TY - JOUR
T1 - Frustrated drift of an anchored scroll-wave filament and the geodesic principle
AU - Wellner, Marcel
AU - Zemlin, Christian
AU - Pertsov, Arkady M.
PY - 2010/9/30
Y1 - 2010/9/30
N2 - 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 varies in space, in contrast to what was assumed in earlier work. Here, we show that the filament shape results from a metric tensor of the form (detD) D-1, where D is the diffusivity tensor. The filament's shape is solely determined by the diffusivity tensor and is independent of the equation's reaction terms. We derive the analytic solution for the filament and determine conditions for the existence of that solution. The theory is in excellent agreement with numerical simulations.
AB - 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 varies in space, in contrast to what was assumed in earlier work. Here, we show that the filament shape results from a metric tensor of the form (detD) D-1, where D is the diffusivity tensor. The filament's shape is solely determined by the diffusivity tensor and is independent of the equation's reaction terms. We derive the analytic solution for the filament and determine conditions for the existence of that solution. The theory is in excellent agreement with numerical simulations.
UR - http://www.scopus.com/inward/record.url?scp=78651262900&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.82.036122
DO - 10.1103/PhysRevE.82.036122
M3 - Article
C2 - 21230154
AN - SCOPUS:78651262900
SN - 1539-3755
VL - 82
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 3
M1 - 036122
ER -