Passive and Active Deformation Processes of 3D Fibre-Reinforced Caricatures of Cardiovascular Tissues

In this paper, we present a mathematical model of contractile elastic solids meant to simulate various districts of the cardiovascular system, and based on the concepts of active deformation and embedded muscle - bres. Specically, here we deal with the modelling of the gross mechanics of the left ventricle (LV) which is strictly related to its pump function. The muscle bres embedded in the LV walls govern, through their contraction and relaxation, the characteristic phases of the cardiac cycle. Moreover, muscle bres dene the anisotropy directions of the LV wall, and the collagene bres determine the material properties along these directions; thus, to model the mechanical behaviour of the LV, both the passive and the active material properties of the must be accurately accounted for. As is well known, the eectiveness of the pumping action is well represented by the pressure-volume (PV) diagrams that relate the blood pressure to the volume of the LV during the cardiac cycle. Here, we aim at reproducing realistic PV by specifying appropriate sequence of muscle contractio