Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are devastating conditions with poorly understood mechanisms and no known cure. Yet a striking feature of these conditions is the characteristic pattern of invasion throughout the brain, leading to well-codified disease stages visible to neuropathology and associated with various cognitive deficits and pathologies.

The similarities between these diseases has led to the hypothesis that they are prion-like: their evolution is driven by some toxic form of a protein spreading through the brain similar to the better characterized prion diseases (such as scrapie in sheep and Creutzfeldt-Jakob disease). As toxic proteins spread, they accumulate and form aggregates. Eventually, these aggregates form tissue lesions, initiate cell death and induce tissue atrophy, leading invariably to a loss of cognitive functions and, ultimately, death.

This prion-like hypothesis is simple enough that it can be tested mathematically and used as a postulate for modelling the invasion of neurodegenerative diseases. In an article published in Physical Review Letters, Oxford Mathematics's Alain Goriely and a team of fellow scientists from Stanford University and Stevens Institute of Technology, has shown that these patterns can be explained from a mathematical model based on generic effects combining the production of new toxic proteins from native ones and the preferential diffusion along axonal pathways in the brain.

Top row: evolution of the toxic protein through the brain
Middle row: MRI of a patient with Alzheimer’s disease in three successive years
Bottom row: shrinking pattern predicted from the mathematical model

The team ran the mathematical model simulated in full brain geometry obtained from MRI scans but with different initial seeding regions characteristic of each disease. Remarkably, this model reproduces the characteristic evolution of different neurodegenerative diseases, the evolution of the total toxic protein load, as well as the typical atrophy patterns associated with tissue removal. This initial model provides a better qualitative understanding of the mechanisms at work during the evolution of these diseases and opens the door to a new quantitative and physics-based approach to studying the propagation of neurodegenerative diseases and identifying new therapeutic targets.

As Alain Goriely says: "Despite the complexity of these diseases, there are some generic features that can be explained from simple mechanistic models. The evolution of the disease in time through the brain is the result of simple underlying mechanisms. The breakthrough in understanding is that it can, in principle, help us identify the key factors affecting this propagation and give us new ideas for therapeutic targets."


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