Analytical modeling of the instantaneous maximal transvalvular pressure gradient in aortic stenosis

In presence of aortic stenosis, a jet is produced downstream of the aortic valve annulus during systole. The vena contracta corresponds to the location where the cross-sectional area of the flow jet is minimal. The maximal transvalvular pressure gradient (TPG(max)) is the difference between the static pressure in the left ventricle and that in the vena contracta. TPG(max) 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 left ventricular outflow tract. However, it is still unclear how these parameters modify the TPG(max) waveform. We thus derived an explicit analytical model to describe the instantaneous TPG(max) across the aortic valve during systole. This theoretical model was validated with in vivo experiments obtained in 19 pigs with supravalvular aortic stenosis. Instantaneous TPG(max) was measured by catheter and its waveform was compared with the one determined from the derived equation. Our results showed a very good concordance between the measured and predicted instantaneous TPG(max). Total relative error and mean absolute error were on average 9.4+/-4.9% and 2.1+/-1.1 mmHg, respectively. The analytical model proposed and validated in this study provides new insight into the behaviour of the TPG(max) and thus of the aortic pressure at the level of vena contracta. Because the static pressure at the coronary inlet is similar to that at the vena contracta, the proposed equation will permit to further examine the impact of aortic stenosis on coronary blood flow.