Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation

Noninvasive quantitation of the mechanical properties of tissue could impro ve early detection of pathology. Previously a method for detecting displace ment from propagating shear waves using a phase-contrast MRI technique was developed. In this work it is demonstrated how a collection of data represe nting the full vector displacement field could be used to potentially estim ate the full complex stiffness tensor. An algebraic inversion approach usef ul for piece-wise homogeneous materials is described in detail for the gene ral isotropic case, which is then specialized to incompressible materials a s a model for tissue. Results of the inversion approach are presented for s imulated and experimental phantom data that show the technique can be used to obtain shear wave-speed and attenuation in regions where there is suffic ient signal-to-noise ratio in the displacement and its second spatial deriv atives. The sensitivity to noise is higher in the attenuation estimates tha n the shear wave-speed estimates. Magn Reson Med 45:299-310, 2001. (C) 2001 Wiley-Liss, Inc.