Experimental surface strain mapping of porcine peripapillary sclera due to elevations of intraocular pressure

Scleral Cross-Linking in Form-Deprivation Myopic Guinea Pig Eyes Leads to Glaucomatous Changes

Purpose

To investigate the potential glaucomatous changes caused by scleral cross-linking (CXL) in a guinea pig form-deprivation (FD) myopia model.

Methods

Eighty 4-week-old tricolor guinea pigs were divided into four groups: FD only, genipin CXL only, FD plus CXL, and control. Refractive error, axial length (AL), intraocular pressure (IOP), and structural and vasculature optic disc changes in optical coherence tomography (OCT) and OCT angiography (OCTA) were measured at baseline and day 21. CXL efficacy was evaluated by scleral rigidity Young's modulus values. Histological and molecular changes in the anterior chamber angle, retina, and sclera were assessed.

Results

Baseline parameters were similar among groups (P > 0.05). The FD plus CXL group at day 21 had the least increase of AL (0.14 ± 0.08 mm) and highest IOP elevation (31.5 ± 3.6 mmHg) compared with the FD-only group (AL: 0.68 ± 0.17 mm; IOP: 22.2 ± 2.6 mmHg) and the control group (AL: 0.24 ± 0.09 mm; IOP: 17.4 ± 1.8 mmHg) (all P < 0.001). OCT and OCTA parameters of the optic disc in the FD plus CXL group at day 21 showed glaucomatous changes and decreased blood flow signals. Sclera rigidity increased in the CXL and FD plus CXL groups. Advanced glycation end products deposited extensively in the retina, choroid, and sclera of FD plus CXL eyes.

Conclusions

CXL causes increased IOP and subsequent optic disc, anterior segment, and scleral changes while inhibiting myopic progression and axial elongation in FD guinea pig eyes. Therefore, applying CXL to control myopia raises safety concerns.

Ultrasonic elastography to assess biomechanical properties of the optic nerve head and peripapillary sclera of the eye

PURPOSE

To quantitatively investigate both optic nerve head (ONH) and peripapillary sclera (PPS) biomechanical properties of porcine eyes through an ultrasonic elastography imaging system in response to both increasing and decreasing intraocular pressure (IOP).

METHODS

The Young's modulus of the ONH and PPS were assessed using our high resolution ultrasonic imaging system which utilized a mechanical shaker to induce shear waves and an off-axis aligned 40 MHz needle transducer to track micron-level displacement along the direction of wave propagation. In this study, imaging on a total of 8 ex vivo porcine eyes preloaded with IOPs from 6 mmHg to 30 mmHg was performed. To have a better understanding of the effect of varying IOP on biomechanics, both increasing and decreasing IOPs were investigated.

RESULTS

The increase of the Young's modulus of ONH (92.4 ± 13.9 kPa at 6 mmHg to 224.7 ± 71.1 kPa at 30 mmHg) and PPS (176.8 ± 14.3 kPa at 6 mmHg to 573.5 ± 64.4 kPa at 30 mmHg) following IOP elevation could be observed in the reconstructed Young's modulus of the shear wave elasticity (SWE) imaging while the B-mode structural images remained almost unchanged. In addition, for the same IOP level, both ONH and PPS have a tendency to be stiffer with decreasing IOP as compared to increasing IOP.

CONCLUSIONS

Our results demonstrate the feasibility of using our ultrasonic elastography system to investigate the stiffness mapping of posterior eye with high resolution in both increasing and decreasing IOPs, making this technique potentially useful for glaucoma.

The role of lamina cribrosa tissue stiffness and fibrosis as fundamental biomechanical drivers of pathological glaucoma cupping

