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Deep Brain Stimulation (DBS) is a neurosurgical technique in which microelectrodes, embedded in a closely specified target area of the brain, are stimulated by a periodic, rectangular, charge-balanced signal, generated by a stimulator embedded in the chest. It was serendipitously discovered by neurosurgeon Professor Alim-Louis Benabid in Grenoble in 1987 that "high frequency" (of the order of 130Hz) stimulation of the Basal Ganglia in the brain could eliminate the characteristic tremor (about 5 to 8 Hz) associated with Parkinson's disease and also release the associated "locking of gait." Since then the idea has been applied to other neurological diseases such as epilepsy, depression and Tourette syndrome and the phenomenon of "essential tremor." The mode of action of DBS is still incompletely understood. This paper presents attempts made by the authors to develop constructive models of the phenomenology of DBS, based on classical Control Theory tools such as the Nyquist Stability Criterion, the Describing Function, the Root Locus method, Liapunov's theorem of the First Approximation and, above all, the concept of the Equivalent Nonlinearity associated with injection of a "high frequency" wave into a nonlinear feedback loop to quench troublesome "low frequency" oscillations. These models have proved very successful in predicting the dependence of pathological oscillations, observed as Local Field Potentials (LFP), on amplitude and fractional pulse duration of the DBS signal.

Control Theory and Deep Brain Stimulation for Relief from Neurological Diseases