Use of a mathematical model to estimate stress and strain during elevated pressure induced lamina cribrosa deformation

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 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.

Biomechanics of the optic nerve head and sclera in canine glaucoma: A brief review

Glaucoma is a leading cause of irreversible blindness, a progressive optic neuropathy with retinal ganglion cell (RGC) death beginning in the optic nerve head (ONH). A primary risk factor for developing glaucoma is elevated intraocular pressure (IOP). Reducing IOP is the only treatment proven to be effective at delaying disease progression. Nevertheless, even when patients have their IOP reduced, the majority of them continue to lose vision. There are, in both humans and dogs, significant interindividual variabilities in susceptibilities to IOP-induced optic nerve damage. Vision loss progresses much more slowly in Beagles with open-angle glaucoma (OAG) caused by ADAMTS10 mutation. This can be attributed to the mutation-related altered ocular biomechanical properties. The principal site of optic nerve (ON) damage in glaucoma is the ONH. It is suggested that the biomechanical properties of the ONH and the surrounding peripapillary sclera (PPS) contribute to glaucoma development and progression. As far as the beneficial biomechanical properties of the ONH and PPS for a decreased susceptibility and slow progression of glaucoma, data are inconsistent and conflicting. Recent biomechanical studies on beagles with ADAMTS10 mutation demonstrated that the mutant dogs have mechanically weak posterior sclera. This weakness was associated with a reduced collagen density and a lower proportion of insoluble collagen. These changes, observed before glaucoma development, were considered intrinsic characteristics caused by the mutation rather than a secondary effect of IOP elevation. Further studies of ADAMTS10-OAG may elucidate the effects of altered biomechanical properties of ONH and PPS in determining the glaucoma progression.

Analysis of the effects of finite element type within a 3D biomechanical model of a human optic nerve head and posterior pole

BACKGROUND AND OBJECTIVE

Biomechanical stresses and strains can be simulated in the optic nerve head (ONH) using the finite element (FE) method, and various element types have been used. This study aims to investigate the effects of element type on the resulting ONH stresses and strains.

METHODS

A single eye-specific model was constructed using 3D delineations of anatomic surfaces in a high-resolution, fluorescent, 3D reconstruction of a human posterior eye, then meshed using our simple meshing algorithm at various densities using 4- and 10-noded tetrahedral elements, as well as 8- and 20-noded hexahedral elements. A mesh-free approach was used to assign heterogeneous, anisotropic, hyperelastic material properties to the lamina cribrosa, sclera and pia. The models were subjected to elevated IOP of 45 mmHg after pre-stressing from 0 to 10 mmHg, and solved in the open-source FE package Calculix; results were then interpreted in relation to computational time and simulation accuracy, using the quadratic hexahedral model as the reference standard.

RESULTS

The 10-noded tetrahedral and 20R-noded hexahedral elements exhibited similar scleral canal and laminar deformations, as well as laminar and scleral stress and strain distributions; the quadratic tetrahedral models ran significantly faster than the quadratic hexahedral models. The linear tetrahedral and hexahedral elements were stiffer compared to the quadratic element types, yielding much lower stresses and strains in the lamina cribrosa.

CONCLUSIONS

Prior studies have shown that 20-noded hexahedral elements yield the most accurate results in complex models. Results show that 10-noded tetrahedral elements yield very similar results to 20-noded hexahedral elements and so they can be used interchangeably, with significantly lower computational time. Linear element types did not yield acceptable results.

Use of dual-flow bioreactor to develop a simplified model of nervous-cardiovascular systems crosstalk: A preliminary assessment

Chronic conditions requiring long-term rehabilitation therapies, such as hypertension, stroke, or cancer, involve complex interactions between various systems/organs of the body and mutual influences, thus implicating a multiorgan approach. The dual-flow IVTech LiveBox2 bioreactor is a recently developed inter-connected dynamic cell culture model able to mimic organ crosstalk, since cells belonging to different organs can be connected and grown under flow conditions in a more physiological environment. This study aims to setup for the first time a 2-way connected culture of human neuroblastoma cells, SH-SY5Y, and Human Coronary Artery Smooth Muscle Cells, HCASMC through a dual-flow IVTech LiveBox2 bioreactor, in order to represent a simplified model of nervous-cardiovascular systems crosstalk, possibly relevant for the above-mentioned diseases. The system was tested by treating the cells with 10nM angiotensin II (AngII) inducing PKCβII/HuR/VEGF pathway activation, since AngII and PKCβII/HuR/VEGF pathway are relevant in cardiovascular and neuroscience research. Three different conditions were applied: 1- HCASMC and SH-SY5Y separately seeded in petri dishes (static condition); 2- the two cell lines separately seeded under flow (dynamic condition); 3- the two lines, seeded in dynamic conditions, connected, each maintaining its own medium, with a membrane as interface for biohumoral changes between the two mediums, and then treated. We detected that only in condition 3 there was a synergic AngII-dependent VEGF production in SH-SY5Y cells coupled to an AngII-dependent PKCβII/HuR/VEGF pathway activation in HCASMC, consistent with the observed physiological response in vivo. HCASMC response to AngII seems therefore to be generated by/derived from the reciprocal cell crosstalk under the dynamic inter-connection ensured by the dual flow LiveBox 2 bioreactor. This system can represent a useful tool for studying the crosstalk between organs, helpful for instance in rehabilitation research or when investigating chronic diseases; further, it offers the advantageous opportunity of cultivating each cell line in its own medium, thus mimicking, at least in part, distinct tissue milieu.

Investigation of the Optic Nerve Head Morphology Influence to the Optic Nerve Head Biomechanics - Patient Specific Model

Glaucoma is associated with damage and death of optic nerve fibers within the Lamina Cribrosa (LC) region of the Optic Nerve Head. The pathogenesis of the disease is unclear, and the anterior LC surface morphology of different individuals can be one of the possible contributor of glaucoma development and progression. The current study evaluates the relationship between the LC surface curvature and distribution of shear stresses on the LC surface. The patient-specific reconstructed ocular model was developed and analyzed in a finite element analysis software. In addition, the effect of elastic modulus of both sclera and LC on the shear stress was examined. Results showed that there is a correlation between the shear stress distribution and the curvature of the anterior LC surface. This finding highlights the potential significance of the LC morphology on the distribution of LC shear stress and require further investigation.

In Vivo Measurements of Prelamina and Lamina Cribrosa Biomechanical Properties in Humans

Purpose

To develop and use a custom virtual fields method (VFM) to assess the biomechanical properties of human prelamina and lamina cribrosa (LC) in vivo.

