Network Diffusion Modeling Explains Longitudinal Tau PET Data

Abstract

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.

Keywords: Alzheimer's disease; Neuroimaging; model calibration; network diffusion model; tau PET.

Figure 1

Image data analysis. Workflow for region of interest (ROI) based positron emission tomography (PET) image analysis. For each subject, at each time point, we co-register the PET images to the T1 weighted magnetic resonance images (MRI), which we segment using FreeSurfer to calculate the standardized uptake value ratios (SUVR) for each region of interest (ROI). Our study contains 46 subjects, 3–4 time points, and 83 regions of interest.

Figure 2

Brain network models. Connectivity-weighted network from the human brain connectome and adjacency matrices of connectivity-weighted intracellular spreading model and distance-weighted extracellular spreading model. The intracellular spreading model features a small number of strong connections within each hemisphere and only few connections between them; the extracellular spreading model features a large number of moderately strong connections across the entire brain. Colors represent the connectivity between two brain regions.

Figure 3

Regional tau PET concentration. Mean tau concentration from PET scans across all 46 subjects with 3–4 annual scans across all brain regions. Red regions consistently exhibit high tau loads in all subjects while blue regions tend to be free of tau in most subjects.

Figure 4

Longitudinal tau PET concentration. Standardized uptake value ratios from PET scans for 46 subjects with 3–4 annual scans in 66 cortical regions and the hippocampus. Regions on the vertical axis are sorted by mean tau load, from top to bottom. Subjects on the horizontal axis are sorted by mean tau load across all regions and visits, from left to right. Each block of columns represents data for one subject. Within each block, each subcolumn represents data from one annual PET scan.

Figure 5

Parameter identification. Personalized production rate α and diffusion coefficient κ for the intracellular and extracellular diffusion models, only including the 21 subjects with a positive production rate. For the connectivity-weighted intracellular spreading model, α = 0.21 ± 0.15 and κ = 0.34 ± 0.43. For the distance-weighted extracellular spreading model, α = 0.20 ± 0.14 and κ = 0.01 ± 0.01.

Figure 6

Model performance. Simulated concentration c^sim and PET-based concentration c^pet of pathogenic tau protein for intracellular and extracellular network diffusion models and null models without production, without diffusion, and without both. Each data point represents the simulated and PET-based concentration for one subject, one visit, and one region of interest. The further a data point is away from the gray line, the worse the prediction. The global residual error err of each model measures the overall prediction error of each model. (*) indicates a subject-wise error significantly higher than for the full model in paired-sample t-test. The correlation coefficient R measures the correlation strength between prediction and observation for each model. (**) indicates a correlation coefficient significantly lower than for the full model using Fisher's R-to-z transform.

Figure 7

Model performance. Inherent data correlation. Baseline and final PET-based concentrations c^pet, and simulated concentration c^sim over PET-based concentration c^pet of pathogenic tau protein for intracellular and extracellular network diffusion models. Each data point represents the PET-based concentration for one subject, one region of interest, and one visit. (**) Correlation coefficient R is significantly lower than for the two proposed models.

Figure 8

Personalized model prediction. Regional tau concentrations from raw and scaled standardized uptake value ratios c^raw and c^pet vs. simulated tau concentrations c^sim with a connectivity-weighted intracellular and a distance-weighted extracellular model for personalized initial conditions, production rates, and diffusion coefficients of subject #12 from Figures 9, 10. Lateral view, left hemisphere.

Figure 9

Personalized model prediction. Regional tau concentrations from raw and scaled standardized uptake value ratios c^raw and c^pet vs. simulated tau concentrations c^sim with a connectivity-weighted intracellular and a distance-weighted extracellular model for personalized initial conditions, production rates, and diffusion coefficients of subject #12 from Figures 9, 10. Medial view, right hemisphere.

Figure 10

Model prediction of intracellular model. Simulated tau concentrations c^sim with connectivity-weighted intracellular model for 21 subjects for 15 years in 66 cortical regions and the hippocampus. Each block of columns represents the simulation for one subject with their personalized initial conditions, production rate α, and diffusion coefficient κ. Within each block, each subcolumn represents simulated concentrations for 1 year.

Figure 11

Model prediction of extracellular model. Simulated tau concentrations c^sim with connectivity-weighted intracellular model for 21 subjects for 15 years in 66 cortical regions and the hippocampus. Each block of columns represents the simulation for one subject with their personalized initial conditions, production rate α, and diffusion coefficient κ. Within each block, each subcolumn represents simulated concentrations for 1 year.