Generating PET scan patterns in Alzheimer’s by a mathematical model

Abstract

Alzheimer disease (AD) is the most common form of dementia. The cause of the disease is unknown, and it has no cure. Symptoms include cognitive decline, memory loss, and impairment of daily functioning. The pathological hallmarks of the disease are aggregation of plaques of amyloid-β (Aβ) and neurofibrillary tangles of tau proteins (τ), which can be detected in PET scans of the brain. The disease can remain asymptomatic for decades, while the densities of Aβ and τ continue to grow. Inflammation is considered an early event that drives the disease. In this paper, we develop a mathematical model that can produce simulated patterns of (Aβ,τ) seen in PET scans of AD patients. The model is based on the assumption that early inflammations, R and R ¯, drive the growth of Aβ and τ, respectively. Recently approved drugs can slow the progression of AD in patients, provided treatment begins early, before significant damage to the brain has occurred. In line with current longitudinal studies, we used the model to demonstrate how to assess the efficacy of such drugs when given years before the disease becomes symptomatic.