Travis B. Thompson

Alzheimer’s disease is characterised by the pathological interaction of two proteins, amyloid-beta (Aβ) and tau, which collectively drive neurodegeneration and cognitive decline. The progression of Aβ, tau, and neurodegeneration biomarkers is captured by the ATN framework, which is a powerful tool for disease classification. However, since the ATN framework is mainly descriptive, it cannot quantify or predict relationships between biomarkers over time. We address this limitation by introducing a dynamical ATN (dATN) model that mechanistically simulates the spatiotemporal progression of Aβ, tau, and neurodegeneration. The dATN model integrates mechanisms of prion-like protein aggregation of Aβ and tau, network-based tau propagation, Aβ-driven catalysis of tau progression, and tau-driven neurodegeneration. We calibrated the model using multimodal longitudinal imaging data from both the ADNI and BioFINDER-2 cohorts and show that it accurately fits longitudinal regional Aβ, tau, and neurodegeneration data. Using the dATN model, we show that Aβ-induced effects predict Braak-like cortical tau progression, that the spatial colocalisation of Aβ and tau is a crucial biomarker of disease acceleration, and that tau-driven atrophy strongly correlates with observed neurodegeneration. Furthermore, by integrating the disease progression model with pharmacokinetic–pharmacodynamic simulations, we present a powerful tool that facilitates regional evaluation of therapeutic strategies targeting Aβ, identification of critical intervention windows, and prediction of heterogeneous treatment effects across brain regions. This framework unifies mechanistic understanding with clinical imaging biomarkers, offering a quantitative approach for forecasting disease progression, testing mechanistic hypotheses, and optimising personalised treatment strategies in AD. One Sentence Summary: Colocalisation of A β and tau predicts regional tau progression and optimal A β -targeted intervention windows, while tau predicts neurodegeneration.

Neurotoxic protein fragments such as amyloid-beta and tau accumulate in characteristic staging patterns in Alzheimer’s disease (AD). The brain clears such metabolic substances via multiple different systems, including via the glymphatic (extracellular/extravascular) pathway. Here, we ask how the distinct features that characterize human glymphatic function would affect the prion-like cascade of protein invasion associated with AD. To address this question, we extract and analyze individual clearance rates from human glymphatic MRI (gMRI) data sets. These clearance rates define subject-specific maps of glymphatic clearance that vary both across cortical lobes and Braak staging regions. We apply these clearance maps as initial states in a computational network model linking misfolded proteins, tissue damage, and local clearance to simulate a series of individual proteinopathy trajectories. Our results show that the spatial heterogeneity in initial clearance induces characteristic propagation patterns, delaying and redirecting the disease progression. Moreover, reducing this spatial heterogeneity accelerates disease progression and induces staging patterns typically associated with AD. A comparison between well-rested subjects and subjects who underwent a single night of sleep deprivation did not reveal differences in initial clearance maps nor in simulated disease progression. These findings suggest that spatial heterogeneity in brain clearance may be a key factor for neurodegenerative resilience.

Microfluidic devices (MDs) present a novel method for detecting circulating tumor cells (CTCs), enhancing the process through targeted techniques and visual inspection. However, current approaches often yield heterogeneous CTC populations, necessitating additional processing for comprehensive analysis and phenotype identification. These procedures are often expensive, time-consuming, and need to be performed by skilled technicians. In this study, we investigate the potential of a cost-effective and efficient hyperuniform micropost MD approach for CTC classification. Our approach combines mathematical modeling of fluid-structure interactions in a simulated microfluidic channel with machine learning techniques. Specifically, we developed a cell-based modeling framework to assess CTC dynamics in erythrocyte-laden plasma flow, generating a large dataset of CTC trajectories that account for two distinct CTC phenotypes. Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) were then employed to analyze the dataset and classify these phenotypes. The results demonstrate the potential effectiveness of the hyperuniform micropost MD design and analysis approach in distinguishing between different CTC phenotypes based on cell trajectory, offering a promising avenue for early cancer detection. Author summary: Early detection is currently the most effective method to combat cancer, as it maximizes treatment options and improves potential survival rates. However, the cost of early detection presents a significant barrier, limiting access for underrepresented groups and discouraging industrial partners from investing in the research and development of screening devices. This study provides an in-silico conceptual validation for the development of an innovative hyperuniform microchip designed to identify circulating tumor cells (CTCs) without the need for biomarker labeling. We created a cell-based modeling framework to examine CTC dynamics in erythrocyte-laden plasma flow, producing an extensive dataset of CTC trajectories that reflect two distinct CTC phenotypes. Two machine learning architectures were utilized to analyze this dataset and classify the phenotypes. The results demonstrate the potential effectiveness of the hyperuniform micropost MD design and analysis approach in distinguishing between different CTC phenotypes based on cell trajectory, offering a promising and cost-effective method for early cancer detection.

