Mathematical Biology Seminar
Andrew Ahern, University of Oxford
Wednesday, March 27, 2024
1:45pm in LCB 222
Title: Bistable dynamics in a model of vascular damage in Alzheimer's disease
Abstract: Alzheimer's disease (AD) is characterised by the accumulation and spread of amyloid beta
(Ab), a protein that is prone to misfolding, aggregation into plaques, and propagation along
axon fibers. For several decades, these features of Ab have been the primary foci of AD
research and the primary target of clinical trials. Recent experimental evidence has
highlighted the important role of Ab-induced capillary damage in AD, suggesting that
capillary bed rarefaction is caused by Ab and conversely, that the resulting ischaemia
aggravates Ab accumulation.
This presentation will have two parts. First, we will present a dynamical system model of
mixed Ab-capillary pathology in AD. Our goal is to understand the consequences of
incorporating ischaemic effects into existing models that treat Ab as a prion, i.e.
``proteinaceous infectious particle". The brain is modelled as a network of regions (nodes)
within which Ab and the local capillary bed interact, with transport between regions
enabled by the structural connectome (edges). We will find that the model has a bistable
character and that this is the key to understanding its behaviour.
Second, we will switch gears to discuss a reduced, 1D continuum version of the above
model, focusing on the question of its steady states' stability properties. We will review the
classic paper of Ludwig, Aronson and Weinberger (1979), whose model of the spruce
budworm is equivalent to our continuum model, and sketch a simple method for assessing
the stability of its steady states that does not resort to comparison methods.
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