IJPAM: Volume 49, No. 4 (2008)

A KINEMATIC MODEL OF WAVE PROPAGATION

John W. Cain
Department of Mathematics
Virginia Commonwealth University
Monte Park Campus, P.O. Box 843 083
1001, W. Main Street, Richmond, Virginia, 23284-2014, USA
e-mail: jwcain@vcu.edu


Abstract.We present a purely kinematic model of wave propagation in an excitable medium, namely cardiac tissue. The kinematic model is constructed from a standard reaction-diffusion model, using asymptotic techniques to track the position and velocity of each propagating wave front and wave back. The kinematic model offers a substantial improvement in computational efficiency without sacrificing the ability to predict the onset of certain arrhythmias. Moreover, the linearized kinematic model equations can be solved exactly in terms of generalized Laguerre polynomials, allowing us to extract valuable physiological information.

Received: August 14, 2008

AMS Subject Classification: 92C50, 33C45, 92C30

Key Words and Phrases: cardiac fiber, pacing, restitution, kinematic model, generalized Laguerre polynomials

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 4