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.
Copyright © 2008 Academic Publications Ltd. This article first appeared in International Journal of Pure and Applied Mathematics 49:4 (2008), 599-605.
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Cain, John W. "A Kinematic Model of Wave Propagation." International Journal of Pure and Applied Mathematics 49, no. 4 (2008): 599-605.