Abstract— The ultrafast scanner has 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. More over, using a new theoretical approach of the strain energy in soft solid [Hamilton, Ilinsky and Zabolotskaya, J. Acoust. Soc. Am., 114, 2436 (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. Index Terms— Shear wave, soft tissues, nonlinear elasticity, transient elastography I. INTRODUCTION COUSTOELASTICITY is a well-established technique [1] to experimentally measure third order elastic constants in solids such as metals [2], crystals [3] or rocks [4]. It consists in measuring the speed of ultrasonic waves in stressed solids. The third order moduli are deduced from the slope of the speed as function of static hydrostatic pressure or uniaxial stress. So far no such measurements have been made in soft tissue since it has long been considered as liquid-like medium from an ultrasonic point of view. However, like in all solids, shear waves do propagate in soft tissues at low frequency (100 Hz typically) [5,6]. As it was shown in a previous paper [7], the speed of these shear waves are modified if the medium is submitted to a uniaxial-stress (which is the evidence of a deviation from the Hooke’s law). The nonlinear coefficients were measured using the transient elastography technique [8]. In these soft solid acoustoelasticity experiments, the main difficulty consists in the establishment of uniform and constant uniaxial stress. The stress field in soft solids is highly dependent on the boundary conditions. Consequently the experimental set-up is enhanced by replacing the mechanical vibrator as a shear wave source by the acoustic radiation pressure technique [9]. The transducer array transmits ultrasound in the gelatin Manuscript received September 10, 2004. S. Catheline, J. Bercoff, JL Gennisson, C. Barrière, M. Fink are with the Laboratory of Ondes et Acoustique, université Paris VII, FRANCE (phone: 33.1.40.79.44.75; fax: 33.1.40.79.44.68; e-mail: stefan.catheline@espci.fr ). based phantom through a wide layer of coupling gel which leaves almost undisturbed the uniaxial stress field. II. EXPERIMENT The experiments are lead in a model of soft tissues: an Agar- gelatin based phantom. A 4.3-MHz transducer array (L4, Vermon, Tours, France, 0.33-mm pitch, 10-mm elevation) is applied at the surface of the phantom so that the ultrasonic beam is horizontal. The transducer array is connected to an ultrafast scanner. Our ultrafast scanner is a fully programmable, multichannel system made of 128 channels connected to the transducer. Each element possesses its own emission/reception electronic board and 2 MB of memory in order to store emission and reception signals. The scanner relies on a 50 MHz sampling frequency and a 80 Vpp voltage (50 Ω). The ultrafast frame rate is achieved by reducing the emitting mode to a single, plane-wave insonification. This technique allows the acquisition of echographic images at a pulse repetition that can reach 6000 Hz. All backscattered radio frequency (RF) echoes are stored in the 2-MB memory of each channel, then transferred to a computer after acquisition. The beamforming process is done only in the receive mode during a postacquisition process. A typical number of 200–300 data sets (for a 6-cm depth) can be Nonlinearity studies in soft tissues with the supersonic shear imaging system S. Catheline, J. Bercoff, J. L. Gennisson, C. Barrière, M. Fink A Fig. 1. Experimental movie of the longitudinal displacement field induced by the radiation force. 1510 0-7803-8412-1/04/$20.00 (c)2004 IEEE. 0-7803-8412-1/04/$20.00 (c)2004 IEEE. 2004 IEEE International Ultrasonics, Ferroelectrics, and Frequency Control Joint 50th Anniversary Conference 2004 IEEE Ultrasonics Symposium