From Resistor Networks to the Human Connectome: Modelling Capillary Network Rarefaction in the Prion Dynamics of Alzheimer’s Disease #

Andrew Ó hEachteirn

10:30 Wednesday in 4Q04.

Part of the Nonlinear dynamics and applications session.

Abstract #

Alzheimer’s disease (AD) is characterised by the accumulation and propagation of toxic proteins (e.g. amyloid beta) in the brain. The resulting aggregates cause progressive neurodegeneration. Mathematical models have been used to describe the prion-like features of these proteins and their spread but none have addressed their coupling with the brain’s vasculature, an area of increasing interest among neuroscientists. In this talk, I will present a multiscale model of AD pathogenesis that couples the prion-like kinetics of amyloid beta with microvascular network damage. We begin at the microscale and ask how the rate of blood flow through a capillary bed decreases in response to percolation-like network damage. At the mesoscale, we pose a simple ODE system intended to describe the kinetics of amyloid beta in a small brain region, observing the ability of capillary damage to destabilise the healthy steady state, thus initiating the prion cascade. At the macroscale, we investigate spatial invasion, first in a toy model of a strip of tissue, then on an MRI-derived network model of the human brain whose nodes and edges represent brain regions and axonal connectivity, respectively. I will discuss the biologically-relevant features of this model, including potential mechanisms for AD initiation and containment, and the next steps to be taken in its development.