Session: 08-07-02: Novel Control of Dynamic System and Design II

Paper Number: 165237

Optimal Control of Populations of Neural Oscillators 

Many challenging problems that consider the analysis and control of neural brain rhythms have been motivated by the advent of deep brain stimulation as a therapeutic treatment for a wide variety of neurological disorders.  In a computational setting, neural rhythms are often modeled using large populations of coupled, conductance-based neurons.  Control of such models comes with a long list of challenges: the underlying dynamics are nonnegligibly nonlinear, high dimensional, and subject to noise; hardware and biological limitations place restrictive constraints on allowable inputs; direct measurement of system observables is generally limited; and the resulting systems are typically highly underactuated.

In this talk, I highlight a collection of recent analysis techniques and control frameworks that have been developed to contend with these difficulties.  Particular emphasis is placed on the problem of desynchronization for a population of pathologically synchronized neural oscillators, a problem that is motivated by applications to Parkinson's disease where pathological synchronization is thought to contribute to the associated motor control symptoms.  Indeed, evidence suggests that deep brain stimulation helps to restore normal function by disrupting this synchronization.

To achieve the desired control objectives, it will be useful to work in a coordinate framework that is more amenable to both mathematical analysis and implementation of nonlinear control algorithms, namely phase coordinates.  The key insight here is that the behavior of a general limit cycle oscillator in response to perturbations can be characterized in terms of the timing of oscillations rather than in reference to the underlying state variables. These ideas have been formalized using the notion of isochrons, i.e., level sets of initial conditions that have the same asymptotic convergence to the limit cycle, and phase response curves, which capture the effect that stimulation has on the phase of an oscillator.

The first control strategy to be covered will be optimal chaotic desynchronization for finding an energy-optimal stimulus which exponentially desynchronizes a population of neurons, based only on a neuron’s phase response curve, and will include recent results on the effect of constraints on stimulus magnitude on the control efficacy.  The second control strategy to be covered will be optimal phase resetting which brings the neurons' states near a phaseless set, so that background noise perturbs the neurons onto random isochrons which randomizes their asymptotic phases, and will include recent results on how accounting for stochasticity in the control design can improve performance.

These algorithms hold great promise for controlling neural oscillator populations with a variety of control objectives. Our hope is that these successes will motivate more research on how to implement them in experimental and clinical studies, opening the door to more effective and more efficient treatments for Parkinson’s disease and other neurological disorders.

 

Presenting Author: Jeff Moehlis University of California, Santa Barbara

Presenting Author Biography: Jeff Moehlis received a Ph.D. in Physics from UC Berkeley in 2000, and was a Postdoctoral Researcher in the Program in Applied and Computational Mathematics at Princeton University from 2000-2003. He joined the Department of Mechanical Engineering at UC Santa Barbara in 2003, and is currently Chair of this department. He was also recently the Chair of the Program in Dynamical Neuroscience at UC Santa Barbara. He has been a recipient of a Sloan Research Fellowship in Mathematics and a National Science Foundation CAREER Award, and was Program Director of the SIAM Activity Group in Dynamical Systems from 2008-2009. Jeff's current research includes applications of dynamical systems and control techniques to neuroscience, cardiac dynamics, and collective behavior. He has published over 100 journal / conference proceedings articles on these and other topics including shear flow turbulence, microelectromechanical systems, energy harvesting, and dynamical systems with symmetry.

Authors:

Jeff Moehlis University of California, Santa Barbara