Deep brain stimulation is a treatment for Parkinson's disease in which current is injected into the appropriate brain region to try to desynchronize pathologically synchronized neurons. This motivates the study of how to control the behavior of neurons. A first step is the development of algorithms which control a single neuron to fire at a desired time; this can be accomplished by exploiting properties of the neuron's phase response curve, which describes the phase-shift of the neuron's dynamics due to an impulsive perturbation as a function of the phase at which the perturbation occurs. Moreover, an event-based feedback control method with fixed stimulus magnitude constraint will be presented which randomizes the asymptotic phase of oscillatory neurons by time-optimally driving the neuron's state to its phaseless set, a point at which its phase is undefined and is extremely sensitive to background noise. When applied to a network of globally coupled neurons that are firing in synchrony, the applied control signal desynchronizes the population in a demand-controlled way, which suggests that this might be useful for improving the efficacy of deep brain stimulation.
Dr. Jeff Moehlis received the B.S. degree in Physics and Mathematics from Iowa State University in 1993, and the Ph.D. degree in Physics from the University of California, Berkeley, in 2000. He 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 the University of California, Santa Barbara, in 2003, and received tenure in 2007. 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 Society of Industrial and Applied Mathematics Activity Group in Dynamical Systems from 2008-2009. Jeff's research interests involve using techniques from dynamical systems theory to understand and control natural and technological systems. His application areas include neuroscience, turbulence, MEMS devices, energy harvesting, and collective behavior.
