Micro Finite Element Modeling of the Lamina Cribrosa in Monkey Eyes

Abstract

Abstract: : Purpose: To estimate intraocular pressure (IOP)–related stress and strain within individual lamina cribrosa beams using finite element (FE) analysis. Methods: Voxel–based volumes of the connective tissues of monkey optic nerve heads (ONHs) were constructed from serial, high resolution images (2.5x2.5 µm/pixel) of the stained block face of an ONH specimen embedded in paraffin and sectioned at 3 µm intervals on a microtome. A continuum FE model was constructed for a single normal monkey ONH (perfusion–fixed at an IOP of 10 mm Hg) in which each element containing lamina was assigned material properties based on the connective tissue volume fraction and predominant orientation of the contained laminar beams. IOP was increased from 10 to 30 mm Hg within the continuum model and the resultant nodal displacements and stress and strain components were calculated. The laminar elastic modulus was adjusted such that the continuum model’s laminar displacement matched histologic displacement reported previously. Due to the computational difficulties associated with FE modeling of the entire lamina cribrosa micro architecture, a sub–structuring approach has been developed. The voxel–based micro architecture of the lamina within a single continuum element (145x160x150 µm region from the superior quadrant) was isolated using 3–dimensional filtering and adaptive segmentation, surfaced, smoothed and converted into a FE model. Isotropic material properties were applied to all micro model elements using the same Young’s modulus (45 MPa) as the parent continuum model. Average displacements of the parent continuum element’s faces were applied as displacement loadings on the micro model at the intersections of the contained laminar beams and the parent element’s faces. Results: At an IOP of 30 mm Hg, average von Mises stress within the parent continuum element was 37 kPa. However, within the laminar micro model, average von Mises stress (across all elements) increased dramatically to 1190 kPa, with large concentrations and gradients in individual laminar beams. Displacement distributions and strain within the micro model were similar to those seen in the parent continuum element. Conclusions: While continuum FE models assess overall ONH biomechanics, micro FE models of the laminar beams are necessary to study the influence of IOP–related stress and strain on laminar beam connective tissue, astrocytes, blood flow, and the adjacent axons. Within these models, individual laminar beam stresses are likely to be much higher than predicted by the continuum modeling approach.

Keywords: optic disc • lamina cribrosa • sclera