Collaborative Research: Multiscale Modeling of Solid Tumor Growth

这个项目的目标是建立肿瘤生长的数学模型，将肿瘤内部的分子和细胞特性与肿瘤的关键行为（如侵袭性）和实验可观察的特性（如形态学）联系起来。该研究小组将(1)对重要组成过程进行新颖的分析和计算研究，(2)将实验数据纳入这些研究中，(3)开发和应用最先进的数值算法进行多时间和空间尺度的大规模计算。通过将实验数据与复杂的、多尺度的数学和计算模型相结合，突破的潜力将极大地促进对肿瘤生物学的理解，从而解决紧迫的国家和全球需求。实体肿瘤是复杂的微观结构材料，其中三维组织结构（形态）和动力学以复杂的非线性方式与细胞特征以及生长环境的分子组成和结构耦合。肿瘤形态与潜在的细胞/分子动力学之间的密切联系具有重要的科学意义，因为产生各种肿瘤形态的细胞动力学也控制着其入侵宿主组织的能力。这使得肿瘤的可观察特性，如其形态，可以用于了解潜在的细胞生理学和预测肿瘤的侵袭潜力。特别是，在肿瘤生长过程中观察到的侵袭的不同形态模式是肿瘤生长环境中分子（组成和结构）不均匀性的定量可预测结果的猜想将得到验证。由于肿瘤细胞与正常细胞具有相似或相同的迁移和增殖机制，并且由于这些过程具有多尺度的性质，因此本项目将进行的数学建模、分析和模拟也将在理解发育、伤口愈合、干细胞分化和组织再生等正常功能过程中具有应用价值。该项目还将在五个机构之间建立新的合作关系，并扩大妇女和少数民族作为研究人员的学员参与研究的范围。群体，从而解决国家的需要。它将在数学和肿瘤细胞生物学的界面上为理论家和实验家提供跨学科的培训。最后，加州大学欧文分校将为高中生开设一个为期一个月的暑期COSMOS（加州州立数学与科学暑期学校）课程。这门课程提高了天才高中生对研究的参与，并有助于招收新的数学和科学本科生，这解决了另一个国家的需求。

The goal of this project, which lies at the interface between mathematics and biology, is to develop mathematical models of tumor growth that connect intra-tumor molecular and cellular properties with critical tumor behaviors, such as invasiveness, and experimentally observable properties such as morphology. The research group will (1) perform novel analytical and computational studies of important constituent processes, (2) incorporate experimental data into these studies, and (3) develop and apply state-of-the-art numerical algorithms to large-scale computations over multiple time and space scales. By integrating experimental data with sophisticated, multi-scale mathematical and computational models, the potential for breakthroughs that will significantly further the understanding of tumor biology are great, thereby addressing a pressing national and global need. Solid tumors are complex micro-structured materials, where the three-dimensional tissue architecture (morphology) and dynamics are coupled in complex, nonlinear ways to cellular characteristics and to molecular composition and structure of the growth environment. This close connection between the tumor morphology and the underlying cellular/molecular dynamics has fundamental scientific importance in that the cellular dynamics that give rise to various tumor morphologies also control its ability to invade the host tissue. This allows observable properties of the tumor, such as its morphology, to be used to both understand the underlying cellular physiology and predict the tumors invasion potential. In particular, the conjecture that diverse morphologic patterns of invasion observed during tumor growth are the quantitatively predictable result of molecular inhomogeneity (of both composition and structure) in the tumors growth environment will be tested. Because tumor cells use similar or identical migration and proliferation mechanisms as normal cells, and because of the multi-scale nature of these processes, the mathematical modeling, analysis and simulation that will be conducted in this project will also have application in understanding normal functional processes during development, wound-healing, stem cell differentiation and tissue regeneration. This project will also establish a new collaboration among five institutions and broadens the participation of women and minorities in research as trainees in the investigators? groups, thereby addressing national needs. It will provide interdisciplinary training with theoreticians and experimentalists at the interface between mathematics and tumor cell biology. Finally, a month-long summer COSMOS (California State Summer School for Mathematics and Science) course at UC Irvine will be developed for high school students on these topics. This course enhances the participation of gifted high school students in research, and helps to recruit new math and science undergraduates, which addresses another national need.