The primary biomechanical driver of pathological glaucomatous cupping remains unknown. Finite element modeling indicates that stress and strain play key roles. In this article, primarily a review, we utilize known biomechanical data and currently unpublished results from our lab to propose a three-stage, tissue stiffness-based model to explain glaucomatous cupping occurring at variable levels of translaminar pressure (TLP). In stage 1, a short-term increase in TLP gradient induces a transient increase in lamina cribrosa (LC) strain. Beyond a critical level of strain, the tissue stiffness rises steeply provoking cellular responses via integrin-mediated mechanotransduction. This early mechanoprotective cellular contraction reduces strain, which reduces tissue stiffness by return of the posteriorly deflected LC to baseline. In stage 2 a prolonged period of TLP increase elicits extracellular matrix (ECM) production leading to fibrosis, increasing baseline tissue stiffness and strain and diminishing the contractile ability/ability to return to the baseline LC position. This is supported by our three-dimensional collagen contraction assays, which show significantly reduced capacity to contract in glaucoma compared with normal LC cells. Second, 15% cyclic strain in LC cells over 24 h elicits a typical increase in ECM profibrotic genes in normal LC cells but a highly blunted response in glaucoma LC cells. Stage 3 is characterized by persistent fibrosis causing further stiffening and inducing a feed-forward ECM production cycle. Repeated cycles of increased strain and stiffness with profibrotic ECM deposition prevent optic nerve head (ONH) recoil from the new deflected position. This incremental maladaptive modeling leads to pathological ONH cupping.

Development of a Nanofabricated Sensor for Monitoring Intraocular Pressure via Ocular Tissue Strain

As the number of individuals developing glaucoma is increasing, researchers and ophthalmologists are exploring new approaches to monitor intraocular pressure, which is a critical measurement for glaucoma detection. Current monitoring methods, such as implantable pressure sensors and wearable contact lenses with sensors, are being explored in eye research clinics. However, these systems currently lack in providing 24 hours data through a practical platform for large-scale use. This paper presents a novel method that provides constant measurements of the scleral strain, which is correlated with the change of intraocular pressure, using a nanofabricated discrete resistor array implant sensor. A preliminary bench-top test was performed using the sensor, and it showed that the nanofabricated 1.6 mm by 2.7 mm resistor array exhibits discrete sensing levels at increments of 41 ohms as a fixture needle traversed approximately half of the array. Though the nanosensor is in the prototype developing stage, it promises a new modality for constant, remote, and around the clock glaucoma monitoring.

Inflation experiments and inverse finite element modelling of posterior human sclera

The complexity of inverse finite element modelling methods used in ocular biomechanics research has significantly increased in recent years in order to produce material parameters that capture microscale tissue behaviour. This study presents a more accessible method for researchers to optimise sclera material parameters for use in finite element studies where macroscale sclera displacements are required. Five human donor sclerae aged between 36 and 72 years were subjected to cycles of internal pressure up to 61 mmHg using a custom-built inflation rig. Displacements were measured using a laser beam and two cameras through a digital image correlation algorithm. Specimen-specific finite element models incorporating regional thickness variation and sclera surface topography were divided into six circumferential regions. An inverse finite element procedure was used to optimise Ogden material parameters for each region. The maximum root mean squared (RMS) error between the numerical and experimental displacements within individual specimens was 17.5 µm. The optimised material parameters indicate a gradual reduction in material stiffness (as measured by the tangent modulus) from the equator to the posterior region at low-stress levels up to 0.005 MPa. The variation in stiffness between adjacent regions became gradually less apparent and statistically insignificant at higher stresses. The study demonstrated how inflation testing combined with inverse modelling could be used to effectively characterise regional material properties capable of reproducing global sclera displacements. The material properties were found to vary between specimens, and it is expected that age could be a contributing factor behind this variation.

Regional Deformation of the Optic Nerve Head and Peripapillary Sclera During IOP Elevation

Purpose

To measure the deformation of the porcine optic nerve head (ONH) and peripapillary sclera (PPS) in response to intraocular pressure (IOP) elevation.

Methods

High-frequency ultrasound was used to image the ONH and PPS of 12 porcine eyes during ex vivo inflation testing from 5 to 30 mm Hg. A speckle tracking algorithm was used to compute tissue displacements in the anterior-posterior direction and expansion of the scleral canal. Through-thickness, in-plane, and shear strains were calculated within the ONH. Regional displacements and strains were analyzed and compared.

Results

The ONH and PPS showed overall posterior displacement in response to IOP elevation. Posterior displacement of the ONH was larger than and strongly correlated with the posterior displacement of the PPS throughout inflation testing. Scleral canal expansion was much smaller and leveled off quicker than ONH posterior displacement as IOP increased. Through-thickness compression was concentrated in the anterior ONH, which also experienced larger in-plane and shear strains than the posterior ONH. Within the anterior ONH, all three strains were significantly higher in the periphery compared with the center, with the shear strain exhibiting the greatest difference between the two regions.

