Supersonic shear imaging: a new technique for soft tissue elasticity mapping

396 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 4, april 2004

Supersonic Shear Imaging: A New Techniquefor Soft Tissue Elasticity Mapping

Jeremy Bercoff, Mickael Tanter, and Mathias Fink

Abstract—Supersonic shear imaging (SSI) is a newultrasound-based technique for real-time visualization ofsoft tissue viscoelastic properties. Using ultrasonic focusedbeams, it is possible to remotely generate mechanical vi-bration sources radiating low-frequency, shear waves insidetissues. Relying on this concept, SSI proposes to create sucha source and make it move at a supersonic speed. In analogywith the “sonic boom” created by a supersonic aircraft, theresulting shear waves will interfere constructively along aMach cone, creating two intense plane shear waves. Thesewaves propagate through the medium and are progressivelydistorted by tissue heterogeneities. An ultrafast scannerprototype is able to both generate this supersonic sourceand image (5000 frames/s) the propagation of the result-ing shear waves. Using inversion algorithms, the shear elas-ticity of medium can be mapped quantitatively from thispropagation movie. The SSI enables tissue elasticity map-ping in less than 20 ms, even in strongly viscous mediumlike breast. Modalities such as shear compounding are im-plementable by tilting shear waves in different directionsand improving the elasticity estimation. Results validatingSSI in heterogeneous phantoms are presented. The first invivo investigations made on healthy volunteers emphasizethe potential clinical applicability of SSI for breast cancerdetection.

I. Introduction

By inducing motion in soft tissue, elastography has be-come a wide medical application field to study soft

tissue mechanical properties. Several techniques arose ac-cording to the type of mechanical excitation chosen (staticcompression, monochromatic, or transient vibration) andthe way these excitations are generated (externally or in-ternally). Different imaging modalities can be used to es-timate the resulting tissue displacements: ultrasound ormagnetic resonance (MR) imaging. Static elastography [1],a pioneer in this field, is limited by various artifacts dueto unknown boundary conditions. The MR elastography[2] gives very good resolution, but the acquisition time(∼20 minutes) limits the application to static organs. Afew years ago, our group introduced transient elastogra-phy in order to overcome these limitations and to providequantitative elasticity maps of tissues [3]. Based on realtime imaging of transient shear waves generated in thebody by an external mechanical vibrator, this techniquehas the advantage of being insensitive to patient motionand boundary condition artifacts and gave promising re-

Manuscript received August 5, 2003; accepted December 15, 2003.The authors are with the Laboratoire Ondes et Acoustique, Ecole

Superieure de Physique et de Chimie Industrielles, National FrenchCenter of Science, Universite Paris VII, 75005, Paris, France (e-mail:[email protected]).

sults on in vivo breast cancer detection. However, the clin-ical applicability of this technique was limited by the useof heavy and bulky external vibrators that vibrate with aunique shear spatial directivity pattern. As a consequence,biased elasticity estimation could occur if some parts of theimage are not reached by the shear wave propagation.

An alternative solution to external vibrations is to usethe acoustic radiation force created by an ultrasonic fo-cused beam to investigate tissues mechanical properties.Several groups are currently investigating this approach.Fatemi and Greenleaf [4] proposed, with the vibroacous-tography technique, the combination of two different ul-trasonic beams with slightly different center frequencies togenerate a low-frequency beat mode that can be detectedwith an external microphone. Another approach, investi-gated by Sarvazyan et al. [5], shear wave elasticity imaging(SWEI) and Nightingale et al. [6], acoustic radiation forceimpulse (ARFI) imaging consists in focusing an ultrasonicbeam deep in tissues during a long time (typically 100 µs)and measuring the resulting displacement at focus usingultrasonic correlation-based techniques. The displacementinduced at focus as a function of time can be linked to thelocal viscoelastic properties of the tissue. However, thesemechanical displacements depend on several parameters,such as the acoustic beam geometry, the ultrasonic ab-sorption coefficient, and the shear wave heterogeneities inthe focal spot, making these techniques unable to providequantitative estimation of tissue viscoelastic parameters.

