Multi-site Delay Feedback Stimulation for Parkinson's Disease and map reduction of neuron models

Deep brain stimulation (DBS) is a surgical procedure used to alleviate debilitating and disrupting symptoms of Parkinson's Disease. The current form of DBS is the conventional high frequency stimulation (HF) that has several drawbacks. Multi-site delay feedback stimulation (MDFS) has been proposed as a feasible alternative to overcome the drawbacks of the conventional DBS. In this study, we explore the effectiveness of MDFS when applied to the subthalamic nucleus (STN) and the globus pallidus internal (GPi) populations in large scale biophysical networks with intermittent Parkinsonian conditions. Our intermittent Parkinsonian network model produces neuronal activities observed in the subthalamic nucleus (STN), the globus pallidus external (GPe), the globus pallidus internal (GPi) and the thalamo-cortical (TC) relay cells recorded in patients and monkeys with Parkinson's Disease (PD). Our network transits between synchronized and desynchronized dynamics. These transitions are important since the brain of a PD patient is likely to transit between a parkinsonian state to a non-parkinsonian state. This study shows that MDFS can improve the fidelity of the TC relay neurons' communication and response to the input motor signal in a realistic Parkinsonian network.;Dimension reduction allows one to study a high dimensional system of ordinary differential equations(ODE) by producing a low dimensional system that captures and keeps the dynamics of original ODEs. We present an novel formulation of a dimensional reduction method based on the attractors in the phase--space. We then apply this approach to reduce the GPi neuron to produce a two dimensional map.