Spatiotemporal Distribution of β-Amyloid in Alzheimer Disease Is the Result of Heterogeneous Regional Carrying Capacities

Abstract

β-amyloid (Aβ) accumulation in the brain is 1 of 2 pathologic hallmarks of Alzheimer disease (AD), and the spatial distribution of Aβ has been studied extensively ex vivo. Methods: We applied mathematical modeling to Aβ in vivo PET imaging data to investigate competing theories of Aβ spread in AD. Results: Our results provided evidence that Aβ accumulation starts in all brain regions simultaneously and that its spatiotemporal distribution is due to heterogeneous regional carrying capacities (regional maximum possible concentration of Aβ) for the aggregated protein rather than to longer-term spreading from seed regions. Conclusion: The in vivo spatiotemporal distribution of Aβ in AD can be mathematically modeled using a logistic growth model in which the Aβ carrying capacity is heterogeneous across the brain but the exponential growth rate and time of half maximal Aβ concentration are constant.

Keywords: Alzheimer disease; PET/CT; image processing; mathematical modeling; neuroimaging; β-amyloid.

FIGURE 1.

Logistic growth model describing Aβ PET imaging signal over time as function of PET NS, K, T₅₀, and r.

FIGURE 2.

Sixteen logistic growth models of Aβ accumulation with example curves from 3 distinct brain regions. Models in gray have regionally different T₅₀s and are consistent with spreading from seed regions, whereas models in white are consistent with local tissue properties driving Aβ accumulation process.

FIGURE 3.

Model fitting of most parsimonious logistic growth model (model 11) to chronological ¹⁸F-AV-45 Aβ PET data in 9 regions. Model accurately describes data for regions of high (top row), medium (middle row), and low (bottom row) accumulation. A = anterior; D = dorsal; inf = inferior.

FIGURE 4.

Parametric images displayed as orthographic projections for K and NS obtained from fitting model 11 at voxel level. Gray matter (GM) and white matter (WM) probability maps are displayed for reference. Highest carrying capacities were in frontal lobe, and lowest were in cerebellum, occipital lobe, and brain stem. NS image is consistent with known NS of ¹⁸F-AV-45 to white matter.