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.