Finite element model for the cardiac pump

Summary form only given. To predict stress values within the myocardium and to explain the pumping action of the left ventricle, an axisymmetrical model has been formulated. The myocardium is a nonhomogeneous continuum made of an elastic matrix, plus a set of crisscrossed unidimensional helical fibers disposed in such a way that torsional motion is prevented. The fiber is characterized by its local orientation and its active tension. The helical fiber pitch angle varies within the wall according to a linear relation. A linear stress-strain relation depending on the activation function is adopted for the fibers. The stress tensor of the myocardium is the sum of two tensors: a stress tensor due to the presence of the fibers and one due to the collagenic matrix. The left ventricle has been modeled as a thick hollow cylinder and then as a thick hollow ellipsoid. The equilibrium of such structures has been studied using a small deformation theory under the assumption that gravitational forces and inertia are negligible