Dynamics of systolic pulmonary venous flow in mitral regurgitation: mathematical modeling of the pulmonary venous system and atrium

Abstract

The noninvasive assessment of mitral regurgitation has been an elusive clinical goal. Recent studies have highlighted the value of pulmonary venous (PV) flow reversal in indicating the presence of severe regurgitation. The purpose of this study was to explore the basic determinants of PV inflow in the presence and absence of regurgitation. In particular, the hypothesis that systolic PV flow depends on the interaction of regurgitant volume with atrial and PV properties (compliance, initial volume, total area of the pulmonary veins at the atrial junction, and the inertia of PV inflow) was tested and further, that the combination of these variables, rather than regurgitant volume alone, determines PV inflow. A mathematical model of the atrium and pulmonary veins was developed. Atrial and PV pressure were modeled as the product of chamber elastance and volume, where atrial elastance varied in time to simulate atrial relaxation and descent of the mitral anulus. A simplification of the modified unsteady Bernoulli equation was used to compute the PV velocities that resulted from the developed pressure gradient. The modeling was performed over a range of initial atrial elastances (0.77 to 0.2 mm Hg/cc), initial atrial volumes (20 to 75 cc), total PV areas (3.12 to 5.12 cm2), and PV inflow inertances (8 to 18 gm/cm2), with and without the addition of two regurgitant jets (regurgitant volume of 20 and 60 cc). The model realistically simulated the systolic PV waveform in magnitude and morphology. As the volume of regurgitation increased, PV peak flow velocity decreased, and eventually late systolic flow reversal occurred. However, the peak flow velocity, the time to peak flow, and the presence and magnitude of flow reversal were influenced by atrial compliance, volume, total atrial inlet area, and PV inflow inertia. This study found that PV flow blunting and reversal increased as atrial compliance, volume, and PV inertia decreased and as atrial inlet area increased. Atrial and PV properties (compliance, volume, total PV atrial inlet area, and PV inflow inertia), acting in combination, mediate the physiologic impact of the regurgitant lesion in terms of the resulting rise in atrial pressure as reflected by the pattern of systolic PV influx. For example, PV flow reversal is more likely in acute compared with chronic regurgitation because the atrium is less compliant and has a smaller initial volume. Therefore, the clinical assessment of mitral regurgitation using changes in systolic PV flow must be viewed in the context of atrial and PV properties.