Hyperelastic Models for Contractile Tissues: Application to Cardiovascular Mechanics

Mathematical models are widely used in biomechanics to represent the contractile activity of living organs. The advancements in experimental and imaging techniques offer scientists a huge amount of data, at several spatial scales, ranging from cells to muscles. Continuum mechanics is an appealing framework to model the active responses of active soft biological tissues at the macroscale. Usually, the activity of the muscles is modeled by adding an active stress term to the stress-strain constitutive law. Another approach, named active-strain, encodes the tissue contraction through a kinematics decomposition, accounting for the active fiber's direction. In this chapter, we illustrate, exemplify, and discuss the implementation of these two formulations of mechanical activity through three applications to cardiovascular mechanics.