Amplitude equation approach to spatiotemporal dynamics of cardiac alternans
Amplitude equation approach to spatiotemporal dynamics of cardiac alternans
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DOI：
10.1103/physreve.76.051911
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发表时间：
2007-11-01
影响因子：
2.4
通讯作者：
Karma, Alain
中科院分区：
文献类型：
--
作者：
Echebarria, Blas;Karma, Alain
振幅方程描述了周期性起搏期间心脏交替的时空动力学。Echebarria和A. Karma，物理学家。与二维同质组织和一维同质组织环的解剖再入。这些方程提供了一个简单的物理理解，动作电位持续时间的周期振荡具有空间变化的相位和振幅，以及明确的定量预测，可以与离子模型模拟或实验进行比较。该方程的形式有望适用于大量的离子模型，但系数仅对双变量离子模型进行了解析推导，并对浦肯野纤维动作电位的原始Noble模型进行了数值计算。在有节奏的组织中，这一理论解释了通过线性不稳定机制形成“空间不协调交替体”，该机制产生交替体的非相位域的周期性模式。该模式的波长等于分离非相域的节点间距的两倍，它取决于由细胞间耦合强度和传导速度（CV）恢复决定的三个基本长度尺度。此外，交替的模式可以是固定节点的平稳模式，也可以是移动节点的移动模式，因此动作电位持续时间的准周期振荡，这取决于CV恢复的不稳定效应和扩散耦合的稳定效应的相对强度。对于环的几何形状，我们恢复了Courtemanche， Glass和Keener [Phys]的结果。由于细胞间扩散偶联，有两个重要的修改。首先，这种耦合打破了无限维Hopf分岔的简并性，使得交替的最不稳定模式对应于环的最长量子化波长。其次，Hopf频率决定了节点沿环的速度，它取决于CV恢复的陡峭度和这种耦合的强度，最终结果是准周期行为可以在恒定的传导速度下出现。在有节奏的几何形状和环状结构中，组织中交替的发生与有节奏的孤立细胞不同。简要讨论了这些结果对二维再入过程中交替动力学的影响。
Amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during periodic pacing of one- [B. Echebarria and A. Karma, Phys. Rev. Lett. 88, 208101 (2002)] and two-dimensional homogeneous tissue and one-dimensional anatomical reentry in a ring of homogeneous tissue. These equations provide a simple physical understanding of arrhythmogenic patterns of period-doubling oscillations of action potential duration with a spatially varying phase and amplitude, as well as explicit quantitative predictions that can be compared to ionic model simulations or experiments. The form of the equations is expected to be valid for a large class of ionic models but the coefficients are derived analytically only for a two-variable ionic model and calculated numerically for the original Noble model of Purkinje fiber action potential. In paced tissue, this theory explains the formation of "spatially discordant alternans" by a linear instability mechanism that produces a periodic pattern of out-of-phase domains of alternans. The wavelength of this pattern, equal to twice the spacing between nodes separating out-of-phase domains, is shown to depend on three fundamental length scales that are determined by the strength of cell-to-cell coupling and conduction velocity (CV) restitution. Moreover, the patterns of alternans can be either stationary, with fixed nodes, or traveling, with moving nodes and hence quasiperiodic oscillations of action potential duration, depending on the relative strength of the destabilizing effect of CV restitution and the stabilizing effect of diffusive coupling. For the ring geometry, we recover the results of Courtemanche, Glass, and Keener [Phys. Rev. Lett. 70, 2182 (1993)] with two important modifications due to cell-to-cell diffusive coupling. First, this coupling breaks the degeneracy of an infinite-dimensional Hopf bifurcation such that the most unstable mode of alternans corresponds to the longest quantized wavelength of the ring. Second, the Hopf frequency, which determines the velocity of the node along the ring, depends both on the steepness of CV restitution and the strength of this coupling, with the net result that quasiperiodic behavior can arise with a constant conduction velocity. In both the paced geometries and the ring, the onset of alternans is different in tissue than for a paced isolated cell. The implications of these results for alternans dynamics during two-dimensional reentry are briefly discussed.