Math can mimic real life to create a virtual 'you'

December 11, 2007 - By Stuart Wolpert

With one tiny slip of a hand, a surgeon accidently kills a patient. But it’s no problem this time. It’s just a matter of starting over again.

Can mathematics make such science fiction a reality?

The day is rapidly approaching when your surgeon will be able to practice on your digital double — a virtual “you” — before starting to cut in earnest, according to mathematician Joseph Teran, who is helping to make virtual surgery a viable, lifesaving technology.

“You can fail spectacularly with no consequences when you use a simulator and then learn from your mistakes,” explained Teran, 30, a new assistant professor in UCLA’s Mathematics Department.

In the near future, a surgeon will be able to practice a procedure tens or hundreds of times even while the real patient is thousands of miles away, waiting to fly in for surgery. All that needs to be done first is for the patient to be scanned so that a 3-D digital double, complete with virtual internal organs, is generated..

There’s just one hitch. “A three-dimensional double of you can be made, but it would now take 20 people six to nine months,” Teran said. “In the future, one person will be able to do it in minutes. It’s going to happen, and it will allow surgeons to make fewer mistakes on actual patients. The only limiting factor is the complexity of the geometry involved. Our job as applied mathematicians is to make these technologies increasingly viable.”

Advances by Teran and other scientists in computational geometry, partial differential equations and large-scale computing are bringing virtual surgery closer. For example, partial differential equations can simulate the way human tissue responds to a surgeon. Tissue, muscle and skin are elastic and behave like a spring, he explained. Their behavior can be accounted for by a classical mathematical theory.

In fact, said the mathematician, who works with a surgeon, “Most of the behavior of everyday life can be described with mathematical equations. It’s very difficult to reproduce natural phenomena without math.”

Fascinated by simulations and the kinds of complex behaviors that can be reproduced on a computer, Teran is also applying his mathematical magic to create eye-popping special effects that are being enjoyed by moviegoers everywhere. His work is part of George Lucas’ Industrial Light & Magic physical simulation engine.

“My work has been used in a number of movies,” the professor said, including the “Pirates of the Caribbean” films where Teran’s algorithms went into creating the Medusa-like beard of Davy Jones. Currently, Teran is wrapping up a fall quarter class on scientific computing for the visual effects industry, delving into such topics as the tetrahedral mesh generation, articulated rigid bodies and Lagrangian deformation.

Teran left New York University, where he was a postdoctoral scholar, for Westwood in July because, he said, UCLA is one of the country’s best universities for applied mathematics, its medical school is among the best nationally and the campus is near Hollywood. He is currently talking with people at Disney’s Pixar Animation Studios now that he is at UCLA.

He is organizing a virtual surgery workshop that will take place on campus from Jan. 7 to 11 as part of UCLA’s Institute for Pure and Applied Mathematics.

For information, visit www.ipam.ucla.edu. (PDF)