Biomedical Engineering and Bioengineering Commons^™

Frustrated Drift Of An Anchored Scroll-Wave Filament And The Geodesic Principle, Marcel Wellner, Christian W. Zemlin, Arkady M. Pertsov

Bioelectrics Publications

We investigate anchored scroll-wave filaments in an excitable medium whose diffusivity matrix, including its determinant, is spatially nonuniform. The study is motivated by cardiological applications where scroll-wave behavior in the presence of diffusivity gradients is believed to play an important role in the development of severe arrhythmias. A diffusivity gradient is expected to make the filament drift, unless drift is prevented ("frustrated") by anchoring to localized defects in the propagation medium. The resulting stationary filament is a geodesic curve, as demonstrated here in the case of a nonzero but constant gradient. That is, the diffusivity matrix has a determinant that …