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Full-Text Articles in Biomedical Engineering and Bioengineering
Refraction Of Scroll-Wave Filaments At The Boundary Between Two Reaction-Diffusion Media, Christian W. Zemlin, Frency Varghese, Marcel Wellner, Arkady M. Pertsov
Refraction Of Scroll-Wave Filaments At The Boundary Between Two Reaction-Diffusion Media, Christian W. Zemlin, Frency Varghese, Marcel Wellner, Arkady M. Pertsov
Bioelectrics Publications
We explore the shape and the dynamics of scroll-wave filaments in excitable media with an abruptly changing diffusion tensor, important for cardiac applications. We show that, similar to a beam of light, the filament refracts at the boundary separating domains with different diffusion. We derive the laws of filament refraction and test their validity in computational experiments. We discovered that at small angles to the interface, the filament can become unstable and develop oscillations. The nature of the observed instabilities, as well as overall theoretical and experimental significance of the findings, is discussed.
Frustrated Drift Of An Anchored Scroll-Wave Filament And The Geodesic Principle, Marcel Wellner, Christian W. Zemlin, Arkady M. Pertsov
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 …