Derivation of a simplified relation for assessing aortic root pressure drop incorporating wall compliance

Aging and some pathologies such as arterial hypertension, diabetes, hyperglycemia, and hyperinsulinemia cause some geometrical and mechanical changes in the aortic valve microstructure which contribute to the development of aortic stenosis (AS). Because of the high rate of mortality and morbidity, assessing the impact and progression of this disease is essential. Systolic transvalvular pressure gradient (TPG) and the effective orifice area are commonly used to grade the severity of valvular dysfunction. In this study, a theoretical model of the transient viscous blood flow across the AS is derived by taking into account the aorta compliance. The derived relation of the new TPG is expressed in terms of clinically available surrogate variables (anatomical and hemodynamic data). The proposed relation includes empirical constants which need to be empirically determined. We used a numerical model including an anatomically 3D geometrical model of the aortic root including the sinuses of Valsalva for their identification. The relation was evaluated using clinical values of pressure drops for cases for which the modified Gorlin equation is problematic (low flow, low gradient AS).