They’re among the most powerful tools for shedding new light on cancer growth and evolution, but mathematical models of the disease for years have faced an either/or stand-off.

Though models have been developed that capture the spatial aspects of tumors, those models typically don’t study genetic changes. Non-spatial models, meanwhile, more accurately portray tumors’ evolution, but not their three-dimensional structure.

A collaboration among Harvard, Edinburgh, and Johns Hopkins Universities including Martin Nowak, director of the Program for Evolutionary Dynamics and a professor of mathematics and of biology at Harvard, has now developed the first model of solid tumors that reflects both their three-dimensional shape and genetic evolution. The new model explains why cancer cells have a surprising number of genetic mutations in common, how driver mutations spread through the whole tumor, and how drug resistance evolves. The study is described in an Aug. 26 paper in Nature.

“Previously, we and others have mostly used non-spatial models to study cancer evolution,” Nowak said. “But those models do not describe the spatial characteristics of solid tumors. Now, for the first time, we have a computational model that can do that.”

A key insight of the new model, Nowak said, is the ability for cells to migrate locally.



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