Simulation-Based Inference for Whole-Brain Network Modeling of Epilepsy using Deep Neural Density Estimators

Whole-brain network modeling of epilepsy is a data-driven approach that combines personalized anatomical information with dynamical models of abnormal brain activity to generate spatio-temporal seizure patterns as observed in brain imaging signals. 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 inference algorithms are required to efficiently estimate the parameters pertaining to the hypothetical areas in the brain, ideally including the uncertainty. In this detailed study, we present simulation-based inference for the virtual epileptic patient (SBI-VEP) model, which only requires forward simulations, enabling us to amortize posterior inference on parameters from low-dimensional data features representing whole-brain epileptic patterns. We use state-of-the-art deep learning algorithms for conditional density estimation to retrieve the statistical relationships between parameters and observations through a sequence of invertible transformations. This approach enables us to readily predict seizure dynamics from new input data. We show that the SBI-VEP is able to accurately estimate the posterior distribution of parameters linked to the extent of the epileptogenic and propagation zones in the brain from the sparse observations of intracranial EEG signals. The presented Bayesian methodology can deal with non-linear latent dynamics and parameter degeneracy, paving the way for reliable prediction of neurological disorders from neuroimaging modalities, which can be crucial for planning intervention strategies.