Chau Hoang , Tuan Anh Phan , Cameron J. Turtle , Jianjun Paul Tian
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引用次数: 0
摘要
在确定性和随机过程混合模型的基础上,我们使用白噪声来解释治疗结果中的患者变异性,使用超参数来表示队列中的患者异质性,并以伊托随机微分方程构建了一个随机模型,用于测试 CAR T 细胞疗法中三种不同治疗方案的疗效。该随机模型有三个遍历不变量,对应于确定性系统的三个不稳定平衡解,而遍历不变量是肿瘤生长某些条件下的吸引子。随机系统的稳定动态反映了治疗的长期结果,而瞬态动态则提供了短期治愈的机会。通过随机模型的瞬态动力学,我们对三种不同的 CAR T 细胞治疗方案进行了数值模拟。治愈时间和进展时间的概率分布展示了不同方案的结果细节,这对当前 CAR T 细胞疗法的临床研究具有重要意义。
A stochastic framework for evaluating CAR T cell therapy efficacy and variability
Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy.
期刊介绍:
Mathematical Biosciences publishes work providing new concepts or new understanding of biological systems using mathematical models, or methodological articles likely to find application to multiple biological systems. Papers are expected to present a major research finding of broad significance for the biological sciences, or mathematical biology. Mathematical Biosciences welcomes original research articles, letters, reviews and perspectives.