MCMC Methods for Parameter Estimation in ODE Systems for CAR-T Cell Cancer Therapy

• Published in: Cancers Vol. 16; no. 18; p. 3132
• Main Authors: Antonini, Elia, Mu, Gang, Sansaloni-Pastor, Sara, Varma, Vishal, Kabak, Ryme
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 11.09.2024; MDPI
• Subjects: Algorithms; Antigens; Antimitotic agents; Antineoplastic agents; Bayesian analysis; Cancer; Cancer therapies; Care and treatment; Cell growth; Cell proliferation; Cell therapy; Chimeric antigen receptors; Cytokines; Cytotoxicity; Differential equations; Genetically modified organisms; Health aspects; Immunotherapy; Lymphocytes; Lymphocytes T; Markov analysis; Markov chains; Markov processes; Mathematical models; Mathematical optimization; Methods; Monte Carlo method; Monte Carlo simulation; Ordinary differential equations; Parameter estimation; Patients; Remission (Medicine); Statistical analysis; T cells; Germany; Markov chain; differential evolution; Monte Carlo; Bayesian; ODEs; immunotherapy; MCMC; Metropolis–Hastings; parameter estimation; CAR-T cell therapy; oncology; Python
• ISSN: 2072-6694; 2072-6694
• DOI: 10.3390/cancers16183132

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.