Numbers Expert

Eliminating errors from computer calculations generates more realistic simulations

Scientists and researchers address many interesting and difficult challenges on a daily basis. Some look for solutions by applying simple observation techniques. Others engage in laboratory science. However, some problems are so complex that they require more data than observation or experiments can provide. That’s when they turn to the power of scientific computing.

“Scientific computing offers another way of getting answers to these problems,” said Steven Wise, associate professor of mathematics at UT. “Many problems in science and technology are continuous in nature,” he explained. “But in order to solve a problem with scientific computing, we have to change something that is continuous in nature to something that is discrete in nature.”

Because computers can deal only with things that are discrete (or finite), the continuous (or infinite) variables and equations must be translated into discrete counterparts to make them suitable for numerical evaluation. The transformation process, known as discretization, is not 100 percent accurate and leaves room for errors, which Wise tries to determine using numerical analysis.

“When you discretize a problem, you always change it and create error,” Wise said. “When we approximate a solution using computer simulation, we’re not getting reality. We are actually a couple of layers away from reality.” Figuring out how to quantify the error is where his expertise comes into play.

One of Wise’s research areas is simulating cancer growth. When a patient presents with symptoms, the medical team has a limited amount of time to diagnose and treat the patient before the tumor takes over. Researching how best to treat the growth is possible with observation and laboratory experiments, but that can be a waste of time and resources.

“Computer simulation is like a black box,” Wise said. “We have to use real data to train our computer model to assign the parameters needed to run the simulation.”

That’s why Wise and his collaborators work with medical professionals who supply data from their cancer patients using MRIs and other tests. The data include information such as the shape of the mass and where it is in the body. Is it near major organs or blood vessels? What kind of cancer is it and how fast does it grow?

Once the data points are entered and the computer understands the model, researchers can start running simulations that represent various treatments or medications to stop or slow the cancer’s growth.

Armed with real-world data, Wise and his collaborators were one of the first groups to successfully simulate the process of growth and neovascularization—an action very similar to how blood vessels grow new vascular tissue to seal a cut on your arm.

Neovascularization occurs when genetically mutated cancer cells send out a chemical signal called tumor angiogenic factor (TAF) to awaken blood vessels near the tumor. The cell walls then begin to break down and grow new vascular tissue. The tissue grows toward the cancer cells in order to replenish their nutrients.

“These cancer cells are haywire,” Wise said. “They are subdividing and doing whatever they can to stay alive.”

After the neovascularization process, cells without the genetic mutation might die. The remaining cells lump together and launch more TAF, which starts the process all over again. Once the tumor gets its own blood supply, it has the ability to break off cells and send them all over the body via the bloodstream.

With this piece of the puzzle in place, Wise and his colleagues can run simulations with a variety of treatment options and medications to try and stop, or at least slow down, the cancer’s growth.

“We’re pretty far away from actual clinical experiments on this process, but we’re trying,” Wise said. As the technology advances, researchers will be able to simulate more complicated activities and move even closer to reality.

Published online, Quest, November 26, 2014

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