Methods

Clinical data of 20 healthy, 20 ocular hypertensive (OHT), 20 primary open-angle glaucoma, and 16 primary angle-closure glaucoma eyes were analyzed. For each eye, the intraocular pressure (IOP) and optical coherence tomography (OCT) images of the optic nerve head (ONH) were acquired at the normal state and after acute IOP elevation. The IOP-induced deformation of the ONH was obtained from the OCT volumes using a three-dimensional tracking algorithm and fed into the VFM to extract the biomechanical properties of the prelamina and the LC in vivo. Statistical measurements and P values from the Mann-Whitney-Wilcoxon tests were reported.

Results

The average shear moduli of the prelamina and the LC were 64.2 ± 36.1 kPa and 73.1 ± 46.9 kPa, respectively. The shear moduli of the prelamina of healthy subjects were significantly lower than those of the OHT subjects. Comparisons between healthy and glaucoma subjects could not be made robustly due to a small sample size.

Conclusions

We have developed a methodology to assess the biomechanical properties of human ONH tissues in vivo and provide preliminary comparisons in healthy and OHT subjects. Our proposed methodology may be of interest for glaucoma management.

Association between peripapillary scleral deformation and choroidal microvascular circulation in glaucoma

Peripapillary vessel density, which is reduced in eyes with glaucoma, has been proposed as a diagnostic tool for the desease and peripapillary choroidal microvasculature dropout(MvD) is considered one of pathophysiological manifestation of glaucomatous damage. However, little is known about the underlying pathogenic mechanism of dropout. According to recent studies, MvD is associated with structural changes in ONH structures. Therefore, we investigated the association between peripapillary scleral deformation and MvD. Data from 62 open-angle glaucoma (OAG) eyes with MvD and 36 eyes without MvD were analyzed in this study. And eyes with MvD were classified into two groups based on location: a juxtapapillary group and a non-juxtapapillary group for further analysis. More eyes with MvD had focal scleral deformation than did those without MvD (64.5% versus 2.8%; P < 0.001). Peripapillary choroidal thickness and focal scleral deformation were significantly associated with MvD. And juxtapapillary group was more associated with focal scleral deformation and coincidental RNFL defects than non-juxtapapillary groups. Peripapillary choroidal MvD was associated with the presence of scleral deformation, especially with juxtapapillary MvD, which was related to corresponding RNFL defects.

Compressive mechanical properties of rat and pig optic nerve head

Glaucoma is the leading cause of irreversible blindness worldwide. Elevated intraocular pressure (IOP), the primary risk factor for glaucoma, is thought to induce abnormally high strains in optic nerve head (ONH) tissues, which ultimately result in retinal ganglion cell damage and vision loss. The mechanisms by which excessive deformations result in vision loss remain incompletely understood. The ability of computational and in vitro models of the ONH to provide insight into these mechanisms, in many cases, depends on our ability to replicate the physiological environment, which in turn requires knowledge of tissue biomechanical properties. The majority of mechanical data published to date regarding the ONH has been obtained from tensile testing, yet compression has been shown to be the main mode of deformation in the ONH under elevated IOP. We have thus tested pig and rat ONH tissue using unconfined cyclic compression. The material constants C₁, obtained from fitting the stress vs. strain data with a neo-Hookean material model, were 428 [367, 488] Pa and 64 [53, 76] Pa (mean [95% Confidence Interval]) for pig and rat optic nerve head, respectively. Additionally, we investigated the effects of strain rate and tissue storage on C1 values. These data will inform future efforts to understand and replicate the in vivo biomechanical environment of the ONH.

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.

In vivo assessment of changes in corneal hysteresis and lamina cribrosa position during acute intraocular pressure elevation in eyes with markedly asymmetrical glaucoma

Purpose

To investigate the biomechanical response of the cornea, lamina cribrosa (LC), and prelaminar tissue (PT) to an acute intraocular pressure (IOP) increase in patients with markedly asymmetrical glaucoma and in healthy controls.

Patients and methods

A total of 24 eyes of 12 patients with markedly asymmetrical primary open-angle glaucoma (POAG) and 12 eyes of 12 healthy patients were examined with spectral-domain optical coherence tomography (SD-OCT) and ocular response analyzer (ORA) at baseline and during acute IOP elevation by means of an ophthalmodynamometer. The displacement of the LC and PT and the change in corneal hysteresis (CH) and corneal resistance factor (CRF) were evaluated.

Results

Following a mean IOP increase of 12.3±2.4 mmHg, eyes with severe glaucoma demonstrated an overall mean anterior displacement of the LC (−6.58±26.09 µm) as opposed to the posterior laminar displacement in eyes with mild glaucoma (29.08±19.28 µm) and in healthy eyes (30.3±10.9; p≤0.001 and p=0.001, respectively). The PT displaced posteriorly during IOP elevation in all eyes. The CH decreased in eyes with severe glaucoma during IOP elevation (from 9.30±3.65 to 6.92±3.04 mmHg; p=0.012), whereas the CRF increased markedly in eyes with mild glaucoma (from 8.61±2.30 to 12.38±3.64; p=0.002) and in eyes with severe glaucoma (from 9.02±1.48 to 15.20±2.06; p=0.002). The increase in CRF correlated with the anterior displacement of the LC in eyes with severe glaucoma.

Conclusion

Eyes with severe glaucoma exhibited a mean overall anterior displacement of the anterior laminar surface, while eyes with mild glaucoma and healthy eyes showed a posterior displacement of the LC during IOP elevation. The CH decreased significantly from baseline only in eyes with severe glaucoma, but the CRF increased significantly in all glaucomatous eyes. The CRF increase correlated with the anterior displacement of the LC in eyes with severe glaucoma.

Study on the deformations of the lamina cribrosa during glaucoma

The lamina cribrosa is the primary site of optic nerve injury during glaucoma, and its deformations induced by elevated intraocular pressure are associated directly with the optic nerve injury and visual field defect. However, the deformations in a living body have been poorly understood yet so far. It is because that integral observation and precise measurement of the deformations in vivo are now almost impossible in the clinical diagnosis and treatment of glaucoma. In the present study, a new mechanical model of the lamina cribrosa is presented by using Reissner's thin plate theory. This model accurately displays the stress and deformation states in the lamina cribrosa under elevated intraocular pressure, in which the shear deformation is not presented by the previous models, however, is demonstrated to play a key role in the optic nerve injury. Further, the deformations of the structures, involving the optic nerve channels and the laminar sheets in the lamina cribrosa, are first investigated in detail. For example, the dislocation of the laminar sheets reaches 18.6μm under the intraocular pressure of 40mmHg, which is large enough to damage the optic nerve axons. The results here confirm some previously proposed clinical speculations on the deformations of the pore shape in the lamina cribrosa under elevated intraocular pressure during glaucoma. Finally, some essentially clinical questions existed during glaucoma, such as the pathological mechanism of the open-angle glaucoma with normal intraocular pressure, are discussed. The present study is beneficial to deeply understanding the optic nerve injury during glaucoma.

