. The maximal BPR change location within the LC volume varied between eyes. BPR deformer eyes had a significantly higher baseline connective tissue volume fraction (CTVF) and lower pore aspect ratio (P = 0.03 and P = 0.04, respectively) compared to BPR non-deformer. In all eyes, the magnitude of BPR changes in the anterior surface was significantly different (either larger or smaller) from the maximal change within the LC (H1-IOP: P = 0.02 and H2-IOP: P = 0.004).

Conclusions

The LC deforms unevenly throughout its depth in response to IOP modulation at fixed ICP. Therefore, analysis of merely the anterior LC surface microstructure will not fully capture the microstructure deformations within the LC. BPR deformer eyes have higher CTVF than BPR non-deformer eyes.

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.

Mechanosensitive channel inhibition attenuates TGFβ2-induced actin cytoskeletal remodeling and reactivity in mouse optic nerve head astrocytes

Astrocytes within the optic nerve head undergo actin cytoskeletal rearrangement early in glaucoma, which coincides with astrocyte reactivity and extracellular matrix (ECM) deposition. Elevated transforming growth factor beta 2 (TGFβ2) levels within astrocytes have been described in glaucoma, and TGFβ signaling induces actin cytoskeletal remodeling and ECM deposition in many tissues. A key mechanism by which astrocytes sense and respond to external stimuli is via mechanosensitive ion channels. Here, we tested the hypothesis that inhibition of mechanosensitive channels will attenuate TGFβ2-mediated optic nerve head astrocyte actin cytoskeletal remodeling, reactivity, and ECM deposition. Primary optic nerve head astrocytes were isolated from C57BL/6J mice and cell purity was confirmed by immunostaining. Astrocytes were treated with vehicle control, TGFβ2 (5 ng/ml), GsMTx4 (a mechanosensitive channel inhibitor; 500 nM), or TGFβ2 (5 ng/ml) + GsMTx4 (500 nM) for 48 h. FITC-phalloidin staining was used to assess the formation of f-actin stress fibers and to quantify the presence of crosslinked actin networks (CLANs). Cell reactivity was determined by immunostaining and immunoblotting for GFAP. Levels of fibronectin and collagen IV deposition were also quantified. Primary optic nerve head astrocytes were positive for the astrocyte marker GFAP and negative for markers for microglia (F4/80) and oligodendrocytes (OSP1). Significantly increased %CLAN-positive cells were observed after 48-h treatment with TGFβ2 vs. control in a dose-dependent manner. Co-treatment with GsMTx4 significantly decreased %CLAN-positive cells vs. TGFβ2 treatment and the presence of f-actin stress fibers. TGFβ2 treatment significantly increased GFAP, fibronectin, and collagen IV levels, and GsMTx4 co-treatment ameliorated GFAP immunoreactivity. Our data suggest inhibition of mechanosensitive channel activity as a potential therapeutic strategy to modulate actin cytoskeletal remodeling within the optic nerve head in 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.

Instant polarized light microscopy for imaging collagen microarchitecture and dynamics

Collagen fibers are a primary load-bearing component of connective tissues and are therefore central to tissue biomechanics and pathophysiology. Understanding collagen architecture and behavior under dynamic loading requires a quantitative imaging technique with simultaneously high spatial and temporal resolutions. Suitable techniques are thus rare and often inaccessible. In this study, we present instant polarized light microscopy (IPOL), in which a single snapshot image encodes information on fiber orientation and retardance, thus fulfilling the requirement. We utilized both simulation and experimental data from collagenous tissues of chicken tendon, sheep eye, and porcine heart to evaluate the effectiveness of IPOL as a quantitative imaging technique. We demonstrate that IPOL allows quantitative characterization of micron-scale collagen fiber architecture at full camera frame rates (156 frames/second herein).

