## Abstract

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 kinematic (lumped parameter) approach. McQueen & Peskin 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. Kovács focuses on the physiology of 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 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.

Original language | English (US) |
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Pages (from-to) | 1299-1314 |

Number of pages | 16 |

Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 359 |

Issue number | 1783 |

DOIs | |

State | Published - Jun 15 2001 |

## Keywords

- Cardiology
- Cardiovascular physiology modelling
- Diastole
- Doppler echocardiography
- Navier-Stokes equations
- Supercomputer

## ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)