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    题名: Optimal Policies of Non-Cross-Resistant Chemotherapy on Goldie and Coldman's Cancer Model
    作者: 陳政輝
    Chen, Jeng-Huei
    郭雅慧
    Kuo, Ya-Hui
    陸行
    Luh, Hsing Paul
    贡献者: 應數系
    关键词: Goldie and Coldman’s model;Drug resistance;Optimal cancer treatment
    日期: 2013.10
    上传时间: 2013-12-09 13:37:00 (UTC+8)
    摘要: Mathematical models can be used to study the chemotherapy on tumor cells. Especially, in 1979, Goldie and Coldman proposed the first mathematical model to relate the drug sensitivity of tumors to their mutation rates. Many scientists have since referred to this pioneering work because of its simplicity and elegance. Its original idea has also been extended and further investigated in massive follow-up studies of cancer modeling and optimal treatment. Goldie and Coldman, together with Guaduskas, later used their model to explain why an alternating non-cross-resistant chemotherapy is optimal with a simulation approach. Subsequently in 1983, Goldie and Coldman proposed an extended stochastic based model and provided a rigorous mathematical proof to their earlier simulation work when the extended model is approximated by its quasi-approximation. However, Goldie and Coldman’s analytic study of optimal treatments majorly focused on a process with symmetrical parameter settings, and presented few theoretical results for asymmetrical settings. In this paper, we recast and restate Goldie, Coldman, and Guaduskas’ model as a multi-stage optimization problem. Under an asymmetrical assumption, the conditions under which a treatment policy can be optimal are derived. The proposed framework enables us to consider some optimal policies on the model analytically. In addition, Goldie, Coldman and Guaduskas’ work with symmetrical settings can be treated as a special case of our framework. Based on the derived conditions, this study provides an alternative proof to Goldie and Coldman’s work. In addition to the theoretical derivation, numerical results are included to justify the correctness of our work.
    關聯: Mathematical Biosciences, 245(2), 282-298
    数据类型: article
    DOI 連結: http://dx.doi.org/10.1016/j.mbs.2013.07.020
    DOI: 10.1016/j.mbs.2013.07.020
    显示于类别:[應用數學系] 期刊論文

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