Usher J R, Henderson D
School of Computer and Mathematical Sciences, Robert Gordon University, Aberdeen, Scotland, UK.
IMA J Math Appl Med Biol. 1996 Jun;13(2):99-126.
The pioneering mathematical analyses for describing the phenomenon of clonal selection, whereby cancer cells mutate and become resistant to treatment, were carried out by Goldie & Coldman (1979, 1983). The present analysis yields more generalized drug-resistant models arising in chemotherapy treatment when cycle-nonspecific (CNS) drugs (i.e. drugs which are toxic to cells irrespective of their position in the cell cycle) are deployed. This is accomplished by modifying models developed by Wheldon (1988) and Usher (1994) for investigating the effect of chemotherapy drugs on homogeneous cell populations (i.e. in the absence of drug resistance); both types of migration, of drug-sensitive cells to drug-resistant cells, and the possibility of a migration of drug-resistant cells to drug-sensitive cells, are incorporated into the models. Subsequently, drug concentrations are sought such that both the drug-resistant cell subpopulation and the drug-sensitive cell subpopulation either simultaneously decay or remain of constant size. The analysis reveals that the role played by the migration of drug-resistant cells to drug-sensitive cells is significant, if it occurs, when seeking appropriate drug concentrations. The qualitative results from these models provide further insight into the effective treatment of cancer by chemotherapy in the presence of drug resistance.
戈迪和戈德曼（1979年、1983年）对克隆选择现象进行了开创性的数学分析，在克隆选择现象中癌细胞发生突变并对治疗产生抗性。当使用周期非特异性（CNS）药物（即对处于细胞周期任何位置的细胞都有毒性的药物）进行化疗时，本分析得出了在化疗治疗中出现的更通用的耐药模型。这是通过修改惠尔登（1988年）和厄舍（1994年）开发的用于研究化疗药物对同质细胞群体（即在无耐药性情况下）影响的模型来实现的；模型纳入了药物敏感细胞向耐药细胞的两种迁移类型，以及耐药细胞向药物敏感细胞迁移的可能性。随后，寻找药物浓度，以使耐药细胞亚群和药物敏感细胞亚群同时衰减或保持恒定大小。分析表明，在寻找合适的药物浓度时，如果发生耐药细胞向药物敏感细胞的迁移，其作用是显著的。这些模型的定性结果为在存在耐药性的情况下通过化疗有效治疗癌症提供了进一步的见解。
