Mathematics for Virtual Surgery

December 4, 2007

Applied mathematician Joseph Teran of the University of California, Los Angeles predicts that one day surgeons will be able to practice on your "digital double." And, when using such a simulator, they'll be allowed to "fail spectacularly with no consequences," he said, and then learn from their mistakes. "It's a cheaper alternative to cadavers," Teran observed, "and a safer alternative to patients." Teran works at UCLA's Center for Advanced Surgical and Interventional Technology.

Teran studies the biomechanical simulation of soft tissues and specializes in solving mathematical equations that govern the physical phenomena of everyday life. Tissue, muscle, and skin are elastic and behave like a spring, for example, and can be modeled by partial differential equations.

In fact, "most of the behavior of everyday life can be described with mathematical equations," Teran said. "It's very difficult to reproduce natural phenomena without math."

Making virtual surgery a reality will require progress not only in solving mathematical equations but also in computational geometry and computer science. "Things in geometry that used to take days and days start to take hours and minutes," Teran said.

Ideally, in the not-too-distant future, patients needing surgery would get scanned, after which surgeons would practice on the resulting three-dimensional digital double. In addition, "you could have a patient in a small town scanned while a surgeon hundreds or thousands of miles away practices the surgery," Teran said.

To help bring the day of virtual surgery a bit closer, Teran has organized a virtual surgery workshop for Jan. 7-11, 2008, as part of UCLA's Institute for Pure and Applied Mathematics.

Source: University of California, Los Angeles, Nov. 26, 2007.