Ali is studying the mathematics of tumor growth with the goal of producing a mathematical model that predicts growth at certain stages of tumor development. A growing number of researchers are bringing their math-related skills to cancer research, for example to model the growth and spread of tumors, and help predict the progress of the cancer and develop or monitor different treatments. Primary malignant tumors are believed to start as small groups of cells that stop responding to normal growth regulation mechanisms. As the tumour grows, it gets larger, invades other tissue, and spreads, and becomes quite complex biologically with its own blood supply. In the early stages, though, the tumor goes through a relatively simple, avascular (lacking a blood supply) growth stage, where it grows quickly at first, but then is slowed by lack of nutrients to the inside of the tumor. Since there is no blood supply to the tumor at this stage, all the nutrients have to diffuse slowly from the outside through the layers of cells. Because this stage is critical to the development of the later tumor stages, it is important to understand how growth is controlled in the avascular stage.
Ali’s summer research has focused on avascular tumor growth, and how tumor shape and volume can affect growth . He has been modeling the roles of individual rate-limiting factors on avascular tumor growth, and also on how the tumor can begin to grow in different ways to invade other tissues. The models are mathematical equations that can be applied to estimate growth and development of tumors under different conditions, therefore letting researchers test how well their therapeutic approaches (treatments) are working.
Student Research