A mathematical model of pathogenesis in idiopathic parkinsonism.

We used our observations relating clinical deficits in idiopathic parkinsonism (IP) to age and to disease duration (Lee et al, Brain 1994; 117: 501-7), to develop a mathematical model of the temporal profile of neurodegeneration in IP. We also examined other sets of relevant published observations and applied three additional assumptions which permitted the formulation of this model. Our model indicates that accelerating or decelerating processes should be excluded as the driving forces behind neuronal death in IP. Mechanisms in accord with the model include: (i) an event that kills some neurons and damages others in such a way that their life expectation is reduced; or (ii) an event that starts a process which is continuously killing healthy neurons at a constant rate. The model enables us to extrapolate back to estimate when the causal event occurred. It also explains why IP proceeds more rapidly in older patients. The model has potential relevance to other neurodegenerative disorders, such as Alzheimer's disease and amyotrophic lateral sclerosis.