Exploring a Mathematical Model for the Kinetics of β-Amyloid Molecular Imaging Probes through a Critical Analysis of Plaque Pathology

Abstract

Amyloid plaques are highly heterogeneous in content, size, density, and macromolecular crowding, as they are composed of masses of fibrils and other cellular material. Given this target architecture, the aggregated microenvironment offers a unique imaging target for ligands and positron emission tomography (PET) molecular imaging probes (MIPs). In this work, we address how the heterogeneous microenvironment of a plaque and its evolution may affect the kinetic rate constant of PET MIPs. We argue that macromolecular crowding will result in anomalous diffusion within plaque regions. To account for anomalous diffusion within plaques, we propose a diffusion-limited ligand-receptor compartmental model. Given the current state of knowledge about the pathological progression of Alzheimer's disease (AD), the model's parameters may be a function of the pathological progression of AD, which could result in biased estimates of the true amyloid load. The bias may be partially overcome through evaluation in conjunction with other measures of AD progression including cerebral glucose metabolism rate, neuronal cell loss, and activated inflammatory presence.