A biophysically inspired microelectrode recording-based model for the subthalamic nucleus activity in Parkinson’s disease

The subthalamic nucleus (STN) plays a central role in movement actuation and manifestation of movement disorders (i.e., tremor, rigidity, akynesia and postural instability) in Parkinson's disease (PD) patients. Moreover, it has been recently revealed that an opportune electrical stimulation of the STN, called deep brain stimulation (DBS), can strongly contribute to the annihilation of the PD-related motor disorders. Currently, a great effort is made both in Medicine, Neurosciences and Engineering for understanding and modeling in details how the STN works, how PD determines its pathological behavior and DBS restores the correct motor function. The paper is organized in two parts. Firstly some stochastic properties of the STN electrical activity are obtained by analyzing a preliminary set of experimental data coming from microelectrode recordings (MERs) in two PD patients who underwent the surgical implantation of DBS electrodes. Then, a nonlinear, stochastic, continuous-state model describing the global electrical behavior of the STN in PD patients is proposed. It is inspired by the fundamental physiologic features of the subthalamic cells and a fictitious vector state is introduced to represent the main dynamics. Its numerical parameters and stochastic properties are chosen by fitting the available data.