Department of Pediatric Cardiovascular Surgery, The Heart Institute of Hapan, Tokyo Women's Medical College
Max(<I>d</I>P/<I>d</I>t), Maximum acceleration of blood, Velocity of blood, Velocity of pulse wave
In early systole before the effect of reflected waves from the periphery becomes significant, the following equation holds: PA−PO=ρcu (1), where PA is the instantaneous pressure in the ascending aorta, PO the end-diastolic pressure, ρ the density of the blood, c the velocity of pulse wave in the aorta, and u the velocity of blood. Differentiation of Eq. (1) with respect to time t yields dPA/dt=ρc(du/dt) (2). If there is no aortic stenosis and if the pressure gradient due to the inertia of the blood during acceleration is neglected, the left ventricular pressure (P) is nearly equal to PA during the ejection period. Since both dP/dt and dPA/dt take their maximum values at times close to the time of aortic valve opening, the following equation holds: Max(dP/dt)≈Max(dPA/dt) (3), where Max means the maximum value of a derivative. Eq. (2) reduces to Max(dPA/dt)=ρcMax(du/dt) (4). Substitution of Eq. (4) into Eq. (3) yields Max(dP/dt)≈ρcMax(du/dt) (5). We performed experiments in seven dogs, and found that there was a good linear correlation (Y=1.01X-2, r=0.97) between Max(dP/dt) and ρc Max(du/dt). Therefore, Eq. (5) is a universal equation which holds irrespective of the animal and intervention employed to change hemodynamic state. The absolute value of Max(dP/dt) of the left ventricle can be obtained non-invasively by measuring the velocity of pulse wave and the maximum acceleration of blood in the ascending aorta.