Shock Waves in Mathematical Models of the Aorta

Abstract

If the nonlinear equations for nonsteady blood flow are solved by the method of characteristics, shock discontinuities may develop as a result of omitting from the mathematical model some aspect of the system that becomes significant at rapid flow changes. As an illustration, the flow from the heart into the aorta at the beginning of systole is analyzed. An equation is derived which yields shock formation distances between a few centimeters and several meters depending on the elastic properties of the aorta. Since knowledge of the actual wave form would be useful for computer programming, a few exploratory experiments were performed with an unrestrained latex tube. They indicated wave transitions extending over several tube diameters, but maximum steepening of the wave has not yet been achieved.