STATEMENT OF SIGNIFICANCE

The lamina cribrosa is the primary site of the optic nerve injury induced by elevated intraocular pressure during glaucoma. Under high intraocular pressure, the optic nerve channel near to the periphery of the lamina cribrosa (Channel A) is deformed to become into a tortuous elliptical horn from a straight cylinder, while the optic nerve channel near to the center of the lamina cribrosa (Channel B) is deformed to become into a straight horn from a straight cylinder. These deformations cause both the axoplasm flow obstacle in the axon fibers and the blocked blood flow in the capillaries which pass through the channels, and trigger the visual field defect during glaucoma.

Pro-fibrotic pathway activation in trabecular meshwork and lamina cribrosa is the main driving force of glaucoma

While primary open-angle glaucoma (POAG) is a leading cause of blindness worldwide, it still does not have a clear mechanism that can explain all clinical cases of the disease. Elevated IOP is associated with increased accumulation of extracellular matrix (ECM) proteins in the trabecular meshwork (TM) that prevents normal outflow of aqueous humor (AH) and has damaging effects on the fine mesh-like lamina cribrosa (LC) through which the optic nerve fibers pass. Applying a pathway analysis algorithm, we discovered that an elevated level of TGFβ observed in glaucoma-affected tissues could lead to pro-fibrotic pathway activation in TM and in LC. In turn, activated pro-fibrotic pathways lead to ECM remodeling in TM and LC, making TM less efficient in AH drainage and making LC more susceptible to damage from elevated IOP via ECM transformation in LC. We propose pathway targets for potential therapeutic interventions to delay or avoid fibrosis initiation in TM and LC tissues.

Verification of a virtual fields method to extract the mechanical properties of human optic nerve head tissues in vivo

We aimed to verify a custom virtual fields method (VFM) to estimate the patient-specific biomechanical properties of human optic nerve head (ONH) tissues, given their full-field deformations induced by intraocular pressure (IOP). To verify the accuracy of VFM, we first generated 'artificial' ONH displacements from predetermined (known) ONH tissue biomechanical properties using finite element analysis. Using such deformations, if we are able to match back the known biomechanical properties, it would indicate that our VFM technique is accurate. The peripapillary sclera was assumed anisotropic hyperelastic, while all other ONH tissues were considered isotropic. The simulated ONH displacements were fed into the VFM algorithm to extract back the biomechanical properties. The robustness of VFM was also tested against rigid body motions and noise added to the simulated displacements. Then, the computational speed of VFM was compared to that of a gold-standard stiffness measurement method (inverse finite element method or IFEM). Finally, as proof of principle, VFM was applied to IOP-induced ONH deformation data (obtained from one subject's eye imaged with OCT), and the biomechanical properties of the prelamina and lamina cribrosa (LC) were extracted. From given ONH displacements, VFM successfully matched back the biomechanical properties of ONH tissues with high accuracy and efficiency. For all parameters, the percentage errors were less than 0.05%. Our method was insensitive to rigid body motions and was also able to recover the material parameters in the presence of noise. VFM was also found 125 times faster than the gold-standard IFEM. Finally, the estimated shear modulus for the prelamina and the LC of the studied subject's eye were 33.7 and 63.5 kPa, respectively. VFM may be capable of measuring the biomechanical properties of ONH tissues with high speed and accuracy. It has potential in identifying patient-specific ONH biomechanical properties in the clinic if combined with optical coherence tomography.

Positional and Curvature Difference of Lamina Cribrosa According to the Baseline Intraocular Pressure in Primary Open-Angle Glaucoma: A Swept-Source Optical Coherence Tomography (SS-OCT) Study

Purpose

To investigate the variation of lamina cribrosa (LC) structure based on the baseline intraocular pressure (IOP) in eyes with primary open-angle glaucoma (POAG) and healthy individuals using swept-source optical coherence tomography.

Methods

A total of 108 eyes with POAG and 61 healthy eyes were recruited. Based on the baseline IOP, the POAG eyes were divided into higher-baseline IOP (HTG; baseline IOP > 21 mmHg, n = 38 eyes) and lower-baseline IOP (NTG; baseline IOP ≤ 21 mmHg, n = 70 eyes). The anterior laminar insertion depth (ALID), mean LC depth (mLCD), and the LC curvature index (mLCD–ALID) were measured, and compared among the three groups. The regional variation of LC structure was evaluated by vertical-horizontal ALID difference.

Results

The mLCD and LC curvature index were greatest in HTG eyes (520.3 ± 123.0 and 80.9 ± 30.7 μm), followed by NTG (463.2 ± 110.5 and 64.5 ± 30.7 μm) and healthy eyes (382.9 ± 107.6 and 47.6 ± 25.7 μm, all P < 0.001). However, there were no significant difference in ALID between HTG and NTG eyes. The vertical-horizontal ALID difference was larger in NTG eyes (72.8 ± 56.2 μm) than in HTG (32.7 ± 61.4 μm, P = 0.004) and healthy eyes (25.5 ± 34.8 μm, P < 0.001).

Conclusions

Lamina cribrosa position and curvature differed in POAG eyes with low and high IOP. This would support the theory that IOP induced biomechanical effects on the optic play a role on glaucoma.

The role of lamina cribrosa cells in optic nerve head fibrosis in glaucoma

Glaucoma is a chronic progressive optic neuropathy. There are extracellular matrix (ECM) changes associated with optic disc cupping in the optic nerve head (ONH) and subsequent visual field defects. The primary risk factor for onset and progression of glaucoma is raised intraocular pressure (IOP). Elevated IOP causes deformation at the ONH specifically at the lamina cribrosa (LC) region where there is also deposition of ECM causing the LC to initially undergo thickening and posterior migration with eventual shearing and collapse of the LC plates leading to a thin fibrotic connective tissue structure/scar. Cells that populate the LC region of the ONH are those cells that are positive for GFAP (the astrocytes) and those negative for GFAP (the LC cells). The LC cell plays an integral role in ECM remodelling producing ECM when exposed to high level mechanical stretch, TGF- β1 and a hypoxic environment.

