Braiding Braak and Braak: Staging patterns and model selection in network neurodegeneration

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. Author Summary Network diffusion models of neurodegenerative diseases are a class of dynamical systems that simulate the evolution of toxic proteins on the connectome. These models predict, from an initial seed, a pattern of invasion called staging. The generalized staging problem seeks to systematically study the effect of various model choices on staging. We introduce methods based on braid diagrams to test the possible staging landscape of a model and how it depends on the choice of connectome, as well as the model parameters. Our primary finding is that connectome construction, the choice of the graph Laplacian, and transport models all have an impact on staging that should be taken into account in any study.