Septal and ventricular deformation in a shell model of the human heart: chamber wall geometry and ventricular interdependence

Ventricular interdependence is one of the principal controllers of heart function, and hence a key mediator of most pathological consequences of its impairment. It can only be explained by accounting for overall chamber deformation resulting from internal bending and twisting moments as well as cardiac dimensions and nonlinear material properties, and clinically useful interpretation of imaging data about pathological alterations in chamber geometry is hampered by lack of understanding of its significance to cardiac function. In order to characterise the influence of chamber geometry on ventricular function, a model was developed which describes the ventricles and septum as portions of generalised ellipsoid shells of non-uniform wall thickness whose interacting walls are subject to local and global stresses/strains as well as torques. Chamber configuration is derived as a function of pressure gradients by combining shell element equilibrium equations through static boundary conditions applied at the sulcus, where the walls exhibit a mixed state of stress. Diastolic pressure (P)-volume (V) curves are calculated for both ventricles as a function of contralateral (constant) pressure and ventricular interaction is characterized by calculating coupling coefficients represented by surfaces in pressure-volume-contralateral pressure space. Further, the alterations in PV relationships determined by a number of pathological conditions (constrictive pericarditis, septal or left ventricular wall hypertrophy, dilatative cardiomiopathy) are characterized. Our results are in good agreement with experimental literature and clinical data, and our model allows simulation/prediction of cardiac chamber behaviour in a variety of physiopathological circumstances.