A reaction-diffusion model for the progression of Parkinson's disease

The temporal and spatial development of Parkinson's disease has been characterised as the progressive formation of {\alpha}-synuclein aggregations through susceptible neuronal pathways. This article describes a new model for this progression mechanism in which Parkinsonian damage moves over time through the nervous system by the combined effect of the reaction kinetics of pathogenesis and molecular diffusion. In the reaction-diffusion model, the change from a healthy state to the disease state advances through the nervous system as a wave front of Parkinsonian damage, marking its path by accumulations of damaged {\alpha}-synuclein and neurotoxic levels of oxidative species. Progression according to this model follows the most vulnerable routes through the nervous system as described by Braak's staging theory and predicts that damage will advance at differing speeds depending upon the level and number of risk factors, in a manner that gives new insights into the variations with which Parkinson's disease develops.