Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126, USA.
Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa.
J Theor Biol. 2019 Jan 7;460:37-55. doi: 10.1016/j.jtbi.2018.10.008. Epub 2018 Oct 6.
The cancer stem cell hypothesis has gained currency in recent times but concerns remain about its scientific foundations because of significant gaps that exist between research findings and comprehensive knowledge about cancer stem cells (CSCs). In this light, a mathematical model that considers hematopoietic dynamics in the diseased state of the bone marrow and peripheral blood is proposed and used to address findings about CSCs. The ensuing model, resulting from a modification and refinement of a recent model, develops out of the position that mathematical models of CSC development, that are few at this time, are needed to provide insightful underpinnings for biomedical findings about CSCs as the CSC idea gains traction. Accordingly, the mathematical challenges brought on by the model that mirror general challenges in dealing with nonlinear phenomena are discussed and placed in context. The proposed model describes the logical occurrence of discrete time delays, that by themselves present mathematical challenges, in the evolving cell populations under consideration. Under the challenging circumstances, the steady state properties of the model system of delay differential equations are obtained, analyzed, and the resulting mathematical predictions arising therefrom are interpreted and placed within the framework of findings regarding CSCs. Simulations of the model are carried out by considering various parameter scenarios that reflect different experimental situations involving disease evolution in human hosts. Model analyses and simulations suggest that the emergence of the cancer stem cell population alongside other malignant cells engenders higher dimensions of complexity in the evolution of malignancy in the bone marrow and peripheral blood at the expense of healthy hematopoietic development. The model predicts the evolution of an aberrant environment in which the malignant population particularly in the bone marrow shows tendencies of reaching an uncontrollable equilibrium state. Essentially, the model shows that a structural relationship exists between CSCs and non-stem malignant cells that confers on CSCs the role of temporally enhancing and stimulating the expansion of non-stem malignant cells while also benefitting from increases in their own population and these CSCs may be the main protagonists that drive the ultimate evolution of the uncontrollable equilibrium state of such malignant cells and these may have implications for treatment.
癌症干细胞假说近年来得到了广泛关注，但由于研究结果与癌症干细胞（CSC）的全面知识之间存在显著差距，其科学基础仍存在争议。有鉴于此，本文提出并使用了一个考虑骨髓和外周血疾病状态下造血动力学的数学模型来解决有关 CSC 的研究结果。该模型是对最近模型的修改和完善，其发展源于这样一种观点，即需要开发少数目前的 CSC 发育数学模型，为有关 CSC 的生物医学发现提供有见地的基础，因为 CSC 理念正在获得关注。因此，讨论并置放了模型所带来的反映处理非线性现象的一般挑战的数学挑战。所提出的模型描述了在考虑中的不断演化的细胞群体中，离散时间延迟的逻辑发生，这些延迟本身就带来了数学挑战。在具有挑战性的情况下，获得了时滞微分方程模型系统的稳态特性，对其进行了分析，并对由此产生的数学预测进行了解释，并将其置于有关 CSC 的研究结果的框架内。通过考虑反映涉及人类宿主疾病演变的各种实验情况的各种参数方案来进行模型模拟。模型分析和模拟表明，癌症干细胞群体与其他恶性细胞一起出现，导致骨髓和外周血中恶性肿瘤的演化出现更高维度的复杂性，而健康造血的发展则受到影响。该模型预测了异常环境的演变，其中恶性群体特别是在骨髓中表现出达到不可控平衡状态的趋势。从本质上讲，该模型表明 CSC 与非干细胞恶性细胞之间存在结构关系，这使 CSC 能够暂时增强和刺激非干细胞恶性细胞的扩张，同时也受益于其自身种群的增加，而这些 CSCs 可能是驱动此类恶性细胞不可控平衡状态最终演化的主要主角，这可能对治疗产生影响。
