Collaborative Research: Multiscale Modeling of Solid Tumor Growth

这个位于数学和生物学之间的项目的目标是开发肿瘤生长的数学模型，将肿瘤内部的分子和细胞属性与关键的肿瘤行为(如侵袭性)和实验可观察的属性(如形态)联系起来。研究小组将(1)对重要的组成过程进行新的分析和计算研究，(2)将实验数据纳入这些研究，以及(3)开发最先进的数值算法并将其应用于多个时间和空间尺度上的大规模计算。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，将极大地促进对肿瘤生物学的理解的突破的潜力是巨大的，从而满足国家和全球的迫切需求。实体肿瘤是一种复杂的微结构材料，其中三维组织结构(形态)和动力学以复杂的、非线性的方式与细胞特征以及生长环境的分子组成和结构相耦合。肿瘤形态和潜在的细胞/分子动力学之间的这种密切联系具有基本的科学意义，因为导致各种肿瘤形态的细胞动力学也控制着它侵袭宿主组织的能力。这使得肿瘤的可观察属性，如其形态，可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不同形态的侵袭模式是肿瘤生长环境中分子不均质性(成分和结构)的定量可预测结果的猜想将得到检验。由于肿瘤细胞使用与正常细胞相似或相同的迁移和增殖机制，以及这些过程的多尺度性质，本项目中将进行的数学建模、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的正常功能过程中应用。该项目还将在五个机构之间建立新的合作，并扩大妇女和少数群体作为调查员受训人员参与研究的范围。因此，它可以满足各国的需要。它将在数学和肿瘤细胞生物学之间为理论家和实验学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发一个为期一个月的夏季COSMOS(加州州立数学与科学暑期学校)课程。这门课程加强了有天赋的高中生参与研究，并帮助招收新的数学和科学本科生，这满足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.