This hypothesis has led to a new “whole-brain” mathematical and computational model developed at the MOX Laboratory of the Department of Mathematics of Politecnico di Milano. The model is designed to describe in an integrated way the interaction between the spread of amyloid beta and the functioning of the cerebral vascular network. The aim is to provide a tool capable of simulating, on the scale of the whole organ, how small biological or vascular alterations can evolve over time and contribute to neurodegeneration. The model and the accompanying scientific study have been published in the prestigious scientific journal Computer Methods in Applied Mechanics and Engineering.

The model integrates two scales of analysis. On the one hand, it describes the dynamics of the production, transformation, diffusion and elimination of the healthy and pathological forms of amyloid beta. On the other, it describes blood flow through a “macroscopic” description of arteries, capillaries and veins, treating brain tissue as a porous medium perfused by blood vessels, through a macroscopic compartmental model. The two components are then connected to represent the possible mechanism of mutual reinforcement between protein accumulation and vascular dysfunction.

The simulations show a particularly relevant result: the brain can evolve into different states depending on the initial conditions. Small localised amounts of amyloid beta can be eliminated, allowing the system to return to a healthy state. Conversely, larger amounts can trigger a self-sustained spread of the pathology at brain scale.