Teruo Kimura

Stress-strain relation of cardiac muscle determined from ventricular pressure-time relationships during isovolumic contractions

Abstract The stress-strain relation of systolic muscle fibers which constitute the left ventricular wall of a canine heart was derived only from pressure-time relationships at different ventricular volumes of isovolumic beat by using a largely deformable thick spherical shell model as a first approximation. The strain energy function being independent of the magnitude of forces generated by contraction was found to be uniquely determined by assuming those forces as forces caused by an eigen stress. The result based on this assumption was verified by several pressure-volume relationships obtained experimentally.

Residual Stress in the Left Ventricle

The left ventricle is a highly deformable, thick-walled structure that is subjected to intraventricular pressure and myocardial contractile force. Stress in the left-ventricular wall may not be zero even if the intraventricular pressure is not present; such a stress is called the residual stress. The values of stresses must be obtained from the appropriate mathematial model, which should be as simple as possible. In the mathematical models proposed so far, the residual stress has not been considered. If the effect of residual stress is ignored, the extreme concentration of the stress occurs near the endocardium, so that there exists a contradiction between the oxygen consumption and the local mechanical work because of stress and strain along the wall thickness. First, a mathematical model was proposed that was valid for isovolumic and isobaric contractions in which the ventricle was subjected to both intraventricular pressure and myocardial contractile force. Expressions for the stress components were derived without assuming the functional form of the stress-strain relation, thus differing from those; assumed previously by many researchers. The residual strain was obtained from experimental work using canine ventricles. Then, the residual stress was introduced to improve the model to avoid the contradiction just mentioned. As a result, the extreme concentration of stress at the endocardium was largely reduced in the improved ventricular model.