Use of a mathematical model to estimate stress and strain during elevated pressure induced lamina cribrosa deformation

Abstract

Background. High intraocular pressure (IOP), which is generally associated with glaucoma, causes lamina cribrosa retrodisplacement and deformation. Shear stress and strain resulting from lamina cribrosa deformation have been implicated in tissue remodeling, changes in retinal astrocyte function and retinal ganglion cell (RGC) death observed in vivo during glaucoma. Methods. A mathematical model was developed to describe the lamina cribrosa exposed to elevated intraocular pressure (IOP). The model is based on the bending theory of plates, incorporates anatomical properties of the lamina cribrosa, and provides estimates of its biomechanical properties. The model relates IOP, the parameter normally correlated with glaucoma, and lamina cribrosa retrodisplacement to stress and strain experienced by cells, parameters that may be more closely associated with cell injury. Results. We estimate that shear strains of 0.05 occur at the edge of a 200 µm thick lamina cribrosa at an IOP of 25 mm Hg. We estimate greater lamina cribrosa deformation and higher shear stress and strain for thinner lamina cribrosa and lamina cribrosa of larger radii. Conclusion. These results may provide better estimates of the stress and strain experienced by cells in the lamina cribrosa and may further our understanding of the forces that contribute to optic nerve degeneration during glaucoma.