Heart Mechanics Using Mathematical Modelling

Heart failure is a leading cause of death in New Zealand. In order to determine the causesof rhythm disturbances leading to failure a knowledge of the structure and mechanical behaviour of cardiac tissue is important. This paper presents realistic stress and strain distributions for the passive heart that have been reproduced using a three-dimensional finite element model of the ventricles based on finite deformation analysis of elastic bodies. The geometry and structure of the ventricles have been accurately described using a mathematical model that combines a prolate spheroidal coordinate system with high order interpolation schemes to minimise the number of degrees of freedom. A fully orthotropic constitutive relation, based on in vitro biaxial tests and observations of cardiac microstructure, is used to describe the stress-strain properties of myocardial tissue. The parameters of the constitutive relation are estimated using a combination of biaxial stress-strain tests on thin myocardial sections and 3D deformation fields derived from non-invasive MRI tagging techniques.