Diffuse shear wave spectroscopy for soft tissue viscoelastic characterization.

In order to limit and slow the development of diseases, they have to be diagnosed early as possible to treat patients in a better and more rapid manner. In this paper, we focus on a noninvasive and quick method based on diffuse fields in elastography to detect diseases that affect the stiffness of organs. To validate our method, a phantom experiment numerically pre-validated is designed. It consists of seven vibrators that generate white noises in a bandwidth of [80-300] Hz and then a complex acoustic field in a phantom. Waves are tracked by a linear ultrasound probe L11-4v linked to a Verasonics Vantage System and are converted into a particle velocity 2D map as a function of time. The phase velocity of the shear waves is calculated using a temporal and 2D spatial Fourier transform and an adapted signal-processing method. Shear wave velocity dispersion measurement in the frequency bandwidth of the vibrators enables one to characterize the dynamic hardness of the material through the viscoelastic parameters µ and η in an acquisition time shorter than a second (Tacq = 300 ms). With the aim of estimating the consistency of the method, the experiment is performed N = 10 times. The measured elastic modulus and viscous parameter that quantify the dynamic properties of the medium correspond to the expected values: µ = 1.23 ± 0.05 kPa and η = 0.51 ± 0.09 Pa∙s.

Exploration of trabecular bone nonlinear elasticity using time-of-flight modulation.

Bone tissue contains microcracks that may affect its mechanical properties as well as the whole trabecular structure. The relationship between crack density and bone strength is nevertheless poorly understood. Linear ultrasound techniques being almost insensitive to the level of damage, we propose a method to measure acoustic non- linearity in trabecular bone using time-of-flight modulation (TOFM) measurements. Ultrasonic short bursts times-of- flight (TOF) are modulated as a result of nonlinear interaction with a low-frequency (LF) wave in the medium. TOF variations are directly related to elastic modulus variations. Classical and nonclassical nonlinear parameters beta, delta, and alpha can be derived from these measurements. The method was validated in materials with classical, quadratic, nonlinear elasticity. In dense trabecular bone region, TOFM related to classical, quadratic, nonlinear elasticity as a function of the LF pressure exhibits tension-compression asymmetry. The TOFM amplitude measured in dense areas of trabecular bone is almost one order of magnitude higher than in a low-density area, but the linear parameters show much smaller variations: 5% for ultrasound propagation velocity and 100% for broadband ultrasonic attenuation (BUA). In high-density trabecular bone regions, beta depends on the LF pressure amplitude and can reach 400 at 50 kPa.

Transient displacement induced in shear wave elastography: comparison between analytical results and ultrasound measurements.

It is now accepted that an effective way to investigate the elastic properties of soft tissues is to generate a localized transient acoustic radiation force and to follow the associated displacements in the time/space domain. Shear waves induced by this stress field are particularly interesting in this kind of medium because they are governed by the shear elastic modulus mu, which is directly linked to the Young modulus, and spatial distribution and temporal evolution of the transient motion induced must therefore be obtained in detail. We report here a model based on the elastodynamic Green's function formalism to describe these displacements. 3D simulation of radiation force in homogenous elastic media was performed and the displacement curves computed at different radial distances for different temporal force profiles. Amplitude and duration of displacement were found to be reliable parameters to characterize the elastic properties of the medium. Experimental measurements were performed in a homogeneous agar-gelatin tissue-mimicking phantom, and two transducers were used to generate the radiation force and follow the induced displacements. Displacements obtained from different lateral locations around the applied force axis were then used to reconstruct the shear-wave propagation in a scan plane as a function of time. The experimental displacements/curves agreed with the theoretical profiles obtained by the elastodynamic Green's function formalism.

Influence of acousto-optic interactions on the determination of the diffracted field by an array obtained from displacement measurements.

