The aim of this article is to infer the connectivity structures of brain regions before and during epileptic seizure. Our contributions are fourfold. First, we propose a 6N-dimensional stochastic differential equation for modelling the activity of N coupled populations of neurons in the brain. This model further develops the (single population) stochastic Jansen and Rit neural mass model, which describes human electroencephalography (EEG) rhythms, in particular signals with epileptic activity. Second, we construct a reliable and efficient numerical scheme for the model simulation, extending a splitting procedure proposed for one neural population. Third, we propose an adapted Sequential Monte Carlo Approximate Bayesian Computation algorithm for simulation-based inference of both the relevant real-valued model parameters as well as the {0,1}-valued network parameters, the latter describing the coupling directions among the N modelled neural populations. Fourth, after illustrating and validating the proposed statistical approach on different types of simulated data, we apply it to a set of multi-channel EEG data recorded before and during an epileptic seizure. The real data experiments suggest, for example, a larger activation in each neural population and a stronger connectivity on the left brain hemisphere during seizure.

翻译：本文旨在推断癫痫发作前及发作期间脑区连接结构。我们的贡献分为四点。首先，我们提出了一个6N维随机微分方程，用于建模大脑中N个耦合神经元群体的活动。该模型进一步发展了（单群体）随机Jansen和Rit神经质量模型，该模型描述了人类脑电图（EEG）节律，特别是具有癫痫活动的信号。其次，我们为模型模拟构建了可靠且高效的数值方案，扩展了为单个神经群体提出的分裂过程。第三，我们提出了一个自适应序列蒙特卡罗近似贝叶斯计算算法，用于基于模拟的推断，推断相关的实值模型参数以及{0,1}值网络参数，后者描述了N个建模神经群体之间的耦合方向。第四，在将所提出的统计方法在不同类型模拟数据上进行验证后，我们将其应用于癫痫发作前及发作期间记录的一组多通道脑电图数据。真实数据实验表明，例如，在癫痫发作期间，每个神经群体中的激活更强，且左脑半球上的连接性更强。