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Application of Numerical Methods to Elasticity Imaging

Benjamin Castaneda, Juvenal Ormachea, Paul Rodríguez, Kevin J. Parker§
Laboratorio de Imágenes Médicas, Pontificia Universidad Católica del Perú
Laboratorio de Imágenes Médicas, Pontificia Universidad Católica del Perú
Laboratorio de Procesamiento Digital de Se ˜ nales, Pontificia Universidad Católica del Perú
§ Electrical and Computer Engineering, University of Rochester

Molecular & Cellular Biomechanics 2013, 10(1), 43-65. https://doi.org/10.3970/mcb.2013.010.043

Abstract

Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity.

Keywords

Elasticity imaging, inverse problems, FEM, total variation, shear velocity estimation, AM-FM

Cite This Article

Castaneda, B., Ormachea, J., Rodríguez, P., Parker, K. J. (2013). Application of Numerical Methods to Elasticity Imaging. Molecular & Cellular Biomechanics, 10(1), 43–65.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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