2009/08/27 by Radostin D. Simitev, Simitev, R. D., V. N. Biktashev +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Electron Spin Resonance Studies #FOS: Biological sciences #Nonlinear Dynamics and Pattern Formation #Tissues and Organs (q-bio.TO) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.0908.3923
openalex publication_date 2009/08/27 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. 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 compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh-Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified "caricature" of the Noble (1962) model and the Beeler and Reuter (1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler-Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method.