The interaction between intracranial pressure, intraocular pressure and lamina cribrosal compression in glaucoma

This review examines some of the biomechanical consequences associated with the opposing intraocular and intracranial forces. These forces compress the lamina cribrosa and are a potential source of glaucomatous pathology. A difference between them creates a displacement force on the lamina cribrosa. Increasing intraocular pressure and/or decreasing intracranial pressure will increase the trans-lamina cribrosa pressure difference and the risk of its posterior displacement, canal expansion and the formation of pathological cupping. Both intraocular pressure and intracranial pressure can be elevated during a Valsalva manoeuvre with associated increases in both anterior and posterior lamina cribrosa loading as well as its compression. Any resulting thinning of or damage to the lamina cribrosa and/or retinal ganglion cell axons and/or astrocyte and glial cells attached to the matrix of the lamina cribrosa and/or reduction in blood flow to the lamina cribrosa may contribute to glaucomatous neuropathy. Thinning of the lamina cribrosa reduces its stiffness and increases the risk of its posterior displacement. Optic nerve head posterior displacement warrants medical or surgical lowering of intraocular pressure; however, compared to intraocular pressure, the trans-lamina cribrosa pressure difference may be more important in pressure-related pathology of the optic nerve head region. Similarly important could be increased compression loading of the lamina cribrosa. Reducing participation in activities which elevate intraocular and intracranial pressure will decrease lamina cribrosa compression exposure and may contribute to glaucoma management and may have prognostic significance for glaucoma suspects.

Automated segmentation of the lamina cribrosa using Frangi's filter: a novel approach for rapid identification of tissue volume fraction and beam orientation in a trabeculated structure in the eye

The lamina cribrosa (LC) is a tissue in the posterior eye with a complex trabecular microstructure. This tissue is of great research interest, as it is likely the initial site of retinal ganglion cell axonal damage in glaucoma. Unfortunately, the LC is difficult to access experimentally, and thus imaging techniques in tandem with image processing have emerged as powerful tools to study the microstructure and biomechanics of this tissue. Here, we present a staining approach to enhance the contrast of the microstructure in micro-computed tomography (micro-CT) imaging as well as a comparison between tissues imaged with micro-CT and second harmonic generation (SHG) microscopy. We then apply a modified version of Frangi's vesselness filter to automatically segment the connective tissue beams of the LC and determine the orientation of each beam. This approach successfully segmented the beams of a porcine optic nerve head from micro-CT in three dimensions and SHG microscopy in two dimensions. As an application of this filter, we present finite-element modelling of the posterior eye that suggests that connective tissue volume fraction is the major driving factor of LC biomechanics. We conclude that segmentation with Frangi's filter is a powerful tool for future image-driven studies of LC biomechanics.

Comparison of lamina cribrosa thickness in normal tension glaucoma patients with unilateral visual field defect

PURPOSE

To compare the lamina cribrosa thickness, measured by swept-source optical coherence tomography (SS OCT), between each eye of normal tension glaucoma (NTG) patients with unilateral visual field (VF) defect and to investigate the correlation between lamina cribrosa thickness and VF loss.

DESIGN

Prospective, cross-sectional study.

METHODS

Optic nerve heads were scanned using SS OCT, and laminar thickness was measured on mid-superior, central, and mid-inferior regions of vertical midline of the optic disc. The inter-eye differences of lamina cribrosa thickness in NTG patients with unilateral VF defect and the intra-eye difference of lamina cribrosa thickness in VF-affected eyes were analyzed using the paired t test. We evaluated the correlation between lamina cribrosa thickness and mean deviation, measured using standard automated perimetry, in NTG patients.

RESULTS

This study included 102 eyes in 51 NTG patients with unilateral VF defect and 47 eyes in 47 normal subjects without glaucomatous change in either eye. The mean lamina cribrosa thickness of normal fellow eyes was thicker than VF-affected eyes in NTG patients (P < .001), but thinner than normal subject eyes (P < .001). Within VF-affected eyes, lamina cribrosa thickness of regions correlated with visual field defect was thinner than horizontally contralateral locations (P < .001). The mean deviation was statistically correlated with inter-eye difference of lamina cribrosa thickness in NTG patients (n = 51; r(2) = 0.12; P = .01).

CONCLUSIONS

The lamina cribrosa was thinner in VF-unaffected eyes of NTG patients than in normal subject eyes, in VF-affected eyes than in normal fellow eyes of NTG patients, and in regions correlated with visual field loss than in horizontally contralateral ones in VF-affected eyes.

Effect of intraocular pressure on the hemodynamics of the central retinal artery: a mathematical model

Retinal hemodynamics plays a crucial role in the pathophysiology of several ocular diseases. There are clear evidences that the hemodynamics of the central retinal artery (CRA) is strongly affected by the level of intraocular pressure (IOP), which is the pressure inside the eye globe. However, the mechanisms through which this occurs are still elusive. The main goal of this paper is to develop a mathematical model that combines the mechanical action of IOP and the blood flow in the CRA to elucidate the mechanisms through which IOP elevation affects the CRA hemodynamics. Our model suggests that the development of radial compressive regions in the lamina cribrosa (a collagen structure in the optic nerve pierced by the CRA approximately in its center) might be responsible for the clinically-observed blood velocity reduction in the CRA following IOP elevation. The predictions of the mathematical model are in very good agreement with experimental and clinical data. Our model also identifies radius and thickness of the lamina cribrosa as major factors affecting the IOP-CRA relationship, suggesting that anatomical differences among individuals might lead to different hemodynamic responses to IOP elevation.

Biomechanics of the Posterior Eye: A Critical Role in Health and Disease

The posterior eye is a complex biomechanical structure. Delicate neural and vascular tissues of the retina, choroid, and optic nerve head that are critical for visual function are subjected to mechanical loading from intraocular pressure, intraocular and extraorbital muscles, and external forces on the eye. The surrounding sclera serves to counteract excessive deformation from these forces and thus to create a stable biomechanical environment for the ocular tissues. Additionally, the eye is a dynamic structure with connective tissue remodeling occurring as a result of aging and pathologies such as glaucoma and myopia. The material properties of these tissues and the distribution of stresses and strains in the posterior eye is an area of active research, relying on a combination of computational modeling, imaging, and biomechanical measurement approaches. Investigators are recognizing the increasing importance of the role of the collagen microstructure in these material properties and are undertaking microstructural measurements to drive microstructurally-informed models of ocular biomechanics. Here, we review notable findings and the consensus understanding on the biomechanics and microstructure of the posterior eye. Results from computational and numerical modeling studies and mechanical testing of ocular tissue are discussed. We conclude with some speculation as to future trends in this field.

Ocular hemodynamics and glaucoma: the role of mathematical modeling

PURPOSE

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma.

METHODS

We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation.

RESULTS

Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression.

