  Background: Despite the striking efforts in investigating neurobiological
factors behind the acquisition of amyloid-\b{eta} (A), protein tau (T), and
neurodegeneration ([N]) biomarkers, the mechanistic pathways of how AT[N]
biomarkers spreading throughout the brain remain elusive. Objectives: To
disentangle the massive heterogeneities in AD progressions and identify
vulnerable/critical brain regions to AD pathology. Methods: In this work, we
characterized the interaction of AT[N] biomarkers and their propagation across
brain networks using a novel bistable reaction-diffusion model, which allows us
to establish a new systems biology underpinning of Alzheimer's disease (AD)
progression. We applied our model to large-scale longitudinal neuroimages from
the ADNI database and studied the systematic vulnerability and criticality of
brains. Results: Our model yields long term prediction that is statistically
significant linear correlated with temporal imaging data, produces clinically
consistent risk prediction, and captures the Braak-like spreading pattern of
AT[N] biomarkers in AD development. Conclusion: Our major findings include (i)
tau is a stronger indicator of regional risk compared to amyloid, (ii) temporal
lobe exhibits higher vulnerability to AD-related pathologies, (iii) proposed
critical brain regions outperform hub nodes in transmitting disease factors
across the brain, and (iv) comparing the spread of neuropathological burdens
caused by amyloid-\b{eta} and tau diffusions, disruption of metabolic balance
is the most determinant factor contributing to the initiation and progression
of Alzheimer's disease.
