Department of Physics, University of California, San Diego, La Jolla, California 92093, USA.
Phys Rev E. 2019 Jan;99(1-1):012407. doi: 10.1103/PhysRevE.99.012407.
Spatially extended excitable systems can exhibit spiral defect chaos (SDC) during which spiral waves continuously form and disappear. To address how this dynamical state terminates using simulations can be computationally challenging, especially for large systems. To circumvent this limitation, we treat the number of spiral waves as a stochastic population with a corresponding birth-death equation and use techniques from statistical physics to determine the mean episode duration of SDC. Motivated by cardiac fibrillation, during which the heart's electrical activity becomes disorganized and shows fragmenting spiral waves, we use generic models of cardiac electrophysiology. We show that the duration can be computed in minimal computational time and that it depends exponentially on domain size. Therefore, the approach can result in efficient and accurate predictions of mean episode duration which may be extended to more complex geometries and models.
空间扩展的兴奋系统在其过程中会表现出螺旋缺陷混沌（SDC），在此期间，螺旋波会不断形成和消失。使用模拟来确定这种动态状态的终止方式在计算上可能具有挑战性，特别是对于大型系统。为了规避这一限制，我们将螺旋波的数量视为具有相应的生死方程的随机种群，并使用统计物理学的技术来确定 SDC 的平均发作持续时间。受心动纤维性颤动的启发，在这种情况下，心脏的电活动变得紊乱，并表现出碎片化的螺旋波，我们使用了心脏电生理学的通用模型。我们表明，在最小的计算时间内可以计算出持续时间，并且它与域大小呈指数关系。因此，该方法可以有效地预测平均发作持续时间，并可以将其扩展到更复杂的几何形状和模型。
