Optimisation of time-scheduled regimen for anti-cancer drug infusion
Optimisation of time-scheduled regimen for anti-cancer drug infusion
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DOI：
10.1051/m2an:2005052
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发表时间：
2005-11-01
期刊：
影响因子：
--
通讯作者：
Lévi, F
中科院分区：
文献类型：
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作者：
Basdevant, C;Clairambault, J;Lévi, F
时间疗法概念利用细胞生理学的昼夜节律，最大限度地提高对目标的治疗效果，同时最大限度地减少对健康器官的毒性。本论文的目的是研究数学和数值上的最佳策略，在癌症的时间治疗。为此，已经推导出描述奥沙利铂抗肿瘤治疗的效率和毒性的时间演变的数学模型。然后，我们采用了最优控制技术，以寻找最佳的药物输注法。数学模型是一组六个耦合微分方程，控制肿瘤细胞群（格拉斯哥骨肉瘤细胞，一种小鼠肿瘤）和成熟空肠肠上皮细胞群的时间演变，以避免奥沙利铂治疗期间的不良副作用。从已知的肿瘤和绒毛群体开始，并给出时间依赖性的游离铂Pt（活性药物）输注法，数学模型允许计算肿瘤和绒毛群体的时间演变。肿瘤群体增长基于Gompertz定律，Pt抗肿瘤疗效考虑了昼夜节律。类似地，肠上皮细胞群体也受到昼夜毒性节律的影响。该模型已得到使用，尽可能，实验数据。我们研究两个不同的优化问题。根除问题在于找到能够最小化肿瘤细胞数量同时保留绒毛群体的最低水平的药物输注法。另一方面，遏制问题寻找一种准周期性的治疗，能够保持肿瘤人口在尽可能低的水平，同时保留绒毛细胞。这些方法的独创性在于，我们使用的目标和约束函数是L-无穷准则。我们能够推导出它们相对于输注速率的梯度，然后实施有效的优化算法。
The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control technique to search for the best drug infusion laws. The mathematical model is a set of six coupled differential equations governing the time evolution of both the tumour cell population (cells of Glasgow osteosarcoma, a mouse tumour) and the mature jejunal enterocyte population, to be shielded from unwanted side effects during a treatment by oxaliplatin. Starting from known tumour and villi populations, and a time dependent free platinum Pt ( the active drug) infusion law being given, the mathematical model allows to compute the time evolution of both tumour and villi populations. The tumour population growth is based on Gompertz law and the Pt anti-tumour efficacy takes into account the circadian rhythm. Similarly the enterocyte population is subject to a circadian toxicity rhythm. The model has been derived using, as far as possible, experimental data. We examine two different optimisation problems. The eradication problem consists in finding the drug infusion law able to minimise the number of tumour cells while preserving a minimal level for the villi population. On the other hand, the containment problem searches for a quasi periodic treatment able to maintain the tumour population at the lowest possible level, while preserving the villi cells. The originality of these approaches is that the objective and constraint functions we use are L-infinity criteria. We are able to derive their gradients with respect to the infusion rate and then to implement efficient optimisation algorithms.