In this paper we report a new technique, called super-sonic shear imaging (SSI), providing quantitative shearmodulus mapping of an organ in less than 30 ms. Combin-ing the advantages of the different approaches presentedabove, SSI relies on the acoustic radiation force to remotelygenerate low-frequency shear waves in tissues and can beachieved using the same piezoelectric arrays as the onesused in conventional ultrasonic scanners. This radiationforce acts as a dipolar source of shear waves and mainlyradiates in transverse directions. We propose, with SSI,to create quasiplane shear waves of stronger amplitude bymoving the shear source at a supersonic speed. Such ashear source, which moves faster than the shear waves, canbe created by successively focusing the ultrasonic “push-ing” beam at different depths. All resulting shear wavesinterfere constructively along a Mach cone, creating twoquasiplane shear wave fronts propagating in opposite di-rections. The angle between the two plane waves is propor-tional to the ratio between the shear-wave speed and thespeed of the moving source, i.e., to the Mach number. Theultrafast, ultrasonic scanner developed for the technique is

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bercoff et al.: technique for inducing and ultrafast imaging of shear waves 397

able to generate this supersonic shear source and image thepropagation of the resulting transient plane shear waves byreaching frame rates of a few kilohertz. Shear modulus canbe estimated by imaging the shear-wave propagation in asource-free region. This approach, which differs from otherradiation force techniques that try to extract viscoelasticproperties from displacements at focus, has the advantageto be quantitative and realizable in a few milliseconds.

Furthermore, establishing such a supersonic regimebrings several essential innovations. First, constructive in-terference between shear waves creates a cumulative effectthat induces high-mechanical displacements in the medium(up to 100 µm in phantoms and 40 µm in vivo). This isan indispensable condition for the in vivo feasibility of thetechnique, particularly in strongly viscous media (breast,liver). Second, the supersonic regime generates two spa-tially extended plane shear waves, increasing the area inwhich mechanical shear information is available. Third,changing the speed of the moving “pushing” beam al-lows us to change the Mach cone angle, then insonify thesame medium with different steered plane waves. With thismethod, called shear compounding, it is possible to gatherthe same mechanical information from different angles ofview and, therefore, to improve the robustness of the tech-nique.

In Section II, we show the experimental feasibility ofimaging transient shear waves resulting from the radiationforce. Results will be compared to a numerical simulationbased on a Green’s function formalism. Section III detailsthe principles of SSI and describes the experimental pro-tocol and SSI implementation in the ultrafast scanner. InSection IV, the inversion algorithm to compute quantita-tive elasticity maps from the shear-wave propagation ispresented, and in vitro results are given in homogeneousand heterogeneous tissue mimicking phantoms. Section Vdetails an interesting modality of SSI: the ability to doshear compounding. The modality is described, in vitroexperiments are presented, and improvements in elastic-ity estimation are quantified and discussed. Section VIpresents, after having taken into account safety consid-erations, the first in vivo results and shows the potentialclinical applicability of the technique.

II. Ultrafast Imaging of Remotely Induced

Shear Waves

A. The Acoustic Radiation Force in Soft Tissues

1. The Acoustic Radiation Force: By focusing an ultra-sonic beam at a given location, it is possible to create avolumic radiation force inside a dissipative medium. Thisforce is due to the momentum transfer from the acousticwave to the medium, caused by dissipation or reflectionof the acoustic wave [7]. For a dissipative medium, it iscommon to write:

F (r, t) =2αI(r, t)

c, (1)

where c is the speed of sound in the medium, α is the ultra-sound attenuation, and I is the local intensity of the ultra-sonic beam that is proportional to the square of the acous-tic pressure-field pattern. This force will generate bulk andshear waves propagating in the medium with respectivespeeds, depending on the elastic moduli λ and µ of themedium.

