Collaborative Research: Optimal Control of Mathematical Models for Cancer Treatments

合作研究：癌症治疗数学模型的优化控制

• 批准号: 0405848
• 负责人: Heinz Schaettler
• 金额: $ 4.38万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-15 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405848&HistoricalAwards=false
• 关键词: Collaborative; Research; Optimal; Control; Mathematical

In this project mathematical models for various cancer treatments will be investigated with the methods of modern optimal control theory. A class of models based on chemotherapy with single or multiple killing agents will be formulated and analyzed under evolving drug resistance. In the case of a single drug this leads to bilinear structures, but for the multiple drug case unconventional formulations arise and new tools need to be applied. Aside from problems involving drug resistance, attention also will be directed to models representing treatments with angiogenic inhibitors (which slow tumor growth by depriving it from recruiting new blood vessels). The dynamics in these models is fully nonlinear and its analysis within the framework of geometric methods of optimal control is expected to answer some open questions about this novel therapy. Drug resistance and other side effects related to chemo-, radio- or antiangiogenic therapy naturally lead to the need for combination treatments. Mathematically such treatments provide a challenge not only in the formulation of the complex dynamics, but also in the choice of proper objectives which would capture the various and multi-fold aspects reflecting the medical criteria by which to judge these therapies. All of these efforts will serve the overall goal of finding the optimal control, which could aid in designing improved therapy protocols.Conventional cancer treatments aim at directly killing tumor cells, be it by means of drugs in chemotherapy or by means of radiation in radiation treatments. However, there exist many limiting factors and probably the single most important, and what has been called "certainly the most frustrating one," is drug resistance. As of today no medical solution exists for this obstacle to developing effective cancer treatments. In the project tools of modern optimal control theory will be employed to analyze a variety of mathematical models representing cancer treatments with the focus on the important medical issue of drug resistance. New models that capture these phenomena will be analyzed in an effort to better reflect the underlying biological situation and goals of the treatment. The research conducted will provide mathematical insights into an understanding of these important biomedical models aimed at designing more effective therapy protocols which may be difficult, or at least very expensive, if not impossible, to test in a laboratory setting. It will also contribute to optimal control theory by developing and employing new techniques aimed at significant applications. Due to its applied and interdisciplinary character the project is of interest to students and consequently will contain a substantial educational component.

在这个项目中，各种癌症治疗的数学模型将与现代最优控制理论的方法进行研究。 一类模型的基础上化疗与单一或多种杀伤剂将制定和分析下不断发展的耐药性。 在单一药物的情况下，这导致双线性结构，但对于多种药物的情况下，非常规的配方出现，需要应用新的工具。 除了涉及耐药性的问题外，还将关注代表血管生成抑制剂治疗的模型（通过剥夺肿瘤招募新血管来减缓肿瘤生长）。 在这些模型中的动态是完全非线性的，其最优控制的几何方法的框架内的分析，预计回答一些开放的问题，这种新的治疗。 与化疗、放疗或抗血管生成治疗相关的耐药性和其他副作用自然导致需要联合治疗。 从数学上讲，这种治疗不仅在复杂动力学的制定方面，而且在选择适当的目标方面都提出了挑战，这些目标将捕捉反映判断这些治疗的医学标准的各种和多方面。 所有这些努力都将服务于找到最佳控制的总体目标，这可以帮助设计改进的治疗方案。传统的癌症治疗旨在直接杀死肿瘤细胞，无论是化学疗法中的药物还是放射治疗中的放射。 然而，存在许多限制因素，其中最重要的可能是耐药性，也被称为“最令人沮丧的因素”。 到目前为止，还没有医学解决方案来解决开发有效癌症治疗的这一障碍。 在该项目中，现代最优控制理论的工具将被用来分析代表癌症治疗的各种数学模型，重点是耐药性的重要医学问题。 将对捕捉这些现象的新模型进行分析，以更好地反映潜在的生物学情况和治疗目标。 进行的研究将提供数学见解，以了解这些重要的生物医学模型，旨在设计更有效的治疗方案，这些方案可能很难，或者至少非常昂贵，如果不是不可能的话，在实验室环境中进行测试。 它还将有助于最优控制理论的发展和采用新技术，旨在显着的应用。 由于其应用和跨学科的特点，该项目是感兴趣的学生，因此将包含大量的教育组成部分。