Constitutive Relations for Pressure Driven Stiffening in Poroelastic Tissues

Abstract

Vascularized biological tissue has been shown to increase in stiffness with increased perfusion pressure. The interaction between blood in the vasculature and other tissue components can be modeled with a poroelastic, biphasic approach. The ability of this model to reproduce the pressuredriven stiffening behavior exhibited by some tissues depends on the choice of the mechanical constitutive relation, defined by the Helmholtz free energy density of the skeleton. We analyzed the behavior of a number of isotropic poroelastic constitutive relations by applying a swelling pressure, followed by homogeneous uniaxial or simpleshear deformation. Our results demonstrate that a strainstiffening constitutive relation is required for a material to show pressuredriven stiffening, and that the strainstiffening terms must be volumedependent.