Spotlight on Research: Prof. Uses Mathematical Optimization to Solve Medical Problem
Posted: October 22, 2002 at 1:00 am, Last Updated: November 30, -0001 at 12:00 am
Liver cancer and deaths caused by the disease are increasing; prostate cancer is the most frequently diagnosed cancer in American men, other than skin cancer, and their second leading cause of cancer-related death. As a result, researchers around the country are focusing their attention on fighting these diseases through new methods of diagnosis and treatment.
In an example of outside-the-box thinking, Ariela Sofer, professor and chair of the Systems Engineering and Operations Research Department, has looked at ways her field of mathematical optimization can contribute to these efforts, and she has had promising results.
For more than a year, Sofer has been using optimization – the technology of finding the best solution to a problem represented by a mathematical model – to help fine-tune a relatively new medical procedure called radiofrequency ablation. The procedure is used to kill liver tumors in patients who are not candidates for surgery.
“Ablation kills the tumor by applying heat,” Sofer says. “The physician inserts a needle and electrical current in the range of radiofrequency is applied. That cooks the tumor. The key is to apply the heat at the right spot. You don’t want to damage large blood vessels or vital tissue.
“Our part is to determine how to place one to three needles to maximize effectiveness of the procedure,” says Sofer. She and her doctoral student, Masami Stahr, joined an interdisciplinary team established by Bradford Wood, an interventional radiologist from the National Institutes of Health, to work on the problem. Their objective is to develop the optimization method and software that will give the physician a feasible path of entry for the needle to kill the tumor and a margin around it, while minimizing damage to healthy tissue. The tumor’s location is determined from CT (computerized tomography) scans, and ultrasound imaging is used during the procedure to monitor the needle’s path.
Sofer, who spent a sabbatical at Georgetown University Medical Center, has also been working with another team for several years on a similar project for prostate cancer. In this effort, however, the Georgetown team’s goal is to improve a biopsy procedure.
Usually a PSA (prostatic specific antigen) blood test is used to screen for prostate cancer, and if the results suggest cancer, a biopsy is performed. For the biopsy, needles are inserted in the prostate to extract a bit of tissue. If the physician can’t actually feel a tumor, six needles are placed in standard positions. But “recent studies have shown a high level of false negative biopsies with this method,” Sofer explains. The goal of her team is to determine the best locations to insert the needles for optimum results.
Using 300 reconstructed models of prostates removed via prostatectomy, Sofer built a math model to maximize the probability of detecting cancer. Inserting six needles in the traditional way will detect cancer in 67 percent of patients with the disease, Sofer says. In the optimized model, however, 79 percent of cancers will be detected. “Even this small percentage difference affects thousands of patients,” she points out.
The team’s results were presented in a medical conference last year. “There was some enthusiasm, but the medical community is not entirely convinced by mathematical data. They’d like to see proof on real patients,” Sofer says. She estimates that the technique can be used on patients on a limited basis within a year.
Sofer’s experiences with the liver and prostate cancer research have convinced her that optimization in medicine is a promising field, although challenging. “These are very, very large problems,” Sofer says, “but I get a sense of satisfaction knowing that this work may actually do some good for human beings.”
– By Robin Herron