CONCLUSION

Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

The role of cerebrospinal fluid pressure in glaucoma and other ophthalmic diseases: A review

Glaucoma is one of the most common causes of blindness in the world. Well-known risk factors include age, race, a positive family history and elevated intraocular pressures. A newly proposed risk factor is decreased cerebrospinal fluid pressure (CSFP). This concept is based on the notion that a pressure differential exists across the lamina cribrosa, which separates the intraocular space from the subarachnoid fluid space. In this construct, an increased translaminar pressure difference will occur with a relative increase in elevated intraocular pressure or a reduction in CSFP. This net change in pressure is proposed to act on the tissues within the optic nerve head, potentially contributing to glaucomatous optic neuropathy. Similarly, patients with ocular hypertension who have elevated CSFPs, would enjoy a relatively protective effect from glaucomatous damage. This review will focus on the current literature pertaining to the role of CSFP in glaucoma. Additionally, the authors examine the relationship between glaucoma and other known CSFP-related ophthalmic disorders.

Perspectives on biomechanical growth and remodeling mechanisms in glaucoma()

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

A gimbal-mounted pressurization chamber for macroscopic and microscopic assessment of ocular tissues

The biomechanical model of glaucoma considers intraocular pressure-related stress and resultant strain on load bearing connective tissues of the optic nerve and surrounding peripapillary sclera as one major causative influence that effects cellular, vascular, and axonal components of the optic nerve. By this reasoning, the quantification of variations in the microstructural architecture and macromechanical response of scleral shells in glaucomatous compared to healthy populations provides an insight into any variations that exist between patient populations. While scleral shells have been tested mechanically in planar and pressure-inflation scenarios the link between the macroscopic biomechanical response and the underlying microstructure has not been determined to date. A potential roadblock to determining how the microstructure changes based on pressure is the ability to mount the spherical scleral shells in a method that does not induce unwanted stresses to the samples (for instance, in the flattening of the spherical specimens), and then capturing macroscopic and microscopic changes under pressure. Often what is done is a macroscopic test followed by sample fixation and then imaging to determine microstructural organization. We introduce a novel device and method, which allows spherical samples to be pressurized and macroscopic and microstructural behavior quantified on fully hydrated ocular specimens. The samples are pressurized and a series of markers on the surface of the sclera imaged from several different perspectives and reconstructed between pressure points to allow for mapping of nonhomogenous strain. Pictures are taken from different perspectives through the use of mounting the pressurization scheme in a gimbal that allows for positioning the sample in several different spherical coordinate system configurations. This ability to move the sclera in space about the center of the globe, coupled with an upright multiphoton microscope, allows for collecting collagen, and elastin signal in a rapid automated fashion so the entire globe can be imaged.

IOP-induced lamina cribrosa displacement and scleral canal expansion: an analysis of factor interactions using parameterized eye-specific models

PURPOSE

To study the anterior-posterior lamina cribrosa deformation (LCD) and the scleral canal expansion (SCE) produced by an increase in IOP and identify the main factors and interactions that determine these responses in the monkey.

METHODS

Eye-specific baseline models of the LC and sclera of both eyes of three normal monkeys were constructed. Morphing techniques were used to generate 888 models with controlled variations in LC thickness, position and modulus (stiffness), scleral thickness and modulus, and scleral canal size and eccentricity. Finite element modeling was used to simulate an increase in IOP from 10 to 15 mm Hg. A two-level, full-factorial experimental design was used to select factor combinations and to determine the sensitivity of LCD and SCE to the eight factors, independently and in interaction.

RESULTS

LCD was between 53.6 μm (posteriorly) and -12.9 μm (anteriorly), whereas SCE was between 0.5 and 15.2 μm (all expansions). LCD was most sensitive to laminar modulus and position (24% and 21% of the variance in LCD, respectively), whereas SCE was most sensitive to scleral modulus and thickness (46% and 36% of the variance in SCE, respectively). There were also strong interactions between factors (35% and 7% of the variance in LCD and SCE, respectively).

CONCLUSIONS

IOP-related LCD and SCE result from a complex combination of factors, including geometry and material properties of the LC and sclera. This work lays the foundation for interpreting the range of individual sensitivities to IOP and illustrates that predicting individual ONH response to IOP will require the measurement of multiple factors.

Finite element modeling of the human sclera: influence on optic nerve head biomechanics and connections with glaucoma

Scleral thickness, especially near the optic nerve head (ONH), is a potential factor of interest in the development of glaucomatous optic neuropathy. Large differences in the dimensions of the sclera, the principal load-bearing tissue of the eye, have been observed between individuals. This study aimed to characterize the effects of these differences on ONH biomechanics. Eleven enucleated human globes (7 normal and 4 ostensibly glaucomatous) were imaged using high-field microMRI and segmented to produce 3-D individual-specific corneoscleral shells. An identical, idealized ONH geometry was inserted into each shell. Finite element modeling predicted the effects of pressurizing the eyes to an IOP of 30 mmHg, with the results used to characterize the effect of inter-individual differences in scleral dimensions on the biomechanics of the ONH. Measurements of the individual-specific corneoscleral shells were used to construct a 2-D axisymmetric idealized model of the corneoscleral shell and ONH. A sensitivity analysis based on this model quantified the relative importance of different geometrical characteristics of the scleral shell on the biomechanics of the ONH. Significant variations were observed in various measures of strain in the idealized lamina cribrosa (LC) across the seven normal corneoscleral shells, implying large differences in individual biomechanics due to scleral anatomy variations alone. The sensitivity analysis revealed that scleral thickness adjacent to the ONH was responsible for the vast majority of variation. Remarkably, varying peripapilary scleral thickness over the physiologically measured range changed the peak (95th percentile) first principal strain in the LC and radial displacement of the ONH canal by an amount that was equivalent to a change in IOP of 15 mmHg. Inter-individual variations in scleral thickness, particularly peripapillary scleral thickness, can result in vastly different biomechanical responses to IOP. These differences may be significant for understanding the interactions between IOP and scleral biomechanics in the pathogenesis of glaucomatous optic neuropathy. The relationship between scleral thickness and material properties needs to be studied in human eyes.

