Localized estimation of electromagnetic sources underlying event-related fields using recurrent neural networks

Objective. To use a recurrent neural network (RNN) to reconstruct neural activity responsible for generating noninvasively measured electromagnetic signals. Approach. Output weights of an RNN were fixed as the lead field matrix from volumetric source space computed using the boundary element method with co-registered structural magnetic resonance images and magnetoencephalography (MEG). Initially, the network was trained to minimise mean-squared-error loss between its outputs and MEG signals, causing activations in the penultimate layer to converge towards putative neural source activations. Subsequently, L1 regularisation was applied to the final hidden layer, and the model was fine-tuned, causing it to favour more focused activations. Estimated source signals were then obtained from the outputs of the last hidden layer. We developed and validated this approach with simulations before applying it to real MEG data, comparing performance with beamformers, minimum-norm estimate, and mixed-norm estimate source reconstruction methods. Main results. The proposed RNN method had higher output signal-to-noise ratios and comparable correlation and error between estimated and simulated sources. Reconstructed MEG signals were also equal or superior to the other methods regarding their similarity to ground-truth. When applied to MEG data recorded during an auditory roving oddball experiment, source signals estimated with the RNN were generally biophysically plausible and consistent with expectations from the literature. Significance. This work builds on recent developments of RNNs for modelling event-related neural responses by incorporating biophysical constraints from the forward model, thus taking a significant step towards greater biological realism and introducing the possibility of exploring how input manipulations may influence localised neural activity.