Conclusions

High-resolution ultrasound speckle tracking revealed the full-thickness mechanical response of the posterior eye to IOP elevation. A mismatch in posterior displacement was found between the ONH and PPS, and regional analyses showed a concentration of strains within the periphery of the anterior porcine ONH. These deformation patterns may help in understanding IOP-associated optic nerve damage and glaucoma susceptibility.

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.

Anisotropic Finite Element Modeling Based on a Harmonic Field for Patient-Specific Sclera

Purpose. This study examined the influence of anisotropic material for human sclera. Method. First, the individual geometry of patient-specific sclera was reproduced from a laser scan. Then, high quality finite element modeling of individual sclera was performed using a convenient automatic hexahedral mesh generator based on harmonic field and integrated with anisotropic material assignment function. Finally, comparison experiments were designed to investigate the effects of anisotropy on finite element modeling of sclera biomechanics. Results. The experimental results show that the presented approach can generate high quality anisotropic hexahedral mesh for patient-specific sclera. Conclusion. The anisotropy shows significant differences for stresses and strain distribution and careful consideration should be given to its use in biomechanical FE studies.

Biomechanical assessment in models of glaucomatous optic neuropathy

The biomechanical environment within the eye is of interest in both the regulation of intraocular pressure and the loss of retinal ganglion cell axons in glaucomatous optic neuropathy. Unfortunately, this environment is complex and difficult to determine. Here we provide a brief introduction to basic concepts of mechanics (stress, strain, constitutive relationships) as applied to the eye, and then describe a variety of experimental and computational approaches used to study ocular biomechanics. These include finite element modeling, direct experimental measurements of tissue displacements using optical and other techniques, direct experimental measurement of tissue microstructure, and combinations thereof. Thanks to notable technical and conceptual advances in all of these areas, we are slowly gaining a better understanding of how tissue biomechanical properties in both the anterior and posterior segments may influence the development of, and risk for, glaucomatous optic neuropathy. Although many challenging research questions remain unanswered, the potential of this body of work is exciting; projects underway include the coupling of clinical imaging with biomechanical modeling to create new diagnostic tools, development of IOP control strategies based on improved understanding the mechanobiology of the outflow tract, and attempts to develop novel biomechanically-based therapeutic strategies for preservation of vision in glaucoma.

Mapping 3D Strains with Ultrasound Speckle Tracking: Method Validation and Initial Results in Porcine Scleral Inflation

This study aimed to develop and validate a high frequency ultrasound method for measuring distributive, 3D strains in the sclera during elevations of intraocular pressure. A 3D cross-correlation based speckle-tracking algorithm was implemented to compute the 3D displacement vector and strain tensor at each tracking point. Simulated ultrasound radiofrequency data from a sclera-like structure at undeformed and deformed states with known strains were used to evaluate the accuracy and signal-to-noise ratio (SNR) of strain estimation. An experimental high frequency ultrasound (55 MHz) system was built to acquire 3D scans of porcine eyes inflated from 15 to 17 and then 19 mmHg. Simulations confirmed good strain estimation accuracy and SNR (e.g., the axial strains had less than 4.5% error with SNRs greater than 16.5 for strains from 0.005 to 0.05). Experimental data in porcine eyes showed increasing tensile, compressive, and shear strains in the posterior sclera during inflation, with a volume ratio close to one suggesting near-incompressibility. This study established the feasibility of using high frequency ultrasound speckle tracking for measuring 3D tissue strains and its potential to characterize physiological deformations in the posterior eye.

