A theoretical model for myocardial tissue deformability

Early detection of cardiac disease is based on the quantitative interpretation of left ventricular wall motion throughout the cardiac pumping cycle. Wall deformations result from complex fluid-wall interactions wherein muscle fibre orientation, intraventricular pressure and regional variations of myocardial wall rheology play a crucial role. A reliable theoretical model would be of intrinsic value in aiding the cardiologist in his interpretation of clinical diagnostic results, particularly through the incorporation of microprocessor-based algorithms permitting automatic processing of clinical data within the framework of such a model. As a step in this direction, a theoretical analysis is formulated for a relatively simple characterization of the left ventricle in terms of a truncated ellipsoidal shell. The myocardial wall contains contractile muscle fibres of known orientation. The stress tensor is derived on the basis of an inviscid fluid-fibre continuum. Principal stresses are calculated in terms of regional wall deformations and intraventricular pressure. These are determined from an inviscid fluid dynamic model for left ventricular contraction, subject to an appropriate Neumann condition on wall velocity as obtained from cineangiography. Local “defects” in wall velocity simulate the inhibition of wall contractility associated with the development of myocardial infarct. The theoretical model makes it possible to evaluate local variations in wall stress at those sites and to calculate both regional and overall changes in heart work as a noninvasive indicator of cardiomyopathies or valvular defects. Graphic results are presented depicting the role of myocardial tissue rheology on the dynamics of cardiac performance during the ejection phase, on the basis of the present theoretical model.