THE INFERENCE OF THE CHANGES OF AXONAL TRANSPORT OF OPTIC NERVE BY DEFORMATIONS OF LAMINA CRIBROSA

Understanding the relationship between the changes in the axonal transport of the optic nerve (ON) and lamina cribrosa (LC) deformation will be helpful to estimate the degree of axonal transport block by measuring the LC deformation in vivo. First, the changes in the axonal transport of the ON were studied using an acute high intraocular pressure (IOP) model, which was established by perfusing saline water into the anterior chamber of cats. The IOP of cat was unilaterally elevated to and maintained at 30, 40, and 50[Formula: see text]mmHg. The axonal transport of the ON was examined by confocal laser scanning microscope. Then the deformations and stress distributions of the LC and ON were calculated using a three-dimensional finite element model of the LC microstructure including ON. The results showed axonal transport changes of ON increased with elevation of the IOPs. While Young’s modulus of the LC and ON were assumed as 0.1[Formula: see text]MPa and 0.03[Formula: see text]MPa, the numerical simulation results showed that LC had displacements of 0.02, 0.03, and 0.04[Formula: see text]mm backward at the IOPs of 30, 40, and 50[Formula: see text]mmHg, respectively. The calculated compressive strain applied to the ON were 0.0425, 0.0567, and 0.0709 under 30, 40, and 50[Formula: see text]mmHg IOP, respectively. The results of strain and stress analysis of LC and ON showed that the deformation of LC would compress the ON. The axonal transport abnormalities could be inferred by measuring the LC deformation in vivo.

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.

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.

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.

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.

Seeing the Hidden Lamina: Effects of Exsanguination on the Optic Nerve Head

Purpose

To introduce an experimental approach for direct comparison of the primate optic nerve head (ONH) before and after death by exsanguination.

Method

The ONHs of four eyes from three monkeys were imaged with spectral-domain optical coherence tomography (OCT) before and after exsanguination under controlled IOP. ONH structures, including the Bruch membrane (BM), BM opening, inner limiting membrane (ILM), and anterior lamina cribrosa (ALC) were delineated on 18 virtual radial sections per OCT scan. Thirteen parameters were analyzed: scleral canal at BM opening (area, planarity, and aspect ratio), ILM depth, BM depth; ALC (depth, shape index, and curvedness), and ALC visibility (globally, superior, inferior, nasal, and temporal quadrants).

Results

All four ALC quadrants had a statistically significant improvement in visibility after exsanguination (overall P < 0.001). ALC visibility increased by 35% globally and by 36%, 37%, 14%, and 4% in the superior, inferior, nasal, and temporal quadrants, respectively. ALC increased 4.1%, 1.9%, and 0.1% in curvedness, shape index, and depth, respectively. Scleral canals increased 7.2%, 25.2%, and 1.1% in area, planarity, and aspect ratio, respectively. ILM and BM depths averaged -7.5% and -55.2% decreases in depth, respectively. Most, but not all, changes were beyond the repeatability range.

Conclusions

Exsanguination allows for improved lamina characterization, especially in regions typically blocked by shadowing in OCT. The results also demonstrate changes in ONH morphology due to the loss of blood pressure. Future research will be needed to determine whether there are differences in ONH biomechanics before and after exsanguination and what those differences would imply.

All roads lead to glaucoma: Induced retinal injury cascades contribute to a common neurodegenerative outcome

Glaucoma describes a distinct optic neuropathy with complex etiology and a variety of associated risk factors, but with similar pathological endpoints. Risk factors such as age, increased intraocular pressure (IOP), low mean arterial pressure, and autoimmune disease, can all be associated with death of retinal ganglion cells (RGCs) and optic nerve head remodeling. Today, IOP management remains the standard of care, even though IOP elevation is not pathognomonic of glaucoma, and patients can continue to lose vision despite effective IOP control. A contemporary view of glaucoma as a complex, neurodegenerative disease has developed, along with the recognition of a need for new disease modifying retinal treatment strategies and improved outcomes. However, the distinction between risk factors triggering the disease process and retinal injury responses is not always clear. In this review, we attempt to distinguish between the various triggers, and their association with subsequent key RGC injury mechanisms. We propose that distinct glaucomatous risk factors result in similar retinal and optic nerve injury cascades, including oxidative and metabolic stress, glial reactivity, and altered inflammatory responses, which induce common molecular signals to induce RGC apoptosis. This organization forms a coherent disease framework and presents conserved targets for therapeutic intervention that are not limited to specific risk factors.

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.

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.