The advances in the mathematical explanation of the dynamics underlying treated cancer has opened the door to the mathematical design of optimal therapies. In parallel, the improvements and cost reductions in experimentation and data analysis techniques have made the formulation of personalized therapies possible. However, the design of cancer therapies making use of optimal control theory has not fully considered this possibility in detail. In this paper we contribute to the existing literature by analyzing the diverse alternatives that optimal therapy models offer to design personalized treatments. Taking as the starting point the Chronic Myeloid Leukemia (CML) optimal therapy model in [25], we design personalized optimal therapy models for patients with: CML; CML with intrinsic and/or induced resistance to the administered drug; CML and suffering high drug toxicity and/or allergy to the administered drug; and CML with presence of adverse factors. Along the paper we show that the clinical and medical applicability -the ultimate objective of this biomathematical research- of our proposed personalized models relies on the joint and proper use of the implemented calibration, simulation, and mathematical approaches and techniques. All the theoretical results generated by our personalized optimal therapy models are corroborated by clinical evidence.

中文翻译：

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利用最佳控制问题设计个性化癌症治疗方法：慢性粒细胞白血病病例

对治疗癌症背后的动力学进行数学解释的进展为最佳疗法的数学设计打开了大门。同时，实验和数据分析技术的改进和成本的降低使个性化疗法的制定成为可能。但是，利用最佳控制理论设计的癌症疗法并未充分考虑这种可能性。在本文中，我们通过分析最佳治疗模型为设计个性化治疗提供的多种选择，为现有文献做出了贡献。以[25]中的慢性粒细胞白血病（CML）最佳治疗模型为起点，我们针对以下患者设计个性化的最佳治疗模型：对所用药物具有固有和/或诱导耐药性的CML；CML且对所用药物有高度的药物毒性和/或过敏；以及存在不利因素的CML。在本文中，我们表明，我们提出的个性化模型的临床和医学适用性（此生物数学研究的最终目的）依赖于已实施的校准，模拟以及数学方法和技术的联合和正确使用。我们的个性化最佳治疗模型所产生的所有理论结果均得到临床证据的证实。模拟以及数学方法和技巧。我们的个性化最佳治疗模型所产生的所有理论结果均得到临床证据的证实。模拟以及数学方法和技巧。我们的个性化最佳治疗模型所产生的所有理论结果均得到临床证据的证实。