Modelling cardiac fluid dynamics and diastolic function

Two complementary mathematical modelling approaches are covered. They contr ast the degree of mathematical and computational sophistication that can be applied to cardiovascular physiology problems and they highlight the diffe rences between a fluid dynamic versus kinematic (lumped parameter) approach . McQueen & Peskin model cardiovascular tissue as being incompressible, hav ing essentially uniform mass density, and apply a modified form of the Navi er-Stokes equations to the four chambered heart and great vessels. Using a supercomputer their solution provides fluid, wall and valve motion as a fun ction of space and time. Their computed results are consistent with flow at tributes observed in vivo via cardiac MRI. Kovacs focuses on the physiology of diastole. The suction pump attribute of the filling ventricle is modell ed as a damped harmonic oscillator. The model predicts transmitral flow-vel ocity as a function of time. Using the contour of the clinical Doppler ecoc ardiographic E and A-wave as input, unique solution of Newton's Law allows solution of the 'inverse problem' of diastole. The model quantifies diastol ic function in terms of model parameters accounting for (lumped) chamber st iffness,, chamber viscoelasticity and filling volume. The model permits der ivation of novel (thermodynamic) indexes of diastolic function, facilitates non-invasive quantitation of diastolic function and can predict 'new' phys iology from first principles.