Math professor wins Iorio award for medical imaging study

by Dalton Karwacki

For his foray into the medical field using mathematics, Dr. Andrew Markoe, a professor in the Department of Mathematics, was honored at Rider’s annual Dominick A. Iorio faculty research award luncheon last Friday.

The Dominick A. Iorio award was established in 1997 after Iorio’s retirement as dean of Liberal Arts and Sciences.  The award is given to a faculty member in recognition of his or her research.
The award is given on Founder’s Day in November, but a luncheon is held later in the year to honor the winner. At the luncheon, the recipient is asked to present his or her research publicly.
Markoe’s presentation was entitled “Tomography: Medical Imaging from the Mathematical Point of View.”  Tomography, as Markoe explained, is the science behind medical CT scans (the T stands for tomography).

“Tomography does [something different from traditional x-rays]; it concentrates on one slice of the body,” he said.

Markoe’s presentation mainly focused on the basic process of tomography, but the underlying mathematics made an appearance toward the end.

“So what is tomography about?” Markoe asked. “We would like to find out what is inside [an object] without opening it up. And that’s really what tomography is about.”

A CT machine puts imaginary planes through the desired area in order to see what is inside, “but one plane doesn’t tell us very much, so therefore we slice [the object] with every possible plane.”

He explained that each of these planes is assigned a number corresponding to the total density. Through a mathematical process known as back projection, these planes are analyzed based on the angle at which the plane passed through the object. Individually, this is of little use, but when taken in the context of all possible planes through the object, a mostly accurate representation of the object can be extrapolated.

This image is mathematically “filtered” to create a clearer image, which is then rendered in what is called the filtered back projection. Markoe gave examples of this process, both with simple geometric shapes as well as actual images of brains.

He made a conscious effort to make the presentation as accessible as possible to everybody, including non-mathematicians. He included jokes throughout the presentation, at times leaving notes to do so in his PowerPoint slides.  When he started explaining the sophisticated mathematics that drive the processes of tomography, he did his best to ensure that the entire audience was able to follow it.
Members of the faculty and several of Markoe’s students attended the luncheon.  Throughout the presentation, he answered questions from the audience. He also took some good-natured heckling right off the bat, which he took in stride.

“Gee, I expected to get heckled, but I didn’t expect it on the first slide,” he said.

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