Measuring of viscoelastic properties of homogeneous soft solid using transient elastography: an inverse problem approach.

Two main questions are at the center of this paper. The first one concerns the choice of a rheological model in the frequency range of transient elastography, sonoelasticity or NMR elastography for soft solids (20-1000 Hz). Transient elastography experiments based on plane shear waves that propagate in an Agar-gelatin phantom or in bovine muscles enable one to quantify their viscoelastic properties. The comparison of these experimental results to the prediction of the two simplest rheological models indicate clearly that Voigt's model is the better. The second question studied in the paper deals with the feasibility of quantitative viscosity mapping using inverse problem algorithm. In the ideal situation where plane shear waves propagate in a sample, a simple inverse problem based on the Helmholtz equation correctly retrieves both elasticity and viscosity. In a more realistic situation with nonplane shear waves, this simple approach fails. Nevertheless, it is shown that quantitative viscosity mapping is still possible if one uses an appropriate inverse problem that fully takes into account diffraction in solids.

[1]  K. Parker,et al.  Sonoelasticity imaging: results in in vitro tissue specimens. , 1991, Radiology.

[2]  Johannes Bernarding,et al.  Analysis of wave patterns in MR elastography of skeletal muscle using coupled harmonic oscillator simulations. , 2002, Magnetic resonance imaging.

[3]  W. Walker,et al.  A fundamental limit on the performance of correlation based phase correction and flow estimation techniques , 1994, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[4]  R L Ehman,et al.  Complex‐valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation , 2001, Magnetic resonance in medicine.

[5]  D. C. Gakenheimer,et al.  Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface , 1969 .

[6]  M. Fink,et al.  Time-Resolved Pulsed Elastography with Ultrafast Ultrasonic Imaging , 1999, Ultrasonic imaging.

[7]  M Fink,et al.  A solution to diffraction biases in sonoelasticity: the acoustic impulse technique. , 1999, The Journal of the Acoustical Society of America.

[8]  K D Paulsen,et al.  Elasticity reconstruction from experimental MR displacement data: initial experience with an overlapping subzone finite element inversion process. , 2000, Medical physics.

[9]  B. Garra,et al.  Elastography of breast lesions: initial clinical results. , 1997, Radiology.

[10]  Mathias Fink,et al.  Transient elastography in anisotropic medium: application to the measurement of slow and fast shear wave speeds in muscles. , 2003, The Journal of the Acoustical Society of America.

[11]  S. Levinson,et al.  Sonoelastic determination of human skeletal muscle elasticity. , 1995, Journal of biomechanics.

[12]  M. Ziol,et al.  Transient elastography: a new noninvasive method for assessment of hepatic fibrosis. , 2003, Ultrasound in medicine & biology.

[13]  H. Oestreicher.  Field and Impedance of an Oscillating Sphere in a Viscoelastic Medium with an Application to Biophysics , 1951 .

[14]  M. Djabourov,et al.  Gelation of aqueous gelatin solutions. II. Rheology of the sol-gel transition , 1988 .

[15]  M. Fink,et al.  Diffraction field of a low frequency vibrator in soft tissues using transient elastography , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[16]  D B Plewes,et al.  Visualizing tissue compliance with MR imaging , 1995, Journal of magnetic resonance imaging : JMRI.

[17]  A. Manduca,et al.  Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. , 1995, Science.

[18]  Michael F. Insana,et al.  Ultrasonic mechanical relaxation imaging of pH in biopolymers , 2004, SPIE Medical Imaging.

[19]  Francis Loth,et al.  Surface response of a viscoelastic medium to subsurface acoustic sources with application to medical diagnosis. , 2003, The Journal of the Acoustical Society of America.

[20]  M. Fink,et al.  Shear modulus imaging with 2-D transient elastography , 2002, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[21]  M. Fink,et al.  Shear elasticity probe for soft tissues with 1-D transient elastography , 2002, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[22]  E. Madsen,et al.  Ultrasonic shear wave properties of soft tissues and tissuelike materials. , 1983, The Journal of the Acoustical Society of America.

[23]  F. S. Lamb,et al.  On the Propagation of Tremors over the Surface of an Elastic Solid , 1904 .

[24]  Sarah A. Klemuk,et al.  Methodology for rheological testing of engineered biomaterials at low audio frequencies. , 2004, The Journal of the Acoustical Society of America.

[25]  U. Klose,et al.  Comparison of quantitative shear wave MR‐elastography with mechanical compression tests , 2003, Magnetic resonance in medicine.

[26]  J Bercoff,et al.  In vivo breast tumor detection using transient elastography. , 2003, Ultrasound in medicine & biology.

[27]  Jonathan Ophir,et al.  The feasibility of using elastography for imaging the Poisson's ratio in porous media. , 2004, Ultrasound in medicine & biology.