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Amyloid-β and hyperphosphorylated tau protein are known drivers of neuropathology in Alzheimer's disease. Tau in particular spreads in the brains of patients following a spatiotemporal pattern that is highly sterotypical and correlated with subsequent neurodegeneration. Novel medical imaging techniques can now visualize the distribution of tau in the brain in vivo , allowing for new insights to the dynamics of this biomarker. Here we personalize a network diffusion model with global spreading and local production terms to longitudinal tau positron emission tomography data of 76 subjects from the Alzheimer's Disease Neuroimaging Initiative. We use Bayesian inference with a hierarchical prior structure to infer means and credible intervals for our model parameters on group and subject levels. Our results show that the group average protein production rate for amyloid positive subjects is significantly higher with 0.019±0.27/yr, than that for amyloid negative subjects with −0.143±0.21/yr ( p = 0.0075). These results support the hypothesis that amyloid pathology drives tau pathology. The calibrated model could serve as a valuable clinical tool to identify optimal time points for follow-up scans and predict the timeline of disease progression. 

Alzheimer's disease is associated with the cerebral accumulation of neurofibrillary tangles of hyperphosphorylated tau protein. The progressive occurrence of tau aggregates in different brain regions is closely related to neurodegeneration and cognitive impairment. However, our current understanding of tau propagation relies almost exclusively on postmortem histopathology, and the precise propagation dynamics of misfolded tau in the living brain remain poorly understood. Here we combine longitudinal positron emission tomography and dynamic network modeling to test the hypothesis that misfolded tau propagates preferably along neuronal connections. We follow 46 subjects for three or four annual positron emission tomography scans and compare their pathological tau profiles against brain network models of intracellular and extracellular spreading. For each subject, we identify a personalized set of model parameters that characterizes the individual progression of pathological tau. Across all subjects, the mean protein production rate was 0.21 ± 0.15 and the intracellular diffusion coefficient was 0.34 ± 0.43. Our network diffusion model can serve as a tool to detect non-clinical symptoms at an earlier stage and make informed predictions about the timeline of neurodegeneration on an individual personalized basis. 

The prion hypothesis states that misfolded proteins can act as infectious agents that template the misfolding and aggregation of healthy proteins to transmit a disease. Increasing evidence suggests that pathological proteins in neurodegenerative diseases adopt prion-like mechanisms and spread across the brain along anatomically connected networks. Local kinetic models of protein misfolding and global network models of protein spreading provide valuable insight into several aspects of prion-like diseases. Yet, to date, these models have not been combined to simulate how pathological proteins multiply and spread across the human brain. Here, we create an efficient and robust tool to simulate the spreading of misfolded protein using three classes of kinetic models, the Fisher–Kolmogorov model, the Heterodimer model and the Smoluchowski model. We discretize their governing equations using a human brain network model, which we represent as a weighted Laplacian graph generated from 418 brains from the Human Connectome Project. Its nodes represent the anatomic regions of interest and its edges are weighted by the mean fibre number divided by the mean fibre length between any two regions. We demonstrate that our brain network model can predict the histopathological patterns of Alzheimer’s disease and capture the key characteristic features of finite-element brain models at a fraction of their computational cost: simulating the spatio-temporal evolution of aggregate size distributions across the human brain throughout a period of 40 years takes less than 7 s on a standard laptop computer. Our model has the potential to predict biomarker curves, aggregate size distributions, infection times, and the effects of therapeutic strategies including reduced production and increased clearance of misfolded protein.