Simple Summary Chimeric antigen receptor (CAR)-T cell therapy is a promising treatment for highly resistant blood cancers, using genetically modified T cells from the patient or a donor. While CAR-T therapy has been successful in pre-clinical and clinical stages for cancer treatment, it also presents challenges, including cytokine release syndrome. To improve the efficacy and reduce side effects, there is a need to better understand CAR-T cell behavior. We aimed to develop a mathematical framework that describes CAR-T behavior using ordinary differential equations (ODEs) and Bayesian parameter estimation (using advanced algorithms including Metropolis-Hastings, DEMetropolis, and DEMetropolisZ). This model will help to understand CAR-T behavior and, by extension, help to improve the effectiveness and efficacy of therapy in a clinical setting.Abstract Chimeric antigen receptor (CAR)-T cell therapy represents a breakthrough in treating resistant hematologic cancers. It is based on genetically modifying T cells transferred from the patient or a donor. Although its implementation has increased over the last few years, CAR-T has many challenges to be addressed, for instance, the associated severe toxicities, such as cytokine release syndrome. To model CAR-T cell dynamics, focusing on their proliferation and cytotoxic activity, we developed a mathematical framework using ordinary differential equations (ODEs) with Bayesian parameter estimation. Bayesian statistics were used to estimate model parameters through Monte Carlo integration, Bayesian inference, and Markov chain Monte Carlo (MCMC) methods. This paper explores MCMC methods, including the Metropolis-Hastings algorithm and DEMetropolis and DEMetropolisZ algorithms, which integrate differential evolution to enhance convergence rates. The theoretical findings and algorithms were validated using Python and Jupyter Notebooks. A real medical dataset of CAR-T cell therapy was analyzed, employing optimization algorithms to fit the mathematical model to the data, with the PyMC library facilitating Bayesian analysis. The results demonstrated that our model accurately captured the key dynamics of CAR-T cell therapy. This conclusion underscores the potential of parameter estimation to improve the understanding and effectiveness of CAR-T cell therapy in clinical settings.
