CDS&E: Mathematical Models and Computational Methods for the Tumor Microenvironment

本工作的主要目的是在体内和体外微流控装置中为导管原位癌（DCIS）的出现和向浸润性导管癌（IDC）的过渡建立综合的微尺度数学模型和计算方法。研究者和他的同事们开发了基于集成二阶有限体积方法的微环境模型的计算方法，用于每个系统组件-流体力学，散装流体中的化学和离子传输，细胞膜上的反应，通过细胞膜的运输以及弹性生物细胞的流体/结构相互作用。建模创新包括将离子传输、反应和扩散结合到一个基于细胞的模型中，该模型具有详细的膜反应动力学和膜传输。这与单个细胞的内部动力学和生长过程相结合。另一个创新是将拉格朗日网格模型用于矩阵和细胞外矩阵的粘弹性特性。乳腺癌是发达国家妇女死亡的第二大原因。仅在美国，2011年就有230,480名女性被诊断为浸润性乳腺癌，估计有57,650名女性被检测为非浸润性导管癌（DCIS）阳性。虽然DCIS本身并不危及生命，但如果不及时治疗，它很有可能发展为IDC。在本项目中，研究者及其同事研究了DCIS的肿瘤微环境及其向IDC的进展。这个项目的成功完成为肿瘤进化建模提供了一个根本性的改变，其中每个细胞的身份是重要的。虽然重点放在导管癌的建模上，但人们可以将这些技术扩展到各种生物过程的研究中。许多研究领域受益于这项工作。这些学科包括细胞生物学、系统生物学、生物医学工程、计算流体力学以及应用与计算数学。除了这种技术影响之外，该项目还为在多学科环境中培训研究生和本科生以及高中教师提供了独特的教育机会。

The main objective of this work is to develop comprehensive mathematical models and computational methods at the microscale for the emergence of ductal carcinoma in situ (DCIS) and the transition to invasive ductal carcinoma (IDC) both in vivo and in vitro microfluidic devices. The investigator and his colleagues develop computational methods for the microenvironment models based on integrated second-order finite volume methods for each of the system components - fluid mechanics, chemical and ion transport in the bulk fluid, reactions on the cell membrane, transport through the cell membrane, and fluid/structure interaction of the elastic biological cells. The modeling innovation includes the incorporation of ion transport, reaction, and diffusion in a cells-based model with detailed membrane reaction kinetics and membrane transport. This is coupled with internal kinetics and growth processes of individual cells. Another innovation is the incorporation of Lagrangian mesh based models for the viscoelastic properties of matrigel and extracellular matrix.Breast cancer is the second-leading cause of death in women in developed countries. In USA alone, 230,480 women were diagnosed with invasive breast cancer in 2011 and an estimated 57,650 women were tested positive with non invasive ductal carcinoma (DCIS). Although DCIS itself is not life-threatening, it has a high probability of progression to IDC if left untreated. In this project, the investigator and his colleagues study tumor microenvironments in DCIS and its progression to IDC. Successful completion of this project provides a fundamental change in modeling of tumor evolution where the identity of each cell is of importance. Although focus has been placed on modeling ductal carcinoma, one can extend these techniques to the study of variety of biological processes. A number of research fields are benefited from this work. These include cell biology, systems biology, biomedical engineering, computational fluid mechanics, and applied and computational mathematics. In addition to this technical impact, the project provides a unique educational opportunity to train graduate and undergraduate students as well as high school teachers in multidisciplinary environments.