2. Viscoelastic Green’s Function: The mechanical dis-placements induced by such a volumic force in an infiniteand viscoelastic medium can be calculated using a Green’sfunction formalism simulation. The Green’s function in apurely elastic medium has been calculated by Aki andRichards [8]. We recently generalized this mathematicalformulation to a viscous and elastic medium [9]. In suchmedia, the mechanical Green’s function can be written asa sum of three contributions:

gij(r, t) = gpij(r, t) + gs

ij(r, t) + gpsij (r, t), (2)

defined in (3) (see next page), where cp and cs are, re-spectively, the P-wave and S-wave propagation speeds, ρis the medium density, ν is the shear viscosity. The threeelementary axis of the spatial coordinates system are de-noted ei, with i = 1, 2, 3. Based on this coordinate sys-tem, the three components of r are (x1, x2, x3) and themodulus r is given by r =

√x2

1 + x22 + x2

3. The unitaryvector pointed by r is given then by er = (γ1, γ2, γ3),with γ1 = xi/r. δij represents the Kronecker symbol withδij = 1 if i = j, and 0 otherwise. j represents the compo-nent of the Green’s solution, and i is the direction of thepunctual source ([i, j] ∈ [1, 2, 3]).

Three mechanical waves are generated in the medium: acompressional one gp

ij(r, t), of large wavelength, that prop-agates instantaneously in the medium (cl = 1500 m/s), alow frequency shear wave gs

ij(r, t), and a coupling term be-tween both waves of lower amplitude gps

ij (r, t). Compres-sional viscosity is assumed to be negligible compared tothe shear one. gp

ij(r, t) is then identical to Aki’s formula-tion. gs

ij(r, t) has been derived using a Voigt model to takeinto account shear viscoelasticity. It can be considered asa “propagative” diffusion Green’s function. Such formula-tion is realistic, assuming that the attenuation length ismuch larger than the wavelength; that is to say, that vis-cosity only acts on the wave amplitude but does not influ-ence the shear-propagation speed in a significant way. Atthe frequencies generated by the radiation pressure, thisassumption is realistic in most biological tissues. Com-parison between the simulations based on the viscoelas-tic Green’s function and experiments will be presented inthe next paragraph. However, the complete derivation ofthis analytical formulation, its discussion, and experimen-tal validation is beyond the scope of this paper and willbe published later [10].

3. Simulating Radiation Pressure in Viscoelastic Me-dia: To model the volumic force, a three-dimensional (3-D) beam pressure pattern was simulated in an homoge-neous attenuating medium using an impulse diffraction


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

gpij(r, t) =

14πρc2

p

γiγj1rδ

(t − r

cp

)

gsij(r, t) =

14πρcs

1√2πνSt

δij − γiγj

re

(t−τ)2c2s2νtt

gpsij (r, t) =

14πρ

(3γiγj − δij)1r3

[ √νst√

2πcs

[e

t2c2t

2νtt − e(t r

cs )2c2s

2νtt

]

+t

2

⎡⎣Erf

(cst√2νt

)− Erf

⎛⎝cs

(t − r

cs

)√

2νt

⎞⎠

⎤⎦ − tH(t)H

(r

cp− t

)⎤⎦

(3)

code (Phased Array Simulation Software (PASS) devel-oped by D. Cassereau). A 4.3-Mhz ultrasound transducerwas modeled. The acoustic beam intensity was calculated,and the resulting volumic force was deduced from (1) andused in the Green’s function simulation. Fig. 1 representsthe longitudinal displacements induced by the acoustic-beam pattern at different time steps. The shear wave hasa bipolar directivity pattern and mainly propagates alongthe transverse direction. Its velocity, typically a few me-ters per second in soft tissues, is directly linked to shearelasticity if the medium is assumed to be purely elastic:

µ = ρc2, (4)

where c is the speed of the shear wave and ρ is the densityof the medium. This assumption is still valid in our vis-coelastic model as we assumed that dispersion induced byviscosity is negligible. As a consequence, we will considerin the rest of the paper that (4) is correct, and it will beused for shear-elasticity estimations.

As we are dealing with soft tissues, λ µ, the Young’smodulus of the medium can be quantitatively estimatedby measuring the shear-wave speed:

E ≈ 3µ = 3ρc2. (5)

This estimation is not possible along the acoustic beamaxis in which the shear term is negligible. The small dis-placements along this axis are induced by the couplingterm and vanish quickly in the near field of the radiationforce source. In the presence of noise, the estimation ofelastic parameters is not relevant. At focus, Sarvazyan etal. [5] have linked the rise time of the longitudinal displace-ments to the local shear modulus:

µ = ρ

(aD

tmax

)2

, (6)

where µ is the shear modulus, tmax is the rising time,a is the Gaussian profile parameter of the beam (φ =exp

(− r2

a2

)), and D is a dimensionless diffraction parame-

ter.However, this expression assumes a perfect Gaussian ul-

trasound beam that is not necessarily the case. As a con-sequence, techniques relying on the measurement of axialdisplacements at focus are not quantitative.