This paper deals with the influence of acousto-optic interactions on the displacement measurements performed over transducer array and their effects on the predicted diffraction field. Changes on the temporal/spatial responses and the plane wave decomposition of the displacement are discussed. Modifications made on the directivity pattern are shown. A theoretical analysis of acousto-optic phenomenon, based on the plane wave decomposition of radiated field by the array is developed. Theoretical and experimental results are compared, showing first that waves with phase velocity near the one of the fluid are greatly amplified. Second, the interaction of laser beam with edge wave produced by the vertical size of elements induces a parasitic temporal pulse on the x-t diagram and so an interference pattern in the omega-k diagram. Corrections are proposed to eliminate errors induced by acousto-optic interactions and validated by comparing predicted diffraction field with measurements.

Presence of nonlinear interference effects as a source of low frequency excitation force in vibro-acoustography.

The vibro-acoustography imaging method consists of forming an image of the deformability of a tissue submitted to a low frequency fLF stress field. This sound field can be created locally by means of a focused annular array emitting two primary beams driven at two close frequencies fa and fb = fa + fLF. In the existing literature, the origin of this stress field has been identified as the low frequency radiation pressure of the two primary beams. However, this work intends to show that another contribution to this internal stress is the low frequency field distributed in the object volume and created by the nonlinear interferences of the two primary beams. This nonlinear field was calculated in the case of multiple ring annular arrays and compared with the qLF beam experimentally measured in a water tank. The agreement between the theoretical and experimental curves provides information on the possibility that this nonlinear effect takes place in vibro-acoustography.

Time-domain modeling of nonlinear distortion of pulsed finite amplitude sound beams.

This work aims to validate a time domain numerical model for the nonlinear propagation of a short pulse of finite amplitude sound beam propagation in a tissue-mimicking liquid. The complete evolution equation is simply derived by a superposition of elementary operators corresponding to the 'one effect equation'. Diffraction LD, absorption and dispersion LAD, and nonlinear distortion LNL effects are treated independently using a first order operator-splitting algorithm. Using the method of fractional steps, the normal particle velocity and the acoustical pressure are calculated plane by plane, at each point of a two-dimensional spatial grid, from the surface of the plane circular transducer to a specified distance. The LA operator is a time convolution between the particle velocity and the causal attenuation filter built after the Kramers-Kroning relations. The LNL operator is a time-based transformation obtained by following an implicit Poisson analytic solution. The LD operator is the usual Rayleigh integral. We present a comparison between theoretical and experimental temporal pressure waveform and axial pressure curves for fundamental (2.25 MHz), second, third and fourth harmonics, obtained after spectral analysis.

High-frequency estimation of the ultrasonic attenuation coefficient slope obtained in human skin: simulation and in vivo results.

In vivo ultrasonic characterization of the skin was performed at 40 MHz by estimating the slope of the attenuation coefficient in the human dermis. The centroid algorithm was first tested on simulated backscattered RF lines with a second-order autoregressive model to carry out the spectral analysis. A relative error of less than 8.5% and a relative precision of less than 6% were predicted for a 2-mm tissue thickness and for temporal window sizes ranging from 0.25 to 0.45 micros. In vivo measurements performed on 138 healthy volunteers yielded values of the attenuation coefficient slope ranging from 0.8 to 3.6 dB/cm MHz. A decrease was observed with advancing age, but no significant difference appeared between men and women. The results from this study suggest that this acoustic parameter shows the effect of the ageing process on normal skin tissue in vivo.

Noncontact measurement of vibration using airborne ultrasound.

A noncontact ultrasonic method for measuring the surface normal vibration of objects was studied. The instrument consists of a pair of 420 kHz ultrasonic air transducers. One is used to emit ultrasounds toward the moving surface, and the other receives the ultrasound reflected from the object under test. Two effects induce a phase modulation on the received signal. The first effect results from the variation of the round trip time interval tau required for the wavefront to go from the emitter to the moving surface and back to the receiver. This is the Doppler effect directly proportional to the surface displacement. The second effect results from the nonlinear parametric interactions of the ultrasonic beams (forward and backward) with the low frequency sound field emitted in the air by the vibrating surface. This latter phenomenon, which is a volume effect, is proportional to the velocity of the vibrating surface and increases with the distance between the transducers and the surface under test. The relative contribution of the Doppler and parametric effects are evaluated, and both have to be taken into account for ultrasonic interferometry in air.