Collaborative Research: Regular synthesis for multi-input optimal control problems with applications to biomedicine

合作研究：多输入最优控制问题的常规综合及其在生物医学中的应用

• 批准号: 1311729
• 负责人: Heinz Schaettler
• 金额: $ 17.5万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-10-01 至 2016-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1311729&HistoricalAwards=false
• 关键词: Collaborative; Research; Regular; synthesis; multi

In this project, fully interacting nonlinear multi-input control systems will be analyzed as optimal control problems. The motivation for this research comes from a systematic study of mathematical models for cancer treatment that combine various structures that form the tumor microenvironment. In modern oncology, a tumor is viewed as not just cancerous cells, but as a system of interacting components that in various ways aid and abet the tumor (e.g., the tumor vasculature), but also fight it (e.g., the immune system). Current treatments therefore are multi-targeted therapies that not only kill cancer cells, but also include antiangiogenic therapy, immunotherapy and many other options. The search for best ways of administering these therapeutic agents naturally leads to formulations as multi-input nonlinear optimal control problems. The aim of the research is to develop local syntheses of optimal controls for such systems, a difficult task even for single-input systems with only partial results known. These new results will be developed in connection with the study of systems that describe (i) cancer treatment within the complex context of the tumor microenvironment and (ii) optimal strategies for the control of the spread of diseases in epidemiology. In the latter field, mathematical models have been a relevant tool in analyzing the underlying dynamics, whereas in this project a much less explored optimal control approach to the problem will be pursued. While one aim is to develop general methods and procedures that have wide applicability, a second important aspect of the research is to provide qualitative and quantitative insights into the structure of optimal solutions for important real-life problems. Motivated by timely problems in biomedicine, like how to design metronomic chemotherapy protocols, challenging problems in optimal control theory will be considered whose solutions require developing new tools and methods. Because of its applied and interdisciplinary character, the project is expected to be of strong interest to students from mathematics and engineering and consequently it contains a substantial educational component. Efforts to attract women and minorities will be continued and expanded by reaching out to engineering students where participation of these groups is particularly low.In modern oncology, a tumor is viewed as not just cancerous cells, but as a system of interacting components that in various ways aid and abet the tumor (e.g., the tumor vasculature), but also fight it (e.g., the immune system). Current treatments therefore are multi-targeted therapies that not only kill cancer cells, but also include antiangiogenic therapy, immunotherapy and many other options. It is very difficult and expensive to test complex multi-target protocols in medical trials. For this reason, the analysis of mathematical models becomes of intrinsic value. The medical community has become more and more aware that not only what drug is given, but also how it is administered, i.e., dosage, frequency and sequencing, can have a major impact on the outcome of the treatment. This led to a recently launched "Metronomics Global Health Initiative". The proposed research is motivated by the biomedical ideas of this initiative and the investigators believe that the tools of geometric optimal control are best suited to give mathematical answers to these questions and thus provide insights into how a metronomic protocol should be designed. Regarding a second topic, infectious diseases continue to be one of the most important health problems worldwide. In this project, the investigators seek theoretical results that can give practical guidelines how to pursue joint efforts of vaccination and treatment in an optimal way to maximize the effectiveness and minimize the social economic cost. Because of its applied and interdisciplinary character, the project is expected to be of strong interest to students from mathematics and engineering and consequently it contains a substantial educational component. Efforts to attract women and minorities will be continued and expanded by reaching out to engineering students where participation of these groups is particularly low.

在本计画中，完全互动的非线性多输入控制系统将被分析为最佳控制问题。这项研究的动机来自于对癌症治疗数学模型的系统研究，这些模型结合了形成肿瘤微环境的各种结构，这些结构是联合收割机。在现代肿瘤学中，肿瘤不仅被视为癌细胞，而且被视为以各种方式帮助和助长肿瘤的相互作用组分的系统（例如，肿瘤脉管系统），但也可以对抗它（例如，免疫系统）。因此，目前的治疗方法是多靶向治疗，不仅可以杀死癌细胞，还包括抗血管生成治疗，免疫治疗和许多其他选择。寻找最佳的方式给予这些治疗剂自然导致制剂作为多输入非线性最优控制问题。研究的目的是开发本地合成的最优控制，这样的系统，一个艰巨的任务，即使是单输入系统，只有部分结果已知。这些新结果将与描述（i）肿瘤微环境复杂背景下的癌症治疗和（ii）流行病学中控制疾病传播的最佳策略的系统研究相关。在后一个领域，数学模型一直是分析潜在动力学的相关工具，而在本项目中，将追求一种更少探索的问题的最优控制方法。虽然一个目的是开发具有广泛适用性的一般方法和程序，研究的第二个重要方面是提供定性和定量的见解，为重要的现实生活中的问题的最佳解决方案的结构。在生物医学中及时的问题，如如何设计节拍化疗方案的动机，在最优控制理论的挑战性问题将被认为是其解决方案需要开发新的工具和方法。由于其应用和跨学科的特点，该项目预计将是强烈的兴趣，从数学和工程的学生，因此它包含了大量的教育组成部分。将继续努力吸引女性和少数族裔，并通过接触工程专业的学生来扩大吸引这些群体的努力，因为这些群体的参与度特别低。在现代肿瘤学中，肿瘤不仅被视为癌细胞，而且被视为一个相互作用的成分系统，这些成分以各种方式帮助和教唆肿瘤（例如，肿瘤脉管系统），但也可以对抗它（例如，免疫系统）。 因此，目前的治疗方法是多靶向治疗，不仅可以杀死癌细胞，还包括抗血管生成治疗，免疫治疗和许多其他选择。在医学试验中，测试复杂的多目标协议是非常困难和昂贵的。因此，数学模型的分析具有内在价值。医学界越来越意识到，不仅要给药，而且要知道如何给药，即，剂量、频率和顺序可能对治疗结果产生重大影响。这导致了最近发起的“Metronomics全球健康倡议”。拟议的研究是由生物医学的想法，这一举措的动机和研究人员认为，几何最优控制的工具是最适合给这些问题的数学答案，从而提供了如何设计一个节拍协议的见解。关于第二个主题，传染病仍然是全世界最重要的健康问题之一。在本项目中，研究人员寻求理论结果，这些理论结果可以为如何以最佳方式进行疫苗接种和治疗的共同努力提供实际指导，以最大限度地提高效果，并最大限度地减少社会经济成本。由于其应用和跨学科的特点，该项目预计将是强烈的兴趣，从数学和工程的学生，因此它包含了大量的教育组成部分。将继续努力吸引妇女和少数民族，并扩大其范围，向工程专业学生伸出援手，因为这些群体的参与率特别低。