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Uncovering Tumors, Hidden Subs, and Cracks in Airplanes Using Math

August 14, 2001

Uncovering Tumors, Hidden Subs, and Cracks in Airplanes Using Math

Rensselaer Researchers Receive $1 Million From the National Science Foundation

Troy, N.Y. — Four researchers at Rensselaer Polytechnic Institute have received a $1 million grant from the National Science Foundation to solve a range of problems — including using the elastic properties of tissue to detect tumors in the human body — with a branch of mathematics known as inverse problems.

The recipients of the grant are: Joyce McLaughlin, Ford Foundation Professor of Mathematical Sciences; Margaret Cheney, professor of mathematics; Antoinette Maniatty, associate professor of mechanical engineering; and Clifford Nolan, assistant professor of mathematics.

"It is unusual for mathematicians to get a grant of this size, and while it is not a diversity program, three of the researchers are women. I am proud of that," McLaughlin said.

Inverse problems is a branch of applied mathematics in which researchers develop non-invasive methods to gain information about inaccessible regions — for example, in the human body or in remote regions of the earth — by probing them with elastic or electromagnetic waves.

The three-year program is a "Focus Group" award given by the Division of Mathematical Sciences at NSF to groups of researchers working collaboratively. The first project at Rensselaer will be to develop an algorithm for a procedure that will enable doctors, using low-frequency elastic waves, to detect abnormal human tissue such as that found in tumors.

The other projects are:

* Locating sources and objects by time-reversing received signals, as in reversing a digital tape. The procedure will locate submerged objects such as submarines, mines, or even kidney stones.
* Advancing near-field electromagnetic imaging systems to improve detection of small objects, especially in the human body. This work has medical imaging and nondestructive testing applications such as finding cracks and corrosion in airplanes.
* Developing airborne and satellite-borne radar for locating partially hidden objects and enhancing detailed topographic maps.

"Advances in the field of inverse problems depend on a wide range of expertise — mathematical analysis, engineering, mathematical modeling, and scientific computation," McLaughlin said. "The team for each problem brings expertise in all these areas."

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Founded in 1824, Rensselaer Polytechnic Institute is America’s first technological research university. Rensselaer encompasses five schools, 32 research centers, more than 145 academic programs, and a dynamic community made up of more than 7,900 students and more than 100,000 living alumni. Rensselaer faculty and alumni include more than 145 National Academy members, six members of the National Inventors Hall of Fame, six National Medal of Technology winners, five National Medal of Science winners, and a Nobel Prize winner in Physics. With nearly 200 years of experience advancing scientific and technological knowledge, Rensselaer remains focused on addressing global challenges with a spirit of ingenuity and collaboration.