DYNAMICAL FINITE ELEMENT MODELING OF SOFT TISSUES AS CHEMOELECTRIC POROUS MEDIA

Abstract

An implicit mixed finite element formulation of hydrated soft biological tissues, based on the Simon model, is presented that incorporates the coupling of solid, fluid, and ion phases as well as the viscoelasticity of soft tissue in the dynamical process. The tissues are modeled as a multi-field viscoelastic body subject to finite deformation. In addition to a three-field (u-w-p) modeling of the porous matrix, the study also includes an ion phase for the ionic solution. After presenting the formulation, an efficient staggered solution scheme is presented: within each time step, the ion charge equation is solved first to give the distribution of the charge concentration, the charge induced osmotic water pressure is then employed in solving the u-w-p equations. The resulting u field becomes a forcing term to the solution of the ion charge concentration equations for iteration. This methodology and codes developed for the study have been verified with one-dimensional (1D) analytical solutions. A 2D chemical electric swelling model illustrates the important role of viscoelasticity. A brain tissue impact example demonstrates the potential application of the model.