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.
