title: Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation.
abstract: Noninvasive quantitation of the mechanical properties of tissue could improve early detection of pathology. Previously a method for detecting displacement from propagating shear waves using a phase-contrast MRI technique was developed. In this work it is demonstrated how a collection of data representing the full vector displacement field could be used to potentially estimate the full complex stiffness tensor. An algebraic inversion approach useful for piece-wise 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 simulated and experimental phantom data that show the technique can be used to obtain shear wave-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 the shear wave-speed estimates. Magn Reson Med 45:299-310, 2001.
authors.affiliation: Ultrasound Research Laboratory, Mayo Foundation, 200 First Street SW, Rochester, MN 55905, USA.
authors.forename: T E
authors.initials: TE
authors.lastname: Oliphant
authors.forename: A
authors.initials: A
authors.lastname: Manduca
authors.forename: R L
authors.initials: RL
authors.lastname: Ehman
authors.forename: J F
authors.initials: JF
authors.lastname: Greenleaf
mesh_terms: D003198:Computer Simulation; D004548:Elasticity; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008433:Mathematics; D008962:Models, Theoretical; D019047:Phantoms, Imaging