Thermodynamic derivation of a non-linear poroelastic model describing hemodynamics-mechanics interplay in the lamina cribrosa

In this paper we formulate a poroelastic model starting from a model of species di usion in an elastic material. The model is applied to study the mechanics of the lamina cribrosa (LC) in the eye. The LC is a porous tissue at the head of the optic nerve. Deformation of this tissue and impairment of blood flow induced by tissue deformation are considered to be related to the pathogenesis of glaucoma. The governing equations are derived from general thermomechanical principles. We carefully revise the role of the energy-stress Eshelby tensor, mutuated from the framework of tissue growth, in describing the hemo-mechanical behaviour of the tissue. The model accounts for non-linear deformations of the solid matrix and deforma- tion-induced changes in porosity and permeability. The model provides a qualitative better undertanding of the phatophysiology and pathogenesis of glaucoma in terms of coupling between tissue deformation and the resulting impaired hemodynamics inside the LC.