Estimation of Complex-Valued Stiffness Using Acoustic Waves Measured with Magnetic Resonance

  • Travis E. Oliphant
  • Richard L. Ehman
  • James F. Greenleaf
Part of the Topics in Applied Physics book series (TAP, volume 84)


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.


Transverse Magnetization Bloch Equation Magnetic Resonance Elastography Shear Speed Lagrangian Coordinate System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. Gao, K. J. Parker, R. M. Lerner, S. F. Levinson, Imaging of the elastic properities of tissue, Ultrasound Med. Biol. 22, 959–977 (1996)CrossRefGoogle Scholar
  2. 2.
    S. Catheline, F. Wu, M. Fink, A solution to diffraction biases in sonoelasticity: The acoustic impulse technique, J. Acoust. Soc. Am. 105, 2941–2950 (1999)CrossRefADSGoogle Scholar
  3. 3.
    M. Fatemi, J. F. Greenleaf, Ultrasound-stimulated vibro-acoustic spectrography, Science 280, 82–85 (1998)CrossRefADSGoogle Scholar
  4. 4.
    A. P. Sarvazyan, O. V. Rudenko, S. D. Swanson, J. B. Fowlkes, S. Y. Emelianov, Shear wave elasticity imaging: a new ultrasonic technology of medical diagnosis, Ultrasound Med. Biol. 24, 1419–1435 (1998)CrossRefGoogle Scholar
  5. 5.
    C. Sumi, K. Nakayama, A robust numerical solution to reconstruct a globally relative shear modulus distribution from strain measurements, IEEE Trans. Med. Imag. 17, 419–428 (1998)CrossRefGoogle Scholar
  6. 6.
    C. Sumi, A. Suzuki, K. Nakayama, Estimation of shear modulus distribution in soft tissue from strain distribtution, IEEE Trans. Biomed. Eng. 42, 193–202 (1995)CrossRefGoogle Scholar
  7. 7.
    T. L. Chenevert, A. R. Skovoroda, M. O’Donnell, S. Y. Emelianov, Elasticity reconstructive imaging via stimulated echo MRI, Magn. Res. Med. 39, 482–490 (1998)CrossRefGoogle Scholar
  8. 8.
    E. E. W. Van Houten, K. D. Paulsen, M. I. Miga, F. E. Kennedy, J. B. Weaver, An overlapping subzone technique for MR-based elastic property reconstruction, Magn. Res. Med. 42, 779–786 (1999)CrossRefGoogle Scholar
  9. 9.
    R. Muthupillai, D. J. Lomas, P. J. Rossman, J. F. Greenleaf, A. Manduca, R. L. Ehman, Magnetic resonance elastography by direct visualization of propagating acoustic strain waves, Science 269, 1854–1857 (1995)CrossRefADSGoogle Scholar
  10. 10.
    R. Muthupillai, P. J. Rossman, D. J. Lomas, J. F. Greenleaf, S. J. Riederer, R. L. Ehman, Magnetic resonance imaging of transverse acoustic strain waves, Magn. Res. Med. 36, 266–274 (1996)CrossRefGoogle Scholar
  11. 11.
    A. J. Romano, J. J. Shirron, J. A. Bucaro, On the noninvasive determination of material parameters from a knowledge of elastic displacements: Theory and simulation, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 751–759 (1998)CrossRefGoogle Scholar
  12. 12.
    V. Dutt, R. R. Kinnick, R. Muthupillai, T. E. Oliphant, R. L. Ehman, J. F. Greenleaf, Acoustic shear-wave imaging using echo ultrasound compared to magnetic resonance elastography, Ultrasound Med. Biol. 26,3, 397–403 (2000)CrossRefGoogle Scholar
  13. 13.
    Y. Yamakoshi, J. Sato, T. Sato, Ultrasonic imaging of internal vibration of soft tissue under forced vibration, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37, 45–53 (1990)CrossRefGoogle Scholar
  14. 14.
    E. U. Condon, Handbook of Physics, 2nd edn., (McGraw-Hill, New York 1967)Google Scholar
  15. 15.
    M. A. Bernstein, X. J. Zhou, J. A. Polzin, K. F. King, A. Ganin, N. J. Pelc, G. H. Glover, Concomitant gradient terms in phase contrast MR: Analysis and correction, Magn. Res. Med. 39, 300–308 (1998)CrossRefGoogle Scholar
  16. 16.
    H. Knutsson, C.-F. Westin, G. Granlund, Local multiscale frequency and bandwidth estimation, In Proc. ICIP-94, Vol. 1, Los Alamitos, CA (IEEE Computer Society 1994) p. 36–40CrossRefGoogle Scholar
  17. 17.
    T. E. Oliphant, A. Manduca, R. L. Ehman, J. F. Greenleaf, Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation, Magn. Res. Med. 45,2, 299–310 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Travis E. Oliphant
    • 1
  • Richard L. Ehman
    • 1
  • James F. Greenleaf
    • 1
  1. 1.Mayo FoundationRochesterUSA

Personalised recommendations