A biomathematical model for pressure-dependent lamina cribrosa behavior

Investigating the relationship between intraocular pressure and the behavior of the lamina cribrosa (the primary site of the optic nerve damage in glaucoma) is important to insight into the pathogenesis of glaucomatous optic neuropathy. In most previous studies, unsuitable approaches were used since the lamina cribrosa was not taken as the main target. In the present study, a linear model of elastic mechanics theory on the bending of thin circular plate was developed for this purpose. The structural features of the lamina cribrosa and the forces acting on the lamina cribrosa were analyzed, and the constitutive equation was formulated. The general solution on a class of Kármán Equation and the analytic solution on fixed boundary conditions were obtained, and from them, the morphological changes and the mechanical properties such as retrodisplacement and force distributions of the lamina cribrosa under pressure were derived. Some of the clinical phenomena occurring in glaucoma damage were explained with the results. Theoretical values were compared with the experimental data obtained by other investigators. The effects of structural parameters on susceptibilities to glaucoma damage were discussed. The biomathematical model, serving as formalistic expressions of the well-known hypothesis of pressure-dependent optic nerve damage in glaucoma, should make it possible for us to further understand and manage this disease.