Experimental scleral cross-linking increases glaucoma damage in a mouse model

The purpose of this study was to assess the effect of a scleral cross-linking agent on susceptibility to glaucoma damage in a mouse model.CD1 mice underwent 3 subconjunctival injections of 0.5 M glyceraldehyde (GA) in 1 week, then had elevated intraocular pressure (IOP) induced by bead injection. Degree of cross-linking was measured by enzyme-linked immunosorbent assay (ELISA), scleral permeability was measured by fluorescence recovery after photobleaching (FRAP), and the mechanical effects of GA exposure were measured by inflation testing. Control mice had buffer injection or no injection in 2 separate glaucoma experiments. IOP was monitored by Tonolab and retinal ganglion cell (RGC) loss was measured by histological axon counting. To rule out undesirable effects of GA, we performed electroretinography and detailed histology of the retina. GA exposure had no detectable effects on RGC number, retinal structure or function either histologically or electrophysiologically. GA increased cross-linking of sclera by 37% in an ELISA assay, decreased scleral permeability (FRAP, p = 0.001), and produced a steeper pressure-strain behavior by in vitro inflation testing. In two experimental glaucoma experiments, GA-treated eyes had greater RGC axon loss from elevated IOP than either buffer-injected or control eyes, controlling for level of IOP exposure over time (p = 0.01, and 0.049, multivariable regression analyses). This is the first report that experimental alteration of the sclera, by cross-linking, increases susceptibility to RGC damage in mice.

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.

Finite element modeling of the viscoelastic responses of the eye during microvolumetric changes

A linear viscoelastic finite element model was built to investigate factors that influenced the intraocular pressure (IOP) elevations due to micro-volumetric changes in the eye at three different rates. The viscoelastic properties of the cornea and the sclera, including the instantaneous modulus, equilibrium modulus, and relaxation time constants, parametrically varied to examine their effects on IOP elevations at different rates of volumetric changes. The simulated responses were in good agreement with the previously reported experimental results obtained from porcine globes, showing the general trend of higher IOP elevations at faster rates. The simulations showed that all viscoelastic properties influenced the profile of the dynamic IOP due to volumetric changes, and the relative significance of a specific parameter was highly dependent on the rate of change.

Ultrasonic measurement of scleral cross-sectional strains during elevations of intraocular pressure: method validation and initial results in posterior porcine sclera

BACKGROUND

Scleral biomechanical properties may be important in the pathogenesis and progression of glaucoma. The goal of this study is to develop and validate an ultrasound method for measuring cross-sectional distributive strains in the sclera during elevations of intraocular pressure (IOP).

METHOD OF APPROACH

Porcine globes (n = 5) were tested within 24 hs postmortem. The posterior scleral shells were dissected and mounted onto a custom-built pressurization chamber. A high-frequency (55-MHz) ultrasound system (Vevo660, VisualSonics Inc., Toronto) was employed to acquire the radio frequency data during scans of the posterior pole along both circumferential and meridian directions. The IOP was gradually increased from 5 to 45 mmHg. The displacement fields were obtained from correlation-based ultrasound speckle tracking. A least-square strain estimator was used to calculate the strains in both axial and lateral directions. Experimental validation was performed by comparing tissue displacements calculated from ultrasound speckle tracking with those induced by an actuator. Theoretical analysis and simulation experiments were performed to optimize the ultrasound speckle tracking method and evaluate the accuracy and signal-to-noise ratio (SNR) in strain estimation.

RESULTS

Porcine sclera exhibited significantly larger axial strains (e.g., -5.1 ± 1.5% at 45 mmHg, meridian direction) than lateral strains (e.g., 2.2 ± 0.7% at 45 mmHg, meridian direction) during IOP elevations (P's < 0.01). The strain magnitudes increased nonlinearly with pressure increase. The strain maps displayed heterogeneity through the thickness. The lateral strains were significantly smaller in the circumferential direction than the meridian direction at 45 mmHg (P < 0.05). Experimental validation showed that the ultrasound speckle tracking method was capable of tracking displacements at the accuracy of sub-micron to micron. Theoretical analysis predicted the dependence of the strain estimation SNR on the strain level, as well as signal processing parameters such as kernel size. Simulation results showed that ultrasound speckle tracking had a high accuracy for estimating strains of 1-5% and a high SNR for strains of 0.5-5%.

CONCLUSIONS

A new experimental method based on ultrasound speckle tracking has been developed for obtaining cross-sectional strain maps of the posterior sclera. This method provides a useful tool to examine distributive strains through the thickness of the sclera during elevations of IOP.

