Dynamic modeling and statistical characterization of subthalamic nucleus neural activity in Parkinson´s disease patients

The neural spiking activity of the subthalamic nucleus (STN) is devoted to modulate movement actuation and correct movement disorders (i.e. tremor at rest, rigidity, akynesia and postural instability) in Parkinson´s disease (PD) patients. Moreover, it has been recently revealed that an opportune electrical stimulation, called deep brain stimulation (DBS), can annihilate, if associated with the most common L-dopa based pharmacological therapies, PD-related motor disorders. Currently, a great effort is made both in medicine and engineering for understanding and modeling in details how the STN works, how PD determines its pathological behavior and how DBS restores the correct motor function. The paper presents a nonlinear, stochastic, continuous-state model describing the global electrical behavior of the STN in PD patients: inspired by the fundamental physiologic features of subthalamic cells, a fictitious vector state is introduced to represent the main dynamics. Its numerical parameters and stochastic properties are chosen by fitting experimental data coming from two PD patients during the surgical implantation of stimulation electrodes in the brain