Pathological pattern formation and cortical propagation of epileptic seizures
Pathological pattern formation and cortical propagation of epileptic seizures
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DOI：
10.1098/rsif.2004.0028
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发表时间：
2005-03-22
影响因子：
3.9
通讯作者：
Szeri, AJ
中科院分区：
文献类型：
--
作者：
Kramer, MA;Kirsch, HE;Szeri, AJ
Steyn-Ross 及其同事提出的随机偏微分方程（SPDE）构成了人类皮层介观电活动的模型。忽略空间变化和随机输入的简化产生常微分方程（ODE），它可以通过动力系统理论技术进行分析。针对皮层下激励增加的常微分方程开发了分岔图，表明该模型可以预测大范围参数中的振荡电活动。完整的 ISPDE 具有增加的皮层下兴奋，产生电活动的行波。将这些模型结果与在癫痫发作的人类受试者的两个硬膜下电极记录的皮层电数据进行比较。模型和观测结果在癫痫发作期间在两个重要方面一致：（i）最大功率的平均频率，以及（ii）电压峰值的空间传播速度。这表明人类皮质上的夺取活动可以被理解为病理模式形成的一个例子。其中包括对这些结果的应用和局限性的讨论。
The stochastic partial differential equations (SPDEs) stated by Steyn-Ross and co-workers constitute a model of mesoscopic electrical activity of the human cortex. A simplification in which spatial variation and stochastic input are neglected yields ordinary differential equations (ODEs), which are amenable to analysis by techniques of dynamical systems theory. Bifurcation diagrams are developed for the ODEs with increased subcortical excitation, showing that the model predicts oscillatory electrical activity in a large range of parameters. The full ISPDEs with increased subcortical excitation produce travelling waves of electrical activity. These model results are compared with electrocortical data recorded at two subdural electrodes from a human subject undergoing a seizure. The model and observational results agree in two important respects during seizure: (i) the average frequency of maximum power, and (ii) the speed of spatial propagation of voltage peaks. This suggests that seizing activity on the human cortex may be understood as an example of pathological pattern formation. Included is a discussion of the applications and limitations of these results.