Modelling of anti-inflammatory treatment in the Alzheimer disease: optimal regimen and outcome

The application of non-steroidal anti-inflammatory drugs (NSAIDs) for Alzheimer's disease is considered to be a promising therapeutic approach. Epidemiological studies suggest potential benefits of NSAIDs; however, these findings are not consistently supported by clinical trials. This long-standing discrepancy has persisted for decades and remains a significant barrier to developing effective treatment strategies. To assess the efficacy of NSAIDs in Alzheimer's disease, we have developed a mathematical model based on a system of ordinary differential equations. The model captures the dynamics of key players in disease progression, including A $\beta$ -monomers, oligomers, pro-inflammatory mediators (M1 microglial cells and pro-inflammatory cytokines), and anti-inflammatory mediators (M2 microglial cells and anti-inflammatory cytokines). The effects of NSAIDs are modeled through a reduction in the production rate of inflammatory cytokines (IC). While a single NSAID administration temporarily reduces IC levels, their concentration eventually returns to baseline due to drug elimination. The return time depends on the drug dose, resulting in a patient-specific return time function. By analyzing this function, we propose an optimal treatment regimen and identify conditions under which NSAID treatment is most effective in reducing IC levels. Our results suggest that NSAID efficacy in Alzheimer's disease is influenced by the stage of the disease (with earlier intervention being more effective), patient-specific parameters, and the treatment regimen. The approach developed here can also be generalized to evaluate the efficacy of anti-inflammatory treatments for other diseases.