Bifurcation analysis points towards the source of beta neuronal oscillations in Parkinson's disease
Parkinson disease is the second most common neurodegenerative disorder after Alzheimer, affecting 0.16% of the population in the USA1. This disease is most common in the elderly, what makes it a prominent health problem in developed countries, where the elder population is expected to importantly increase in the future. The mechanism generating the disease is the death of dopaminergic neurons in the substantia nigra pars compacta (SNc), a small brain region from the brain stem. These neurons release the neurotransmitter dopamine to the basal ganglia, a large and complex brain structure implicated in motor control and reinforcement learning. Once SNc neurons have died, the basal ganglia starts showing prominent features of malfunction, and the characteristics symptoms of Parkinson's disease began to be observed in the patient (i.e. general difficulty or inability to execute motor movements and limb tremor, among others). Modern theory of Parkinson's disease focuses on the abnormal brain activity oscillations observed in the basal ganglia, which are consistently observed in parkinsonian patients and correlate with their symptoms. This paper develops a mathematical model of the basal ganglia, which reproduces the experimentally recorded neuronal activity of this brain structure in health and disease. Studying this model numerical and analytically, we draw conclusion on how and where these oscillations are generated within the brain. If the conclusions of this mathematical model are further confirmed experimentally, we think they pave the way towards controlling such oscillations pharmacologically or through electrode stimulation in the future.