XDL-ESI: Electrophysiological Sources Imaging via explainable deep learning framework with validation on simultaneous EEG and iEEG.

Electroencephalography (EEG) or Magnetoencephalography (MEG) source imaging aims to estimate the underlying activated brain sources to explain the observed EEG/MEG recordings. Solving the inverse problem of EEG/MEG Source Imaging (ESI) is challenging due to its ill-posed nature. To achieve a unique solution, it is essential to apply sophisticated regularization constraints to restrict the solution space. Traditionally, the design of regularization terms is based on assumptions about the spatiotemporal structure of the underlying source dynamics. In this paper, we propose a novel paradigm for ESI via an Explainable Deep Learning framework, termed as XDL-ESI, which connects the iterative optimization algorithm with deep learning architecture by unfolding the iterative updates with neural network modules. The proposed framework has the advantages of (1) establishing a data-driven approach to model the source solution structure instead of using hand-crafted regularization terms; (2) improving the robustness of source solutions by introducing a topological loss that leverages the geometric spatial information applying varying penalties on distinct localization errors; (3) improving the reconstruction efficiency and interpretability as it inherits the advantages from both the iterative optimization algorithms (interpretability) and deep learning approaches (function approximation). The proposed XDL-ESI framework provides an efficient, accurate, and interpretable paradigm to solve the ESI inverse problem with satisfactory performance in both simulated data and real clinical data. Specially, this approach is further validated using simultaneous EEG and intracranial EEG (iEEG).