B. Experimental Protocol

To provide a quantitative elasticity map of the medium,it is necessary to image the propagation of the shear-waveoff-axis and to measure its velocity. As these waves typi-cally propagate at a few meters per second, a frame rate ofseveral kilohertz is needed. This is not possible using con-ventional ultrasound scanners (they typically reach a 50-Hz frame rate). The experiment has been realized with ourultrafast, ultrasonic scanner that is able to remotely gen-erate the mechanical shear wave by focusing ultrasound ata given location, and image the medium during the wavepropagation at a very high-frame rate (up to 6000 im-ages/s). The characteristics of the experiment conductedare described below and illustrated on Fig. 2.

1. The Ultrafast Scanner: Our ultrafast scanner is afully programmable, multichannel system made of 128channels connected to the transducer. Each element pos-sesses its own emission/reception electronic board and2 MB of memory in order to store emission and recep-tion signals. The scanner relies on a 50 MHz samplingfrequency and a 80 Vpp voltage (50 Ω). The ultrafastframe rate is achieved by reducing the emitting mode toa single, plane-wave insonification. This technique allowsthe acquisition of echographic images at a pulse repeti-tion that can reach 6000 Hz. All backscattered radio fre-quency (RF) echoes are stored in the 2-MB memory ofeach channel, then transferred to a computer after acqui-sition. The beamforming process is done only in the receivemode during a postacquisition process. A typical numberof 200–300 data sets (for a 6-cm depth) can be acquiredduring one acquisition sequence. In addition to the channelmemories devoted to store, transmit, and receive signals, a512 kB random access memory (RAM) allows the storageof the acquisition sequences that are programmed by theoperator. This memory controls the temporal behavior ofeach programmable board. For each elementary transmit-receive sequence, parameters such as the delays before andafter emission (to create focalized or flat transmits), thepointer addresses of transmit and receive signals can befixed on each channel independently. A set of successiveelementary sequences can be executed at a pulse repeti-tion frequency (PRF) fixed by the operator (this PRF can


Fig. 1. Green’s function formalism simulation. Mechanical displace-ments induced in the medium by the acoustic radiation force at dif-ferent sampling times: 1 ms (top), 6 ms (middle), 13 ms (bottom).Grayscale images represents the longitudinal displacement ampli-tude. Superimposed arrows indicate the local displacement direction.

be changed from one sequence to the next). The ultrafastscanner is connected to a 4.3-MHz ultrasound array (L4,Vermon, Tours, France, 0.33-mm pitch, 10-mm elevation).

2. Phantom: Experiments are conducted in elasticagar-gelatin phantoms. These phantoms can be consid-ered as elastic solids for the low-frequency, shear wavesgenerated. The percentage in gelatin will fix the stiffnessof the phantom, and agar particles will act as ultrasoundscatterers. The experiment presented was realized in anagar-gelatin homogeneous phantom in which the shear-wave speed was about 1.5 m/s.

3. Generation of the Radiation Force: To generate theradiation force, the ultrafast scanner is used to create anultrasound-focused beam in the phantom at a chosen lo-cation The typical ultrasound pulse is made of 400 oscil-lations at 4.3 MHz. This corresponds to a “pushing time”of 100 µs.

4. Acquisition Sequence: A first plane-wave insonifica-tion is done to realize a reference echographic image of themedium. The “pushing” sequence then is realized by focus-ing the ultrasound beam at a chosen location. Just afterthe generation of the “pushing” beam, the scanner beginsan ultrafast imaging sequence by sending plane-wave in-sonifications at a high-frame rate (3000 Hz) in order tocatch the shear wave created by the “push.”

5. Signal Processing: The RF data stored in the scan-ner memory are transferred to the computer. A classicalbeamforming process then is applied to the data to com-pute the set of echo images. All the images acquired af-ter the “push” then are correlated with the reference echoimage using a 1-D correlation algorithm. The results are aset of images giving the displacement induced by the shearwave at each sample time.

