A Kinematic Model of Wave Propagation

John W. Cain, University of Richmond


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.