Sun Yi, Rangan Aaditya V, Zhou Douglas, Cai David
Statistical and Applied Mathematical Sciences Institute, 19 T.W. Alexander Drive, P.O. Box 14006, Research Triangle Park, NC 27709, USA.
J Comput Neurosci. 2012 Feb;32(1):55-72. doi: 10.1007/s10827-011-0339-7. Epub 2011 May 20.
We present an event tree analysis of studying the dynamics of the Hodgkin-Huxley (HH) neuronal networks. Our study relies on a coarse-grained projection to event trees and to the event chains that comprise these trees by using a statistical collection of spatial-temporal sequences of relevant physiological observables (such as sequences of spiking multiple neurons). This projection can retain information about network dynamics that covers multiple features, swiftly and robustly. We demonstrate that for even small differences in inputs, some dynamical regimes of HH networks contain sufficiently higher order statistics as reflected in event chains within the event tree analysis. Therefore, this analysis is effective in discriminating small differences in inputs. Moreover, we use event trees to analyze the results computed from an efficient library-based numerical method proposed in our previous work, where a pre-computed high resolution data library of typical neuronal trajectories during the interval of an action potential (spike) allows us to avoid resolving the spikes in detail. In this way, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable statistical accuracy in terms of average firing rate and power spectra of voltage traces. Our numerical simulation results show that the library method is efficient in the sense that the results generated by using this numerical method with much larger time steps contain sufficiently high order statistical structure of firing events that are similar to the ones obtained using a regular HH solver. We use our event tree analysis to demonstrate these statistical similarities.
我们展示了一种用于研究霍奇金-赫胥黎（HH）神经元网络动力学的事件树分析方法。我们的研究依赖于通过对相关生理可观测量的时空序列（如多个神经元的放电序列）进行统计收集，将其粗粒度投影到事件树以及构成这些树的事件链上。这种投影能够快速且稳健地保留关于网络动力学的多方面信息。我们证明，即使输入存在微小差异，HH网络的某些动力学状态在事件树分析中的事件链中也包含足够高阶的统计量。因此，这种分析对于区分输入中的微小差异是有效的。此外，我们使用事件树来分析我们之前工作中提出的一种基于高效库的数值方法所计算的结果，在该方法中，一个预先计算的动作电位（尖峰）间隔期间典型神经元轨迹的高分辨率数据库使我们能够避免详细解析尖峰。通过这种方式，我们可以使用比不使用该数据库解析轨迹时所用的典型时间步长大一阶的时间步长来演化HH网络，同时在平均放电率和电压迹线的功率谱方面实现相当的统计精度。我们的数值模拟结果表明，该库方法是有效的，即使用这种具有大得多的时间步长的数值方法生成的结果包含与使用常规HH求解器获得的结果相似的足够高阶的放电事件统计结构。我们使用事件树分析来展示这些统计相似性。
