A ventricular-vascular coupling model in presence of aortic stenosis

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 ventricular-valvular-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 = 0.99x - 2.36 with a coefficient of determination r(2) = 0.98. There was also very good agreement between estimated and measured stroke volumes (y = 1.03x + 2.2, r(2) = 0.96, SEE = 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.