Richard T. Hart

The optic nerve head as a biomechanical structure: a new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage.

We propose here a conceptual framework for understanding the optic nerve head (ONH) as a biomechanical structure. Basic principles of biomechanical engineering are used to propose a central role for intraocular pressure (IOP)-related stress and strain in the physiology of ONH aging and the pathophysiology of glaucomatous damage. Our paradigm suggests that IOP-related stress and strain (1) are substantial within the load-bearing connective tissues of the ONH even at low levels of IOP and (2) underlie both ONH aging and the two central pathophysiologies of glaucomatous damage--mechanical failure of the connective tissues of the lamina cribrosa, scleral canal wall, and peripapillary sclera, and axonal compromise within the lamina cribrosa by a variety of mechanisms. Modeling the ONH as a biomechanical structure generates a group of testable hypotheses regarding the central mechanisms of glaucomatous damage and provides a logic for classifying the principal components of the susceptibility of an individual ONH to a given level of IOP.

Functional adaptation in long bones: Establishing in vivo values for surface remodeling rate coefficients

In this paper we describe a computational means, based on beam theory, for application of the theory of adaptive elasticity to examples of real bone geometries. The results of the animal experiments were taken from the literature, and each documented the temporal evolution of a change in bone shape after a significant change in the mechanical loading environment of the bone. For each of these studies, we establish preliminary estimates of the in vivo values of the surface remodeling rate coefficients--the key parameters in the theory of surface remodeling. Our preliminary parameter estimates are established by comparison of published animal experimental results with surface remodeling theory predictions generated by the computational method.

Viscoelastic Characterization of Peripapillary Sclera: Material Properties by Quadrant in Rabbit and Monkey Eyes

In this report we characterize the viscoelastic material properties of peripapillary sclera from the four quadrants surrounding the optic nerve head in both rabbit and monkey eyes. Scleral tensile specimens harvested from each quadrant were subjected to uniaxial stress relaxation and tensile ramp to failure tests. Linear viscoelastic theory, coupled with a spectral reduced relaxation function, was employed to characterize the viscoelastic properties of the tissues. We detected no differences in the stress-strain curves of specimens from the four quadrants surrounding the optic nerve head (ONH) below a strain of 4 percent in either the rabbit or monkey. While the peripapillary sclera from monkey eyes is significantly stiffer (both instantaneously and in equilibrium) and relaxes more slowly than that from rabbits, we detected no differences in the viscoelastic material properties (tested at strains of 0-1 percent) of sclera from the four quadrants surrounding the ONH within either species group.

Fibers in the Extracellular Matrix Enable Long-Range Stress Transmission between Cells

Cells can sense, signal, and organize via mechanical forces. The ability of cells to mechanically sense and respond to the presence of other cells over relatively long distances (e.g., ∼100 μm, or ∼10 cell-diameters) across extracellular matrix (ECM) has been attributed to the strain-hardening behavior of the ECM. In this study, we explore an alternative hypothesis: the fibrous nature of the ECM makes long-range stress transmission possible and provides an important mechanism for long-range cell-cell mechanical signaling. To test this hypothesis, confocal reflectance microscopy was used to develop image-based finite-element models of stress transmission within fibroblast-seeded collagen gels. Models that account for the gels fibrous nature were compared with homogenous linear-elastic and strain-hardening models to investigate the mechanisms of stress propagation. Experimentally, cells were observed to compact the collagen gel and align collagen fibers between neighboring cells within 24 h. Finite-element analysis revealed that stresses generated by a centripetally contracting cell boundary are concentrated in the relatively stiff ECM fibers and are propagated farther in a fibrous matrix as compared to homogeneous linear elastic or strain-hardening materials. These results support the hypothesis that ECM fibers, especially aligned ones, play an important role in long-range stress transmission.

