Optimal open-loop desynchronization of neural oscillator populations

Area of Science:

• Neuroscience
• Computational Neuroscience
• Mathematical Biology

Background:

• Deep brain stimulation (DBS) is a clinical therapy for neurological disorders.
• DBS efficacy is linked to desynchronizing neuronal activity, but mechanisms remain unclear.
• Mathematical models are needed to understand how periodic stimulation affects neural synchrony.

Purpose of the Study:

• To develop a mathematical framework for analyzing the desynchronizing effects of periodic stimulation on coupled neurons.
• To design optimal open-loop stimulation waveforms using control theory.
• To investigate the influence of noise and heterogeneity on stimulation efficacy.

Main Methods:

• Utilized a phase-amplitude reduction framework to model coupled oscillators.
• Applied optimal control theory to design stimulation parameters.
• Analyzed system nonlinearities and Floquet exponents.
• Investigated the role of phase response curves in weak coupling limits.

Main Results:

• Demonstrated that periodic stimulation can destabilize synchronized solutions and stabilize rotating block solutions.
• Showcased that weak coupling requires only phase response curve information.
• Presented numerical results considering noise and heterogeneity.

Conclusions:

• The developed framework provides insights into the mathematical mechanisms of DBS-induced desynchronization.
• This approach can inform the design of more effective DBS waveforms.
• Potential for improved therapeutic outcomes in neurological diseases treated with DBS.