Core 1: Mathematical Core

摘要-数学建模核心 了解肿瘤发生、发展和发展过程中发生的肿瘤生态学(“∆生态学”)的变化 治疗需要仔细研究涉及多个尺度的复杂动力系统-从分子到 从细胞到组织再到全身。这项研究的一个重要工具是使用数学模型，它可以 弥合临床和实验数据之间的时间差距。来自患者的生态组织学数据是困难的和 虽然对梳理机制和测试假说至关重要，但很少能获得和实验工作， 不能完全复制人类的疾病背景。数学建模是连接这两个领域的纽带 方法，允许从体外和体内研究的机制中产生的生态学原理在 患者设置，根据可用的患者数据进行校准。数学建模核心将发展这些 模型，使用各种方法。关键是使用基于空间代理的模型，它可以处理 细胞类型和分子的丰富多样性，以及肿瘤生态学和 进化论。我们已经建立了一个快速而灵活的开发这些模型的平台，包括许多 将为本提案的两个项目中的科学服务的附加组件。此外，我们在非空间领域的专业知识 模型将并行应用，因为这些方法可以捕捉到肿瘤生长和 对治疗的反应具有显著的可翻译潜力，正在进行的试验证明了这一点 莫菲特的进化疗法。除了构建这些模型之外，我们还将开发初始化工具， 根据每个项目收集的临床和临床前数据对模型进行校准和分析。这将是 使用虚拟的“第一阶段”试验，在该试验中，虚拟患者/老鼠是从一个模型生成的， 考虑参数的不确定性。总之，核心模型将提供对生态环境的洞察 在肿瘤生长和治疗过程中发生的过程。

Summary – Mathematical Modeling Core Understanding the changes in tumor ecology (“∆-Ecology”) that occur during tumor initiation, progression, and therapy requires careful study of a complex dynamical system involving multiple scales – from molecular to cellular to tissue to systemic. An important tool in this study is the use of mathematical models, which can bridge temporal gaps in clinical and experimental data. Ecological histology data from patients is difficult and rare to obtain, and experimental work, while crucial for teasing apart mechanism and testing hypotheses, cannot fully reproduce the human setting of disease. Mathematical modeling serves as a link between these approaches, allowing ecological principles arising from mechanisms studied in vitro and in vivo to play out in the patient setting, calibrated to available patient data. The Mathematical Modeling Core will develop these models, using a variety of approaches. Key is the use of spatial agent-based models, which can handle the rich diversity of cell types and molecules, as well as the multiple scales involved in tumor ecology and evolution. We have built a platform for developing these models that is fast and flexible, including numerous add-ons that will serve the science in the two projects of this proposal. In addition, our expertise in non-spatial models will be applied in parallel, as these approaches can capture the broad dynamics of tumor growth and the response to treatment in ways that have significant translatable potential, as evidenced by ongoing trials in Evolutionary Therapy at Moffitt. In addition to constructing these models, we will develop tools for initializing, calibrating, and analyzing models based on clinical and pre-clinical data collected in each project. This will involve the use of virtual “Phase i” trials, where virtual patients/mice are generated from a model, taking parameter uncertainty into account. In summary, the Core models will provide insight into the ecological processes that occur during tumor growth and treatment.