An attempt to describe heart attacks via continuum damage mechanics

Abstract

In an earlier paper the author expressed evolution equations of classical continuum damage mechanics in terms of unit dissipated power and proposed an extension to biological materials in vivo, adding a term describing recovery. In the present paper an analogy with evolution of coronary artery disease is established. If we denote by S (relative stenosis) one minus the ratio of current luminal area to the initial area, then the condition S = 1 at a certain point of the artery means complete blockage at this point resulting in a heart attack (myocardial infarction). This corresponds to the condition of critical state D = 1 in damage mechanics, where D denotes a scalar measure of damage. Making use of this analogy, an evolution equation for S is proposed with unit dissipated power replaced by unit power of flow in individual cross-sections of coronary arteries and, subsequently, by the heart power. Further, another evolution equation describes the required heart power in terms of external loadings acting on the organism as a whole. Numerical integration of the evolution equations proposed makes it possible to distinguish loadings leading to a myocardial infarction from those subject to recovery. Also, the description of stable and unstable angina pectoris is discussed and illustrated by numerical examples.