Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome.

The prion-like hypothesis of neurodegenerative diseases states that the accumulation of misfolded proteins in the form of aggregates is responsible for tissue death and its associated neurodegenerative pathology and cognitive decline. Some disease-specific misfolded proteins can interact with healthy proteins to form long chains that are transported through the brain along axonal pathways. Since aggregates of different sizes have different transport properties and toxicity, it is important to follow independently their evolution in space and time. Here, we model the spreading and propagation of aggregates of misfolded proteins in the brain using the general Smoluchowski theory of nucleation, aggregation, and fragmentation. The transport processes considered here are either anisotropic diffusion along axonal bundles or discrete Laplacian transport along a network. In particular, we model the spreading and aggregation of both amyloid-ß and τ molecules in the brain connectome. We show that these two models lead to different size distributions and different propagation along the network. A detailed analysis of these two models also reveals the existence of four different stages with different dynamics and invasive properties.

Bayesian Physics-Based Modeling of Tau Propagation in Alzheimer's Disease.

Amyloid-ß 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.

Effects of B.1.1.7 and B.1.351 on COVID-19 Dynamics: A Campus Reopening Study.

The timing and sequence of safe campus reopening has remained the most controversial topic in higher education since the outbreak of the COVID-19 pandemic. By the end of March 2020, almost all colleges and universities in the United States had transitioned to an all online education and many institutions have not yet fully reopened to date. For a residential campus like Stanford University, the major challenge of reopening is to estimate the number of incoming infectious students at the first day of class. Here we learn the number of incoming infectious students using Bayesian inference and perform a series of retrospective and projective simulations to quantify the risk of campus reopening. We create a physics-based probabilistic model to infer the local reproduction dynamics for each state and adopt a network SEIR model to simulate the return of all undergraduates, broken down by their year of enrollment and state of origin. From these returning student populations, we predict the outbreak dynamics throughout the spring, summer, fall, and winter quarters using the inferred reproduction dynamics of Santa Clara County. We compare three different scenarios: the true outbreak dynamics under the wild-type SARS-CoV-2, and the hypothetical outbreak dynamics under the new COVID-19 variants B.1.1.7 and B.1.351 with 56% and 50% increased transmissibility. Our study reveals that even small changes in transmissibility can have an enormous impact on the overall case numbers. With no additional countermeasures, during the most affected quarter, the fall of 2020, there would have been 203 cases under baseline reproduction, compared to 4727 and 4256 cases for the B.1.1.7 and B.1.351 variants. Our results suggest that population mixing presents an increased risk for local outbreaks, especially with new and more infectious variants emerging across the globe. Tight outbreak control through mandatory quarantine and test-trace-isolate strategies will be critical in successfully managing these local outbreak dynamics.

Network Diffusion Modeling Explains Longitudinal Tau PET Data.

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.

Prion-like spreading of Alzheimer's disease within the brain's connectome.

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.

Towards Patient-Specific Computational Modelling of Articular Cartilage on the Basis of Advanced Multiparametric MRI Techniques.

Cartilage degeneration is associated with tissue softening and represents the hallmark change of osteoarthritis. Advanced quantitative Magnetic Resonance Imaging (qMRI) techniques allow the assessment of subtle tissue changes not only of structure and morphology but also of composition. Yet, the relation between qMRI parameters on the one hand and microstructure, composition and the resulting functional tissue properties on the other hand remain to be defined. To this end, a Finite-Element framework was developed based on an anisotropic constitutive model of cartilage informed by sample-specific multiparametric qMRI maps, obtained for eight osteochondral samples on a clinical 3.0 T MRI scanner. For reference, the same samples were subjected to confined compression tests to evaluate stiffness and compressibility. Moreover, the Mankin score as an indicator of histological tissue degeneration was determined. The constitutive model was optimized against the resulting stress responses and informed solely by the sample-specific qMRI parameter maps. Thereby, the biomechanical properties of individual samples could be captured with good-to-excellent accuracy (mean R2 [square of Pearson's correlation coefficient]: 0.966, range [min, max]: 0.904, 0.993; mean Ω [relative approximated error]: 33%, range [min, max]: 20%, 47%). Thus, advanced qMRI techniques may be complemented by the developed computational model of cartilage to comprehensively evaluate the functional dimension of non-invasively obtained imaging biomarkers. Thereby, cartilage degeneration can be perspectively evaluated in the context of imaging and biomechanics.