(by Dr. Alexander Anderson)
Biomathematics Group Develops
Mathematical Models
Of Cancer Invasion
The Department of Mathematics’ Biomathematics Study Group is playing a key role in a $12.5 million research project to develop mathematical models of cancer invasion. Four members of the Biomath Study Group will develop the mathematics that will be used to create computer simulations of tumor invasion. Researchers hope the models will ultimately provide a tool that can be used to predict the progress of tumors in patients.
The “Multiscale Mathematical Modeling of Cancer Invasion” project is an interdisciplinary effort involving Vanderbilt scientists from several specialties, including chemical engineering, imaging, mathematics, oncology, and cancer biology. It’s funded by a five-year grant awarded in October 2004 by the National Institute of Health’s National Cancer Institute (NCI). The grant designates Vanderbilt as one of nine new Integrative Cancer Biology Centers under an NCI initiative to foster interdisciplinary teams to develop computational models of cancer.
“Bringing mathematics into a central role in cancer research represents a new direction for the National Cancer Institute and the National Institutes of Health,” says Prof. Philip Crooke, vice director of the Biomathematics Study Group. “This is a high-profile attempt to bring mathematics to bear on a very important problem – how solid tumors invade tissue.”
“If we’re going to understand cancer invasion, we have to consider a large number of variables,” explains Dr. Vito Quaranta of Vanderbilt’s Department of Cancer Biology, the project’s principal investigator.
Parameters known to affect cancer invasion include cell proliferation and death, migration, metabolism, cell-cell adhesion, angiogenesis, and extracellular matrix properties, as well as numerous microenvironmental factors. Predicting how all these will interact to produce cancer is a highly complex task.
“It can’t be done intuitively, the way we’ve been doing biology so far,” says Quaranta. “We need a mathematical model.”
Vanderbilt’s mathematicians were instrumental in developing the successful grant proposal last fall. “In fact, Vanderbilt was already known as a place where people are interested in mathematical models of cancer, even before the grant opportunity was announced,” says Mathematics Professor Glenn Webb. “The Biomathematics Study Group has been in existence since 2001, and we had a Workshop on Mathematical Models of Cancer here at Vanderbilt in May 2002 that attracted more than 50 U.S. and international researchers. So it was quite natural that our group began meeting with the biologists to develop this proposal when NCI announced the initiative.”
In addition to Crooke and Webb, members of the Biomathematics Study Group involved in the project are BSG Director Emmanuele DiBenedetto and Assistant Professor Daphne Manoussaki. The mathematicians’ role is to extend and refine a model of tumor growth developed by Dr. Alexander Anderson of the University of Dundee in Scotland, a co-investigator on the project. Peter Cummings of the Department of Chemical Engineering also consults on the modeling and computations.
Anderson’s model of tumor invasion includes four variables: the number of cells and their rate of growth, the cellular matrix, enzymes to degrade the cellular matrix, and the oxygen concentration in the environment of the cells. His model uses a combination of nonlinear and discretized partial differential equations to model tumor invasion.
Working with Anderson, the Biomathematics Study Group will add mathematical descriptions of cellular and microenvironment invasion parameters, such as cell-cell adhesion, cell migration, metabolism, and angiogenesis. The modeling will be based on actual measurements of these processes taken in the lab by experimental biologists on the team. As the model is developed, additional experiments will test its validity. Continuous interaction between the mathematicians and the biologists will fine-tune the model to more accurately represent the behavior of actual tumor cells.
“The interplay between the biologists and the mathematicians is an essential element in this research,” says Crooke. “The biologists perform experimental validation of the model as it develops, and we adjust the mathematics based on those results. We also give the biologists feedback from our calculations, so they can adjust their experimental processes. We believe we’re at the forefront of how scientific interdisciplinary teams should work together.”
The research here at Vanderbilt, as well as at the other eight Integrative Cancer Biology Centers created by the NCI, demonstrates the new role math is increasingly playing in all areas of biology. Cancer researchers, in particular, are recognizing the value of using high-level mathematics to better understand the disease. The hope, as expressed in the NCI’s 2004 annual plan, is that “computational models for cancer, once refined and validated, will not only yield insights and knowledge about cancer, but will also be used to help diagnose cancer patients and to plan and monitor treatment strategies.”
The “Multiscale Mathematical Modeling of Cancer Invasion” project has also been featured in The VUMC Reporter. Click here to read that story.
Visit the Vanderbilt Integrative Cancer Biology Center website.
Date Posted: March 9, 2005