Whole globe inflation testing of exogenously crosslinked sclera using genipin and methylglyoxal

Exogenous collagen cross-linking has been investigated as method of reinforcing scleral biomechanics, with the goal of counteracting scleral weakening that occurs at the onset of myopia. This study uses whole globe inflation testing to investigate the biomechanical effect of treating posterior sclera with the collagen cross-linking agents methylglyoxal and genipin. Pairs of porcine eyes were treated in four ways. Three groups involved 1% methylglyoxal: two-hour (Group I) or thirty-minute (Group II) incubation of the whole globe, and thirty-minute incubation of only the posterior sclera of the intact eye (Group III). Group IV consisted of a thirty-minute incubation of the posterior sclera in 1% genipin. Following treatment, each eye was subjected to inflation testing under physiological pressure levels (0-150 mmHg); four strain markers on the posterior pole were tracked, providing displacement measurements in two directions. Results were used to derive load versus deformation behavior and to calculate stiffness at 0.25% strain (toe stiffness) and at peak strain (peak stiffness). Toe stiffness of Group I was 4.8 and 1.3 times greater than controls (sagittal and transverse directions, respectively: 5.23 ± 0.39 vs. 0.90 ± 0.08 mHg, P < 0.001; and 3.41 ± 0.19 vs. 1.51 ± 0.22 mHg, P < 0.01; values in mean ± SE). Group II was 7.4 and 4.3 times stiffer than controls (sagittal and transverse directions, respectively: 5.26 ± 0.49 vs. 0.63 ± 0.10 mHg, P < 0.02; and 3.44 ± 0.44 vs. 0.65 ± 0.07 mHg, P < 0.003). Group III was 3.6 and 3.4 times stiffer than controls (sagittal and transverse directions, respectively: 5.21 ± 0.39 vs. 1.13 ± 0.31 mHg, P < 0.01; and 4.94 ± 1.48 vs. 1.13 ± 0.25, P < 0.01), while Group IV was 8.2 and 2.8 times stiffer than controls (sagittal and transverse: 12.36 ± 1.96 vs. 1.35 ± 0.14 mHg, P < 0.01; and 12.45 ± 1.34 vs. 3.27 ± 0.50 mHg, P < 0.05). In all groups, there was no significant difference in peak stiffness after scleral cross-linking (SXL). At low strain, the posterior sclera was stiffer in both measured directions following methylglyoxal and genipin treatments, however at peak strain the treated sclera was not stiffer. Additionally, the saturation level of scleral stiffening by methylglyoxal can be reached within thirty minutes of treatment.

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.

Scleral mechanics: comparing whole globe inflation and uniaxial testing

The purpose of this study was to assess fundamental differences between the mechanics of the posterior sclera in paired eyes using uniaxial and whole globe inflation testing, with an emphasis on the relationship between testing conditions and observed tissue behavior. Twenty porcine eyes, consisting of matched pairs from 10 pigs, were used in this study. Within pairs, one eye was tested with 10 cycles of globe pressurization to 150 mmHg (∼10× normal IOP) while biaxial strains were tracked via an optical system at the posterior sclera. An excised posterior strip from the second eye was subjected to traditional uniaxial testing in which mechanical hysteresis was recorded from 10 cycles to a peak stress of 0.13 MPa (roughly equivalent to the circumferential wall stress produced by an IOP of 150 mmHg under the thin-walled pressure vessel assumption). For approximately equivalent loads, peak strains were more than twice as high in uniaxial tests than in inflation tests. Different trends in the load-deformation plots were seen between the tests, including an extended "toe" region in the uniaxial test, a generally steeper curve in the inflation tests, and reduced variability in the inflation tests. The unique opportunity of being able to mechanically load a whole globe under near physiologic conditions alongside a standard uniaxially tested specimen reveals the effects of testing artifacts relevant to most uniaxially tested soft tissues. Whole globe inflation offers testing conditions that significantly alter load-deformation behavior relative to uniaxial testing; consequently, laboratory studies of interventions or conditions that alter scleral mechanics may greatly benefit from these findings.

Biomechanical changes in the sclera of monkey eyes exposed to chronic IOP elevations

PURPOSE

To characterize scleral biomechanics in both eyes of eight monkeys in which chronic intraocular pressure (IOP) elevation was induced in one eye.

METHODS

Each posterior sclera was mounted on a pressurization apparatus, IOP was elevated from 5 to 45 mm Hg while the 3D displacements of the scleral surface were measured by speckle interferometry. Finite element (FE) models of each scleral shell were constructed that incorporated stretch-induced stiffening and multidirectionality of the collagen fibers. FE model predictions were then iteratively matched to experimental displacements to extract unique sets of scleral biomechanical properties.

