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Inverse Problems in Biomechanics

Assad Oberai, PhD

Certain types of diseases lead to changes in the microstructural organization of tissue. Altered microstructure in turn leads to altered macroscopic tissue properties, which are often easier to image than the microstructure itself. Thus the measurement of macroscopic properties offers a window into tissue microstructure and health. In Elastography, or more generally Biomechanical Imaging (BMI), we aim to utilize this association between the macroscopic mechanical properties of tissue and its health by generating images of the mechanical properties and using these to infer tissue microstructure and health.

At the heart of BMI lies the solution of an inverse problem in continuum mechanics: given the deformation of the medium (tissue) and a constitutive model, determine the spatial distribution of the material properties. In this talk, I will discuss the well-posedness of this inverse problem and describe efficient and robust algorithms for solving it. I will also describe the development of new constitutive models that are motivated by tissue microstructure, applications of Biomechanical Imaging that include improved non-invasive diagnosis of breast cancer, and quantification of elastic properties from the sub-cellular level to the level of an organ.

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