Principle of a noninvasive method of measuring Max(dP/dt) of the left ventricle: Theory and experiments

Summary

In early systole, before the effects of reflected waves from the periphery become significant, the following equation applies:

$$PA - PO = \rho cu$$

((1))

where PA and PO are the instantaneous and end-diastolic pressures in the ascending aorta,ρ the density of blood, c the velocity of the pulse wave in the aorta, and u the velocity of blood. Differentiation of Eq. (1) with respect to time t yields:

$$dPA/dt = \rho c(du/dt)$$

((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 applies:

$$Max(dP/dt) \fallingdotseq Max(dPA/dt)$$

((3))

where Max signifies the maximum value of a derivative. Equation (2) reduces to:

$$Max(dPA/dt) = \rho cMax(du/dt)$$

(4)

Substitution of Eq. (4) into Eq. (3) yields:

$$Max(dP/dt) \fallingdotseq \rho cMax(du/dt)$$

((5))

Experiments were performed on seven dogs. Max(dP/dt), Max(du/dt), and c were measured during volume loading, pressure loading and unloading, and before and after administration of positive and negative inotropic agents.

There was a good linear correlation (Y=1.01X−2, r=0.97) between Max(dP/dt) andρcMax(du/dt). Therefore, Eq. (5) is a universal equation which holds, irrespective of the dogs and interventions employed to change the hemodynamic state. The absolute value of Max(dP/dt) of the left ventricle can be obtained by measuring noninvasively the velocity of the pulse wave and the maximum acceleration of blood in the ascending aorta.