During the summer of 2008, Dustin Phan held an internship with the Wiseman Research Group in Los Angeles. During that time, he learned about the clinical trial process for developing FDA approved vaccines and developed an interest in cancer. When he came back to school that Fall, Dustin was fortunate enough to find Dr. John S. Lowengrub working on mathematical cancer modeling. He worked with Dr. Lowengrub in developing and analyzing a discrete mathematical model of solid tumor growth called a cellular automaton model. Dustin was accepted into the UCI Mathematical, Computation, and Systems Biology graduate program, allowing him to continue research in both fields after graduation.

Tumor growth is a complex biological process often studied through the use of both in vivo and in vitro experimentation. Mathematical models provide a complementary approach by using a controlled environment in which a system can be described quantitatively. This can also yield prognostic data after thorough analysis by the modeler. In an effort to study the characteristics that increase cell fitness, this paper presents a discrete cellular automaton model that uses computer simulation to describe the invasion of healthy tissue by cancer cells. A mechanistic approach is used in which the proliferation, migration, and death of cells is controlled through preset parameters. Values can be adjusted and corresponding simulations can be analyzed. During simulation, cells with high migration probabilities create morphologies with considerably less population density than those with low migration probabilities, thereby creating space into which other cells may proliferate or migrate. Furthermore, these highly migratory cells display greater rates of population growth compared to less migratory cells with the same proliferation rate. The model also shows that tumor cell invasion times can decrease even when increasing only the cells’ tendency to migrate. Results show that the population growth rate of non-migratory cells may be achieved by cells with smaller proliferation rates but larger migration rates.

John S. Lowengrub School of Physical Sciences

Cancer cells compete with each other and host cells in a fast paced evolutionary system. Typically, mutations are introduced into the genome of cancer cells, and it is important to understand what types of mutations ensure that one mutant is more fit than another and is also more fit than the host cells. This work uses a mathematical model that tracks the motion and interaction of discrete cells. The results demonstrate that there is a nontrivial trade-off between migration and proliferation. This can have profound implications for traditional cancer treatment, which typically only targets highly proliferative cells. Being involved in state-of-the-art research, such as described in this paper, provides undergraduates with a unique opportunity to bridge classroom mathematics experience and knowledge with real world applications.