Numerical study of flow through models of aortic valve stenoses and assessment of Gorlin equation

Gorlin equation has been applied in clinical practice for evaluating the aortic valve area (AVA) of vascular and aortic valve stenosis for past sixty years [1]. It was derived using the Bernoulli equation across the stenosis with the assumption that the velocity of the fluid behind the stenosis is much greater than the velocity upstream of the stenosis. Because of this assumption, the calculated stenosed area may have large error if the flow rate across the valve is low or the stenosis is mild [2]. In a recent paper, Okpara and Agarwal [3] proposed a new equation (Agarwal - Okpara equation) which significantly decreases the evaluation error compared to the Gorlin Equation. The purpose of this paper is to modify the Agarwal - Okpara equation to generalize its applicability based on additional data calculated from the commercial CFD software FLUENT as well as the clinical data obtained from the literature. A total of ten cases are computed using CFD to assess the range of validity of the Gorlin equation and the Agarwal - Okpara equation. In addition, eighty clinical data points were obtained from the papers of Minners et al. [4] and Hakii et al. [5] covering a large range of severity of stenosis. The error in AVA computed from Gorlin equation and Agarwal - Okpara equation varied from 7.44 to 82.14% and 0.06 to 27.26% respectively compared to the CFD simulation data, and 41.47 to 83.60% and 8.88 to 33.98% respectively compared to the clinical data; however, AVA calculated using the Agarwal - Okpara - Bao equation presented in this paper gives results within 0.42 to 9.6% error compared to the exact AVA used in FLUENT simulations, and from 4.76 to 24.13% compared to the clinical data. The Agarwal - Okpara - Bao equation agrees with the clinical data for all relevant flow rates and full range of severity of stenosis. Thus, the use of Agarwal - Okpara -Bao equation to evaluate AVA in clinical practice is suggested.