Frustrated drift of an anchored scroll-wave filament and the geodesic principle.
Frustrated drift of an anchored scroll-wave filament and the geodesic principle.
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DOI：
10.1103/physreve.82.036122
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
M. Wellner;C. Zemlin;A. Pertsov
中科院分区：
文献类型：
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作者：
M. Wellner;C. Zemlin;A. Pertsov
我们研究了可兴奋介质中的锚定滚动波细丝，其扩散矩阵（包括其行列式）在空间上不均匀。这项研究的动机是心脏病学应用，其中扩散梯度存在下的滚动波行为被认为在严重心律失常的发展中发挥重要作用。扩散率梯度预计会使细丝漂移，除非通过锚定到传播介质中的局部缺陷来防止（“阻止”）漂移。由此产生的固定细丝是测地曲线，如此处在非零但恒定梯度的情况下所示。也就是说，扩散矩阵具有随空间变化的行列式，这与早期工作中的假设相反。在这里，我们证明细丝形状由 (det D)D{-1} 形式的度量张量产生，其中 D 是扩散率张量。细丝的形状仅由扩散张量决定，并且与方程的反应项无关。我们推导出灯丝的解析解并确定该解存在的条件。该理论与数值模拟非常吻合。
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 (det D)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.