Optimal Entrainment of Neural Oscillator Ensembles

TL;DR

This paper derives a minimum-energy control method to entrain neural oscillator ensembles to a desired frequency, demonstrating its effectiveness on Hodgkin-Huxley models and potential for low-energy brain stimulation therapies.

Contribution

It introduces a novel optimal control approach using phase reduction and averaging, applicable to large-scale neural systems with parameter uncertainties.

Findings

Optimal control achieves effective entrainment with minimal energy.

Method successfully applied to Hodgkin-Huxley neural models.

Controls are practical for deep brain stimulation applications.

Abstract

In this paper, we derive the minimum-energy periodic control that entrains an ensemble of structurally similar neural oscillators to a desired frequency. The state space representation of a nominal oscillator is reduced to a phase model by computing its limit cycle and phase response curve, from which the optimal control is derived by using formal averaging and the calculus of variations. We focus on the case of a 1:1 entrainment ratio, and introduce a numerical method for approximating the optimal controls. The method is applied to asymptotically control the spiking frequency of neural oscillators modeled using the Hodgkin-Huxley equations. This illustrates the optimality of entrainment controls derived using phase models when applied to the original state space system, which is a crucial requirement for using phase models in control synthesis for practical applications. The results of this work can be used to design low energy signals for deep brain stimulation therapies for neuropathologies, and can be generalized for optimal frequency control of large-scale complex oscillating systems with parameter uncertainty.