Estimation of Complex-Valued Stiffness Using Acoustic Waves Measured with Magnetic Resonance
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Tissue stiffness can be a useful indicator of diseased tissue. Noninvasive quantitation of the mechanical properties of tissue could improve early detection of such pathology. A method for detecting displacement from propagating shear waves using a phase-contrast MRI technique has been developed previously. In this chapter the principles behind the measurement technique are reviewed, and the mechanical properties that can be determined from the displacement data are investigated for isotropic materials. An algebraic inversion approach useful for piecewise homogeneous materials is described in detail for the general isotropic case, which is then specialized to incompressible materials as a model for tissue. Results of the inversion approach are presented for an experimental phantom and in-vivo breast tumor. These results show that the technique can be used to obtain shearwave speed and attenuation in regions where there is sufficient signal-to-noise ratio in the displacement and its second spatial derivatives. The sensitivity to noise is higher in the attenuation estimates than in the shear-wave speed estimates.
KeywordsTransverse Magnetization Bloch Equation Magnetic Resonance Elastography Shear Speed Lagrangian Coordinate System
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