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.
嵌合抗原受体（CAR）-T细胞疗法代表了治疗耐药性血液癌症的一项突破性进展。该方法基于对来自患者或供体的T细胞进行基因改造。尽管近年来其应用日益广泛，但CAR-T疗法仍面临诸多挑战，例如相关的严重毒性反应，包括细胞因子释放综合征。为模拟CAR-T细胞的动态过程，重点关注其增殖和细胞毒性活性，我们建立了一个基于常微分方程（ODEs）的数学框架，并采用贝叶斯参数估计方法。通过蒙特卡洛积分、贝叶斯推断和马尔可夫链蒙特卡洛（MCMC）方法进行模型参数估计。本文探讨了多种MCMC方法，包括Metropolis-Hastings算法以及融合差分进化策略以提升收敛速度的DEMetropolis和DEMetropolisZ算法。理论发现与算法通过Python和Jupyter Notebooks平台进行了验证。通过分析真实的CAR-T细胞疗法医疗数据集，采用优化算法使数学模型与数据拟合，并借助PyMC库进行贝叶斯分析。结果表明，我们的模型能准确捕捉CAR-T细胞疗法的关键动态特征。这一结论凸显了参数估计在提升临床环境中对CAR-T细胞疗法的理解与疗效方面的潜力。
MCMC Methods for Parameter Estimation in ODE Systems for CAR-T Cell Cancer Therapy
肿瘤(癌症)患者之家