Active contraction of the cardiac ventricle and distortion of the microstructural architecture

The shortening of the myocardial fibers is the microstructural engine that produces the contraction of the cardiac muscle. The complex interplay between fibers shortening and elastic macroscopic strain is functional to the ejection of blood into the pulmonary and arterial networks. Here, we address the contraction of the left ventricle in a finite elasticity framework, adopting the 'prolate ellipsoid' geometry and the invariants-based strain energy proposed by Holzapfel and Ogden, where the mechanical role of fibers and sheets is accounted for. We show that a microstructurally motivated mathematical model of active strain type reproduces the main indicators of normal cardiac function along the whole PV-loop without introduction of any further ad hoc law. The bare-bones mathematical model depends on one measurable parameter only, that is, the shortening ratio of the sarcomere units, which we assume to be nearly independent on the prestretch. Strict enforcement of incompressibility and novel treatment of boundary conditions are shown to be crucial to simulate the correct muscle torsion.