A critique: relationship of the time derivative of pressure to blood flow

Abstract

The relationship of the time derivative of pressure to instantaneous aortic blood flow was studied in six dogs. Pressure was measured with calibrated high-fidelity manometry and flow with an electromagnetic flowmeter. The true time constants of the equation of fluid motion (relating blood flow to the pressure gradient) were calculated and compared to the magnitude of time constants necessary to produce flow contours computed from the pressure time derivative that empirically “matched” flows measured by the electromagnetic flowmeter. It was found that time constants which produced acceptable “matching” were approximately 20 times too large. This observation demonstrated that 1) the time derivative of pressure is not proportional to the pressure gradient and 2) the similarity of measured and computed flows, using the pressure derivative, depends not on the laws of fluid motion but rather on the accidental similarity of the final form of the equation of fluid motion (with pressure derivative substituted for pressure gradient) to an empirical equation describing the hydraulic input impedance to the aorta. pressure gradient technique; blood velocity; analog computer Submitted on September 30, 1964