Mathematical Analysis of Spatial Cancer Models

空间癌症模型的数学分析

基本信息

批准号：
1614838
负责人：
Richard Durrett
金额：
$ 28.72万
依托单位：
Duke University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-07-01 至 2020-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1614838&HistoricalAwards=false
关键词：
Mathematical Analysis Spatial Cancer Models

项目摘要

Successful prevention, early detection, and treatment of cancer requires an understanding of the underlying mechanisms by which cancer evolves spatially and temporally. The occurrence of different cell types in different parts of a tumor, the spatial heterogeneity of the tumor, can lead to failure of therapy that is directed only against one type of cancer cell. Furthermore, spatial heterogeneity is associated with a worse prognosis in many cancer types, and the spatial distribution of nutrients and oxygen can favor the development of more aggressive tumor cell populations. By analyzing spatial cancer models, this research will provide new insights into the mechanistic underpinnings of intra-tumor heterogeneity in solid tumors, and into the role of cellular mobility in shaping tumor phenotypes with poor prognosis. To guarantee that the results are relevant to treatment, the project will be carried out in collaboration with physicians and a cancer biologist. The involvement of graduate students in this research will enhance their ability to work at the interface between mathematics and biology. This project addresses critical challenges in the quest for more effective diagnostic tools and therapeutic approaches in the fight against cancer. Complex agent-based models have often been employed to investigate the impact of space on cancer evolution. However, even if a simulation successfully reproduces observed phenomena, it does not mean that the true underlying mechanism has been found. For this project the investigators plan to extend prior work on spatial Moran models by adding new features to the basic model. To further reduce the gap between analytically tractable and complex computational models, the behavior of the new systems will be analyzed mathematically. The biological questions to be addressed by the project are motivated by recent experimental findings, including studies of the impact of cancer cell migration on solid tumor growth and elucidation of the role of cancer stem cells in driving cancer evolution. Mathematical models that can include genomic data will be used to study genealogies and intra-tumor heterogeneity in colon cancer. Rigorous results for hybrid models that describe tumor-microenvironment interactions will also be derived. More generally, the rigorous analyses of the models will require the development of novel mathematical techniques that will contribute to a deeper understanding of spatial stochastic systems and the behavior of genealogies in an expanding population.

成功的预防，早期检测和治疗癌症需要了解癌症在空间和时间上演变的潜在机制。在肿瘤的不同部位（肿瘤的空间异质性）中，不同细胞类型的发生可能导致治疗失败，而治疗仅针对一种类型的癌细胞。此外，空间异质性与许多癌症类型的预后较差有关，养分和氧气的空间分布可以有利于更具侵略性的肿瘤细胞种群的发展。通过分析空间癌模型，这项研究将为实体瘤中肿瘤内异质性的机械基础提供新的见解，以及细胞迁移率在塑造预后不良的肿瘤表型中的作用。为了确保结果与治疗有关，该项目将与医生和癌症生物学家合作进行。研究生参与这项研究将增强他们在数学和生物学之间界面上工作的能力。该项目解决了寻求更有效的诊断工具和对抗癌症的治疗方法的关键挑战。经常采用基于复杂的代理模型来研究空间对癌症进化的影响。但是，即使模拟成功地再现了观察到的现象，也不意味着已经找到了真正的潜在机制。对于该项目，调查人员计划通过在基本模型中添加新功能来扩展空间Moran模型的先前工作。为了进一步降低分析可牵引和复杂的计算模型之间的差距，将通过数学分析新系统的行为。该项目将要解决的生物学问题是由最近的实验发现激发的，包括研究癌细胞迁移对实体瘤生长的影响以及阐明癌症干细胞在驱动癌症进化中的作用的影响。可以包括基因组数据的数学模型将用于研究结肠癌中的家谱和肿瘤内异质性。还将得出描述肿瘤微环境相互作用的混合模型的严格结果。更一般而言，对模型的严格分析将需要开发新颖的数学技术，这将有助于更深入地了解空间随机系统以及在不断扩展的人群中的家谱行为。