Journal of Theoretical Medicine
Volume 3 (2001), Issue 4, Pages 221-230

Shape Parameterization of the Time-Dependent Geometry of the Heart for Steady Fluid Dynamical Analysis

Department of Applied Mathematics, University of Leeds, LS2 9JT, UK

Received 8 November 2000; Accepted 15 March 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A parametric model of the complex time-dependent geometry of the ventricles of the human heart is constructed. The geometry model is created by means of a boundary value approach, solving an elliptic partial differential equation to generate a representation of the inner surface of the ventricles. The technique provides a closed-form description of the geometry with the advantage that the geometry can be readily changed without introducing holes or discontinuities in the surface. It also allows a straightforward link to analysis, facilitating the calculation of physical properties such as those relevant to fluid dynamics. As an application of this work, the geometry model is combined with commercial CFD software to analyse the blood flow in the heart. Steady-state calculations are performed at various time steps to follow the evolution of the fluid flow.