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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.