Application of Describing Function Analysis to a Model of Deep Brain Stimulation

Deep brain stimulation effectively alleviates motor symptoms of medically refractory Parkinson´s disease, and also relieves many other treatment-resistant movement and affective disorders. Despite its relative success as a treatment option, the basis of its efficacy remains elusive. In Parkinson´s disease, increased functional connectivity and oscillatory activity occur within the basal ganglia as a result of dopamine loss. A correlative relationship between pathological oscillatory activity and the motor symptoms of the disease, in particular bradykinesia, rigidity, and tremor, has been established. Suppression of the oscillations by either dopamine replacement or DBS also correlates with an improvement in motor symptoms. DBS parameters are currently chosen empirically using a “trial and error” approach, which can be time-consuming and costly. The work presented here amalgamates concepts from theories of neural network modeling with nonlinear control engineering to describe and analyze a model of synchronous neural activity and applied stimulation. A theoretical expression for the optimum stimulation parameters necessary to suppress oscillations is derived. The effect of changing stimulation parameters (amplitude and pulse duration) on induced oscillations is studied in the model. Increasing either stimulation pulse duration or amplitude enhanced the level of suppression. The predicted parameters were found to agree well with clinical measurements reported in the literature for individual patients. It is anticipated that the simplified model described may facilitate the development of protocols to aid optimum stimulation parameter choice on a patient by patient basis.