Formulation and Computational Implementation of Constitutive Models for Cardiovascular Soft Tissue Simulations

Abstract

Predictive computational modeling of the cardiovascular system has often been utilized as a powerful investigative tool. Motivated by the need for a deeper understanding of the underlying physiology, the identification of pathological initiators, as well as the development of bioprosthetic devices, a broad variety of modeling approaches have been introduced into the literature. Central to system- and organ-level functional simulations is the need for robust and physiologically meaningful constitutive models of the underlying soft tissue structures. While studied for many decades, Y.C. Fung popularized the field of soft tissue mechanics through a set of influential books which demonstrated the unique challenges involved in the mathematical characterization of living tissue mechanical behaviors. Overall, his main contribution was to establish constitutive relationships for the purpose of examining biological tissues in a continuum mechanics framework. Particular challenges in soft tissue constitutive modeling are encountered due to their complex mechanical behavior. For example, because of their oriented fibrous structures, they often exhibit pronounced mechanical anisotropy, nonlinear stress–strain relationships, large deformations, viscoelasticity, poroelasticity, and strong mechanical coupling. Taken as a whole, soft biological tissues defy simple material models. The focus of this chapter is the description and computational application of relevant biomechanical constitutive theories. Throughout this chapter, we will utilize the assumption of hyperelastic behavior as fundamental to soft tissue biomechanics, utilizing the concept of pseudo-elasticity, so that the loading response is modeled only.