Mathematicians at George Mason University are developing sophisticated mathematical models that can help tune and improve the efficiency and safety of various imaging and therapeutic devices:
Sofer, who chairs SEOR in the Volgenau School of Information Technology and Engineering, was one of the first researchers to focus on the application of operations research to medical treatment and diagnosis, and she has become a leader in the effort to make operations research in medicine into a field.
She became interested in the medical applications of mathematical optimization nearly 10 years ago when she collaborated with Calvin Johnson, a doctoral student who worked at the National Institutes of Health (NIH) on the problem of image reconstruction in positron emission tomography, a medical imaging technique for investigating the level of metabolism and blood flow in an organ.
Sofer and Johnson developed reconstruction methodology and software that outperformed leading methods both in the quality of image and in the solution time. Through this research she says she discovered how rewarding it was to work on applications that could help save or extend human lives.
In her current work, Sofer has been using optimization to help fine-tune the application of a relatively new medical procedure called radiofrequency ablation. The procedure is used to kill liver tumors in patients who are not candidates for surgery. She is collaborating in this research with NIH physician Bradford Wood, an interventional radiologist.
"Ablation kills the tumor by applying heat," Sofer explains. "The physician inserts a needle, and electrical current in the range of radiofrequency is applied. That cooks the tumor; however, it also kills adjacent healthy tissue. The key is to apply the heat in exactly the right region. You don’t want to damage vital tissue or structures."
Computed tomography scans and ultrasound imaging are used to determine the tumor’s location and monitor the needle’s path.
Sofer has been working on the problem of determining how to place one or more needles to maximize the effectiveness of the procedure. It’s not as easy as it sounds. As in the radiation example, there are many variables. Not only must she consider how many needles should be used and where the needle or needles should be inserted, but also the angle and depth of insertion. Other questions that come into play are how to minimize the number of insertion points when multiple needles must be used. And in a real-life situation, this optimization must often be determined in a matter of minutes.
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