Fragility in Dynamic Networks: Application to Neural Networks in the Epileptic Cortex
Fragility in Dynamic Networks: Application to Neural Networks in the Epileptic Cortex
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DOI：
10.1162/neco_a_00644
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发表时间：
2014-10-01
影响因子：
2.9
通讯作者：
Sarma, Sridevi V.
中科院分区：
文献类型：
--
作者：
Sritharan, Duluxan;Sarma, Sridevi V.
癫痫是一种网络现象，其特征在于癫痫发作期间神经元和群体水平的非典型活动，包括强直性尖峰、尖峰速率异质性增加和同步化。癫痫的病因尚不清楚，但提出的机制中的一个共同主题是神经元之间的结构连接被改变。据推测，癫痫不是由连接性的随机变化引起的，而是由网络中最脆弱的节点或神经元的特定结构变化引起的。在这封信中，最小能量扰动功能连接所需的线性网络不稳定的推导。然后将扰动结果应用于在稳定固定点处操作的概率非线性神经网络模型。也就是说，如果对网络施加一个小的刺激，每个神经元的激活概率会短暂地做出反应，但最终会恢复到它们的基线值。当扰动网络不稳定时，激活概率会转移到更大或更小的值，或者在施加小刺激时振荡。最后，结构修改的神经网络，实现功能的扰动。未扰动和扰动网络的模拟定性地反映了癫痫患者中观察到的神经元活动，这表明由于不稳定扰动导致的网络动力学变化，包括出现不稳定流形或稳定极限环，可能指示癫痫发作期间的神经元或群体动力学。也就是说，癫痫皮层总是处于不稳定的边缘，与最脆弱的节点相关的突触权重的微小变化可能会突然破坏网络的稳定，导致癫痫发作。最后，这里开发的理论及其对癫痫网络的解释使得能够设计一个简单的反馈控制器，该控制器首先检测网络何时不稳定，然后应用线性状态反馈控制来引导网络回到稳定状态。
Epilepsy is a network phenomenon characterized by atypical activity at the neuronal and population levels during seizures, including tonic spiking, increased heterogeneity in spiking rates, and synchronization. The etiology of epilepsy is unclear, but a common theme among proposed mechanisms is that structural connectivity between neurons is altered. It is hypothesized that epilepsy arises not from random changes in connectivity, but from specific structural changes to the most fragile nodes or neurons in the network. In this letter, the minimum energy perturbation on functional connectivity required to destabilize linear networks is derived. Perturbation results are then applied to a probabilistic nonlinear neural network model that operates at a stable fixed point. That is, if a small stimulus is applied to the network, the activation probabilities of each neuron respond transiently but eventually recover to their baseline values. When the perturbed network is destabilized, the activation probabilities shift to larger or smaller values or oscillate when a small stimulus is applied. Finally, the structural modifications to the neural network that achieve the functional perturbation are derived. Simulations of the unperturbed and perturbed networks qualitatively reflect neuronal activity observed in epilepsy patients, suggesting that the changes in network dynamics due to destabilizing perturbations, including the emergence of an unstable manifold or a stable limit cycle, may be indicative of neuronal or population dynamics during seizure. That is, the epileptic cortex is always on the brink of instability and minute changes in the synaptic weights associated with the most fragile node can suddenly destabilize the network to cause seizures. Finally, the theory developed here and its interpretation of epileptic networks enables the design of a straightforward feedback controller that first detects when the network has destabilized and then applies linear state feedback control to steer the network back to its stable state.