Monday 18 Nov 2013Conduction velocity restitution in models of electrical excitation in the heart (Taylor and Francis sponsored)

Radostin Simitev - University of Glasgow

Harrison 101 15:00-16:00

Conduction velocity restitution is the simplest nontrivial spatially
extended problem in excitable media, and in the case of cardiac tissue it
is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a nonlinear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We propose a non-Tikhonov asymptotic embedding of a typical single-cell ionic model of cardiac excitability and an asymptotic method for calculation of conduction velocity restitution curves. We take particular care to demonstrate the well-posedness of the corresponding boundary-value problem. We highlight mathematical features specific to cardiac excitation models and possible applications of the developed method.

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