C. Results

The resulting axial displacement movie is given onFig. 3 and compared to the simulation results based onGreen functions formalism at the same sampling times.The shear-wave speed is, in both cases, 1.5 m/s.

From a mechanical point of view, the radiation force ex-citation can be considered as a short impulse. From a largebroadband excitation rises a low-frequency, shear wave ofa few hundred hertz center frequency. This is explained bythe fact that diffraction (due to the spatial extension ofthe source) and viscosity act as low-pass filters. The ex-periment and the viscoelastic Green’s function simulationare in very good agreement.

III. Supersonic Shear Imaging: Principles

A. Basic Principles

In Section II we showed that we are able, by using aclassical ultrasound array driven by the ultrafast scan-ner, to generate a mechanical shear wave in the medium


Fig. 2. Experimental protocol realized.

Fig. 3. Experimental movie of longitudinal displacements induced by the radiation force. (a) experiment, (b) simulation.


Fig. 4. Generation of the supersonic shear source: the source issequentially moved along the beam axis, creating two plane- andintense-shear waves.

and image its propagation in a few tens of seconds. Com-pared to classical external vibrators [3], the use of theacoustic radiation force as a mechanical source enablesmuch more versatility regarding the shear wave genera-tion. Shear sources can be created at any location in themedium at any time by focusing appropriate ultrasoundbeams. The idea of SSI is to create a shear source mov-ing through the medium at a supersonic speed. This shearsource, which moves faster than the shear waves it induces,is created by successively focusing the ultrasonic “pushing”beam at different depths. All resulting shear waves inter-fere constructively along a Mach cone creating two planeand intense shear waves propagating in opposite directions(Fig. 4). This regime is an analog in soft tissues of a “sonicboom” created by a supersonic aircraft. The sound wavesthen are confined below the aircraft in a Mach cone whichangle depends on the airplane speed.

As ultrasonic waves, which create the mechanicalsource, have a much higher speed than the mechanicalshear waves generated (typically 1500 m/s compared to1 m/s), supersonic regimes of extremely high Mach number(or hypersonic regimes) can be generated in the medium(in principle up to Mach 1500!).

Fig. 5 shows the Green’s formalism simulation of a Mach3 supersonic regime using the Green’s function-based simu-lation introduced in Section II. The resulting movie clearlyshows the constructive interferences between bipolar shearwaves leading to the generation of two-plane shear wavesalong the Mach cone.

B. Sequence

These plane-shear waves can be generated and imagedwith the ultrafast scanner presented in Section II. Fig. 6presents the emission sequence realized by the ultrafastscanner to implement SSI. The sequence consist in threesteps:

• A reference ultrasonic image of the medium is ac-quired. It will be used for the calculation of the dis-placements induced by the shear-wave propagation.

• Then the supersonic source is activated by succes-sively focusing a “pushing” beam (typically 100 µslong) at different depths (three depths in this exam-ple). The “pushing” beam should be moved faster thanthe shear-wave speed. Between each push, a set of ul-trasonic images can be acquired at an ultrafast framerate (3000 Hz) to monitor the activation of the super-sonic source.

• A set of ultrafast, ultrasonic images are acquired to fol-low the propagation of the supersonic-generated shearwaves through the medium.

Our ultrafast scanner is able to instantaneously switchbetween the “pushing” mode and the imaging mode, thenfollow in real time the activation of the supersonic sourceand the propagation of the resulting shear waves. The to-tal sequence duration lasts no more than a few tens ofmilliseconds.

C. Results

Initial experiments were conducted in (3%,3%) agar-gelatin homogeneous phantom. The previous sequence wasrealized by the ultrafast scanner. The postacquisition sig-nal processing, detailed in Section II, was applied to thedata. Fig. 7 shows the experimental realization of a Mach3 supersonic regime. The supersonic source was generatedwith five “pushing” beams of 100 µs long.

Activating the supersonic regime enables the generationof high amplitude displacements (up to 100 µm in phan-toms and 40 µm in vivo) and spatially extended planewaves. This leads, as it can be seen on Fig. 7, to an in-creased penetration depth of the shear wave that propa-gates through the whole imaged area, potentially provid-ing, as will be shown in Section IV, the elasticity mapcomputation of the whole imaged medium.

