Closed-Loop Current Stimulation Feedback Control of a Neural Mass Model Using Reservoir Computing

Transcranial electrical stimulation (tES) is a non-invasive neuromodulatory technique that alters ongoing neural dynamics by injecting an exogenous electrical current through the scalp. Although tES protocols are becoming more common in both clinical and experimental settings, the neurophysiological mechanisms through which tES modulates cortical dynamics are unknown. Most existing tES protocols ignore the potential effect of phasic interactions between endogenous and exogenous currents by stimulating in an open-looped fashion. To better understand the mechanisms of closed-loop tES, we first instantiated a two-column Jansen and Rit model to simulate neuronal dynamics of pyramidal cells and interneurons. An echo-state network (ESN) reservoir computer inverted the dynamics of the model without access to the internal state equations. After inverting the model dynamics, the ESN was used as a closed-loop feedback controller for the neural mass model by predicting the current stimulation input for a desired future output. The ESN was used to predict the endogenous membrane currents of the model from the observable pyramidal cell membrane potentials and then inject current stimulation to destructively interfere with endogenous membrane currents, thereby reducing the energy of the PCs. This simulation approach provides a framework for a model-free closed-loop feedback controller in tES experiments.