A ventricular-vascular coupling model in presence of aortic stenosis

Abstract

In patients with aortic stenosis, the left ventricular afterload is determined by the degree of valvular obstruction and the systemic arterial system. We developed an explicit mathematical model formulated with a limited number of independent parameters that describes the interaction among the left ventricle, an aortic stenosis, and the arterial system. This ventricularvalvular-vascular (V 3 ) model consists of the combination of the time-varying elastance model for the left ventricle, the instantaneous transvalvular pressure-flow relationship for the aortic valve, and the three-element windkessel representation of the vascular system. The objective of this study was to validate the V 3 model by using pressure-volume loop data obtained in six patients with severe aortic stenosis before and after aortic valve replacement. There was very good agreement between the estimated and the measured left ventricular and aortic pressure waveforms. The total relative error between estimated and measured pressures was on average (standard deviation) 7.5% (SD 2.3) and the equation of the corresponding regression line was y ϭ 0.99x Ϫ 2.36 with a coefficient of determination r 2 ϭ 0.98. There was also very good agreement between estimated and measured stroke volumes (y ϭ 1.03x ϩ 2.2, r 2 ϭ 0.96, SEE ϭ 2.8 ml). Hence, this mathematical V 3 model can be used to describe the hemodynamic interaction among the left ventricle, the aortic valve, and the systemic arterial system. mathematical modeling; cardiovascular system; cardiac catheterization; left ventricle LEFT VENTRICULAR (LV) pressure, aortic pressure, and cardiac output result from a matching among the oxygen demand of the body, the LV performance, and the LV afterload. The presence of an aortic valve stenosis causes an obstruction to LV outflow, thus resulting in an increase in LV afterload (20). Patients with aortic stenosis also often have concomitant diseases, including hypertension, hyperlipidemia, diabetes, and atherosclerosis (1,6,22,25). These diseases have been shown to alter the structural and functional properties of the systemic arterial system (8,40). More specifically, they may reduce arterial elasticity and/or increase arteriolar resistance. Hence in patients with aortic stenosis, the left ventricle is often facing a double load: a valvular load imposed by the aortic stenosis and an arterial load caused by a decrease in systemic arterial compliance (C) and/or an increase in systemic vascular resistance (R). Briand et al. (3) have recently shown that reduced C is a frequent occurrence in patients with aortic stenosis where it independently contributes to increase afterload and decrease LV function. In addition, Antonini-Canterin et al. (1) have reported that symptoms of aortic stenosis develop at a lesser degree of valvular obstruction in hypertensive compared with normotensive patients. It is thus important to assess the respective contributions of the aortic valve and the systemic arterial system to the LV workload in such patients. This information could be ...

Systemic Arterial Response to Exercise in Patients With Aortic Valve Stenosis

“…In general, this blunted stroke response has been attributed to abnormal left ventricular filling dynamics, 26 -30 although the role of increased afterload has been much discussed. [31][32][33][34] More recently, there has been increased interest in the relationship between systemic arterial hemodynamics and measures of stenosis severity 12,13,15,35 and ventricular function. 12,13 The latter studies were performed under resting conditions; thus, extrapolation to the exercise state is problematic.…”

“…12,13 However, the dependence of arterial compliance on arterial pressure, intrinsic arterial wall pathology, age, and other clinical conditions is likely to confound any association between compliance and ventricular performance. Likewise, studies of patients in the resting state provide no insight into the behavior of compliance on exercise or the clinical and hemodynamic significance of physiological perturbations in compliance.…”

Multi-scale modeling of the human cardiovascular system with applications to aortic valvular and arterial stenoses

“…In the case of severe AV stenosis, the transvalvular pressure drop is dominated by the energy loss associated with a sudden flow expansion from the vena contracta to the ascending aorta. In this study, we adopted the model proposed by Garcia et al [8][9][10], in which the pressure drop (DP av ) is expressed as a function of the transvalvular flow rate (Q av ), the cross-sectional area of the flow jet at the vena contracta [generally termed effective orifice area (EOA)], and the cross-sectional area of the ascending aorta (A ao ):…”

The Future of Cardiovascular Imaging

“…Una enfermedad común tal como la hipertensión con estenosis aórtica eleva la impedancia en serie y, cuando se acopla con aumento de la rigidez aórtica, acompaña al envejecimiento y la ateroesclerosis y contribuye a la carga del VI y el desarrollo de los síntomas en una forma importante. [31][32][33][34][35] Los avances en las imágenes están ahora permitiendo una comprensión más profunda de la biopatología de la enfermedad más que simplemente una comprensión de las consecuencias hemodinámicas de la enfermedad valvular. Un objetivo de la imagen multimodal es facilitar el diagnóstico temprano así como potencialmente afectar su progreso.…”