Back to Departmental Colloquium: Fall 2013
Departmental Colloquium
Date: Thursday, Sep 26, 2013
Time: 4:00PM
Location: LCB 219
Jonathan Rubin
University of Pittsburgh
Title |
Irregular (neural) dynamics: how to get it and how to restore it |
Abstract |
Baseline healthy activity in many brain regions is believed to be irregular, with little correlation in firing times of different neurons. On the other hand, excessive regularity has been associated with disorders such as Parkinson’s disease. Mathematically, neuronal irregularity has been represented as an asynchronous state that can be stable under so-called balance conditions that yield cancellation of correlations. I will discuss a mechanism by which irregular, apparently chaotic activity emerges naturally in small networks, such as certain neuronal networks involved in parkinsonism, that lack such balance. Moreover, I will describe a one-dimensional map that captures this activity as well as analysis of how expansion, folding, and contraction emerge in a corresponding phase plane, as expected in chaotic dynamics. Once this irregularity is lost and parkinsonism arises, symptoms can be alleviated with implantation of an electrode to deliver periodic high frequency current pulses, known as deep brain stimulation (DBS). I will also present the mathematics of two possible mechanisms by which DBS may work, including a transformation from periodic stimulation to restored irregularity. |
Mathematical Biology
Dynamical Systems