Aaron Abajian has devoted his undergraduate research experience to developing computer tools for use in biology. For this project, under the mentorship of Professor Lowengrub, Aaron has combined the fields of computer science, biology and mathematics to create a unique mathematical tumor model. He has found the novelty of his project particularly exciting, especially as it has helped him truly understand many difficult concepts for the first time. Aaron is currently enrolled in a Credential and Master’s Program in Urban Education at Loyola Marymount University, while teaching high school as part of the Teach for America Program.

Tumor development is a complex and multi-faceted process that cannot be captured in a single formula, yet the ability to predict a maturing tumor’s magnitude and direction of growth would provide significant clinical benefits. In-vitro trials provide only limited predictive data since it is nearly impossible to chemically reproduce the exact environmental conditions surrounding a tumor. Moreover, each trial is necessarily unique to a specific tumor and cannot be quickly modified to satisfy the requirements of another. Mathematical models provide a virtual solution to this problem by implementing the core processes of tumor development in software. We present a model for tumor development from the single-cell stage to early microinvasion. An overlying nutrient field determines a cell’s status as living, quiescent, mutant, or nonviable. Interactions between tumor cells are simulated using a competing exponential function and nutrient influx is modeled using the diffusion equation. The object-oriented implementation allows the introduction of multiple nutrient and chemical fields. The model may be applied to a variety of emerging tumors by carefully defining the constants that determine the tumors’ development pathway and microenvironment. We present simulation results that demonstrate the flexibility of the model and its future applicability.

John S. Lowengrub School of Physical Sciences

This research introduces an agent-based model for simulating solid tumor growth. Mathematical modeling and numerical simulation have the potential to provide important insight into the root causes of solid tumor invasion and metastasis. Such models have been widely used for healthy cells but not for cancer modeling; however, the mechanisms are thought to be similar. An important feature of cancer is the communication and adhesion among the cancer cells and the extracellular matrix. At the time this research was performed, previous agent-based models did not consider this effect. Now, several other models account for these effects, although none consider the questions asked here. Research projects such as this provide undergraduates with a unique opportunity to bridge classroom experience and knowledge with important real world applications.