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Numerical Methods

With funding from the National Science Foundation and the Department of Energy, Kapila is part of a team attempting to describe, mathematically, the dynamics of explosions. All of the work involves conventional, nonnuclear explosives.   

“We are trying to precisely identify the conditions under which things will go off or not go off, and mechanisms that make things go off. Some explosives will detonate only under very specific conditions, while others are more sensitive. We are very interested in assessing how aging affects the performance of an explosive,” says Kapila, one of the original organizers of the Mathematical Problems in Industry workshops.   

Like several of his colleagues in the Department of Mathematical Sciences, Kapila has never received an academic degree in mathematics. He studied physics and mechanical engineering as an undergraduate in India, and his Ph.D. from Cornell University is in theoretical and applied mechanics.

“It’s a somewhat unconventional department, in that several of us don’t even have degrees in mathematics, or we have additional degrees along with mathematics. We are not cloistered at all. We are not cloistered at all. We familiarize ourselves with other disciplines and work with colleagues from those disciplines. People here are driven by application,” says Kapila.   

Just as his father’s heart attack led David Isaacson, with the assistance of several Rensselaer colleagues, to develop a conductivity imaging device, a different disease has inspired him and Biomedical Engineering Professor Jonathan Newell to create yet another means of peering electronically into the human body. In the mid-1990s, Isaacson’s wife was diagnosed with breast cancer.   

“You’re devastated at first, of course. You’re in shock. Then we started researching our best options. What we are developing is a screening tool. It will be an adjunct to mammography. It won’t replace it, but it may provide an improvement,” Isaacson says.   

His device, which delivers real-time images, is called adaptive current tomography (ACT), and does not expose the patient to radiation. The system, developed with the aid of a grant from the New York State Department of Health, uses low-level electrical currents to measure conductivity (the ability to let electricity flow through matter) and permittivity (the ability to store an electrical charge) within the body. Isaacson’s chief partners






Images from the adaptive current tomography (ACT) device show the increase in resistivity in the lungs in proportion to the amount of air that is taken in. They get progressively “redder” because the resistivity is increasing as air fills the lungs. (Contributed by D. Isaacson.)

on the project are Newell and Gary Saulnier ’80, professor of electrical, computer, and systems engineering at Rensselaer.  

Using electrodes applied to the breast, researchers transmit currents through the affected area. A computer records and measures changes in the flow of the current, and turns the data into video images. A healthy breast will show up as a uniform, circular pattern, while a tumor is displayed as a dark spot on the screen. The device is in use at Albany Medical Center.   

“This method is cheaper than traditional mammography. The image isn’t as clear as X-rays or CT scans, but it may improve the sensitivity and there’s no exposure to radiation,” Isaacson says.   

The ACT system may also be used to detect blood clots in post-surgical patients, to find fluid buildups in the brains of premature infants, and to diagnose pulmonary edema.   

“This probably sounds a little unusual coming from a mathematician, but the thing I’m most excited about is understanding cancer from the molecular level. While I was reading these cancer drug papers when my wife was sick, every once in a while I would forget why I was doing it and I’d just start to enjoy it. Isn’t that odd, the idea of enjoying modeling the cell cycle in cancer?” Isaacson says.

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