RESULTS

For all eyes, the posterior sclera exhibited inhomogeneous, anisotropic, nonlinear biomechanical behavior. Biomechanical changes caused by chronic IOP elevation were complex and specific to each subject. Specifically: (1) Glaucomatous eyes in which the contralateral normal eyes displayed large modulus or thickness were less prone to biomechanical changes; (2) glaucomatous scleral modulus associated with an IOP of 10 mm Hg decreased (when compared with that of the contralateral normal) after minimal chronic IOP elevation; (3) glaucomatous scleral modulus associated with IOPs of 30 and 45 mm Hg increased (when compared with that of the contralateral normal) after moderate IOP elevation; and (4) FE-based estimates of collagen fiber orientation demonstrated no change in the glaucomatous eyes.

CONCLUSIONS

Significant stiffening of the sclera follows exposure to moderate IOP elevations in most eyes. Scleral hypercompliance may precede stiffening or be a unique response to minimal chronic IOP elevation in some eyes. These biomechanical changes are likely to be the result of scleral extracellular matrix remodeling.

Cortical surface strain estimation using stereovision

We present a completely noninvasive technique to estimate soft tissue surface strain by differentiating three-dimensional displacements obtained from optical flow motion tracking using stereo images. The implementation of the strain estimation algorithm was verified with simulated data and its application was illustrated in three open cranial neurosurgical cases, where cortical surface strain induced by arterial blood pressure pulsation was evaluated. Local least squares smoothing was applied to the displacement field prior to strain estimation to reduce the effect of noise during differentiation. Maximum principal strains (epsilon1) of up to 7% were found in the exposed cortical area on average, and the largest strains (up to -18%) occurred near the craniotomy rim with the majority of epsilon1 perpendicular to the boundary, indicating relative stretching along this direction. The technique offers a new approach for soft tissue strain estimation for the purpose of biomechanical characterization.

The in vitro inflation response of mouse sclera

The purpose of this research was to develop a reliable and repeatable inflation protocol to measure the scleral inflation response of mouse eyes to elevations in intraocular pressure (IOP), comparing the inflation response exhibited by the sclera of younger and older C57BL/6 mice. Whole, enucleated eyes from younger (2 month) and older (11 month) C57BL/6 mice were mounted by the cornea on a custom fixture and inflated according to a load-unload, ramp-hold pressurization regimen via a cannula connected to a saline-filled programmable syringe pump. First, the tissue was submitted to three load-unload cycles from 6 mmHg to 15 mmHg at a rate of 0.25 mmHg/s with ten minutes of recovery between cycles. Next the tissue was submitted to a series of ramp-hold tests to measure the creep behavior at different pressure levels. For each ramp-hold test, the tissue was loaded from 6 mmHg to the set pressure at a rate of 0.25 mmHg/s and held for 30 min, and then the specimens were unloaded to 6 mmHg for 10 min. This sequence was repeated for set pressures of: 10.5, 15, 22.5, 30, 37.5, and 45 mmHg. Scleral displacement was measured using digital image correlation (DIC), and fresh scleral thickness was measured optically for each specimen after testing. For comparison, scleral thickness was measured on untested fresh tissue and epoxy-fixed tissue from age-matched animals. Comparing the apex displacement of the different aged specimens, the sclera of older animals had a statistically significant stiffer response to pressurization than the sclera of younger animals. The stiffness of the pressure-displacement response of the apex measured in the small-strain (6-15 mmHg) and the large-strain (37.5-45 mmHg) regime, respectively, were 287 ± 100 mmHg/mm and 2381 ± 191 mmHg/mm for the older tissue and 193 ± 40 mmHg/mm and 1454 ± 93 mmHg/mm for the younger tissue (Student t-test, p<0.05). The scleral thickness varied regionally, being thickest in the peripapillary region and thinnest at the equator. Fresh scleral thickness did not differ significantly by age in this group of animals. This study presents a reliable inflation test protocol to measure the mechanical properties of mouse sclera. The inflation methodology was sensitive enough to measure scleral response to changes in IOP elevations between younger and older C57BL/6 mice. Further, the specimen-specific scleral displacement profile and thickness measurements will enable future development of specimen-specific finite element models to analyze the inflation data for material properties.

