A Biphasic Poroelasticity Model for Soft Tissue

Poroelastic media are characterized by biphasic structure, consisting of a solid matrix permeated by a fluid-filled pore space. Originally conceived for soil mechanics, poroelastic models have been used to study the mechanics of biological tissues, where the matrix consists of cells or the extracellular matrix, and the fluid compartment is comprised of the vascular tree, interstitial fluid, cerebro-spinal fluid, or a combination of these. Unlike simpler monophasic models, poroelasticity predicts two longitudinal (compressional) wave modes with different wave speeds. The poroelastic equations of motion depend on two interaction or coupling parameters that describe the transfer of energy or momentum between the two phases, thus leading to a system of coupled equations. In this chapter, we will explain the poroelastic tissue model, present a poroelastic version of the wave equation, and complement this theoretical part with numerical simulations.