Effect of diffusivity of amyloid beta monomers on the formation of senile plaques

Alzheimers disease (AD) presents a perplexing question: why does its development span decades, even though individual amyloid beta (A{beta}) deposits (senile plaques) can form rapidly in as little as 24 hours, as recent publications suggest? This study investigated whether the formation of senile plaques can be limited by factors other than polymerization kinetics alone. Instead, their formation may be limited by the diffusion-driven supply of A{beta} monomers, along with the rate at which the monomers are produced from amyloid precursor protein (APP) and the rate at which A{beta} monomers undergo degradation. A mathematical model incorporating the nucleation and autocatalytic process (via the Finke-Watzky model), as well as A{beta} monomer diffusion, was proposed. The obtained system of partial differential equations was solved numerically, and a simplified version was investigated analytically. The computational results predicted that it takes approximately 7 years for A{beta} aggregates to reach a neurotoxic concentration of 50 M. Additionally, a sensitivity analysis was performed to examine how the diffusivity of A{beta} monomers and their production rate impact the concentration of A{beta} aggregates.