Numerical modeling of ventricular filling

The fluid dynamical and physiological assumptions underlying general mathematical modeling of ventricular filling are outlined. We then describe the use of a lumped parameter model and computer simulation to study how the early transmitral velocity profile is affected by isolated changes in ventricular compliance and relaxation, atrial pressure and compliance, and valvular morphology. We show that the transmitral velocity is fundamentally affected by two physical determinants: the transmitral pressure difference and the net compliance of the atrium and the ventricle. These physical determinants in turn are specified by the various physiologic parameters of interest. This approach has shown that peak velocity is most strongly affected by initial left atrial pressure, lowered somewhat by prolonged relaxation, low atrial and ventricular compliance, and systolic dysfunction. Peak acceleration is directly affected by atrial pressure and inversely affected by the time constant of isovolumic relaxation, with little influence of compliance, whereas the deceleration rate is almost purely given by mitral valve area divided by instantaneous atrioventricular compliance at the end of the rapid filling wave.