Amortized Bayesian inference on generative dynamical network models of epilepsy using deep neural density estimators

Whole-brain modeling of epilepsy combines personalized anatomical data with dynamical models of abnormal activities to generate spatio-temporal seizure patterns as observed in brain imaging data. Such a parametric simulator is equipped with a stochastic generative process, which itself provides the basis for inference and prediction of the local and global brain dynamics affected by disorders. However, the calculation of likelihood function at whole-brain scale is often intractable. Thus, likelihood-free algorithms are required to efficiently estimate the parameters pertaining to the hypothetical areas, ideally including the uncertainty. In this study, we introduce the simulation-based inference for the virtual epileptic patient model (SBI-VEP), enabling us to amortize the approximate posterior of the generative process from a low-dimensional representation of whole-brain epileptic patterns. The state-of-the-art deep learning algorithms for conditional density estimation are used to readily retrieve the statistical relationships between parameters and observations through a sequence of invertible transformations. We show that the SBI-VEP is able to efficiently estimate the posterior distribution of parameters linked to the extent of the epileptogenic and propagation zones from sparse intracranial electroencephalography recordings. The presented Bayesian methodology can deal with non-linear latent dynamics and parameter degeneracy, paving the way for fast and reliable inference on brain disorders from neuroimaging modalities.