Development of a 1D Model for Assessing the Aortic Root Pressure Drop With Viscosity and Compliance

Aging and some pathologies such as arterial hypertension, diabetes, hyperglycemia, and hyperinsulimenia cause some geometrical and mechanical changes in the aortic valve microstructure. Cupsal thickening and lost of extensibility (increasing stiffness) are the consequences of these changes in the aortic valve which have a negative impact on the function of the valve [1]. The most frequent form of diseases of the aortic valve is the calcific aortic stenosis which is responsible for 80% of the North American deaths due to valvular heart diseases [2]. In this pathology, calcified nodules on the valve leaflets occur which lead to the thickening and stiffening of the leaflets and restricting the natural motion of the valve which presents an increased resistance to forward blood flow during the ejection phase of the cardiac cycle. To reduce the mortality and morbidity from the aortic stenosis, clinical management and proper diagnosis are essential [3]. Tranvalvular pressure gradient (TPG) and the effective orifice area (EOA), the minimum cross sectional area of the blood flow across the stenosis, are the most commonly used indices for assessing the aortic stenosis [4]. Numerous studies have been done to relate the TPG across the stenosis to the blood flow rate and EOA. Gorlin (1951) was the first to establish a relationship between TPG and EOA [5]. Several studies have reported deviations in valve area calculation by using Gorlin formula. This formula was derived based on some assumptions such as rigid circular orifice, non viscous and steady flow, while valvular orifices are compliant and the flow through them is viscous and pulsatile [6]. Several corrections have been proposed. However, even with these improved formula, significant deviations are still reported [7]. Calark (1978), Bermejo et al (2002) and Garcia et al (2006), by presenting a theoretical model, tried to express TPG in terms of the blood flow rate and EOA [8–10]. None of these studies considered the effect of the aortic root compliance on TPG. Nobari et al reported that the stiffening of the aorta changes the pressure drop and affects the leaflets motion [11]. Therefore, the objective of this study is to develop a 1D model for assessing the aortic pressure drop for the transient viscous blood flow across the aortic stenosis, by taking into account the vessel wall compliance. The derived TPG will be expressed in terms of the surrogate variables which are anatomical and hemodynamic data meaningful and accessible for physicians.

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