The cancer stem cell hypothesis states that tumors are heterogeneous and comprised of several different cell types that have a range of reproductive potentials. Cancer stem cells (CSCs), represent one class of cells that has both reproductive potential and the ability to differentiate. These cells are thought to drive the progression of aggressive and recurring cancers since they give rise to all other constituent cells within a tumor. With the development of immunotherapy in the last decade, the specific targeting of CSCs has become feasible and presents a novel therapeutic approach. In this paper, we construct a mathematical model to study how specific components of the immune system, namely dendritic cells and cytotoxic T-cells interact with different cancer cell types (CSCs and non-CSCs). Using a system of ordinary differential equations, we model the effects of immunotherapy, specifically dendritic cell vaccines and T-cell adoptive therapy, on tumor growth, with and without chemotherapy. The model reproduces several results observed in the literature, including temporal measurements of tumor size from in vivo experiments, and it is used to predict the optimal treatment schedule when combining different treatment modalities. Importantly, the model also demonstrates that chemotherapy increases tumorigenicity whereas CSC-targeted immunotherapy decreases it.

中文翻译：

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癌症干细胞靶向免疫疗法的数学模型。

癌症干细胞假说指出，肿瘤是异质性的，由几种具有一定繁殖潜能的不同细胞类型组成。癌症干细胞（CSC）代表一类具有生殖潜能和分化能力的细胞。这些细胞被认为可驱动侵袭性和复发性癌症的发展，因为它们会引起肿瘤内所有其他组成细胞的出现。随着近十年来免疫疗法的发展，对CSCs的特异性靶向已经变得可行并提出了一种新颖的治疗方法。在本文中，我们构建了一个数学模型来研究免疫系统的特定组成部分，即树突状细胞和细胞毒性T细胞如何与不同类型的癌细胞（CSC和非CSC）相互作用。使用常微分方程组，我们模拟了免疫疗法（特别是树突状细胞疫苗和T细胞过继疗法）对有无化疗的肿瘤生长的影响。该模型再现了文献中观察到的几种结果，包括体内实验中肿瘤大小的时间测量，并且当组合不同的治疗方式时，可用于预测最佳治疗方案。重要的是，该模型还证明了化学疗法可增加致瘤性，而以CSC为靶点的免疫疗法可降低其致癌性。结合不同的治疗方式时，可用于预测最佳治疗方案。重要的是，该模型还证明了化学疗法可增加致瘤性，而以CSC为靶点的免疫疗法可降低其致癌性。结合不同的治疗方式时，可用于预测最佳治疗方案。重要的是，该模型还证明了化学疗法可增加致瘤性，而以CSC为靶点的免疫疗法可降低其致癌性。