The angle between the two plane waves is proportionalto the ratio between the shear-wave speed and the speed ofthe moving source (i.e., to the Mach number). By varyingthe source speed in a given medium, it is possible to steerplane-shear waves in different directions. This modality,called shear compounding, will be discussed in detail inSection V.

IV. Elasticity Mapping Using SSI

A. Inverse Problem of the Shear-Wave Propagation

As we have measured the local displacements inducedby the shear-wave propagation as a function of time in thewhole imaged area, it is possible to use this informationto recover the medium elasticity map [11], [12]. The nextparagraph briefly details the equations and the assump-tions made to write the wave propagation inverse problem.

As we assumed that viscosity does not significantly af-fect the shear-wave speed, we neglect it in the inverse prob-lem formulation. The medium is assumed to be purely elas-tic, infinite, isotropic, and locally homogeneous. It also ishypothesized that λ µ, this is to say, that the bulk


Fig. 5. Simulation of a Mach 3 supersonic regime; displacements induced at different time steps: 1 ms (left), 1.5 ms (center), and 2 ms(right).

Fig. 6. Emission sequence for a supersonic regime.

wave propagates instantaneously. After application of theradiation force, the motion equation in the medium can bereduced to a shear-wave propagation equation [11]:

ρ∂2u

∂t2= µ∆u, (7)

where µ is the shear elastic modulus, u is the displacementvector, and ρ is the density of the medium. It is importantto note that, using the hypothesis above, the three com-ponents of the displacement are independent solutions ofthe wave equation. As our 1-D correlation algorithm onlygives access to the z-component of the displacement, theequation used is:

ρ∂2uz

∂t2= µ∆uz. (8)

The image area corresponds to the (x, z) plane. Onlytwo of the second order spatial derivatives in the Laplacianterm can be calculated. It is then assumed that:

∂2uz

∂y2 ∂2uz

∂x2 +∂2uz

∂z2 , (9)

and then:

∆uz ≈ ∂2uz

∂x2 +∂2uz

∂z2 .

This assumption implies that the shear wave does notsignificantly diffract in the elevation direction y (i.e., out-side of the imaging plane). As the displacement is a func-tion of time, the local inverse problem relation can be writ-ten in the Fourier domain:

µ(x, z) =ρ

N

∑ω

F

(∂2uz(x, z)

∂t2

)

F

(∂2uz(x, z)

2x2 +∂2uz(x, z)

∂z2

)

where F represents the Fourier transform in the time do-main, and N is the number of frequencies taken into ac-count. N is chosen using a threshold in the Laplacian spec-trum around the shear-wave center frequency.

This inversion algorithm provides local, quantitative,shear-elasticity estimation in the area covered by the


(a)

(b)

Fig. 7. Experimental Mach 3 supersonic regime in an elastic phantom: displacements induced in the medium at 6 different time steps.

shear-wave propagation. Considering the previous assump-tions, the elasticity estimation will not be accurate:

• In the area in which the radiation force is applied.As the inversion algorithm is based on a free-sourcewave equation, it does not include the volumic source(which is not known) in the motion equation. Thisleads to an overestimation of the shear velocity at theshear-source location.

• Along the beam axis where, as it has been shown inSection II, the shear term is extremely weak. The cou-pling term does not provide sufficient axial displace-ment to ensure relevant shear-modulus estimation.

B. Experimental Tests in Homogeneous Medium

Experiments were conducted on (5%,1%) gelatin-agarphantom in which shear waves propagate at 2.5 m/s (6 kPaphantom). A Mach 10 supersonic shear source was gener-ated in the homogeneous phantom by focusing the ultra-sound beam at five different locations along the beam axis:focus ∈ [15 20 25 30 35] mm. After calculating the displace-ments induced by the shear-wave propagation, the inver-sion algorithm was applied to the spatio-temporal data.The resulting elasticity map is shown on Fig. 8.

