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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2004-2005 MATHEMATICS COLLOQUIUM SERIES 02/04/05 Colloquium Dr. Jeong-Rock Yoon Department of Mathematical Sciences Rensselaer Polytechnic Institute Elastography: Creating Elasticity Images of Tissue Using Propagating Shear Waves Abstract:   Elastography is an innovative new medical imaging technique that provides high resolution/contrast images of elastic stiffness identifying abnormalities not seen by standard ultrasound. Since the elastic stiffness increases significantly (up to 10 times) in cancerous tissue, elastography shows tumor as a bright spot in the reconstructed image. Our data is the time dependent (10,000 frames/sec) interior displacements (0.3mm grid spacing) initiated by a short-time pulse. While standard inverse problems utilizing only boundary data suffer from the inherent ill-posedness, our inverse problem for elastography doesn't because it utilizes interior information. For the isotropic tissue model, a series of uniqueness results for our inverse problem are presented, and a fast stable algorithm to reconstruct the shear stiffness based on arrival time is explained. For the anisotropic tissue model, we assume an incompressible transversely isotropic model. It is important to consider anisotropic tissue models, since some tumors exhibit anisotropy and the structure of fiber orientation has a strong correlation with the malignancy of tumor. In this model, two shear stiffness and the fiber orientation are reconstructed by four measurements of SH-polarized shear waves, which are initiated by line sources in the interior of human body based on supersonic remote palpation and interior excitation. Dr. Yoon received the Ph.D. in Mathematics from Korea Advanced Institute of Science and Technology in February 2001. Presently, he is a postdoctoral fellow in the Department of Mathematical Sciences at Rensselaer Polytechnic Institute. His primary research interest involves inverse problems for PDE's which arise in real-world applications.