A three-dimensional analytical (rheological) model of the human left ventricle in passive-active states. Nontraumatic determination of the in vivo values of the rheological parameters.

In this paper a three-dimensional continuum model of a mammalian left ventricle is formulated. The stresses in the model satisfy the conditions of zero stress on the outer (epicardial surface-representing) boundary. The strains of the model are obtained from the actual dynamic geometry measurements (obtained from cineangiocardiography). Since the left ventricular muscle is incompressible, the dilatational strain is zero and hence the (three-dimensional) deviatric stress components are related to the corresponding strain components by Maxwell and Voigt rheological model analogues of one-dimensional systems; the parameters of the model are series and parallel elastic (SE, PE) elements and the contractile element (CE) (representing the sarcomere). The incorporation of the rheological features of the cardiac muscle into the three-dimensional constitutive equations (for the three-dimensional continuum model of the left ventricle) is a feature of this paper. A procedure is presented to determine the parameters of the constitutive equations (i.e., the SE, PE, and the parameters of the force-velocity relation for the CE) for the left ventricle of a subject from data on the dimensions and chamber pressure of the left ventricle. The values of these parameters characterize the rheology of the left ventricular muscle of the subject. In order to demonstrate clinical application of the analyses, in vivo data of the subjects' left ventricular pressure and dimensions are obtained, and the analyses are applied to the data to determine (for each subject) the values and characteristics of the elastic elements and CEs.