Mathematical model that characterizes transmitral and pulmonary venous flow velocity patterns

The transmitral and pulmonary venous flow velocity (TMFV and PVFV, respectively) patterns are related to the physiological state of the left heart by use of an electrical analog model. Filling of left ventricle (LV) through the mitral valve is characterized by a quadratic Bernoulli's resistance in series with an inertance. Filling of the left atrium (LA) through the pulmonary veins is represented by a lumped network of linear resistance, capacitance, and inertance. LV and LA are each represented by a time-varying elastance. A volume dependency is incorporated into the LV model to produce physiological pressure-volume loops and Starling curves. The state-space representation of the analog model consists of 10 simultaneous differential equations, which are solved by numerical integration. Model validity is supported by the following. First, the expected effects of aging and decreasing LV compliance on TMFV and PVFV are accurately represented by the model. Second, the model-generated TMFV and PVFV waveforms fit well to pulsed-Doppler recordings in normal and postinfarct patients. It is shown that the TMFV deceleration time is prolonged by the increase in LV compliance and, to a lesser extent, by the increase in LA compliance. A shift from diastolic dominance to systolic dominance in PVFV occurs when LA compliance or pulmonary perfusion pressure increases or when LV compliance or mitral valve area decreases. The present model should serve as a useful theoretical basis for echocardiographic evaluation of LV and LA functions.