A Subdomain Method for Mapping the Heterogeneous Mechanical Properties of the Human Posterior Sclera

Abstract

Although strongly correlated with elevated intraocular pressure, primary open-angle glaucoma (POAG) occurs in normotensive eyes. Mechanical properties of the sclera around the optic nerve head (ONH) may play a role in this disparity. The purpose of this study is to present an automated inverse mechanics based approach to determine the distribution of heterogeneous mechanical properties of the human sclera as derived from its surface deformations arising from pressure in fl ation experiments. The scleral shell of a 78 year old European Descent male donor eye was utilized to demonstrate the method; the sclera was coated with a speckle pattern on the outer surface and was subjected to in fl ation pressures of 5, 15, 30, and 45 mmHg. The speckle pattern was imaged at each pressure, and a displacement fi eld was calculated for each pressure step using a previously described sequential digital image correlation(S-DIC) technique. The fiber splay and fiber orientation of the sclera collagen were determined experimentally, and the thickness across the scleral globe was determined using micro CT images. The displacement fi eld from the in fl ation test was used to calculate the strain and also used as an input for inverse mechanics to determine the heterogeneity of material properties. The scleral geometry was divided into subdomains using the first principal strain. The Holzapfel anisotropic material parameters of matrix and fiber stiffness were estimated within each individual subdomain using an inverse mechanics approach by minimizing the sum of the square of the residuals between the computational and experimental displacement fields. The mean and maximum error in displacement across all subdomains were 8.9 +/- 3.0 mu m and 13.2 mu m, respectively. The full pressure-inflation forwardmechanics experiment was done using subdomain-specific mechanical properties on the entire scleral surface. The proposed approach is effective in determining the distribution of heterogeneous mechanical properties of the human sclera in a user-independent manner. Our research group is currently utilizing this approach to better elucidate how scleral stiffness influences those at high risk for POAG.