Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are associated with the prion-like propagation and aggregation of toxic proteins. A long standing hypothesis that amyloid-beta drives Alzheimer’s disease has proven the subject of contemporary controversy; leading to new research in both the role of tau protein and its interaction with amyloid-beta. Conversely, recent work in mathematical modeling has demonstrated the relevance of nonlinear reaction-diffusion type equations to capture essential features of the disease. Such approaches have been further simplified, to network-based models, and offer researchers a powerful set of computationally tractable tools with which to investigate neurodegenerative disease dynamics. Here, we propose a novel, coupled network-based model for a two-protein system that includes an enzymatic interaction term alongside a simple model of aggregate transneuronal damage. We apply this theoretical model to test the possible interactions between tau proteins and amyloid-beta and study the resulting coupled behavior between toxic protein clearance and proteopathic phenomenology. Our analysis reveals ways in which amyloid-beta and tau proteins may conspire with each other to enhance the nucleation and propagation of different diseases, thus shedding new light on the importance of protein clearance and protein interaction mechanisms in prion-like models of neurodegenerative disease.
A hallmark of Alzheimer’s disease is the aggregation of insoluble amyloid-beta plaques and tau protein neurofibrillary tangles. A key histopathological observation is that tau protein aggregates follow a structured progression pattern through the brain. Mathematical network models of prion-like propagation have the ability to capture such patterns, but a number of factors impact the observed staging result, thus introducing questions regarding model selection. Here, we introduce a novel approach, based on braid diagrams, for studying the structured progression of a marker evolving on a network. We apply this approach to a six-stage ‘Braak pattern’ of tau proteins, in Alzheimer’s disease, motivated by a recent observation that seed-competent tau precedes tau aggregation. We show that the different modeling choices, from the model parameters to the connectome resolution, play a significant role in the landscape of observable staging patterns. Our approach provides a systematic way to approach model selection for network propagation of neurodegenerative diseases that ensures both reproducibility and optimal parameter fitting.
Misfolded tau proteins are a classical hallmark of Alzheimer's disease. Increasing evidence indicates that tau-and not amyloid-is the main agent in driving neurodegeneration and tissue atrophy in Alzheimer's brains. However, the precise correlation between tau and atrophy remains insufficiently understood. Here we explore tau-atrophy interactions by integrating a multiphysics brain network model and longitudinal neuroimaging data for n = 61 subjects from the Alzheimer's Disease Neuroimaging Initiative. Using Bayesian inference with a hierarchical prior structure, we personalize subject-level parameter distributions for each individual subject and infer group-level parameter distributions for amyloid positive and negative groups. Our results show that the group-level tau growth for amyloid positive subjects of 0.0161/year is significantly larger (p=0.0036) than for amyloid negative subjects of Correlating tau pathology to brain atrophy -0.2042/year. Similarly, the group-level tau-induced atrophy for amyloid positive subjects of 0.0165/year is significantly larger (p=0.0048) than for amyloid negative subjects of 0.0111/year. These findings support the hypothesis that amyloid pathology has a magnifying effect on tau pathology and tissue atrophy. Our model may serve as a descriptive tool to quantify the correlation between tau and atrophy, as well as a predictive tool to estimate personalized tau pathology, atrophy, and cognitive impairment timelines from a sequence of medical images.
For more than 25 years, the amyloid hypothesis--the paradigm that amyloid is the primary cause of Alzheimer's disease--has dominated the Alzheimer's community. Now, increasing evidence suggests that tissue atrophy and cognitive decline in Alzheimer's disease are more closely linked to the amount and location of misfolded tau protein than to amyloid plaques. However, the precise correlation between tau pathology and tissue atrophy remains unknown. Here, we integrate multiphysics modeling and Bayesian inference to create personalized tau-atrophy models using longitudinal clinical images from the the Alzheimer's Disease Neuroimaging Initiative. For each subject, we infer three personalized parameters, the tau misfolding rate, the tau transport coefficient, and the tau-induced atrophy rate from four consecutive annual tau positron emission tomography scans and structural magnetic resonance images. Strikingly, the tau-induced atrophy coefficient of 0.13/year (95% CI: 0.097-0.189) was fairly consistent across all subjects suggesting a strong correlation between tau pathology and tissue atrophy. Our personalized whole brain atrophy rates of 0.68-1.68%/year (95% CI: 0.5-2.0) are elevated compared to healthy subjects and agree well with the atrophy rates of 1-3%/year reported for Alzheimer's patients in the literature. Once comprehensively calibrated with a larger set of longitudinal images, our model has the potential to serve as a diagnostic and predictive tool to estimate future atrophy progression from clinical tau images on a personalized basis.
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