that scleral material properties may influence the onset of glaucoma [1-4]. Open-angle glaucoma is the progressive loss of vision due to the death of retinal ganglion cells (RGCs). These neurons bundle through the back of the sclera via the optic nerve head (ONH) to transmit visual information to the brain. It is known that intraocular pressure (IOP) plays an important role in the damage to RGCs [1-3], however the relationship between the mechanical properties of the scleral connective tissue and how it affects RGC death is not well understood. Despite recent therapeutic advances to reduce vision loss in glaucoma patients, the rate of blindness remains high [5, 6]. The focus of this paper is to discuss an experimental and modeling study that quantifies scleral material properties measured for a bulge inflation response of an excised and intact mouse sclera. The mouse model was pursued because of the ability to mechanically test tissue that has been altered through age, disease, and genetic manipulation, and to determine how each of these factors influences the deformation response of scleral tissue to increases in IOP. The experimental methodology for the mouse sclera bulge tests has been described in detail in Myers et al. [7], and the nonlinear, anisotropic, distributed fiber material model that was used to fit the data has been described in Nguyen and Boyce [8]. This paper details the inverse finite element method and optimization scheme that was employed to fit the material model to measured scleral edge displacements for different aged wild-type C57BL/6 mouse sclera. The resulting best-fit material parameters were compared between different aged animals. METHODS Inflation tests were conducted on intact ex-vivo mouse eyes using a method previously described elsewhere [7]. Three 2 month old and three 11 month old C57BL/6 mouse scleral specimens were tested. Briefly, eyes were enucleated, cleaned of orbital fat and muscle, mounted by the cornea to a custom fixture, cannulated and immersed in PBS. A programmable pressure-controlled syringe pump inflated the cannulated eyes in a series of load-unload tests to 2kPa (15mmHg) and ramp-hold creep tests to 2, 4 and 6kPa. A CCD video camera (Pt. Grey Research GRAS-20S4M/C) attached to a microscope (Zeiss Stemi) imaged the expanding scleral surface at 0.5Hz (5µm/pixel). Scleral displacement for locations adjacent to the ONH to the holder was measured with a DIC program (Vic 2D, Correlated Solutions Inc.). After testing, fresh tissue thickness measurements were taken on scleral slices at multiple locations under a light microscope. Because mouse scleral tissue has a varying thickness profile and contains a stress concentration at the optic nerve head, a finite element (FE) model of the scleral specimens was developed to determine the complex stress state of the posterior portion of the eye. To quantify material properties, parameters of a nonlinear, anisotropic, distributed fiber material model [8] were optimized such that the FE model predictions matched the deformation response of the expanding scleral edge during inflation. The finite element (FE) model was constructed for each specimen using the scleral geometry measured from the DIC camera at a reference pressure of 0.8kPa (6mmHg). After extracting the coordinates of the reference position of the scleral edge, a geometric representation was constructed by first fitting a conic section to one half of the measured scleral edge. A second conic section was fit to the inner scleral surface based on the measured thickness profile. Lastly, the inner and outer surface geometries were revolved 90° to form a quarter model of the scleral shell, with the optic nerve head (ONH) located at 100μm from the apex. The sclera was modeled as a composite material with a nearly incompressible Neo-Hookean matrix embedded with regions of non-linear transversely isotropic and anisotropic fibers. To summarize the details of the material model [8], the matrix was characterized by a shear μmatrix and bulk κmatrix modulus, with κmatrix orders of magnitude larger than μmatrix. The non-linear response of the collagen fibers was modeled with a phenomenological exponential function with model parameters [β, αo = 4αβ], with β charactering the strain-stiffening and αo representing the initial stiffness of the fibers. 88
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