Aggregation of the hyperphosphorylated tau protein is a central driver of Alzheimer’s disease, and its accumulation exhibits a rich spatio-temporal pattern that unfolds during the course of the disease, sequentially progressing through the brain across axonal connections. It is unclear how this spatio-temporal process is orchestrated – namely, to what extent the spread of pathologic tau is governed by transport between brain regions, local production or both. To address this, we develop a mechanistic model from tau PET data to describe tau dynamics along the Alzheimer’s disease timeline. Our analysis reveals longitudinal changes in production and transport dynamics on two independent cohorts, with subjects in early stage of the disease exhibiting transport-dominated spread, consistent with an initial spread of pathologic tau seeds, and subjects in late stage disease (Braak stage 3/4 onwards) characterised primarily by local production of tau. Furthermore, we demonstrate that the model can accurately predict subject-specific longitudinal tau accumulation at a regional level, potentially providing a new clinical tool to monitor and classify patient disease progression. Teaser: A mechanistic model reveals tau protein dynamics in Alzheimer’s, showing stage-specific shifts in transport and local production.

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 medical research showing that clearance plays an important role in the etiology, progression, and treatment of Alzheimer’s disease.

The multiple-network poroelasticity (MPET) equations describe deformation and pressures in an elastic medium permeated by interacting fluid networks. In this paper, we (i) place these equations in the theoretical context of coupled elliptic–parabolic problems, (ii) use this context to derive residual-based a posteriori error estimates and indicators for fully discrete MPET solutions and (iii) evaluate the performance of these error estimators in adaptive algorithms for a set of test cases: ranging from synthetic scenarios to physiologically realistic simulations of brain mechanics.

Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key problem is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? Here, motivated by the study of toxic protein propagation in neurodegenerative diseases, we present and compare three different estimates for the arrival time in order of increasing analytical complexity: the linear arrival time, obtained by linearizing the underlying dynamical system; the Lambert time, obtained by considering the interaction of pairs of nodes; and the nonlinear arrival time, obtained by asymptotic techniques. We use the classic Fisher–Kolmogorov–Petrovsky–Piskunov equation as a paradigm for the dynamics and show that each method provides different insights but consistent time estimates. Further, we show that the nonlinear asymptotic method also gives an approximate solution, valid in the entire domain, and the correct ordering of arrival regions over large regions of parameters and initial conditions.

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 medical research showing that clearance plays an important role in the etiology, progression and treatment of Alzheimer’s disease.

Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key question is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? Here, motivated by the study of toxic protein propagation in neurodegenerative diseases, we present and compare three different estimates for the arrival time in order of increasing analytical complexity: the linear arrival time, obtained by linearizing the underlying system; the Lambert time, obtained by considering the interaction of two nodes; and the nonlinear arrival time, obtained by asymptotic techniques. We use the classic Fisher-Kolmogorov-Petrovsky-Piskunov equation as a paradigm for the dynamics and show that each method provides different insight and time estimates. Further, we show that the nonlinear asymptotic method also gives an approximate solution valid in the entire domain and the correct ordering of arrival regions over large regions of parameters and initial conditions.