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VIGRE seminar, summer 2000: Mathematical Problems in Biomedical Engineering

Instructors
Jay Walton, David Dobson
Students enrolled
Xue Bai, Wei Guo, Dinara Khalmanova, Haewon Nam, Mahendra Panagoda, Wendy Poling, John Ryan, Xudong Yao, Qu Zhou (graduate mathematics students); Parag Ravindran (graduate mechanical engineering student)
Description
This VIGRE course was, in part, a continuation of the one offered during the previous spring. The subject was soft tissue mechanics, only now the issue was developing a mathematical model for ultrasound modulated soft tissue imaging. This project was undertaken in collaboration with Li-Hong Wang of the Biomedical Engineering Department who is a leading developer of this imaging technique. He and his colleagues needed help in development of algorithms for doing enhanced image reconstruction. The clinical application is the early detection of breast tumours. The advantages of the imaging technique is that it uses low power non-ionizing radiation, and hence is safer and is much less costly than traditional imaging technologies. This problem turned out to be a bit too ambitious for a five week summer term. The students did background reading with each presenting to the group reports on papers they were assigned to read on various topics relevant to the problem. This part worked well and was very instructive for the students. They were given about two to three weeks of lectures by the instructors on various relevant mathematical topics then began to develop models for the scattering of laser photons in soft tissue and for the focusing of ultrasound beams. There was not enough time to combine the two into a model of their interaction, which is needed to fully model the imaging technique. Consequently, they weren't able to even begin the inverse problem which is needed for image reconstruction. However, one of the students, Hae-won Nam, continued to work on the problem after the class ended, and is now finishing her Ph.D. dissertation on this topic under the direction of Professor Dobson.
Impact
This VIGRE class spawned one Ph.D. dissertation by student Hae-won Nam and one or more papers. The reconstruction algorithm Nam and Dobson are developing shows nice promise of helping to enhance the usefulness of the medical imaging technique.