Minimum energy desynchronizing control for coupled neurons

Authors:
Ali Nabi;Mohammad Mirzadeh;Frederic Gibou;Jeff Moehlis
Affiliations:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106-5070;Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106-5070;Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106-5070;Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106-5070
Venue:
Journal of Computational Neuroscience
Year:
2013

Citing 11
Cited 0

Uniformly high order accurate essentially non-oscillatory schemes, 111

Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes

Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations

SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes

Journal of Computational Physics
Mathematical physiology

Mathematical physiology
Strong Stability-Preserving High-Order Time Discretization Methods

SIAM Review
On the Phase Reduction and Response Dynamics of Neural Oscillator Populations

Neural Computation
Control of Neuronal Synchrony by Nonlinear Delayed Feedback

Biological Cybernetics
Event-based minimum-time control of oscillatory neuron models: Phase randomization, maximal spike rate increase, and desynchronization

Biological Cybernetics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II

Journal of Computational Physics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We employ optimal control theory to design an event-based, minimum energy, desynchronizing control stimulus for a network of pathologically synchronized, heterogeneously coupled neurons. This works by optimally driving the neurons to their phaseless sets, switching the control off, and letting the phases of the neurons randomize under intrinsic background noise. An event-based minimum energy input may be clinically desirable for deep brain stimulation treatment of neurological diseases, like Parkinson's disease. The event-based nature of the input results in its administration only when it is necessary, which, in general, amounts to fewer applications, and hence, less charge transfer to and from the tissue. The minimum energy nature of the input may also help prolong battery life for implanted stimulus generators. For the example considered, it is shown that the proposed control causes a considerable amount of randomization in the timing of each neuron's next spike, leading to desynchronization for the network.