Stefan Catheline

Measurement 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 Voigts 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.

Diffraction field of a low frequency vibrator in soft tissues using transient elastography

For the last 10 years, interest has grown in low frequency shear waves that propagate in the human body. However, the generation of shear waves by acoustic vibrators is a relatively complex problem, and the directivity patterns of shear waves produced by the usual vibrators are more complicated than those obtained for longitudinal ultrasonic transducers. To extract shear modulus parameters from the shear wave propagation in soft tissues, it is important to understand and to optimize the directivity pattern of shear wave vibrators. This paper is devoted to a careful study of the theoretical and the experimental directivity pattern produced by a point source in soft tissues. Both theoretical and experimental measurements show that the directivity pattern of a point source vibrator presents two very strong lobes for an angle around 35/spl deg/. This paper also points out the impact of the near field in the problem of shear wave generation.

Measurement of elastic nonlinearity of soft solid with transient elastography

Transient elastography is a powerful tool to measure the speed of low-frequency shear waves in soft tissues and thus to determine the second-order elastic modulus mu (or the Youngs modulus E). In this paper, it is shown how transient elastography can also achieve the measurement of the nonlinear third-order elastic moduli of an Agar-gelatin-based phantom. This method requires speed measurements of polarized elastic waves measured in a statically stressed isotropic medium. A static uniaxial stress induces a hexagonal anisotropy (transverse isotropy) in solids. In the special case of uniaxially stressed isotropic media, the anisotropy is not caused by linear elastic coefficients but by the third-order nonlinear elastic constants, and the medium recovers its isotropic properties as soon as the uniaxial stress disappears. It has already been shown how transient elastography can measure the elastic (second-order) moduli in a media with transverse isotropy such as muscles. Consequently this method, based on the measurement of the speed variations of a low-frequency (50-Hz) polarized shear strain waves as a function of the applied stress, allows one to measure the Landau moduli A, B, C that completely describe the third-order nonlinearity. The several orders of magnitude found among these three constants can be justified from the theoretical expression of the internal energy.

Acoustic impact localization in plates: properties and stability to temperature variation

Localizing an impact generated by a simple finger knock on plate-shaped solid objects is made possible in an acoustic time reversal experiment. It is shown that the technique works with a single accelerometer. To better understand the phenomenon and to know exactly the nature of the created waves, a two-dimensional (2-D) elastic simulation is used, showing that in a very good approximation the A0 Lamb mode is the only propagating one. However, it is shown that, within one wavelength distance from the edges, evanescent waves must be taken into account. As a first consequence, the ability to distinguish two neighboring impacts improves when the plate thickness decreases and the frequency increases. As a second consequence, it is expected theoretically that temperature variations lead to a stretching or a contraction of acoustic signatures. The experimental demonstration used a heterodyne interferometer to measure the impulse responses created by a knock on a plate during the cooling. A simple algorithm is shown to perfectly compensate for temperature impacts, which demonstrates the feasibility of the technique for outdoor time reversal interactive experiments

Real-time focusing using an ultrasonic one channel time-reversal mirror coupled to a solid cavity

Focusing and beam steering is achieved by using a time-reversal process and a single transducer coupled to a solid cavity that is immersed in water. This low-cost technique makes it possible to focus acoustic energy anywhere on a 3D domain with a spatio-temporal resolution comparable to that of multiple transducers array. A short pulse is emitted from a transducer stuck at the surface of the solid cavity. The multiple-scattered field is measured in front of the solid cavity using a hydrophone needle at a reference point. This signal is then time reversed and remitted by the transducer. Around the reference point, one can observe a spatio-temporal recompression. The sidelobe level as well as the focal width no longer depend on the transducer aperture but on the dimensions of the solid cavity and the multiple paths covered by the acoustic waves in the solid. Moreover, it is shown how the experimental impulse responses on the front face of the cavity can be used to control the emitting ultrasonic field. This...

Ultra high speed imaging of elasticity

Ultrafast ultrasonic imaging seems to have a strong potential for medical imaging applications. During the past five years, it has been applied successfully to quantitative assessment of soft tissues elasticity. An ultrafast ultrasonic scanner was built in our lab for quantitatively mapping the shear elasticity of soft tissues. The ultrafast Scanner provides images of the echogenecity of tissues similar to a standard echographic device but with a 200 times higher a frame rate. It allows to detect fast tissue motion induced by low frequency shear waves inside the body. From these displacements, a shear elasticity map is constructed using inverse problem algorithms. Preliminary in vivo results in breast demonstrate that this technique, known as transient elastography, is very sensitive to the presence of hard tumors. The same technique can also be combined with remote palpation induced par ultrasonic radiation pressure to replace the usual external vibrating system The same probe allows both to generate and detect shear waves propagation by using an unusual emission-reception sequence.

Nonlinearity studies in soft tissues with the supersonic shear imaging system

The ultrafast scanner has been shown to be a powerful tool to detect shear wave propagation within soft tissues in transient elastography experiments. More recently it was also used to generate shear waves thanks to the acoustic radiation pressure. This technique, the supersonic shear imaging, can easily be implemented in an acoustoelasticity experiment. Thus the association of static elastography with dynamic elastography can reveal the nonlinear properties of soft materials. Moreover, using a new theoretical approach of the strain energy in soft solid (Hamilton et al. (2003)), it is shown that the acoustoelasticity experiment can be greatly simplified. Instead of measuring shear wave speed for three different polarizations in order to completely determine the nonlinearity of standard solids, one is sufficient in soft solids to characterize the nonlinear shear elasticity.

Tactile time reversal interactivity: experiment and modelization

Thanks to the Time Reversal theory, a technique of localization of an impact generated by a simple finger knock on plate-shaped solid objects has been developed. It is shown that the technique works with only one cheap accelerometer, and that adding sensors increases the contrast of the localization pattern but not the resolution. To better understand the phenomenon and to know exactly the nature of the created waves, a 2D elastic simulation is used, showing that in a very good approximation the A0 Lamb mode is the only propagating one. Moreover, at around 1 cm from the edges, even the non-propagating modes are negligible compared with the A0 mode. Furthermore, the stability of the technique to temperature changes is studied. Indeed, the TR theory predicts that the localization is effective only if the acoustic medium reciprocity has not been broken by any change in the medium including wave speed variation due to temperature change. To this end, a laser interferometer coupled to a low frequency demodulator measures the impulse responses created by a knock on a plate during the cooling. Given that there is only one propagating wave (A0), it is expected that temperature variations lead to a stretching of acoustic signatures that can be compensated for thanks to a simple contraction: this is observed experimentally. This shows the feasibility of the technique for outdoor Time Reversal interactive experiment.