2012 Proceedings - International Tissue Elasticity Conference

033 TOWARDS QUANTITATIVE ELASTICITY ESTIMATION BY CROSS-CORRELATION OF SHEAR
WAVES.
Nicolás Benech 1 , Javier Brum 1 , Stefan Catheline 2 , Carlos A. Negreira 1 .
1 Laboratorio de Acústica Ultrasonora, Facultad de Ciencias, Montevideo, URUGUAY; 2 LabTAU
INSERM U–1032, University of Lyon, Lyon, FRANCE.
Background: Green’s function retrieval by cross–correlation of diffuse fields has been widely
investigated in many areas of physics including elastography [1,2]. In an ideal equipartitioned field, the
cross–correlation (CC) computation is equivalent to a perfect time–reversal (TR) experiment [3]. Under this
condition, two inversion methods were developed to estimate the shear elastic modulus, µ, in soft tissues:
the focal size and the phase method [4]. The focal size method is based on the fact that the focal size of
the TR focusing is limited by the shear wavelength. Thus, computing the focal spot size locally would bring
a direct estimation of the shear wavelength, λ, if the relationship between them is known. The phase
method is based in estimating the time–of–flight of the TR field around the focus. Both methods attempt to
estimate the shear wave speed, C, which is related to µ as µ = ρC 2 , where ρ is the material density of the
tissue. In previous work, they were applied to image the shear elastic modulus in liver in vivo [5].
Aims: The aim of this work is to deepen the investigation of both inversion methods to bring quantitative
estimation of the local shear elasticity in soft tissues. In particular, the goal is to establish an analytical
relationship between the focal size and λ. On the other hand, a relationship between the time–of–flight
and the shear wave speed should also be investigated since it is known that near field effects give
diffraction corrections in this case [6].
Methods: In this work a complex low frequency wave field is created in the volume of a tissue–mimicking
phantom by randomly tapping its surface with fingers [5]. This wave field is imaged during a 6 second
window using an ultrafast electronic (Multichannel device 1000 fps, Lecoeur Electronique, France) with a
linear, 64–element array at a frequency of 6MHz. The low frequency field is imaged by a standard speckle
tracking technique in a 64x50 points grid within the volume of the sample. The CC field is computed between
an arbitrary position, r0, and all other positions of the observation points grid. According to theoretical
derivations, the CC field is equivalent to a TR field which converges at r0 and then diverges. In order to
estimate µ from this data, an analytical expression for the TR process in elastic solids is needed. In this work,
the spatial focusing profile is derived from the elasto–dynamic Green’s function adapted to the soft–solid case.
Results: The analytical expression for the TR field allows for developing inversion algorithms to estimate
the shear elastic modulus. Diffraction corrections, coming from near field effects, are easily implemented
in both methods to estimate the shear wave speed. When tested in homogeneous phantoms, the results
obtained are in good agreement with independent estimations from transient elastography experiments.
When tested in heterogeneous phantoms, the quality of the results depends on the contrast between the
inclusion and the background. In some cases, artifacts on the final image are observed.
Conclusions: The work presented here represents a step forward in elasticity estimation from the CC
field interpreted in the frame of TR. The diffraction corrections included in the inversion algorithm
improve the final elasticity image in soft tissues. The results obtained here can be used in imaging
modalities like passive elastography from physiological noise [5]. The experimental data suggest that the
eventual presence of image artifacts around inclusions are due to scattered waves not taken into account
in the inversion algorithm. This topic will be addressed in future works.
References:
[1] J. Brum, S.Catheline, N. Benech, C. Negreira: Shear Elasticity Estimation from Surface Waves: The Time–Reversal
Approach. J. Acoust. Soc. Am., 124 (6), pp. 3377–3380, 2008.
[2] S. Catheline, N. Benech, J. Brum, C. Negreira: Time-Reversal of Elastic Waves in Soft–Solids. Phys. Rev. Lett,
100, p. 064301, 2008.
[3] F. Sánchez–Sesma, J. Pérez–Ruiz, F. Luzón, M. Campillo, A. Rodríguez–Castellanos: Diffusive Fields in Dynamic
Elasticity. Wave Motion, 45, pp. 641–654, 2008.
[4] N. Benech, S. Catheline, J. Brum, T. Gallot, C. Negreira: 1D Elasticity Assessment in Soft–Solids from Shear Wave
Correlation: The Time–Reversal Approach. IEEE Trans. Ultras. Ferroelec. Freq. Control, 56 (11), pp. 2400–2411, 2009.
[5] T. Gallot, S. Catheline, P. Roux, J. Brum, N. Benech, C. Negreira: Passive Elastography: Shear Wave Tomography
From Physiological Noise Correlation In Soft Tissues. IEEE Trans. Ultras. Ferroelc. Freq. Control, 58 (6), pp.
1122–1125, 2011.
[6] L. Sandrin, D. Cassereau, M. Fink: The Role of the Coupling Term in Transient Elastography. J. Acoust. Soc.
Am., 115 (1), pp. 73–83, 2004.
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