Computer Simulation of Intraventricular Flow and Pressure Gradients During Diastole

Abstract

A two-dimensional axisymmetric computer model is developed for the simulation of the filling flow in the left ventricle (LV). The computed results show that vortices are formed during the acceleration phases of the filling waves. During the deceleration phases these are amplified and convected into the ventricle. The ratio of the maximal blood velocity at the mitral valve (peak E velocity) to the flow wave propagation velocity (WPV) of the filling wave is larger than 1. This hemodynamic behavior is also observed in experiments in vitro (Steen and Steen, 1994, Cardiovasc. Res., 28, pp. 1821-1827) and in measurements in vivo with color M-mode Doppler echocardiography (Stugaard et al., 1994, J. Am. Coll. Cardiol., 24, 663-670). Computed intraventricular pressure profiles are similar to observed profiles in a dog heart (Courtois et al., 1988, Circulation, 78, pp. 661-671). The long-term goal of the computer model is to study the predictive value of noninvasive parameters (e.g., velocities measured with Doppler echocardiography) on invasive parameters (e.g., pressures, stiffness of cardiac wall, time constant of relaxation). Here, we show that higher LV stiffness results in a smaller WPV for a given peak E velocity. This result may indicate an inverse relationship between WPV and LV stiffness, suggesting that WPV may be an important noninvasive index to assess LV diastolic stiffness, LV diastolic pressure and thus atrial pressure (preload).

Diastolic Filling and Pressure Imaging: Taking Advantage of the Information in a Colour M-mode Doppler Image

“…This concept is illustrated in Fig. 3 Vierendeels et al [46] , using a numerical model, confirmed this close relationship between the position of the vortex core and the position of the maximum velocities along the base-apex axis.…”

“…Phase II is the propagation of the maximum velocity that can be associated with the propagation of a vortex ring as described before. The biphasic filling pattern is observed in vitro [45] , in numero [46] and in vivo [30,41,49,50] .…”

“…The higher peak E-velocity, compared to v p , is observed in vitro and in numero [42][43][44][45][46] , and in vivo [47][48][49] .…”

“…Courtois et al [79] observed a significant sub-basal-apical early diastolic pressure gradient along the left ventricular inflow tract with minimum pressure in the apex speculating suction of the blood toward the left ventricular apex. In contrast, using a 1D numerical model, Verdonck et al [80] , and using an axisymmetric three-dimensional model, Vierendeels et al [46] demonstrated that such pressure gradients are not a rigorous proof of elastic recoil. Intra-ventricular pressure gradients yield potential important clinical useful information.…”

Fluid Flow inside Deformable Vessels and in the Left Ventricle

“…An intriguing aspect of the left heart dynamics is the hypothesised occurrence of diastolic vortices within the ventricular chamber. Their presence and properties have been analyzed in theoretical (Reul et al, 1981;Wieting & Stripling, 1984), experimental (Steen & Steen, 1994), and numerical models (Vierendeels et al, 2000;Baccani et al, 2002 ), and introduced also in medical observations (Kim et al, 1994;Kim et al, 1995;ab Kilner et al, 2000). The presence of vorticity makes the fluid dynamics approach relevant for the understanding of the possible patterns and their relation with the mechanical properties of the surrounding tissues.…”