Jarrett Angela M, Faghihi Danial, Ii David A Hormuth, Lima Ernesto A B F, Virostko John, Biros George, Patt Debra, Yankeelov Thomas E
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA.
Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX 78712, USA.
J Clin Med. 2020 May 2;9(5):1314. doi: 10.3390/jcm9051314.
Optimal control theory is branch of mathematics that aims to optimize a solution to a dynamical system. While the concept of using optimal control theory to improve treatment regimens in oncology is not novel, many of the early applications of this mathematical technique were not designed to work with routinely available data or produce results that can eventually be translated to the clinical setting. The purpose of this review is to discuss clinically relevant considerations for formulating and solving optimal control problems for treating cancer patients. Our review focuses on two of the most widely used cancer treatments, radiation therapy and systemic therapy, as they naturally lend themselves to optimal control theory as a means to personalize therapeutic plans in a rigorous fashion. To provide context for optimal control theory to address either of these two modalities, we first discuss the major limitations and difficulties oncologists face when considering alternate regimens for their patients. We then provide a brief introduction to optimal control theory before formulating the optimal control problem in the context of radiation and systemic therapy. We also summarize examples from the literature that illustrate these concepts. Finally, we present both challenges and opportunities for dramatically improving patient outcomes the integration of clinically relevant, patient-specific, mathematical models and optimal control theory.
最优控制理论是数学的一个分支，旨在优化动态系统的解决方案。虽然将最优控制理论用于改进肿瘤治疗方案的概念并不新颖，但这种数学技术的许多早期应用并非设计用于处理常规可得的数据，也无法产生最终可转化到临床环境中的结果。本综述的目的是讨论在为癌症患者制定和解决最优控制问题时的临床相关考量。我们的综述聚焦于两种应用最广泛的癌症治疗方法，即放射治疗和全身治疗，因为它们自然适用于最优控制理论，作为一种以严谨方式实现治疗方案个性化的手段。为了给最优控制理论应用于这两种治疗方式提供背景，我们首先讨论肿瘤学家在为患者考虑替代治疗方案时面临的主要局限性和困难。然后，在将最优控制问题应用于放射治疗和全身治疗的背景下，我们简要介绍最优控制理论。我们还总结了文献中说明这些概念的示例。最后，我们阐述了通过整合临床相关的、针对患者的数学模型和最优控制理论来显著改善患者治疗效果所面临的挑战和机遇。
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