Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, 600 N Wolfe Street, Carnegie 568, Baltimore, MD, USA.
Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, 600 N Wolfe Street, Carnegie 568, Baltimore, MD, USA; IHU Liryc, Electrophysiology and Heart Modeling Institute, Fondation Bordeaux Université, F-33600, Pessac-Bordeaux, France.
Comput Biol Med. 2019 Jan;104:291-298. doi: 10.1016/j.compbiomed.2018.11.005. Epub 2018 Nov 14.
Spiral waves are considered to be one of the potential mechanisms that maintain complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the organizing manifolds of information flow at multiple scales.
We simulated spiral waves using a numerical model of cardiac excitation in a two-dimensional (2-D) lattice. We created a renormalization group by coarse graining and re-scaling the original time series in multiple spatiotemporal scales, and quantified the Lagrangian coherent structures (LCS) of the information flow underlying the spiral waves. To quantify the scale-invariant structures, we compared the value of the finite-time Lyapunov exponent between the corresponding components of the 2-D lattice in each spatiotemporal scale of the renormalization group with that of the original scale.
Both the repelling and the attracting LCS changed across the different spatial and temporal scales of the renormalization group. However, despite the change across the scales, some LCS were scale-invariant. The patterns of those scale-invariant structures were not obvious from the trajectory of the spiral waves based on voltage mapping of the lattice.
Some Lagrangian coherent structures of information flow underlying spiral waves are preserved across multiple spatiotemporal scales.
螺旋波被认为是维持复杂心律失常（如心房和心室颤动）的潜在机制之一。本研究的目的是定量螺旋波的复杂动力学，作为信息流在多个尺度上的组织流形。
我们使用二维（2-D）晶格中心脏兴奋的数值模型来模拟螺旋波。我们通过粗粒化和重新缩放原始时间序列在多个时空尺度上创建重整化群，并量化螺旋波下信息流的拉格朗日相干结构（LCS）。为了量化具有标度不变性的结构，我们将重整化群中每个时空尺度上的 2-D 晶格对应分量的有限时间李雅普诺夫指数值与原始尺度上的该值进行比较。
排斥和吸引 LCS 都在重整化群的不同时空尺度上发生变化。然而，尽管存在尺度上的变化，但有些 LCS 是具有标度不变性的。基于晶格的电压映射，这些具有标度不变性结构的模式并不明显。
螺旋波下信息流的一些拉格朗日相干结构在多个时空尺度上得到了保持。
