Analytical modeling of the instantaneous pressure gradient across the aortic valve

Abstract

Aortic stenosis is the most frequent valvular heart disease. The mean systolic value of the transvalvular pressure gradient (TPG) is commonly utilized during clinical examination to evaluate its severity and it can be determined either by cardiac catheterization or by Doppler echocardiography. TPG is highly time-dependent over systole and is known to depend upon the transvalvular flow rate, the effective orifice area (EOA) of the aortic valve and the cross-sectional area of the ascending aorta. However it is still unclear how these parameters modify the TPG waveform. We thus derived a simple analytical model from the energy loss concept to describe the instantaneous TPG across the aortic valve during systole. This theoretical model was validated with orifice plates and bioprosthetic heart valves in an in vitro aortic flow model. Instantaneous TPG was measured by catheter and its waveform was compared with the one determined from the transvalvular flow rate, the valvular EOA and the aortic cross-sectional area, using the derived equation. Our results showed a very good concordance between the measured and predicted instantaneous TPG. The analytical model proposed and validated in this study provides a comprehensive description of the aortic valve hemodynamics that can be used to accurately predict the instantaneous transvalvular pressure gradient in native and bioprosthetic aortic valves. The consideration of this model suggests that: (1) TPG waveform is exclusively dependent upon transvalvular flow rate and flow geometry, (2) the frequently applied simplified Bernoulli equation may overestimate mean TPG by more than 30% and (3) the measurement of ejection time by cardiac catheterization may underestimate the actual ejection time, especially in patients with mild/moderate aortic stenosis and low cardiac output.