It is now well recognized that a host of imaging modalities (a list that includes Ultrasound, MRI, Optical Coherence Tomography, and optical microscopy) can be used to “watch” tissue as it deforms in response to an internal or external excitation. The result is a detailed map of the deformation field in the interior of the tissue. This deformation field can be used in conjunction with a material mechanical response to determine the spatial distribution of material properties of the tissue by solving an inverse problem. Images of material properties thus obtained can be used to quantify the health of the tissue. Recently, they have been used to detect, diagnose and monitor cancerous lesions, detect vulnerable
plaque in arteries, diagnose liver cirrhosis, and possibly detect the onset of Alzheimer’s disease. In this talk I will describe
the mathematical and computational aspects of solving this class of inverse problems, and their applications in biology
In particular, I will discuss the well-posedness of these problems and quantify the amount of displacement data necessary to obtain a unique property distribution. I will describe an efficient algorithm for solving the resulting inverse problem. I will also describe some recent developments based on Bayesian inference in estimating the variance in the estimates of material properties. I will conclude with the applications of these techniques in diagnosing breast cancer and in characterizing the mechanical properties of cells with sub-cellular resolution.
Assad A. Oberai, "Inverse problems biomechanical imaging
(Conference Presentation)," Proc. SPIE 9710, Optical Elastography and Tissue Biomechanics III, 97100W (Presented at SPIE BiOS: February 14, 2016; Published: 27 April 2016); https://doi.org/10.1117/12.2216702.4848677997001.
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