As expected, the velocity map is not accurate in thesource zone, but it gives a very good quantitative estima-

Fig. 8. Elasticity map of a 6 kPa homogeneous phantom computedfrom a Mach 10 supersonic regime.

tion of the shear elasticity (6 kPa with 3% variance) inthe areas in which the shear wave has propagated. Thiscorresponds to the whole imaged area except the beamaxis. In the supersonic mode, the source moves along thebeam axis, that is to say, in the area in which the elas-


b)

Fig. 9. a) Picture of the elastic phantom containing a harder inclusion. (b) Shear waves from a Mach 3 supersonic regime propagationthrough the same phantom: displacements induced in the medium at 3 different time steps: 2 ms (left), 12 ms (center), and 17 ms (right).The shear wave is sensitive to the harder inclusion.

Fig. 10. Elasticity map of the phantom containing a 20-mm hardinclusion.

ticity could not be recovered anyway. As a consequence,increasing the spatial extension of the shear source (bymoving it) increases the propagation area, but it does notchange the misestimated area. It then is possible to definea “well reconstructed” area for a given supersonic mode:In this large area the elastic parameters can be quantita-tively recovered in less than 30 ms using SSI. One shouldnote that recovering the shear elasticity in the source areais a very complicated problem as it strongly depends onthe ultrasonic beam pattern inducing the radiation force.This experiment emphasizes the interest of looking outsidethe source location to estimate elastic parameters.

C. Experimental Tests in Heterogeneous Medium

Experiments were conducted on (5%,1%) gelatin-agarphantom containing a harder cylindrical inclusion. This in-clusion had a 20-mm diameter and was made with (8%,1%)gelatin-agar mixture that corresponds approximately to anelastic tissue twice as hard as the surrounding phantom. A


picture of the experimental phantom is shown on Fig. 9(a).A colored ink was added in the inclusion phantom to makeit visible. A supersonic shear source has been created nearthe inclusion by successively focusing five pushing beamsat different depths at a 1500-Hz rate. The resulting dis-placement movie is shown on Fig. 9(b).

The shear wave, propagating initially in a Mach cone,is progressively distorted and accelerated when passingthrough the harder inclusion. This information is used forelasticity estimation. The shear-elasticity map resultingfrom the local inversion algorithm is given on Fig. 10.

If the harder inclusion is not visible on the echographicimage, it clearly can be identified on the elasticity map.The shear modulus inside it has a mean value of 4.1 kPawith a 12% variance. Outside the inclusion, the mean shearelasticity is estimated to 2 kPa with a 2% variance. Theshear-elasticity map has 1-mm spatial resolution.

V. Shear Compounding

A. Principles

As explained in Section III, it is possible, by choosingthe speed of the supersonic source, to fix the angle be-tween the two plane-shear waves (which is directly linkedto the Mach number). Varying the source speed in a givenmedium allows us to steer plane-shear waves in differentdirections and to insonify the medium from different an-gles of view. Such an approach has been studied alreadyfor ultrasonic waves, in which a given medium is insonifiedwith several steered-focused beams. This modality, calledcompound imaging, has been successfully implemented incommercial ultrasonic scanners and enhance in a signif-icant way the image quality [13]. We have shown previ-ously [14] the interest of compound imaging in the estima-tion of 2-D vector displacements induced by shear wavesin soft tissues. We propose here to explore the capabil-ities of SSI and apply this concept to mechanical shearwaves. A given medium is insonified, using SSI, with sev-eral steered plane-shear waves. For each insonification, anelasticity map is computed. All the reconstructed maps areaveraged to compute a final one. The next paragraph stud-ies how the average of a set of elasticity maps can improvethe quality and the robustness of the technique. This shearcompound modality also will be tested for hard inclusiondetection.

The ability of SSI to steer plane-shear waves in differentdirections has been tested in a homogenous tissue mimick-ing phantom. Fig. 11 shows a Mach 3, a Mach 10, anda Mach −3 supersonic regimes. Mach −3 corresponds toa supersonic source moving toward the transducer. Theangle is shifted by π compared to a Mach 3 regime.

Supersonic regimes from Mach 1 to Mach 5 can begenerated in tissues to provide tilted plane waves. Forhigher Mach numbers, the planes are quasiparallel, andthe change in angle is no longer significant. As a conse-quence, shear compounding can be realized by averaging

elasticity maps coming from up to 10 tilted waves. Influ-ence on the variance of elasticity maps is studied in thenext paragraph.

