Modelling cardiac fluid dynamics and diastolic function. (English) Zbl 0994.92016

Kovács, Sándor J.; McQueen, David M.; Peskin, Charles S.

Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 359, No. 1783, 1299-1314 (2001).

Summary: Two complementary mathematical modelling approaches are covered. They contrast the degree of mathematical and computational sophistication that can be applied to cardiovascular physiology problems and they highlight the differences between a fluid dynamic versus a kinematic (lumped parameter) approach. D.M. McQueen and C.S. Peskin [Comput. Graph. 34, 56-60 (2000); J. Supercomput. 11, No. 3, 213-236 (1997); see also J. Comput. Phys. 81, No. 2, 372-405 (1989; Zbl 0668.76159), ibid. 82, No. 2, 289-297 (1989; Zbl 0701.76130)] model cardiovascular tissue as being incompressible, having essentially uniform mass density, and apply a modified form of the Navier-Stokes equations to the four chambered heart and great vessels. Using a supercomputer their solution provides fluid, wall and valve motion as a function of space and time. Their computed results are consistent with flow attributes observed in vivo via cardiac MRI.
S.J. Kovács [Int. J. Cardiovasc. Med. Sci. 1, 109 ff (1997)] focuses on the physiology of the diastole. The suction pump attribute of the filling ventricle is modelled as a damped harmonic oscillator. The model predicts transmitral flow-velocity as a function of time. Using the contour of the clinical Doppler echocardiographic \(E\)- and \(A\)-wave as input, unique solution of Newton’s Law allows solution of the ‘inverse problem’ of the diastole. The model quantifies diastolic function in terms of model parameters accounting for (lumped) chamber stiffness, chamber viscoelasticity and filling volume. The model permits derivation of novel (thermodynamic) indexes of diastolic function, facilitates non-invasive quantitation of diastolic function and can predict ‘new’ physiology from first principles.

MSC:

92C35	Physiological flow
92-08	Computational methods for problems pertaining to biology

Keywords:

cardiovascular physiology modelling; supercomputer; Doppler echocardiography; cardiology; Navier-Stokes equations