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Assad Oberai

Inverse problems play an important role in medicine and biology. They provide the values and distributions of material, shape and boundary parameters that are critical in developing biomedical models. We have developed an efficient, nonlinear optimization-based strategy for solving this class of problems. This strategy relies on the use of adjoint equations, novel continuation methods and efficient preconditioners to solve such problems efficiently.

The mechanical properties of soft tissue are related to the tissue structure, and thus the pathological state of the tissue.  The response of tissue to a dynamic excitation, for example waves propagating from a focused ultrasound pulse, is directly related to the mechanical properties.  This project seeks out ways to image mechanical properties of tissue for medical diagnosis (elastography) based on measured responses of the tissue to dynamic excitation.