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

Magn Reson Med. 2001 Feb;45(2):299-310. doi: 10.1002/1522-2594(200102)45:2<299::aid-mrm1039>3.0.co;2-o.

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.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Computer Simulation
  • Elasticity
  • Magnetic Resonance Imaging / methods*
  • Mathematics
  • Models, Theoretical
  • Phantoms, Imaging