Mathematics and biology are converging to help improve certain cancer treatment strategies. HMC researcher and mathematics Professor Lisette de Pillis and her undergraduate research partners have garnered attention for their work, including notice from the top professional organization for applied mathematicians.

In October 2009, de Pillis, the Norman F. Sprague Professor of Life Sciences and Professor of Mathematics, was featured featured in a front page article of the SIAM News. The Society of Industrial and Applied Mathematics (SIAM) is the leading international professional organization for applied mathematicians, and their monthly publication has a circulation of over 14,000 subscribers. The article highlighted the invited plenary talk delivered by de Pillis at the SIAM Annual Meeting held during July in Denver, Colo.

In her talk, De Pillis describes how she and her colleagues have developed ordinary differential equations models based on clinical and laboratory data that incorporate the nonlinear interactions of tumor cells and immune cells with chemo and immunotherapies. Mathematical optimal control techniques have been implemented to determine improved treatment protocols. The models can use data from an individual's immune system to give insight into conditions and treatment strategies that will maximize healing of a patient while minimizing damaging side-effects.

Her talk included discussion about some basics of cancer cells and work she has done modeling the effect of chemotherapy on the progress of the disease. The research began by trying to answer the question of why tumors sometimes grow when treated with chemotherapy and shrink when not treated. Her answer is tied to a patient's immune system. She and her colleagues have developed models based on ordinary differential equations, that incorporate tumor cells, host cells, immune cells, and drug interaction. The models have been successful keeping patients in a region with a favorable basin of attraction (in which the tumor shrinks) and shifting them there, by gathering data on an individual's immune system and using that data to guide the treatment. The prescribed treatment uses a combination of chemotherapy and immunotherapy. Before her research, patients could be in different basins of attraction and the same chemotherapy treatment would push them further into the region, which is bad for those starting off in the "wrong" region. By knowing the state of a patient's immune system, doctors can identify which region a patient is in, and prescribe treatment based on the region.

De Pillis holds the Norman F. Sprague Chair of Life Sciences, is co-director of the Center for Quantitative Life Sciences, is an investigator on two National Science Foundation-funded mathematical biology projects, and advises for the college’s Mathematical Biology major, one of the first such undergraduate programs in the United States. The mathematical biology program, the only one that meets the Bio2010 recommendations for preparing research scientists in the 21st century, has risen to become a leader in both curriculum and undergraduate research innovation. De Pillis also is serving as the Director of the HMC Global Clinic program.  The October issue of SIAM news also includes an article describing the HMC Clinic and Global Clinic.

De Pillis joined HMC in 1993, but her interest in math and biology dates back further. As a young girl, de Pillis, inspired by her own female pediatrician, wanted to become a medical doctor. Although her undergraduate degree is in mathematics and computer science, her continuing interest in medicine is interwoven throughout her mathematical biology work.

Mathematical biology is the science of solving biological problems using a range of mathematical tools. De Pillis’ ongoing research — curing cancer with mathematics — involves the use of mathematical models to address the complex interactions of growing tumors with the body’s immune system to better treat, and perhaps someday cure, cancer. De Pillis uses differential equations—mathematical sentences — to define the variables involved in tumor growth rates, to identify the effects of different concentrations of immune cells and drugs on tumors, and to anticipate the tumor decay patterns.

One aspect of that research involves the evaluation of two important immune cell types: the more generalized natural killer cells, and T-cells, which are specific to a disease. Using existing data, De Pillis and her team created several models based upon differential equations, making predictions about immune cell response.

“The best way to motivate students to learn new science is to have them work on a problem that must be solved,” she said. “I have a real passion for strengthening the ties between mathematics and the sciences. Will we cure cancer? Perhaps not. Are we training students to speak the multiple scientific languages without being afraid to work across disciplines? Most definitely.”