Ralph Sinkus

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.

4J-3 A New Rheological Model Based on Fractional Derivatives for Biological Tissues

The intuitive use of viscoelastic properties is routinely done by physicians via the palpation. However, such an examination relies on the physician experience and is not quantitative nor reproducible. Thus, elastography has been developed to complement the palpation by reliable and reproducible measurements. The principle of elastography is to image elastic waves propagation in a medium. To evaluate the shear moduli, Helmholtz transforms are applied to the displacement images. Then the waves movie is interpreted using a rheological model. For instance, the Voigt model explains the observed frequency dependence of the measured shear wave speed. It has been shown to be a reliable model for mimicking tissue phantoms such as gelatin based phantoms. However, we show here that neither this model nor the Maxwell model are applicable to biological tissues using in vivo data (breast) and ex vivo data (liver). Although these simple models are widely used in the elastography community, they have been substituted by more relevant models in the micro-rheology community in order to reveal the solid-liquid duality of tissues. Based on these experimental observations, we introduce a new rheological model relying on fractional derivatives closer to the viscoelastic properties of in vivo data. Indeed, we observed that the dynamic modulus (Gd) and the loss modulus (Gl) have the same frequency behavior: a non-integer frequency power law smaller than 1. This frequency behavior is contradictory with the use of the Voigt model or any kind of simple arrangements of dash pots and springs. In order to explain this frequency behavior the concept of spring pot was introduced. Moreover, we observed that the ratio Gl /Gd is constant and not linked to the non-integer power observed, not predicted by the spring pot model. Thus we build a network of spring pots where the basic element is responsible of the frequency power and the network is responsible of the ratio Gl/Gd . The experiments were conducted on fresh liver samples and phantoms between 50 Hz and 100 Hz. The frequency behavior was analyzed by plotting the real and imaginary parts of the complex shear modulus using MR-elastography as well as 3D ultrasound based elastography. By applying the fractional derivatives model to these data sets, we observed that the frequency power law in the liver was equal to 0.75 (a liquid-like behavior), while the ratio parameter of the network was equal to 0.15 (a solid-like behavior). The dispersion curves of Gd and Gl obtained through this model correlates much better with the experimental observations. The model parameters values seem to emphasize the necessity to take into account the solid-liquid duality of tissues in the rheological model choice for elastography reconstructions

3D ultrasound-based dynamic and transient elastography: first in vitro results

3D magnetic resonance (MR) elastography is a well-established technique based on monochromatic mechanical excitations to study soft tissue mechanical properties. MR imaging observations are used to calculate tissue viscoelastic properties and has been validated in vivo, but the technique is limited by the acquisition time (about ten minutes). We study the feasibility of performing 3D dynamic elastography using an ultrasound based imaging system. The ultrasound approach provides a low cost system and reduces the acquisition time by a factor of 300 (to about 2 seconds). Two ultrasonic arrays are moved perpendicularly using a stepper-motor-control positioning system to acquire ultrasonic images in a given volume of interest. Mechanical excitation is induced by a 20 mm square plate linked to an external vibrator. Displacements induced by the vibrator are calculated from ultrasound images using a 2-dimensional estimator (Tanter, M. et al., 2002). Each ultrasonic array is able to calculate in-plane (axial and lateral) displacements. Lateral displacements are the same from both arrays and are averaged. The configuration leads to the estimation of the three displacement components in a full 3D area. Imaging sequences for 3D displacements have been realized. Experiments were conducted in a phantom mimicking heterogeneous tissue with two harder inclusions. 3D shear elasticity, viscosity and anisotropy maps of the studied phantoms are presented and show the feasibility of building a full ultrasound based system for 3D dynamic elastography providing a complete description of tissue mechanical properties in a few seconds.

4J-5 A 3D Elastography System Based on the Concept of Ultrasound-Computed Tomography for In Vivo Breast Examination

Elastography holds great promises for the additional characterization of lesions especially in the domain of breast cancer diagnosis. Most ultrasound based approaches have so far been limited to a one dimensional (1D) or at most two dimensional (2D) displacement estimation in one plane. This leads for the general case to sparse data which cannot be used to solve the full three dimensional (3D) wave equation in an unbiased manner. For instance contributions from the compressional wave cannot be removed via application of the curl operator. In order to overcome this limitation we developed an ultrasound based elastography system which uses the concept of computed tomography for data acquisition in combination with 2D vector displacement estimation within the plane of the ultrasound beam. The vector displacement estimation is achieved using the concept of adaptive subapertures during the receive beamforming process. The object of interest is scanned using a conventional ultrasonic probe (4 MHz, 128 elements) from different directions on a circular orbit. The transducer is translated perpendicular to the orbit (~10 times) for each angle which leads to several block datasets (~30 blocks) each containing 2D displacement information. Thereby, the displacement of each voxel within the object is measured several times from different directions. This provides high resolution volumic 3D displacement fields after regridding each dataset from polar to Cartesian coordinates. The data acquisition system is contained within a water tank underneath a standard breast biopsy table. This enables in vivo measurements with the patient in prone position. Thereby, the 3D acquisition as already developed in the area of magnetic resonance elastography (MRE), is brought to the ultrasonic field. Initial phantom experiments were conducted with steady state mechanical excitation at 150 Hz. Inclusions are clearly visible in the complex shear modulus as reconstructed from inverting the full 3D wave equation. Taking benefit of the ultrafast acquisition speed of our ultrasound system, the proposed method allows to measure volumic datasets within clinically acceptable time. The method provides for each voxel of the 3D volume the frequency dependence of the complex shear modulus which in turn is linked to the underlying rheology of the material. This represents the proof of concept for a spectroscopic approach of elastography suitable for clinical application. The system enables the study of rheological properties of tumors which should further extend the diagnostic gain of elastography

Radiation force localization of HIFU therapeutic beams coupled with magnetic resonance-elastography treatment monitoring in vivo application to the rat brain

Magnetic resonance elastography is feasible in the brain and is a new way to non invasively control the stiffness of the tissue. The thermal HIFU necrosis of the brain results in an increase of its complex shear modulus. Furthermore, MR sequences can be very sensitive to motion and thus give a good tool to detect the acoustic radiation force in in-vivo. This target control can be very valuable in order to assess the quality of the aberration correction when a high power US signal is about to be sent trough the skull. In this context, ex-vivo and in-vivo experiments were conducted with and without an aberrating skull. They confirmed that both the MR localization of the US focal point and the measurement of the tissue stiffness pre and post HIFU, together with temperature control during HIFU are valuable and feasible techniques for the accurate monitoring of HIFU in the brain.

New Devices and Promising approaches for Clinical H.I.F.U. Applications

Bursts of focused ultrasound energy three orders of magnitude more intense than diagnostic ultrasound became during the last decade a noninvasive option for treating cancer from breast to prostate or uterin fibroid. However, many challenges remain to be addressed. First, the corrections of distortions induced on the ultrasonic therapy beam during its propagation through defocusing obstacles like skull bone or ribs remains today a technological performance that still needs to be validated clinically. Secondly, the problem of motion artifacts particularly important for the treatment of abdominal parts becomes today an important research topic. Finally, the problem of the treatment monitoring is a wide subject of interest in the growing HIFU community. For all these issues, the potential of new ultrasonic therapy devices able to work both in Transmit and Receive modes will be emphasized. A review of the work under achievement at L.O.A. using this new generation of HIFU prototypes on the monitoring, motion an...