Mathematical Models and Supercomputers Helping to Advance Tailored Cancer Therapies

Mathematical Models and Supercomputers Helping to Advance Tailored Cancer Therapies

Researchers at the University of Texas at Austin are advancing cancer research using supercomputers and big data to model how cancer behaves — a technique that could be used to improve therapies for prostate cancer.

Thomas Yankeelov, director of the Center for Computational Oncology at UT Austin, believes cancer research is rich in data but needs laws and models. The solution, he said, is to mine large quantities of data to bring mathematics to cancer and find formulas that explain the multiplicity of behaviors of different cancers, which might be useful in improving personalized therapies for patients.

“We’re trying to build models that describe how tumors grow and respond to therapy,” Yankeelov, who is leading the project, said in a press release. “The models have parameters in them that are agnostic, and we try to make them very specific by populating them with measurements from individual patients.”

His research is based on studies completed in 2017. Results showed the research team was able to predict how brain tumors would grow and respond to X-ray radiation therapy much more accurately than other models. They achieved these results by including factors like the mechanical forces that act on cells and tumors.

“We’re at the phase now where we’re trying to recapitulate experimental data so we have confidence that our model is capturing the key factors,” Yankeelov said.

The team developed the mathematically complex models using supercomputers at the Texas Advanced Computing Center (TACC), advancing knowledge that had been “smoldering in the literature for a decade,” as J. Tinsley Oden describes it. Oden is director of UT Austin’s Institute for Computational Engineering and Sciences, of which the Center for Computational Oncology is a part.

The new models were developed following years of work from several efforts in countries around the world, including earlier studies in which researchers were able to predict how large mouse tumors would grow within 5 to 10 percent of their final mass.

“We have examples where we can gather data from lab animals or human subjects and make startlingly accurate depictions about the growth of cancer and the reaction to various therapies, like radiation and chemotherapy,” Oden said.

The latest model included equations based on patient-specific data like positron emission tomography (PET), X-ray computed tomography (CT), magnetic resonance imaging (MRI), biopsies, and other measurements of tumor response.

“You put mathematical models on a computer and tune them and adapt them and learn more,” Oden said. “It is, in a way, an approach that goes back to Aristotle, but it accesses the most modern levels of computing and computational science.”

By modeling biological behavior at the tissue, cellular and cell signaling levels, the team is able to solve partial differential equations for each element, combining them intelligently at the end.

“This is one of the most complicated projects in computational science. But you can do anything with a supercomputer,” Oden said. “There’s a cascading list of models at different scales that talk to each other. Ultimately, we’re going to need to learn to calibrate each and compute their interactions with each other.”

Using the model in earlier experiments, Yankeelov and his group achieved 87 percent accuracy at predicting how a breast cancer patient would respond after just one round of treatment. Now, the team is working to replicate these results and readjust their models by adding new predictors associated with how the tumor might evolve.

Combining mathematical modeling and supercomputers could be a way to overcome the complexity of treatments for cancer, which is not a single disease, but a group of diseases that behave differently according to sub-types, these researchers argue.

The team will continue conducting studies until eventually they can create specific predictions for each patient so that therapies can be optimized to fit their personal needs, which is, as Yankeelov says, their “ultimate goal.”