  It is well known that today nearly one in six of the world's population has
to deal with neurodegenerative disorders. While a number of medical devices
have been developed for the detection, prevention, and treatments of such
disorders, some fundamentals of the progression of associated diseases are in
urgent need of further clarification. In this paper, we focus on Alzheimer's
disease, where it is believed that the concentration changes in amyloid-beta
and tau proteins play a central role in its onset and development. A multiscale
model is proposed to analyze the propagation of these concentrations in the
brain connectome. In particular, we consider a modified heterodimer model for
the protein-protein interactions. Higher toxic concentrations of amyloid-beta
and tau proteins destroy the brain cell. We have studied these propagations for
the primary and secondary and their mixed tauopathy. We model the damage of a
brain cell by the nonlocal contributions of these toxic loads present in the
brain cells. With the help of rigorous analysis, we check the stability
behaviour of the stationary points corresponding to the homogeneous system.
After integrating the brain connectome data into the developed model, we see
that the spreading patterns of the toxic concentrations for the whole brain are
the same, but their concentrations are different in different regions. Also,
the time to propagate the damage in each region of the brain connectome is
different.
