González-Ramírez Laura R, Ahmed Omar J, Cash Sydney S, Wayne C Eugene, Kramer Mark A
Department of Mathematics and Statistics, Boston University, Boston, Massachusetts, United States of America.
Department of Neurology, Massachusetts General Hospital, Boston, Massachusetts, United States of America; Harvard Medical School, Boston, Massachusetts, United States of America.
PLoS Comput Biol. 2015 Feb 17;11(2):e1004065. doi: 10.1371/journal.pcbi.1004065. eCollection 2015 Feb.
Epilepsy--the condition of recurrent, unprovoked seizures--manifests in brain voltage activity with characteristic spatiotemporal patterns. These patterns include stereotyped semi-rhythmic activity produced by aggregate neuronal populations, and organized spatiotemporal phenomena, including waves. To assess these spatiotemporal patterns, we develop a mathematical model consistent with the observed neuronal population activity and determine analytically the parameter configurations that support traveling wave solutions. We then utilize high-density local field potential data recorded in vivo from human cortex preceding seizure termination from three patients to constrain the model parameters, and propose basic mechanisms that contribute to the observed traveling waves. We conclude that a relatively simple and abstract mathematical model consisting of localized interactions between excitatory cells with slow adaptation captures the quantitative features of wave propagation observed in the human local field potential preceding seizure termination.
癫痫——一种反复发作且无明显诱因的病症——表现为具有特征性时空模式的脑电压活动。这些模式包括由聚集的神经元群体产生的刻板半节律活动，以及有组织的时空现象，如波。为了评估这些时空模式，我们开发了一个与观察到的神经元群体活动一致的数学模型，并通过分析确定支持行波解的参数配置。然后，我们利用从三名患者癫痫发作终止前的人类皮质体内记录的高密度局部场电位数据来约束模型参数，并提出导致观察到的行波的基本机制。我们得出结论，一个由具有缓慢适应性的兴奋性细胞之间的局部相互作用组成的相对简单且抽象的数学模型，捕捉到了癫痫发作终止前人类局部场电位中观察到的波传播的定量特征。
