A continuous model for an arterial tissue, incorporating remodeling and volumetric growth

Abstract

A continuum-mechanics approach for the derivation of a model for the behavior, that is, the growth and remodeling, of an arterial tissue under a mechanical load is presented. This behavior exhibits an interplay between two phenomena: continuum mechanics and biology. The tissue is modeled as a continuous mixture of two components: elastin and collagen. Both components are incompressible, but the tissue as a whole can show volumetric growth due to the creation of collagen. Collagen is a fibrous structure, having a strain-induced preferred orientation. Remodeling of the tissue incorporates degradation of elastin and strain-induced creation and degradation of collagen fibers. Both elastin and collagen are considered to be nonlinear elastic media; elastin as a neo-Hookean material and collagen fibers behaving according to an exponential law. The modeling is based on the classical balance laws of mass and momentum.