Glaucomatous cupping of the lamina cribrosa: a review of the evidence for active progressive remodeling as a mechanism

The purpose of this review is to examine the literature in an attempt to elucidate a biomechanical basis for glaucomatous cupping. In particular, this work focuses on the role of biomechanics in driving connective tissue remodeling in the progression of laminar morphology from a normal state to that of an excavated glaucomatous state. While there are multiple contributing factors to the pathogenesis of glaucoma, we focus on laminar extracellular matrix (ECM) remodeling in glaucoma and the feedback mechanisms and signals that may guide progressive laminar cupping. We review the literature on the potential mechanisms of glaucomatous changes in the laminar ECM at the anatomic, structural, cellular and subcellular levels in the context of the biomechanical paradigm of glaucomatous onset and progression. Several conclusions can be drawn from this review. First, extensive remodeling of the lamina cribrosa ECM occurs in primary open angle glaucoma. Second, there is surprisingly little evidence to support acute mechanical damage to the lamina as the principal mechanism of cupping. Third, ONH astrocytes and lamina cribrosa cells can sense their mechanical environment and respond to mechanical stimuli by remodeling the ECM. Fourth, there is evidence suggesting that chronic remodeling of the lamina results in a progressive posterior migration of the laminar insertion into the canal wall, which eventually results in the posterior lamina inserting into the pia mater. Finally, modeling studies suggest that laminar remodeling may be a biomechanical feedback mechanism through which cells modify their environment in an attempt to return to a homeostatic mechanical environment. It is plausible that biomechanics-driven connective tissue remodeling is a mechanism in the progression of laminar morphology from a normal state to that of a cupped, excavated glaucomatous state.

Laminar and prelaminar tissue displacement during intraocular pressure elevation in glaucoma patients and healthy controls

OBJECTIVE

To determine the response of the anterior lamina cribrosa and prelaminar tissue to acute elevation of intraocular pressure (IOP) in glaucoma patients and healthy subjects.

DESIGN

Prospective case-control series.

PARTICIPANTS AND CONTROLS

Patients with open-angle glaucoma (n = 12; mean age ± standard deviation [SD], 66.8 ± 6.0 years), age-matched healthy controls (n = 12; mean age ± SD, 67.1 ± 6.2 years), and young controls (n = 12; mean age ± SD, 36.1 ± 11.7 years).

METHODS

One eye was imaged with spectral-domain optical coherence tomography to obtain 12 high-resolution radial scans centered on the optic disc. Imaging was repeated at precisely the same locations with an ophthalmodynamometer held perpendicular to the globe via the inferior lid to raise the IOP. A line joining Bruch's membrane opening in 4 radial scans was used as reference in the baseline and elevated IOP images. The vertical distance from the reference line to the anterior prelaminar tissue surface and anterior laminar surface was measured at equidistant points along the reference line in the 2 sets of images. The difference between the 2 sets of corresponding measurements were used to determine laminar displacement (LD) and prelaminar tissue displacement (PTD).

MAIN OUTCOME MEASURES

Laminar displacement and PTD.

RESULTS

Intraocular pressure elevation among patients, age-matched controls, and young controls was similar (mean ± SD, 12.4 ± 3.2 mmHg). The mean ± SD LD and PTD were 0.5 ± 3.3 μm and 15.7 ± 15.5 μm, respectively. The LD was not statistically different from 0 (P = 0.366), but PTD was (P < 0.001). The mean ± SD LD was similar among the groups (-0.5 ± 3.7 μm, 0.2 ± 2.0 μm, and 2.0 ± 3.6 μm, respectively; P = 0.366), whereas the mean ± SD PTD was different (6.8 ± 13.7 μm, 20.8 ± 17.5 μm, and 19.6 ± 11.8 μm, respectively; P = 0.045). In all subjects, the PTD was greater than LD. In multivariate regression analyses, LD was negatively associated with optic disc size (P = 0.007), whereas PTD was positively associated with the degree of IOP elevation (P = 0.013).

CONCLUSIONS

In glaucoma patients and controls, the anterior laminar surface is noncompliant to acute IOP elevation. Acute optic disc surface changes represent compression of prelaminar tissue and not laminar displacement.

African Descent and Glaucoma Evaluation Study (ADAGES): II. Ancestry differences in optic disc, retinal nerve fiber layer, and macular structure in healthy subjects

OBJECTIVE

To define differences in optic disc, retinal nerve fiber layer, and macular structure between healthy participants of African (AD) and European descent (ED) using quantitative imaging techniques in the African Descent and Glaucoma Evaluation Study (ADAGES).

METHODS

Reliable images were obtained using stereoscopic photography, confocal scanning laser ophthalmoscopy (Heidelberg retina tomography [HRT]), and optical coherence tomography (OCT) for 648 healthy subjects in ADAGES. Findings were compared and adjusted for age, optic disc area, and reference plane height where appropriate.

RESULTS

The AD participants had significantly greater optic disc area on HRT (2.06 mm(2); P < .001) and OCT (2.47 mm(2); P < .001) and a deeper HRT cup depth than the ED group (P < .001). Retinal nerve fiber layer thickness was greater in the AD group except within the temporal region, where it was significantly thinner. Central macular thickness and volume were less in the AD group.

CONCLUSIONS

Most of the variations in optic nerve morphologic characteristics between the AD and ED groups are due to differences in disc area. However, differences remain in HRT cup depth, OCT macular thickness and volume, and OCT retinal nerve fiber layer thickness independent of these variables. These differences should be considered in the determination of disease status.

Elevated hydrostatic pressure activates sodium/hydrogen exchanger-1 in rat optic nerve head astrocytes

Optic nerve head astrocytes become abnormal in eyes that have elevated intraocular pressure, and cultured astrocytes display altered protein expression after being subjected for > or = 1 days to elevated hydrostatic pressure. Here we show that 2-h elevated hydrostatic pressure (15 or 30 mmHg) causes phosphorylation of ERK1/2, ribosomal S6 protein kinase (p90(RSK)), and Na/H exchanger (NHE)1 in cultured rat optic nerve head astrocytes as judged by Western blot analysis. The MEK/ERK inhibitor U0126 abolished phosphorylation of NHE1 and p90(RSK) as well as ERK1/2. To examine NHE1 activity, cytoplasmic pH (pH(i)) was measured with BCECF and, in some experiments, cells were acidified by 5-min exposure to 20 mM ammonium chloride. Although baseline pH(i) was unaltered, the rate of pH(i) recovery from acidification was fourfold higher in pressure-treated astrocytes. In the presence of either U0126 or dimethylamiloride (DMA), an NHE inhibitor, hydrostatic pressure did not change the rate of pH(i) recovery. The findings are consistent with NHE1 activation due to phosphorylation of ERK1/2, p90(RSK), and NHE1 that occurs in response to hydrostatic pressure. These responses may precede long-term changes of protein expression known to occur in pressure-stressed astrocytes.

