  One of the hallmarks of Alzheimer's disease (AD) is the accumulation and
spread of toxic aggregates of tau protein. The progression of AD tau pathology
is thought to be highly stereotyped, which is in part due to the fact that tau
can spread between regions via the white matter tracts that connect them.
Mathematically, this phenomenon has been described using models of "network
diffusion", where the rate of spread of tau between brain regions is
proportional to its concentration gradient and the amount of white matter
between them. Although these models can robustly predict the progression of
pathology in a wide variety of neurodegenerative diseases, including AD, an
under explored aspect of tau spreading is that it is governed not simply by
diffusion but also active transport along axonal microtubules. Spread can
therefore take on a directional bias, resulting in distinct patterns of
deposition, but current models struggle to capture this phenomenon. Recently,
we have developed a mathematical model of the axonal transport of toxic tau
proteins that takes into account the effects tau exerts on the molecular
motors. Here we describe and implement a macroscopic version of this model,
which we call the Network Transport Model (NTM). A key feature of this model is
that, while it predicts tau dynamics at a regional level, it is parameterized
in terms of only microscopic processes such as aggregation and transport rates;
that is, differences in brain-wide tau progression can be explained by its
microscopic properties. We provide numerical evidence that, as with the
two-neuron model that the NTM extends, there are distinct and rich dynamics
with respect to the overall rate of spread and the staging of pathology when we
simulated the NTM on the hippocampal subnetwork. The theoretical insights
provided by the NTM have broad implications for understanding AD
pathophysiology more generally.
