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的微流控装置中，为导管原位癌(DCIS)的出现和向浸润性导管癌(IDC)的转变，在微观尺度上建立全面的数学模型和计算方法。这位研究人员和他的同事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，这些方法针对系统的每个组件-流体力学、主体流体中的化学和离子传输、细胞膜上的反应、通过细胞膜的传输以及弹性生物细胞的流体/结构相互作用。模型的创新包括将离子传输、反应和扩散纳入基于细胞的模型中，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有关。另一项创新是引入了基于拉格朗日网格的模型，用于描述基质和细胞外基质的粘弹性特性。在发达国家，乳腺癌是女性死亡的第二大原因。仅在美国，2011年就有230,480名妇女被诊断为浸润性乳腺癌，估计有57,650名妇女的非浸润性导管癌(DCIS)检测呈阳性。虽然DCIS本身不会危及生命，但如果不治疗，它很有可能发展为IDC。在这个项目中，研究人员和他的同事研究了DCIS中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的建模提供了一个根本性的变化，其中每个细胞的身份都很重要。虽然人们把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学过程的研究。这项工作使许多研究领域受益。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和计算数学。除了这种技术影响，该项目还提供了一个独特的教育机会，在多学科环境中培训研究生和本科生以及高中教师。

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.