Biomechanics of the optic nerve head

Biomechanical factors acting at the level of the lamina cribrosa (LC) are postulated to play a role in retinal ganglion cell dysfunction and loss in glaucoma. In support of this postulate, we now know that a number of cell types (including lamina cribrosa cells) are mechanosensitive. Here we briefly review data indicating cellular stretching, rate of stretching and substrate stiffness may be important mechanosensitivity factors in glaucoma. We then describe how experiments and finite element modeling can be used to quantify the biomechanical environment within the LC, and how this environment depends on IOP. Generic and individual-specific models both suggest that peripapillary scleral properties have a strong influence on LC biomechanics, which can be explained by the observation that scleral deformation drives much of the IOP-dependent straining of the LC. Elegant reconstructions of the LC in monkey eyes have shown that local strains experienced by LC cells depend strongly on laminar beam microarchitecture, which can lead to large local strain elevations. Further modeling, suitably informed by experiments, is needed to better understand lamina cribrosa biomechanics and how they may be involved in glaucomatous optic neuropathy.

Modeling individual-specific human optic nerve head biomechanics. Part I: IOP-induced deformations and influence of geometry

Glaucoma, the second most common cause of blindness worldwide, is an ocular disease characterized by progressive loss of retinal ganglion cell (RGC) axons. Biomechanical factors are thought to play a central role in RGC loss, but the specific mechanism underlying this disease remains unknown. Our goal was to characterize the biomechanical environment in the optic nerve head (ONH)--the region where RGC damage occurs--in human eyes. Post mortem human eyes were imaged, fixed at either 5 or 50 mmHg pressure and processed histologically to acquire serial sections through the ONH. Three-dimensional models of the ONH region were reconstructed from these sections and embedded in a generic scleral shell to create a model of an entire eye. We used finite element simulations to quantify the effects of an acute change in intraocular pressure from 5 to 50 mmHg on the ONH biomechanical environment. Computed strains varied substantially within the ONH, with the pre-laminar neural tissue and the lamina cribrosa showing the greatest strains. The mode of strain having the largest magnitude was third principal strain (compression), reaching 12-15% in both the lamina cribrosa and the pre-laminar neural tissue. Shear strains were also substantial. The distribution of strains in all ONH tissues was remarkably similar between eyes. Inter-individual variations in ONH geometry (anatomy) have only modest effects on ONH biomechanics, and may not explain inter-individual susceptibility to elevated intraocular pressure. Consistent with previous results using generic ONH models, the displacements of the vitreo-retinal interface and the anterior surface of the lamina cribrosa can differ substantially, suggesting that currently available optical imaging methods do not provide information of the acute deformations within ONH tissues. Predicted strains within ONH tissues are potentially biologically significant and support the hypothesis that biomechanical factors contribute to the initial insult that leads to RGC loss in glaucoma.

Modeling individual-specific human optic nerve head biomechanics. Part II: influence of material properties

Biomechanical factors acting within the optic nerve head (ONH) likely play a role in the loss of vision that occurs in glaucoma. In a companion paper (Sigal et al. 2008), we quantified the biomechanical environment within individual-specific ONH models reconstructed from human post mortem eyes. Our goal in this manuscript was to use finite element modeling to investigate the influence of tissue material properties on ONH biomechanics in these same individual-specific models. A sensitivity analysis was carried out by simulating the effects of changing intraocular pressure on ONH biomechanics as tissue mechanical properties were systematically varied over ranges reported in the literature. This procedure was repeated for each individual-specific model described in the companion paper (Sigal et al. 2008). The outcome measures of the analysis were first and third principal strains, as well as the derived quantity of maximum shear strain, in ONH tissues. Scleral stiffness had by far the largest influence in ONH biomechanics, and this result was remarkably consistent across ONH models. The stiffnesses of the lamina cribrosa and pia mater were also influential. These results are consistent with those obtained using generic ONH models. The compressibility of the pre-laminar neural tissue influenced compressive and shearing strains. Overall, tissue material properties had a much greater influence on ONH biomechanics than did tissue geometry, as assessed by comparing results between our individual-specific models. Material properties of ONH tissues, particularly of the peripapillary sclera, play a dominant role in the mechanical response of an ONH to acute changes in IOP and may be important in the pathogenesis of glaucoma. We need to better understand inter-individual differences in scleral biomechanical properties and whether they are clinically important.

Biomechanical Assessment of Radial Optic Neurotomy

PURPOSE

A biomechanical model was constructed to simulate the potential therapeutic effect that the surgical procedure radial optic neurotomy (RON) would have on an eye with a central retinal vein occlusion.

DESIGN

Experimental study.

CONTROLS

Model eyes undergoing RON were compared to control eyes under the same baseline conditions.

INTERVENTION

Radial optic neurotomy. We modeled the optic nerve, lamina cribrosa, and the sclera separately and then reassembled the components. Material properties of the sclera and lamina cribrosa were extracted from the literature and both stiff and more elastic values were used for the optic nerve. Intraocular and arterial pressures were varied across a wide range in the analysis.

MAIN OUTCOME MEASURE

Change in central retinal vein lumen size.

RESULTS

Over a clinically relevant range of boundary conditions, the increase in the lumen area of the central retinal vein lumen after RON remained trivial, ranging from 1% to a maximum of 5%.

CONCLUSIONS

The biomechanical effect of RON is negligible, and is unlikely to be a procedure that could mechanically ameliorate the clinical sequelae of a central vein occlusion.

A cellular solid model of the lamina cribrosa: mechanical dependence on morphology

The biomechanics of the optic nerve head (ONH) may underlie many of the potential mechanisms that initiate the characteristic vision loss associated with primary open angle glaucoma. Therefore, it is important to characterize the physiological levels of stress and strain in the ONH and how they may change in relation to material properties, geometry, and microstructure of the tissue. An idealized, analytical microstructural model of the ONH load bearing tissues was developed based on an octagonal cellular solid that matched the porosity and pore area of morphological data from the lamina cribrosa (LC). A complex variable method for plane stress was applied to relate the geometrically dependent macroscale loads in the sclera to the microstructure of the LC, and the effect of different geometric parameters, including scleral canal eccentricity and laminar and scleral thickness, was examined. The transmission of macroscale load in the LC to the laminar microstructure resulted in stress amplifications between 2.8 and 24.5xIOP. The most important determinants of the LC strain were those properties pertaining to the sclera and included Young's modulus, thickness, and scleral canal eccentricity. Much larger strains were developed perpendicular to the major axis of an elliptical canal than in a circular canal. Average strain levels as high as 5% were obtained for an increase in IOP from 15 to 50 mm Hg.

