Entrainment of a network of interacting neurons with minimum stimulating charge

TL;DR

This paper extends minimum charge control theory to neural networks, deriving optimal stimulation waveforms to entrain collective oscillations efficiently, with validation on various neuron models.

Contribution

It generalizes single-neuron minimum charge control to networks, providing a formula for optimal waveforms based on the network's phase response curve.

Findings

Optimal waveforms are bang-off-bang type for networks.

The theory is validated on FitzHugh-Nagumo and quadratic integrate-and-fire networks.

Entrainment achieved with minimal stimulation charge.

Abstract

Periodic pulse train stimulation is generically used to study the function of the nervous system and to counteract disease-related neuronal activity, e.g., collective periodic neuronal oscillations. The efficient control of neuronal dynamics without compromising brain tissue is key to research and clinical purposes. We here adapt the minimum charge control theory, recently developed for a single neuron, to a network of interacting neurons exhibiting collective periodic oscillations. We present a general expression for the optimal waveform, which provides an entrainment of a neural network to the stimulation frequency with a minimum absolute value of the stimulating current. As in the case of a single neuron, the optimal waveform is of bang-off-bang type, but its parameters are now determined by the parameters of the effective phase response curve of the entire network, rather than of a single neuron. The theoretical results are confirmed by three specific examples: two small-scale networks of FitzHugh-Nagumo neurons with synaptic and electric couplings, as well as a large-scale network of synaptically coupled quadratic integrate-and-fire neurons.