Applied Mathematics, Statistics, and Scientific Computation Program, Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742, USA.
Proc Natl Acad Sci U S A. 2010 Sep 28;107(39):16766-71. doi: 10.1073/pnas.1007726107. Epub 2010 Sep 8.
Often, resistance to drugs is an obstacle to a successful treatment of cancer. In spite of the importance of the problem, the actual mechanisms that control the evolution of drug resistance are not fully understood. Many attempts to study drug resistance have been made in the mathematical modeling literature. Clearly, in order to understand drug resistance, it is imperative to have a good model of the underlying dynamics of cancer cells. One of the main ingredients that has been recently introduced into the rapidly growing pool of mathematical cancer models is stem cells. Surprisingly, this all-so-important subset of cells has not been fully integrated into existing mathematical models of drug resistance. In this work we incorporate the various possible ways in which a stem cell may divide into the study of drug resistance. We derive a previously undescribed estimate of the probability of developing drug resistance by the time a tumor is detected and calculate the expected number of resistant cancer stem cells at the time of tumor detection. To demonstrate the significance of this approach, we combine our previously undescribed mathematical estimates with clinical data that are taken from a recent six-year follow-up of patients receiving imatinib for the first-line treatment of chronic myelogenous leukemia. Based on our analysis we conclude that leukemia stem cells must tend to renew symmetrically as opposed to their healthy counterparts that predominantly divide asymmetrically.
通常，药物耐药性是癌症治疗成功的障碍。尽管该问题很重要，但控制耐药性演变的实际机制尚未完全了解。在数学建模文献中已经进行了许多尝试来研究耐药性。显然，为了了解耐药性，必须对癌细胞的潜在动力学有一个很好的模型。最近引入快速发展的数学癌症模型库中的主要成分之一是干细胞。令人惊讶的是，这个如此重要的细胞亚群尚未完全纳入现有的耐药性数学模型中。在这项工作中，我们将干细胞可能分裂的各种可能方式纳入耐药性研究中。我们推导出了一种以前未描述的估计方法，用于估计在肿瘤被检测到时产生耐药性的概率，并计算在肿瘤检测时耐药性癌症干细胞的预期数量。为了证明这种方法的重要性，我们将我们以前未描述的数学估计与从最近六年接受伊马替尼一线治疗慢性髓性白血病的患者的临床数据结合起来。基于我们的分析，我们得出结论，白血病干细胞必须倾向于对称地自我更新，而不是像它们的健康对应物那样主要不对称地分裂。
