NSC Seminar Instabilities of Reaction-Diffusion Waves in 2D and 3D Excitable Media: From Spiral Breakup and Scroll Waves to Cardiac Alternans Part I

2007-05-02 13:30 - 2007-05-02 15:00
Prof. Markus Baer (Mathematical Modeling and Data Analysis, Physikalisch-Technische Bundesanstalt (PTB), Berlin. Germany)
Reaction-diffusion patterns often show dramatic changes in behaviour like the transition from regular spiral patterns to chemical turbulence via spiral breakupin 2D or the emergence of Winfree turbulence due to negative linetension in filaments in 3D. Here, we try to link such phenomena found inexperiments and simulations with linear stability analysis of regularpatterns like wavetrains, rotating spiral and scroll waves. Inparticular, it is shown, that different spiral breakup scenarios resultfrom different linear instabilities of rotating spirals. In 3D systems,we analyse experimental data from the Magdeburg biophysics group andrelate the observations to particular scroll wave instabilities like 3Dmeandering or negative line tension with the help of numericalsimulations. Finally, qualitatively different dynamics in paced 3Dcardiac tissue obtained with the modified Beeler-Reuter model inrealistic geometries are considered. Here, 3D simulations aresupplemented by a numerical linear stability analysis of so-calledT-wave alternans, which allows the test of the well-known restitutionhypothesis and a quick scanning of the model in the parameter space asinput for 3D simulations.