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

Putra, Prama Setia; Thompson, Travis; Chaggar, Pavanjit; Goriely, Alain

doi:10.1162/netn_a_00208

Cited by 13 publications

(20 citation statements)

References 39 publications

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“…This analysis suggests that the brain's connectivity may protect regions by allowing them to share the burden of clearing toxic loads with their neighbors. These conceptual observations may be interpreted in the context of neurofibrillary tangle (NFT) staging [53,72]. Indeed, (6) dictates that as toxic protein proliferates through neighboring regions, clearance is reduced below λ crit and the formation of NFTs can result.…”

Section: Perturbation Analysis Of Critical Network Toxic Seedingmentioning

confidence: 99%

“…We will here demonstrate that simple variations in the initial distribution of clearance can elicit variations in the observed patterns of toxic protein progression and explain these AD subtypes. To compare the effect of clearance on the distribution of NFTs, we follow previous studies [55,67,53,60] and augment (6) with a measure of (nodal) NFT production, denoted by q i (t), reflecting damage accumulation following the arrival of toxic proteins. Given a toxic protein concentration p i (t), the (post-processed) NFT aggregation marker is defined as the solution of the damage equation: qi = p i (1 − q i ), q i (0) = 0, i = 1, .…”

Section: Clearance Variation May Promote Ad Subtypesmentioning

confidence: 99%

“…In the case where λ i (0) = λ ∞ for all i , this system reduces to the standard Fisher-Kolmogorov system [20, 75, 53, 61].…”

Section: Modeling Toxic Protein and Clearance Interplaymentioning

confidence: 99%

“…Other normalized forms of the graph Laplacian may and have been used in the literature, but this standard form simultaneously conserves mass and enforces Fick’s constraint, thus guaranteeing that no transport occurs between regions with same concentration [61, Supplementary S1]. Specifically, we select the weighted adjacency matrix with entries , where n ij is the number of fibers along the axonal tract, connecting node i to node j , and ℓ ij is the average fiber length b etween the same two nodes.…”

Section: Modeling Toxic Protein and Clearance Interplaymentioning

confidence: 99%

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The role of clearance in neurodegenerative diseases

Brennan

Thompson

Oliveri

et al. 2022

Preprint

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Alzheimer's disease, the most common form of dementia, is a systemic neurological disorder associated with the formation of toxic, pathological aggregates of proteins within the brain that lead to severe cognitive decline, and eventually, death. In normal physiological conditions, the brain rids itself of toxic proteins using various clearance mechanisms. The efficacy of brain clearance can be adversely affected by the presence of toxic proteins and is also known to decline with age. Motivated by recent findings, such as the connection between brain cerebrospinal fluid clearance and sleep, we propose a mathematical model coupling the progression of toxic proteins over the brain's structural network and protein clearance. The model is used to study the interplay between clearance in the brain, toxic seeding, brain network connectivity, aging, and progression in neurodegenerative diseases such as Alzheimer's disease. Our findings provide a theoretical framework for the growing body of clinical results showing that clearance plays an important role in the etiology, progression and treatment of Alzheimer's disease.

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Section: Perturbation Analysis Of Critical Network Toxic Seedingmentioning

confidence: 99%

Section: Clearance Variation May Promote Ad Subtypesmentioning

confidence: 99%

“…In the case where λ i (0) = λ ∞ for all i , this system reduces to the standard Fisher-Kolmogorov system [20, 75, 53, 61].…”

Section: Modeling Toxic Protein and Clearance Interplaymentioning

confidence: 99%

Section: Modeling Toxic Protein and Clearance Interplaymentioning

confidence: 99%

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The role of clearance in neurodegenerative diseases

Brennan

Thompson

Oliveri

et al. 2022

Preprint

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“…( 4). The resulting equation has recently been studied in the context of neurodegenerative diseases in [35,66] in the case where L represents linear diffusion -f (x) = x, g(x) = 1. For extensions to two species with the same operator see for example [34,67].…”

Section: Insights Into Reaction-diffusion Systemsmentioning

confidence: 99%

From random walks on networks to nonlinear diffusion

Falcó¹

2022

Preprint

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Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great impact on collective movement of the group. For this reason, many models in mathematical biology have incorporated crowding effects and managed to understand their implications. Here, we build on a previously developed framework for random walks on networks to show that in the continuum limit, the underlying stochastic process can be identified with a diffusion partial differential equation. The diffusion coefficient of the emerging equation is in general density-dependent, and can be directly related to the transition probabilities of the random walk. Moreover, the relaxation time of the stochastic process is directly linked to the diffusion coefficient and also to network structure, as it usually happens in the case of linear diffusion. As a specific example, we study the equivalent of a porous-medium type equation on networks, which can be coarse-grained to obtain a known nonlinear equation. These findings also provide insights into reaction-diffusion systems with general diffusion operators, which have appeared recently in some applications.

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Correlating tau pathology to brain atrophy using a physics-based Bayesian model

Schäfer

Chaggar²,

Goriely³

et al. 2022

Engineering with Computers

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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.

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

Cited by 13 publications

References 39 publications

The role of clearance in neurodegenerative diseases

The role of clearance in neurodegenerative diseases

From random walks on networks to nonlinear diffusion

Correlating tau pathology to brain atrophy using a physics-based Bayesian model

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