The Kinetics and Mechanism of Inhibitor Drugs in the Treatment of Alzheimer's Disease

The etiology of Alzheimer's disease (AD) remains elusive. From a pathological point of view, several complex hypotheses, such as impaired neurotransmission, oxidative stress, and aggregation of amyloid- $\beta$ (A $\beta$), are considered crucial contributors to the pathophysiology of AD. Recent studies have primarily focused on AD treatment strategies targeting drugs that intervene in cerebral deposition of aggregated amyloid- $\beta$ (A $\beta$) polymers, often found in the form of amyloid plaques. In this paper, we present intuitive mathematical models that clarify the treatment of AD in the presence of inhibitory drugs. These models elucidate the intricate kinetics involved in A $\beta$ formation and the interaction of drugs with these processes. We discuss two categories of drugs: first, anti-inflammatory drugs (NSAIDs), which act as monomer inhibitors of A $\beta$ aggregation, and second, drugs that directly interact with A $\beta$ aggregated polymers. We initially analyze each drug independently and then assess their combined effects. Our numerical simulations demonstrate that the first type of drug reduces the equilibrium state value of aggregated filaments, whereas the second model of drug exhibits even greater efficacy in reducing the equilibrium state value of aggregated filaments. Furthermore, we conduct simulations of the simultaneous application of both drugs. The results are compared with the experimental data.