β-amyloid (Aβ) accumulation in the brain is one of two pathological hallmarks of Alzheimer's Disease (AD) and its spatial distribution has been studied extensively ex vivo. We apply mathematical modelling to Aβ in vivo PET imaging data in order to investigate competing theories of Aβ spread in AD. Our results provide evidence that Aβ accumulation starts in all brain regions simultaneously and that its spatiotemporal distribution is a result of heterogeneous regional carrying capacities (regional maximum possible concentration of Aβ) for the aggregated protein rather than longer term spreading from seed regions.