Pages 15-16: Mathematics
Page 15: The Math of CT-Scanning: Reconstructing Spiral Computer Tomography
Spiral Computer Tomography (CT), one of the most powerful medical imaging modalities, provides doctors with the ability “to see inside the patient” without actually performing any surgery. The technology, however, poses a difficult challenge for engineers and mathematicians, which UCF’s Alexander Katsevich may have made easier.
The challenge with Spiral CT is to process the vast amounts of data that the scan collects in a timely and accurate manner. Perfect algorithms-which reconstruct the scanned objects flawlessly (at least, in theory) -exist, but they are far too slow to be used. Faster approximate algorithms also exist, but they create inaccuracies in the reconstructed images.
“Unfortunately, this is not very good,” said Katsevich. “You get artifacts (false features in an image or distortions) that could mask a significant problem. Sometimes radiologists go by the tiniest detail when looking for pathology.”
Katsevich found a balance between efficiency and accuracy for Spiral CT reconstruction. He suggested a completely new approach to the reconstruction problem-one that is based on a piecewise constant weight. His solution is referred to as the “1 algorithm” or “Katsevich’s algorithm.”
Katsevich’s algorithm has had a significant impact on the theory of image reconstruction. A number of researchers are now trying to adapt his approach to other problems in tomographic imaging (including non-spiral scanning)-opening a whole new direction of research. “Only time can tell how big it will become in the long run,” Katsevich said.
Currently, Katsevich is continuing to refine his algorithm. He calls the latest version the “3 algorithm” and hopes that it will make considerable improvements in image quality provided by the present scanners.
How Does CT Scanning Work? Both Spiral and non-Spiral CT scanning work by transmitting a narrow beam of x-ray particles through a patient and measuring the energy loss of the beam after the particles have passed through parts of the patient’s body. The energy loss of the x-ray beam is proportional to the total mass of tissues along the path of the beam, thereby allowing the beam to “see” as it traverses the patient. With Spiral CT, the x-ray source is mounted in a gantry, a large doughnut-shaped object, and a detector array is placed directly opposite to the source. The patient, lying on a bench, is moved slowly into the middle of the rotating gantry while the source shoots beams of x-rays from varying directions. CT scanners collect data, which is then reconstructed into an image with the help of the reconstruction algorithm. The results are significantly more detailed than normal x-ray imaging and have numerous diagnostic advantages over older non-Spiral protocols.
More Information: www.math.ucf.edu
Key Faculty: Alexander Katsevich
Page 16: Turbulence Research
Turbulence arises in practically all flow situations in nature and modern technology, but despite its ubiquity, turbulence still remains one of the greatest scientific riddles.
In May 2003, UCF applied mathematicians Drs. Sen Shivamoggi and John Cannon organized a week-long international conference on turbulence that was sponsored by UCF along with Florida State University, University of Florida, Florida A&M University, and Embry Riddle Aeronautical University. At the conference, leading experts from applied mathematics, physics, and engineering who are working on this common problem shared insights from their diverse backgrounds. The conference was a great success; participating experts commented that it was “the best workshop on turbulence,” “a very exciting event,” and “a wonderful experience.”
UCF has a 15-year long history of active turbulence research, and Dr. Shivamoggi, the primary UCF researcher on the subject, has published over 30 articles on the topic, several of which appeared in MIT’s Annals of Physics. Most recently, Dr. Shivamoggi has been identified by the New Journal of Physics as one of about 50 leading researchers in turbulence worldwide. The journal’s upcoming turbulence focus issue will feature Dr. Shivamoggi’s article on collisionless magnetohydrodynamic turbulence—a problem of great interest in fusion and space plasma dynamics.
UCF’s Department of Mathematics has a very active plasma dynamics graduate research group that collaborates with Drs. Shivamoggi and David Rollins (Mathematics), Drs. John Brandenburg and Richard Eastes (Florida Space Institute). Over the past two years the graduate group has made six presentations at the national meetings of the American Physical Society Division of Plasma Physics and holds weekly research seminars. The next presentation of this research will be given in August by Dr. Shivamoggi, who is an invited speaker at the Workshop on Magnetic Reconnection in the Sun and the Magnetosphere at the Isaac Newton Institute of Mathematical Sciences, Cambridge (UK).
More Information: www.math.ucf.edu
Key Faculty: Sen Shivamoggi & John R. Cannon
Page 16: Modeling Expert: Dr. David J. Kaup
Provost Distinguished Research Professor David J. Kaup uses advanced mathematics to create models of human behavior, natural events, and physics. His research is then used to create computer simulations of situations that are too expensive, dangerous, or impossible to create and study in real life. For example, Dr. Kaup and one of his students recently worked on a simulation of an office-building fire. They made mathematical models of pedestrian crowd behavior trying to exit a burning building, in order to test the effectiveness of the building’s fire exits.
Dr. Kaup’s articles have been cited more than 5250 times!
Page 16: Quick Facts
WOMEN IN SCIENCE: UCF’s Department of Mathematics has the highest percentage of full-time female research faculty of all of the Florida Universities. The University has a special program—Women in Science and Engineering (WISE)—that creates female communities in order to encourage women to enter the sciences and prevent them from feeling isolated in those male-dominated disciplines.
CODE WORDS: UCF’s Distinguished Professor of Mathematics Peter Hilton was one of 40 men who broke Germany’s secret-message code during WWII.
CONFERENCES: UCF will host the 8th International Conference on Integral Methods in Science and Engineering on August 2-5, and on October 2-4 the Department will also host the first meeting of the SIAM activity group on nonlinear waves and coherent structures. siam.org/meetings/nw04.
HIGHLY CITED: Professor of Mathematics Mourad Ismail was named a “Highly Cited Researcher” by the Institute of Scientific Information (ISI). The researchers selected for inclusion on ISI Highly Cited list comprise less than .05 % of the nearly five-million researchers in the ISI Citation Database from 1981-1999. Dr. Ismail was the only highly cited mathematical researcher from any of the Florida state universities.
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