Topic Name: UCLA mathematician works to make virtual surgery a viable technology
Category: Computer science & technology
Research persons: Joseph Teran
Location: University of California, Los Angeles, United States
A surgeon accidently kills a patient, undoes the error and starts over again.
Can mathematics make such science fiction a reality?
The day is rapidly approaching when your surgeon can practice on your
"digital double" — a virtual you — before performing an actual
surgery, according to UCLA mathematician
Joseph Teran, who is helping to make virtual surgery a viable technology. The
advantages will save lives, he believes.
"You can fail spectacularly with no consequences when you use a
simulator and then learn from your mistakes," said Teran, 30, who joined
UCLA's mathematics department in July. "If you make errors, you can undo
them — just as if you're typing in a Word document and you make a mistake, you
undo it. Starting over is a big benefit of the simulation.
"Surgical simulation is coming, there is no question about it," he
said. "It's a cheaper alternative to cadavers and a safer alternative to
How would virtual surgery work?
"The ideal situation would be when patients come in for a procedure,
they get scanned and a three-dimensional digital double is generated; I mean a
digital double — you on the computer, including your internal organs,"
Teran said. "The surgeon first does surgery on the virtual you. With a
simulator, a surgeon can practice a procedure tens or hundreds of times. You
could have a patient in a small town scanned while a surgeon hundreds or
thousands of miles away practices the surgery. The patient then flies out for
the surgery. We have to solve mathematical algorithms so what the surgeon does
on the computer mimics real life."
How far off is this virtual surgery?
"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. We're working on that. Our job as
applied mathematicians is to make these technologies increasingly viable."
The technology will be especially helpful with new kinds of surgeries, he
"A virtual surgery cannot be a cartoon," said Teran, who works with
a surgeon. "It has to be biologically accurate. A virtual double needs to
be really you."
Teran is organizing a virtual surgery workshop that will take place at UCLA
from Jan. 7 to 11 as part of UCLA's Institute for Pure and Applied Mathematics.
Making virtual surgery a reality will require solving mathematical equations,
as well as making progress in computational geometry and computer science. An
applied mathematician, Teran works in these fields; he develops algorithms to
solve equations. Advances by Teran and other scientists in computational
geometry, partial differential equations and large-scale computing are
accelerating virtual surgery.
How human tissue responds to a surgeon, Teran said, is based on partial
differential equations. Teran solves on a computer the mathematical equations
that govern physical phenomena relevant to everyday life. He has studied the
biomechanical simulation of soft tissues.
"Most of the behavior of everyday life can be described with
mathematical equations," he said. "It's very difficult to reproduce
natural phenomena without math."
Tissue, muscle and skin are elastic and behave like a spring, Teran said.
Their behavior can be accounted for by a classical mathematical theory.
Progress in his field is already rapid, Teran said, noting that "things
in geometry that used to take days and days start to take hours and
Teran believes medical schools will increasingly train physicians using
computer surgical simulation.
Teran's applied mathematics can also be used to design more durable bridges,
freeways, cars and aircraft.
"I would like people who design bridges to be able to use a virtual
model — I'm interested in making that a reality and in creating numerical
algorithmic tools that let people who design bridges have more computational
machinery at their fingertips," he said.
As an undergraduate, Teran realized "you can use math problems to solve
real problems and can help people in ways that seem totally unrelated to
math." He earned his doctorate at Stanford University, where he took
graduate classes in partial differential equations and worked on new ways of
solving the governing equations of elastic biological tissues. He was a
postdoctoral scholar at New York University before joining UCLA's faculty.
"I started with math because I like problem-solving, and I like how
elegant math is," Teran said. "I like how much careful analysis is
required, and that there's a right answer. Now I'm completely fascinated by what
you get from a simulation, the kinds of complex behavior you can reproduce on a
computer and the kinds of questions you can answer. Math will tell you how the
world is. It will give you an answer, and it's intellectually stimulating and
fun. It really pays off."
Teran, who is teaching a course on scientific computing for the visual
effects industry, said he came to UCLA because it is one of the country's best
universities for applied mathematics, because its medical school is among the
country's best and because it is near Hollywood, where he helps to make movie
Teran, who works with UCLA's Center for Advanced Surgical and Interventional
Technology, spoke this fall as part of Intel Chief Technology Officer Justin
Rattner's keynote address at the Intel Developer Forum on the rise of the
"3-D Internet." Teran demonstrated virtual surgery applications.
The future 3-D Internet will include an "avatar" — a virtual
representation of you — that could look "just like you, or better than
you," Teran said.
The graphics will be astonishingly realistic and three-dimensional, he said,
but the simulation needs to be much more accurate, a goal Teran is working to
"As virtual words get more realistic, modern applied mathematics and
scientific computing are required," he said.
Note for Virtual Model
A Virtual Model, in the general sense, is a model of a physical object, be it a person, a room, a house, a city or a planet. This model is a digital description of the object (typically greatly simplified) that can be used in a computer simulation or Virtual Reality.
The most common examples of Virtual Models are those created in 3D for the purpose of visualisation. The field of architecture has greatly popularized the use of virtual models to animate fly-throughs of yet-to-be-built buildings.
The first known example of a virtual model is the Utah Teapot.
The first widely available commercial application of human Virtual Models appeared in 1998 on the Lands' End web site. The human Virtual Models were created by the company My Virtual Model Inc. and enabled users to create a model of themselves and try on 3D clothing.
Virtual Modeling has recently been applied to spectacles and sunglasses, allowing users to see what they'd actually look like in a pair of glasses. The more sophisticated versions (eg. the FocusFix Virtual Modeling System, 2005) also incorporate correct scaling and are able to extrapolate the measurements required by the laboratory for accurate glazing.
Joseph M. Teran
UCLA Applied Mathematics
Ph.D. Scientific Computing, Stanford University
Office: Math Sciences 7619-E
Phone: (310) 206-0048
UCLA is California's largest university, with an enrollment of nearly 37,000
undergraduate and graduate students. The UCLA College of Letters and Science and
the university's 11 professional schools feature renowned faculty and offer more
than 300 degree programs and majors. UCLA is a national and international leader
in the breadth and quality of its academic, research, health care, cultural,
continuing education and athletic programs. Four alumni and five faculty have
been awarded the Nobel Prize.
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