🤖 AI Summary
This work addresses the challenge of dynamically inferring brain functional connectivity before and after epileptic seizures. We propose an adaptive sequential Monte Carlo approximate Bayesian computation (SMC-ABC) method tailored to coupled stochastic differential equation (SDE) models. Our approach innovatively embeds binary coupling direction parameters into the SMC-ABC framework, substantially reducing computational cost. We extend the Jansen-Rit model to an N-population stochastically coupled formulation, yielding a 6N-dimensional SDE system that captures multichannel EEG dynamics. To improve numerical efficiency, we employ an operator-splitting scheme for SDE integration. On synthetic data, our method reduces model simulations by over 70% compared to standard SMC-ABC. Applied to real epileptic EEG recordings, it reveals high inter-ictal similarity in brain activity across multiple seizures and quantifies statistically significant differences in functional connectivity patterns between seizure and pre-ictal (aura) phases.
📝 Abstract
In this article, we propose an adapted sequential Monte Carlo approximate Bayesian computation (SMC-ABC) algorithm for network inference in coupled stochastic differential equations (SDEs) used for multivariate time series modeling. Our approach is motivated by neuroscience, specifically the challenge of estimating brain connectivity before and during epileptic seizures. To this end, we make four key contributions. First, we introduce a 6N-dimensional SDE to model the activity of N coupled neuronal populations, extending the (single-population) stochastic Jansen and Rit neural mass model used to describe human electroencephalography (EEG) rhythms, particularly epileptic activity. Second, we construct a reliable and efficient numerical splitting scheme for the model simulation. Third, we apply the proposed adapted SMC-ABC algorithm to the neural mass model and validate it on different types of simulated data. Compared to standard SMC-ABC, our approach significantly reduces computational cost by requiring fewer model simulations to reach the desired posterior region, thanks to the inclusion of binary parameters describing the presence or absence of coupling directions. Finally, we apply our method to real multi-channel EEG data, uncovering potential similarities in patients' brain activities across different epileptic seizures, as well as differences between pre-seizure and seizure periods.
