COMPUTATIONAL MODEL FOR HEART TISSUE WITH DIRECT USE OF EXPERIMENTAL CONSTITUTIVE RELATIONSHIPS

Abstract

Heart wall tissue plays a crucial role in living organisms by generating the mechanical force for blood flow. This tissue has a complex internal structure comprised mostly of muscle cells, in which biochemical energy is transformed into mechanical active stress under rhythmical electrical excitation. The overall heart functioning depends, among other physiological conditions, on the mechanical properties of the tissue. Over the past centuries, experimental and theoretical investigations have been conducted in order to establish the constitutive laws governing wall tissue behavior. Regarding computational modeling, many material models have been introduced, from simple elastic anisotropic to more sophisticated ones, based on various formulations of strain potentials. We here present a novel computational model that directly employs experimental constitutive relationships. Therefore, we avoid any fitting of material parameters for a selected analytical form of the constitutive law. Hysteretic characteristics of the tissue are included, as well as either incompressibility or compressibility according to experimentally determined curves. Deformation is split into deviatoric and volumetric parts in order to handle compressibility. The correctness and accuracy of the model is demonstrated through simple cases for loading and unloading conditions. Furthermore, the model was implemented for left ventricle (LV) deformation, where the FE mesh was generated from echocardiography recordings. Here, a specific algorithm, which accounts for LV torsion, was introduced to determine trajectories of material points on the internal LV surface. Hysteresis of the constitutive curves was used to calculate mechanical energy of LV wall tissue deformation. For completeness, the fluid flow within the LV was computed as well.