Effects of scleral stiffness properties on optic nerve head biomechanics

The biomechanical environment within the optic nerve head, important in glaucoma, depends strongly on scleral biomechanical properties. Here we use a range of measured nonlinear scleral stress-strain relationships in a finite element (FE) model of the eye to compute the biomechanical environment in the optic nerve head at three levels of intraocular pressure (IOP). Three stress-strain relationships consistent with the 5th, 50th and 95th percentiles of measured human scleral stiffness were selected from a pool of 30 scleral samples taken from 10 eyes and implemented in a generic FE model of the eye using a hyperelastic five-parameter Mooney-Rivlin material model. Computed strains within optic nerve head tissues depended strongly on scleral properties, with most of this difference occurring between the compliant and median scenarios. Also, the magnitudes of strains were found to be substantial even at normal IOP (up to 5.25% in the lamina cribrosa at 15 mmHg), being larger than previously reported values even at normal levels of IOP. We conclude that scleras that are "weak", but still within the physiologic range, will result in appreciably increased optic nerve head strains and could represent a risk factor for glaucomatous optic neuropathy. Estimations of the deformation at the optic nerve head region, particularly at elevated IOP, should take into account the nonlinear nature of scleral stiffness.

Scleral biomechanics in the aging monkey eye

PURPOSE

To investigate the age-related differences in the inhomogeneous, anisotropic, nonlinear biomechanical properties of posterior sclera from old (22.9 +/- 5.3 years) and young (1.5 +/- 0.7 years) rhesus monkeys.

METHODS

The posterior scleral shell of each eye was mounted on a custom-built pressurization apparatus, then intraocular pressure (IOP) was elevated from 5 to 45 mm Hg while the 3D displacements of the scleral surface were measured with speckle interferometry. Each scleral shell's geometry was digitally reconstructed from data generated by a 3-D digitizer (topography) and 20-MHz ultrasound (thickness). An inverse finite element (FE) method incorporating a fiber-reinforced constitutive model was used to extract a unique set of biomechanical properties for each eye. Displacements, thickness, stress, strain, tangent modulus, structural stiffness, and preferred collagen fiber orientation were mapped for each posterior sclera.

RESULTS

The model yielded 3-D deformations of posterior sclera that matched well with those observed experimentally. The posterior sclera exhibited inhomogeneous, anisotropic, nonlinear mechanical behavior. The sclera was significantly thinner (P = 0.038) and tangent modulus and structural stiffness were significantly higher in old monkeys (P < 0.0001). On average, scleral collagen fibers were circumferentially oriented around the optic nerve head (ONH). No difference was found in the preferred collagen fiber orientation and fiber concentration factor between age groups.

CONCLUSIONS

Posterior sclera of old monkeys is significantly stiffer than that of young monkeys and is therefore subject to higher stresses but lower strains at all levels of IOP. Age-related stiffening of the sclera may significantly influence ONH biomechanics and potentially contribute to age-related susceptibility to glaucomatous vision loss.

Correlation between local stress and strain and lamina cribrosa connective tissue volume fraction in normal monkey eyes

PURPOSE

To investigate the biomechanical response to IOP elevation of normal monkey eyes using eye-specific, three-dimensional (3-D) finite element (FE) models of the ONH that incorporate lamina cribrosa (LC) microarchitectural information.

METHODS

A serial sectioning and episcopic imaging technique was used to reconstruct the ONH and peripapillary sclera of four pairs of eyes fixed at 10 mm Hg. FE models were generated with local LC material properties representing the connective tissue volume fraction (CTVF) and predominant LC beam orientation and used to simulate an increase in IOP from 10 to 45 mm Hg. An LC material stiffness constant was varied to assess its influence on biomechanical response.

RESULTS

Strains and stresses within contralateral eyes were remarkably similar in both magnitude and distribution. Strain correlated inversely, and nonlinearly, with CTVF (median, r (2) = 0.73), with tensile strains largest in the temporal region. Stress correlated linearly with CTVF (median r(2) = 0.63), with the central and superior regions bearing the highest stresses. Net average LC displacement was either posterior or anterior, depending on whether the laminar material properties were compliant or stiff.

