Healthy brain function is marked by neuronal network dynamics at or near the critical phase, which separates regimes of instability and stasis. A failure to remain at this critical point can lead to neurological disorders such as epilepsy, which is associated with pathological synchronization of neuronal oscillations. Using full Hodgkin-Huxley (HH) simulations on a Small-World Network, we are able to generate synthetic electroencephalogram (EEG) signals with intervals corresponding to seizure (ictal) or non-seizure (interictal) states that can occur based on the hyperexcitability of the artificial neurons and the strength and topology of the synaptic connections between them. These interictal simulations can be further classified into scale-free critical phases and disjoint subcritical exponential phases. By changing the HH parameters, we can model seizures due to a variety of causes, including traumatic brain injury (TBI), congenital channelopathies, and idiopathic etiologies, as well as the effects of anticonvulsant drugs. The results of this work may be used to help identify parameters from actual patient EEG or electrocorticographic (ECoG) data associated with ictogenesis, as well as generating simulated data for training machine-learning seizure prediction algorithms.

中文翻译：

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小世界网络上模拟 EEG 信号的临界和发作阶段

健康的大脑功能的标志是处于或接近关键阶段的神经元网络动态，它将不稳定和停滞状态分开。未能保持在这个临界点可能导致神经系统疾病，如癫痫，这与神经元振荡的病理同步有关。在小世界网络上使用完整的霍奇金 - 赫胥黎 (HH) 模拟，我们能够生成合成脑电图 (EEG) 信号，其间隔对应于癫痫发作（发作）或非癫痫发作（发作间期）状态，基于过度兴奋可能发生人工神经元的数量以及它们之间突触连接的强度和拓扑结构。这些间歇模拟可以进一步分为无标度临界阶段和不相交的亚临界指数阶段。通过改变 HH 参数，我们可以模拟由于各种原因引起的癫痫发作，包括外伤性脑损伤 (TBI)、先天性通道病和特发性病因，以及抗惊厥药物的作用。这项工作的结果可用于帮助识别与 ictogenesis 相关的实际患者 EEG 或皮层电图 (ECoG) 数据的参数，以及生成用于训练机器学习癫痫预测算法的模拟数据。