当淋巴细胞遇到其同源抗原时，它们被激活并经历有限次数的细胞分裂，在此期间它们分化为记忆细胞或效应细胞或死亡。虽然单个细胞的动力学通常是异质的，但群体水平的扩张动力学具有高度可重复性，这表明平均场描述。为了生成有限的分裂命运，我们考虑两种情况：细胞在一定次数的迭代后停止分裂，或者它们的死亡率随着每次细胞分裂而增加。组合系统的动力学可以映射到偏微分方程，并且为了选择合适的激活速率，我们获得了总细胞数和每个细胞平均分裂数的简单解析解，可以很好地描述信号-来自体外实验的依赖性 T 细胞扩增动力学。有趣的是，只有分裂停止机制才能产生与实验不矛盾的分裂命运的表达式。我们发现，单个细胞中分裂率的世代依赖性下降导致群体水平上的时间依赖性下降，这与先前提出的分裂命运的“死亡时间”控制机制一致。我们还推导了总细胞数的平均场方程，为将 T 细胞扩增动力学应用于免疫肿瘤学和 CAR-T 细胞疗法的定量系统药理学模型提供了基础。

When lymphocytes encounter their cognate antigen, they become activated and undergo a limited number of cell divisions during which they differentiate into memory or effector cells or die. While the dynamics of individual cells are often heterogeneous, the expansion kinetics at the population level are highly reproducible, suggesting a mean-field description. To generate a finite division destiny, we consider two scenarios: Cells stop dividing after a certain number of iterations or their death rate increases with each cell division. The dynamics of the combined system can be mapped to a partial differential equation, and for a suitable choice of the activation rate, we obtain simple analytical solutions for the total cell number and the mean number of divisions per cell which can well describe the signal-dependent T cell expansion kinetics from in vitro experiments. Interestingly, only the division cessation mechanism yields an expression for the division destiny that does not contradict experiments. We show that the generation-dependent decrease of the division rate in individual cells leads to a time-dependent decrease at the population level which is consistent with a "time-to-die" control mechanism for the division destiny as suggested previously. We also derive mean-field equations for the total cell number which provide a basis for implementing T cell expansion kinetics into quantitative systems pharmacology models for immuno-oncology and CAR-T cell therapies.