CONCLUSIONS

The results show that contralateral eyes exhibit similar mechanical behavior and suggest that local mechanical stress and strain within the LC are correlate highly with local laminar CTVF. These simulations emphasize the importance of developing both high-resolution imaging of the LC microarchitecture and next-generation, deep-scanning OCT techniques to clarify the relationships between IOP-related LC displacement and CTVF-related stress and strain in the LC. Such imaging may predict sites of IOP-related damage in glaucoma.

Peripapillary and posterior scleral mechanics--part I: development of an anisotropic hyperelastic constitutive model

The sclera is the white outer shell and principal load-bearing tissue of the eye as it sustains the intraocular pressure. We have hypothesized that the mechanical properties of the posterior sclera play a significant role in and are altered by the development of glaucoma-an ocular disease manifested by structural damage to the optic nerve head. An anisotropic hyperelastic constitutive model is presented to simulate the mechanical behavior of the posterior sclera under acute elevations of intraocular pressure. The constitutive model is derived from fiber-reinforced composite theory, and incorporates stretch-induced stiffening of the reinforcing collagen fibers. Collagen fiber alignment was assumed to be multidirectional at local material points, confined within the plane tangent to the scleral surface, and described by the semicircular von Mises distribution. The introduction of a model parameter, namely, the fiber concentration factor, was used to control collagen fiber alignment along a preferred fiber orientation. To investigate the effects of scleral collagen fiber alignment on the overall behaviors of the posterior sclera and optic nerve head, finite element simulations of an idealized eye were performed. The four output quantities analyzed were the scleral canal expansion, the scleral canal twist, the posterior scleral canal deformation, and the posterior laminar deformation. A circumferential fiber organization in the sclera restrained scleral canal expansion but created posterior laminar deformation, whereas the opposite was observed with a meridional fiber organization. Additionally, the fiber concentration factor acted as an amplifying parameter on the considered outputs. The present model simulation suggests that the posterior sclera has a large impact on the overall behavior of the optic nerve head. It is therefore primordial to provide accurate mechanical properties for this tissue. In a companion paper (Girard, Downs, Bottlang, Burgoyne, and Suh, 2009, "Peripapillary and Posterior Scleral Mechanics--Part II: Experimental and Inverse Finite Element Characterization," ASME J. Biomech. Eng., 131, p. 051012), we present a method to measure the 3D deformations of monkey posterior sclera and extract mechanical properties based on the proposed constitutive model with an inverse finite element method.

Peripapillary and posterior scleral mechanics--part II: experimental and inverse finite element characterization

The posterior sclera likely plays an important role in the development of glaucoma, and accurate characterization of its mechanical properties is needed to understand its impact on the more delicate optic nerve head--the primary site of damage in the disease. The posterior scleral shells from both eyes of one rhesus monkey were individually mounted on a custom-built pressurization apparatus. Intraocular pressure was incrementally increased from 5 mm Hg to 45 mm Hg, and the 3D displacements were measured using electronic speckle pattern interferometry. Finite element meshes of each posterior scleral shell were reconstructed from data generated by a 3D digitizer arm (shape) and a 20 MHz ultrasound transducer (thickness). An anisotropic hyperelastic constitutive model described in a companion paper (Girard, Downs, Burgoyne, and Suh, 2009, "Peripapillary and Posterior Scleral Mechanics--Part I: Development of an Anisotropic Hyperelastic Constitutive Model," ASME J. Biomech. Eng., 131, p. 051011), which includes stretch-induced stiffening and multidirectional alignment of the collagen fibers, was applied to each reconstructed mesh. Surface node displacements of each model were fitted to the experimental displacements using an inverse finite element method, which estimated a unique set of 13 model parameters. The predictions of the proposed constitutive model matched the 3D experimental displacements well. In both eyes, the tangent modulus increased dramatically with IOP, which indicates that the sclera is mechanically nonlinear. The sclera adjacent to the optic nerve head, known as the peripapillary sclera, was thickest and exhibited the lowest tangent modulus, which might have contributed to the uniform distribution of the structural stiffness for each entire scleral shell. Posterior scleral deformation following acute IOP elevations appears to be nonlinear and governed by the underlying scleral collagen microstructure as predicted by finite element modeling. The method is currently being used to characterize posterior scleral mechanics in normal (young and old), early, and moderately glaucomatous monkey eyes.

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.