Human left ventricular end-systolic pressure-volume relationship in a cylinder model

The relationship between myocardial total force and length at the end of systole appears to be linear, and the slope of this relationship is considered to be an appropriate index of myocardial contractile state, independent of preload and afterload. However, direct measurements of this relation may be impossible in the intact human heart, and thus, alternative indices such as the left ventricular end-systolic stress-length, stress-strain, pressure-volume, and pressure-dimension slopes have been proposed to evaluate myocardial contractility in the intact heart. However, the mathematical relationship between the myocardial end-systolic total force-length relation and any of these left ventricular end-systolic relations remains unclear. In this study, assuming a linear myocardial end-systolic total force-length relation in an intact ventricle, we obtained mathematical formulae for the left ventricular end-systolic stress-strain, pressure-radius, and pressure-volume relations, using a cylinder model of the left ventricle. The results obtained using these formulae and the cylinder model were found to match accurately findings obtained from earlier experimental and clinical studies of these left ventricular end-systolic relations. Thus, this model could mathematically account for the relationships between the slopes of the myocardial end-systolic total force-length relation and these left ventricular end-systolic relations.