A dynamical systems approach to understanding deep brain stimulation
Deep brain stimulation (DBS) is a surgical intervention in which an electrode is implanted in a localized area of a patient's brain, where it delivers high-frequency electric current pulses. This technique has proved particularly effective at tremor suppresion and thus has been implemented in many thousands of Parkinson's disease patients, as well as in patients with other motor pathologies, yet the mechanism by which it works remains largely mysterious. In this talk, I will show how some ideas from dynamical systems theory can be used to explain how one hypothesized mechanism for the efficacy of DBS could work. Further, I will show some results of simulations incorporating experimental data, which support the explanation given by mathematical analysis. Finally, I will briefly discuss a Markov chain analysis that complements these results and that can be used in general to analytically derive statistics characterizing the activity of fast-slow excitable systems satisfying certain assumptions. Note that I will not assume any background knowledge about the brain in this talk!
Jonathan Rubin (Univ. Pittsburgh, USA)
September 06, 2006