Modeling pressure-area relations of coronary blood vessels embedded in cardiac muscle in diastole and systole.

Pressure-cross-sectional area (P-A) relations of a (thick-walled) arteriole and (thin-walled) small vein (both maximally dilated), embedded in cardiac muscle in both static systole and diastole at slack length and at 90% of maximal length (Lmax), were calculated. The elastic properties of cardiac muscle and vessel wall per se were taken into account. Muscle fibers and vessels were assumed to run in parallel. The muscle tissue (fibers + collagen) was assumed to be incompressible, homogeneous, nonlinearly elastic, and transversely isotropic. Cross-fiber stress-strain relations were assumed to be proportional to those in fiber direction. It is predicted that cardiac muscle in diastole has little effect on the P-A relation of the arteriole but strongly affects that of the small vein. In systole, the myocardium strongly affects the P-A relations of both vessels. Isometric transition from static diastole to static systole (isometric "contraction") was found to reduce arteriolar and venous area (at constant pressures of 35 and 7 mmHg, respectively) by approximately 50 and 40, respectively. Contraction with a 14% shortening was found to reduce these areas by 48 and 32%, respectively. The differences in the results for the two vessels were found to be determined mainly by their difference in the ratio of outer to inner radius. Furthermore, it was found that the area reductions are much larger for contractions (with or without shortening) than for muscle stretch per se. It is concluded that the change in elastic properties and, more specifically, development of stress in cross-fiber direction of the cardiac muscle during contraction causes the area reductions of coronary vessels.