Using Mathematics to Help Cure Cancer

November 16, 2009

Cancer is one of the major causes of death in the world, with around 11 million people diagnosed and 7 million dying every year. A virtual model of cancerous tumor growth may provide new insight into the spread of cancer. Mathematician Mark Chaplain led the interdisciplinary team of University of Dundee researchers in developing the model. 

"One of the big challenges in addressing cancer treatment," Chaplain told Plus Magazine, "is that you can have two patients with the same kind of tumor in the same area of the body, but they will react to it completely differently." He said he believes mathematics is the right tool to tackle this obstacle. "The factors which contribute to the creation and growth of cancerous cells can all be measured—most biological processes in the human body involve many different but interconnected phenomena to which mathematical values can be applied."

Cancerous tumors usually begin when a DNA failure causes uncontrolled cell division. The needs of the tumor depend on its volume, and whether they are satisfied depends on the tumor's surface area. Initially, due to the tumor's size, it can adequately meet its requirements. This phase, the pre-invasive phase, has been well modeled mathematically.

When its requirements are not met, the tumor's growth becomes more dangerous. Cells on the surface of the tumor produce chemicals to break down surrounding tissue to increase the mobility of the cancer cells and to secure a steady blood supply. Chaplain and his team wanted their model to include the second stage.

Chaplain's team aimed for a complete model of a cancerous tumor. Taking into account subcellular, cellular, and macroscopic levels of behavior, from individual cell division all the way up to the cooperative process of nutrient transport, their model contains both discrete and continuous parts. The discrete part deals with cancer cells as individual particles, interacting with the environment around them, while the continuous part uses a system of reaction-diffusion equations to track the chemicals released by the cancer cells and their effect on surrounding tissue.

By fighting a complex disease with a complex mathematical model, Chaplain said he hopes his team's work will "give clinicians another valuable tool in diagnosing and treating individual patients."

Source: Plus, Oct. 27, 2009.