Quantification of motor network dynamics in Parkinson's disease by means of landscape and flux theory.

The basal ganglia neural circuit plays an important role in motor control. Despite the significant efforts, the understanding of the principles and underlying mechanisms of this modulatory circuit and the emergence of abnormal synchronized oscillations in movement disorders is still challenging. Dopamine loss has been proved to be responsible for Parkinson's disease. We quantitatively described the dynamics of the basal ganglia-thalamo-cortical circuit in Parkinson's disease in terms of the emergence of both abnormal firing rates and firing patterns in the circuit. We developed a potential landscape and flux framework for exploring the modulatory circuit. The driving force of the circuit can be decomposed into a gradient of the potential, which is associated with the steady-state probability distributions, and the curl probability flux term. We uncovered the underlying potential landscape as a Mexican hat-shape closed ring valley where abnormal oscillations emerge due to dopamine depletion. We quantified the global stability of the network through the topography of the landscape in terms of the barrier height, which is defined as the potential difference between the maximum potential inside the ring and the minimum potential along the ring. Both a higher barrier and a larger flux originated from detailed balance breaking result in more stable oscillations. Meanwhile, more energy is consumed to support the increasing flux. Global sensitivity analysis on the landscape topography and flux indicates how changes in underlying neural network regulatory wirings and external inputs influence the dynamics of the system. We validated two of the main hypotheses(direct inhibition hypothesis and output activation hypothesis) on the therapeutic mechanism of deep brain stimulation (DBS). We found GPe appears to be another effective stimulated target for DBS besides GPi and STN. Our approach provides a general way to quantitatively explore neural networks and may help for uncovering more efficacious therapies for movement disorders.