Mathematical Modeling of the Biomechanics of the Lamina Cribrosa Under Elevated Intraocular Pressures

Comprehensive understanding of the biomechanical performance of the lamina cribrosa (LC) and the optic nerve head is central to understanding the role of elevated intraocular pressures (IOP) in chronic open angle glaucoma. In this paper, six closed-from mathematical models based on different idealizations of the LC are developed and compared. This approach is used to create further understanding of the biomechanical behavior by identifying the LC features and properties that have a significant effect on its performance under elevated IOP. The models developed are based on thin circular plate and membrane theories, and consider influences such as in-plane pretension caused by scleral expansion and large deflections. Comparing the results of the six models against a full ocular globe finite element model suggests the significance of the in-plane pretension and the importance of assuming that the sclera provides the LC with a clamped edge. The model that provided the most accurate representation of the finite element model was also used to predict the behavior of a number of LC experimental tests presented in the literature. In addition to the deflections under elevated IOP, the model predictions include the distributions of stress and strain, which are shown to be compatible with the progression of visual field loss experienced in glaucoma.

En face optical coherence tomography: a new method to analyse structural changes of the optic nerve head in rat glaucoma

AIM

To investigate en face optical coherence tomography (eOCT) and its use as an effective objective technique for assessing changes in the glaucomatous rat optic nerve head (ONH) in vivo, and compare it with confocal scanning laser ophthalmoscopy (cSLO).

METHODS

18 Dark Agouti (DA) rats with surgically induced ocular hypertension were imaged with eOCT and cSLO at regular intervals. Assessment included three dimensional (3D) topographic reconstructions, intensity z-profile plots, a new method of depth analysis to define a "multilayered" structure, and scleral canal measurements, in relation to the degree of intraocular pressure (IOP) exposure.

RESULTS

The increased depth resolution of the eOCT compared to the cSLO was apparent in all methods of analysis, with better discrimination of tissue planes. This was validated histologically. eOCT demonstrated several significant changes in imaged rat ONH which correlated with IOP exposure, including the area of ONH (p<0.01), separation between retinal vessel and scleral layers (p<0.05), and anterior scleral canal opening expansion (p<0.05).

CONCLUSION

eOCT appears to be effective in assessing rat ONH, allowing detailed structural analysis of the multilayered ONH structure. As far as the authors are aware, this is the first report of scleral canal expansion in a rat model. They suggest eOCT as a novel method for the detection of early changes in the ONH in glaucoma.

Ocular biomechanics and biotransport

The eye transduces light, and we usually do not think of it as a biomechanical structure. Yet it is actually a pressurized, thick-walled shell that has an internal and external musculature, a remarkably complex internal vascular system, dedicated fluid production and drainage tissues, and a variety of specialized fluid and solute transport systems. Biomechanics is particularly involved in accommodation (focusing near and far), as well as in common disorders such as glaucoma, macular degeneration, myopia, and presbyopia. In this review, we give a (necessarily brief) overview of many of the interesting biomechanical aspects of the eye, concluding with a list of open problems.

Effect of Cyclical Mechanical Stretch and Exogenous Transforming Growth Factor-??1 on Matrix Metalloproteinase-2 Activity in Lamina Cribrosa Cells from the Human Optic Nerve Head

PURPOSE

Extensive remodeling of the lamina cribrosa extracellular matrix occurs in primary open angle glaucoma. The transforming growth factor-beta (TGF-beta) and matrix metalloproteinase (MMP) protein families are implicated in this process. The authors investigated (a). the effect of cyclical mechanical stretch on TGF-beta1 mRNA synthesis, TGF-beta1 protein secretion, MMP-2 protein activity and (b). the effect of exogenous TGF-beta1 on MMP-2 protein activity in human lamina cribrosa cells in vitro.

METHODS

Primary human lamina cribrosa cells grown on flexible and rigid plates were exposed to cyclical stretch (1Hz, 15%) or static conditions for 12 and 24 hours. Cells grown on 100-mm plates were exposed to human TGF-beta1 (10 ng/ml) or vehicle (4 mM HCl/1% BSA) for 24 hours. TGF-beta1 mRNA synthesis in stretched and static cells was measured using real-time polymerase chain reaction. TGF-beta1 protein secretion in stretched and static cell media was measured using enzyme linked immunosorbent assay. Gelatin zymography measured MMP-2 activity in stretched, static, TGF-beta1- treated and vehicle-treated cell media.

RESULTS

Cyclical stretch induced significant increases in TGF-beta1 mRNA synthesis after 12 hours (**P < 0.01) and TGF-beta1 protein secretion after 24 hours (*P < 0.05). Cyclical stretch significantly (*P < 0.05) increased MMP-2 activity in cell media after 24 hours. Exogenous TGF-beta 1 induced a significant (**P < 0.01) increase in cell media MMP-2 activity after 24 hours.

CONCLUSIONS

These results suggest that cyclical stretch and TGF-beta1 modulate MMP-2 activity in human lamina cribrosa cells. TGF-beta 1 and MMP-2 release from lamina cribrosa cells may facilitate matrix remodeling of the optic nerve head in primary open angle glaucoma.

Responses and signaling pathways in human optic nerve head astrocytes exposed to hydrostatic pressure in vitro

In this study, we examined the effects of mechanical stress induced by elevated hydrostatic pressure (HP) on the migration of human optic nerve head (ONH) astrocytes, using an in vitro model that follows repopulation of a cell-free area (CFA) created on a monolayer of cultured astrocytes. alpha-Tubulin staining detected phenotypic changes in astrocytes exposed to HP. The influence of proliferation in closure of the CFA was determined by incorporation of BrdU under 1.5-cm H2O, control pressure (CP), and 10-cm H2O HP with or without 5-fluorouracil. Under control and experimental conditions, closure of the CFA occurred mostly by migration and less by proliferation. Exposure to 10-cm H2O HP induced faster closure of the CFA at 1, 3, and 5 days. The signaling pathways involved in responses to HP were determined using genistein, tyrphostin A25, AG1478, and AG1295, inhibitors of receptor tyrosine kinases; wortmannin and LY294002, inhibitors of phosphatidyl inositol 3-kinase (PI-3K); and SC58236, an inhibitor of inducible cyclooxygenase-2 (COX2). Genistein and tyrphostin A25 blocked HP-induced migration at 1, 3, and 5 days, but did not affect closure of the CFA under CP. AG1478 and AG1295 blocked HP-induced migration and partially inhibit closure of the CFA under CP. LY294002 blocked HP-induced migration. SC58236 markedly inhibited closure of the CFA under CP by inhibiting COX2 activity. Exposure to HP, a physical stress, induced faster closure of the CFA via activation of members of the epidermal growth factor receptor (EGFR) family and PI-3K pathways. Under CP, closure of the CFA in response to denudation, a form of injury, is due to activation of COX2 in ONH astrocytes.