Effects of Storage Time on the Mechanical Properties of Rabbit Peripapillary Sclera After Enucleation

In the field of biomechanics, little research has been performed to evaluate the effect of storage time on the material properties of ocular tissues. Twenty-four rabbit eyes were divided into six groups with storage times from 3 to 72 hr. A tensile specimen was prepared from the inferior quadrant of each sclera and was subjected to a stress relaxation test. The data were analyzed using linear viscoelastic theory yielding four material parameters (E0, instantaneous elastic modulus; E∞, equilibrium elastic modulus; β, half-width of the Gaussian distribution; τm; mean relaxation time). No statistically significant differences were found in the material properties of each group, which suggests that sclera can be stored up to 3 days without risking mechanical deterioration.

Local bone formation due to combined mechanical loading and intermittent hPTH-(1-34) treatment and its correlation to mechanical signal distributions

We evaluated the local response of cortical bone in the rat tibia due to combined treatment with synthetic parathyroid hormone, hPTH-(1-34), and mechanical stimulation by four-point bending. Forty-eight female retired breeder Sprague-Dawley rats were divided into six groups. Mechanically stimulated animals included the following groups: (1) Bend+PTH, (2) Sham+PTH, (3) Bend+Vehicle, (4) Sham+Vehicle. Non-mechanically stimulated animals included a (5) Control group that received neither loading nor injections, and a (6) PTH group that received only hPTH-(1-34) injections. The right limbs of mechanically loaded animals were exposed to a peak force of 50 N for 36 cycles at 2 Hz, three days per week for four weeks, and PTH-treated animals received injections equivalent to 50 microg/kg BW. Fluorochrome labeling was used to measure local formation at 12 sectors about the endocortical periphery. The distributions of endocortical bone formation were compared to the local formation differences between treatment groups and to a variety of potential mechanical stimuli signals. Results indicated that hPTH-(1-34) exerted a potent anabolic effect with near-uniform formation about the endocortical surface, and that localized formation peaks due to bending were further augmented in the presence of hPTH-(1-34) treatment. Correlation of formation patterns to mechanical signal distributions highlighted several candidate signals including the mid-principal stress, the dilatational strain, and the radial gradient of the local radial strain.

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 Youngs 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.

Characterization of dynamic three-dimensional strain fields in the canine radius

This note describes a method to approximate the 3-D mechanical environment of a long bone during a normal daily activity. Our specific goal was to characterize the temporal and spatial strain distributions in the mid-shaft region of the canine radius during gait. Direct measurement of strains along the entire surface of in vivo bone is not feasible, so we employed a combination of experimental measurements and numerical interpolation techniques to approximate the time-varying longitudinal strain distribution. Using standard in vivo strain gauging techniques, we measured dynamic strains at nine locations (three locations on each of three cross sections, data pooled from two experimental animals) on the canine radius during trotting gait. These in vivo strain measurements were then used to approximate the time course of the strain field for the entire radius mid-shaft region using a 3-D numerical interpolation scheme using finite element basis functions. Despite limitations in the present implementation of the method, the results show that there are considerable time-dependent variations in the strain distribution occurring at different transverse sections along the length of the diaphysis with substantial anteroposterior bending and rotation of neutral axis locations during the gait cycle.

Errors in the orientation of the principal stress axes if bone tissue is modeled as isotropic.

The error in the prediction of the orientation of the principal axes of stress in bone tissue is determined in the case when the tissue is modeled as elastically isotropic rather than as orthotropic, the probable symmetry of bone tissue. Results are two-dimensional and assume the same underlying strain state for both the orthotropic and isotropic cases. The maximum error is 45 degrees, and the typical error is generally significant.

A theoretical study of the influence of bone maturation rate on surface remodeling predictions: Idealized models

The use of a finite element based computational method, RFEM3D, is described for the study of strain-induced bone remodeling. The purpose of the research is to find the potential influence on the predictions of surface bone remodeling when various models for the maturation of newly deposited bone are used. A parameter study is performed using seven hypothetical mechanical descriptions of the bone maturation process. The results show that, theoretically, the process of surface bone maturation may be an efficient mechanism for reducing overload strains in bone, but that differences as a consequence of using any of the proposed maturation rules are rather subtle.