Computational modeling of mechanical anisotropy in the cornea and sclera

Abstract

Purpose: To determine the biomechanical deformation of the cornea resulting from tissue cutting and removal by use of a new computational model and to investigate the effect of mechanical anisotrophy resulting from the fibrillar architecture.

Setting: Department of Mechanical Engineering, Stanford University, Stanford, California, USA.

Methods: A mathematical model for a typical lamella that explicitly accounts for the strain energy of the collagen fibrils, extrafibrillar matrix, and proteoglycan cross-linking was developed. A stromal model was then obtained by generalized averaging of the lamella properties through the stromal thickness, taking into account the preferred orientations of the collagen fibrils, which were obtained from x-ray scattering data.

Results: The model was used to predict astigmatism induced by a tunnel incision in the sclera, such as is used for cataract extraction and intraocular lens implantation. The amount of induced cylinder was in good agreement with published clinical data. Results show it is important for the model to incorporate preexisting corneal physiological stress caused by intraocular pressure.

Conclusions: The mathematical model described appears to provide a framework for further development, capturing the essential features of mechanical anisotropy of the cornea. The tunnel incision simulation indicated the importance of the anisotropy in this case.