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Mathematical and control aspects of deep-brain-stimulation in certain neurological disorders (Parkinson and Essential Tremor)

The talk is in two parts: (a) Applying stochastic differential equations (SDE) to model neuronal activity in the brain (sub-thalamic nucleus) in Parkinson Disease patients. (b) Predictive on-off control of deep-brain-stimulation (DBS) in neurological Essential Tremor (ET), using surface-EMG signals for prediction and control

The role of stochastic calculus in modeling abnormal neuronal firing in neurological disorders is natural, since neuronal firing are random point processes of the kind for which stochastic calculus is natural and where it leads to far simpler models (far fewer parameters) than deterministic approaches. DBS is now a major treatment of several such disorders and understanding, designing and predicting various aspects of stimulation design and its control require such mathematical modeling.

In Part (a) we discuss applying Ornstein-Uhlenbeck stochastic processes (OUP) to model the inter-spike-intervals (ISI) of such neuronal activity to neuronal in vivo data taken a Parkinson patient during implantation of DBS electrodes in her sub-thalamic nucleus (STN). We extract the model parameters from these data via First-Passage Time (FTP) analysis and demonstrate its fit to the patient’s data. We further compare the OUP/FPT model with previous models (Fokker-Planck (FP) equation-based model, Wiener-Process/Inverse-Gaussian (WP/IG) random walk model and Poisson (PP) model, to show the superiority of the OUP/FPT model with respect to FP, WP/IG and PP models for the same data.

Concerning Part (b), we note that all DBS is presently open-loop and its parameters are pre-set at surgery (implantation ). They remain unchanged afterwards, irrespective to patient’s condition that may change from second to second, Part (b) is concerned with predictive-adaptive on-off control of DBS in ET patients. ET is approximately 10 times more prevalent than PD and its treatment with DBS is also becoming more frequent.

In Part (b) we present data taken from an ET patient who had been implanted with DBS electrodes 8 years previously, to show that after each train of DBS pulse of 20-35 seconds, there is a tremor-free interval (without stimulation), lasting for another 15-35 seconds. This implies that stimulation may be stopped for that time duration (which varies from cycle to cycle), to reduce the electric charge applied to the patients thalamus (where DBS is applied). Furthermore, we show that surface EMG recordings, which are noninvasive, allow to predict when tremors re-appear. Once a forthcoming tremor is predicted, stimulation is restarted still ahead of actual tremor.

Both studies have been accepted for publication (Part (a): Biol Cyb., Part (b): Neurol Res.) and are subject to pending patents.

Type of Seminar:
Public Seminar
Prof. Daniel Graupe
University of Illinois at Chicago, USA
Jul 28, 2010   4.00 p.m.

ETH, VAW building, room B1, Gloriastrasse 37/39
Contact Person:

Manfred Morari
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