IEEE Trans Biomed Eng. 2014 Feb;61(2):415-25. doi: 10.1109/TBME.2013.2280189.
The combination of mathematical modeling and optimal control techniques holds great potential for quantitatively describing tumor progression and optimal treatment planning. Hereby, we use a Gompertz-type growth law and a pharmacokinetic-pharmacodynamic approach for modeling the effects of drugs on tumor progression in tumor bearing mice, and we combine these in order to design optimal therapeutic patterns. Specifically, we describe colon cancer progression in both untreated mice as well as mice treated with widely used anticancer agents. We also present a pharmacokinetic model to describe the kinetics of drugs in the body as well as detailed toxicity models to describe the severity of side effects. Finally, we propose a promising methodology by which cancer progression in mice with drug resistance can be controlled. By using optimal control, we demonstrate that the optimal planning of the frequency and magnitude of treatment interruptions is key to the control of cancer progression in subjects with resistance and should be further investigated in an experimental setting, which is currently underway.
数学建模和最优控制技术的结合在定量描述肿瘤进展和优化治疗计划方面具有巨大的潜力。为此，我们使用 Gompertz 型生长规律和药代动力学-药效学方法来模拟药物对荷瘤小鼠肿瘤进展的影响，并将它们结合起来以设计最佳的治疗模式。具体来说，我们描述了未治疗的小鼠以及接受广泛使用的抗癌药物治疗的小鼠中的结肠癌进展。我们还提出了一个药代动力学模型来描述药物在体内的动力学以及详细的毒性模型来描述副作用的严重程度。最后，我们提出了一种有前途的方法，可以控制耐药小鼠的癌症进展。通过使用最优控制，我们证明了治疗中断的频率和幅度的最优规划是控制耐药患者癌症进展的关键，应该在实验环境中进一步研究，目前正在进行中。
