Can control theory throw light on Parkinson´s disease and its treatment with deep brain stimulation?

A simple neural mass model is used to represent oscillatory activity within closed loop circuits of interacting neurons in the basal ganglia area of the brain in Parkinson´s disease. Pathological oscillatory neural activity is generated within the tremor (3-8 Hz), beta (15-30 Hz) and gamma (30-90 Hz) frequency bands. Quenching of the oscillations by means of high frequency deep brain stimulation is illustrated. It is shown that interaction between sub-loops exhibiting tremor and gamma band activity can produce new oscillations within the beta band range, a frequency range clinically associated with increased bradykinesia and akinesia. It is similarly shown that interactions between neural circuits oscillating at the tremor and beta frequencies may result in oscillations at approximately twice the frequency of Parkinsonian tremor.