B. Application to Inclusion Detection

Considering the phantom with an inclusion that is twiceas hard as the surrounding tissues described in Section IV,experiments were conducted to improve the quality of theinclusion detection using shear compound. Three steeredplane-shear waves were generated in the medium corre-sponding to a Mach 2, 3, and 4 supersonic regime. Foreach of them, the inversion algorithm was applied to thepropagation movie, and the resulting elasticity maps wereaveraged.

Fig. 12 shows a scaled picture of the heterogeneousphantom and the corresponding elasticity maps computedwith and without shear compounding.

The variance of the elasticity estimation has decreasedfrom 12% to 4% in the harder inclusion. The resultingelasticity was more homogeneous, and the inclusion wasbetter shaped. The modality seems to be an elegant way toimprove the robustness of the technique and detect smallbreast lesions.

VI. In Vivo Results

A. Safety Considerations

To estimate the feasibility of the technique in clinicalconditions and start working in vivo, it is necessary toverify that SSI is safe for the human body and meets theFood and Drug Administration (FDA) requirements [15].Three parameters with respect to the acoustic output ofthe ultrasound system should be evaluated: the mechanicalindex (MI < 1.9), the spatial peak pulse average intensity(ISPPA < 190 W/cm2), and the spatial peak temporal av-erage intensity (ISPTA < 720 mW/cm2). The values givenare derated values. The derating factor is accounting fora 0.3 dB.cm−1.MHz−1 ultrasonic average attenuation, asfixed by FDA requirements. We consider for our calcula-tion a “pushing” beam focused at 40-mm depth and gen-erated by a 4.3 MHz array.

In our experiments, the maximal acoustic pressure gen-erated by our 4.3 MHz array was measured at focus (40-mm depth) and does not exceed 40 bars in water or aderated value of 20 bars in the normalized attenuatingmedium (0.3 dB.cm−1.MHz−1). Knowing that P0 = 20bars, the three FDA parameters have been estimated withthe chosen experimental conditions:

• MI = 0.96 < 1.9,• ISPPA = P 2

02ρc = 133 W.cm−2 < 190 W.cm−2 where ρ

is the medium density and c is the sound speed in themedium,

• ISPTA = ISPPA ∗ ∆t1 = 13.3 mW/cm2 <

720 mW/cm2, for a classical “pushing” beam dura-tion ∆t of 100 µs.


Fig. 11. Different supersonic regimes generating compounded shear-plane waves. (a) Mach 3, (b) Mach 10, (c) Mach −3.

Knowing that the acoustic power of an ultrafast emit-ting sequence (about 100 plane waves insonifications) isextremely weak (ISPTA ≈ 0.5 mW/cm/MHz), the FDArequirements allow the generation of about 50 “pushes”per second at the same location. As four or five “pushes”are sufficient to recover a complete elasticity map of themedium, the last condition is perfectly met. Here oneshould notice the interest of plane-wave illumination forthe imaging sequence, as flat transmitted beams imposemuch less constraints than classical focused beams.

B. In Vivo ResultsAfter having verified the safety of the technique, a set of

in vivo measurements were realized on breasts of healthyvolunteers. The experiment shown below was conductedon a 24-year-old woman. The echographic image cover a40 ∗ 30-mm area. A supersonic shear source was generatedin the axial direction by creating four “pushing” beams of100 µs. The resulting shear waves were imaged with theultrafast scanner at a 3000 Hz frame rate. The movie, pre-sented in Fig. 13, clearly shows two vertical plane shear


Fig. 12. Scaled phantom picture (right). Corresponding elasticity maps with (center) and without (left) shear compounding.

Fig. 13. Mach shear wave in a healthy breast: displacements at three different time steps: 1 ms (left), 4 ms (center), and 9 ms (right).

Fig. 14. Ultrasound image and corresponding elasticity map of the healthy breast.

waves propagating in opposite directions corresponding,after a shear-wave speed estimation, to a Mach 12 su-personic regime. The maximum amplitude displacementis 28 µm at the center. The plane shear wave is stronglyattenuated during the propagation leading to a 5 µm dis-placement at the edges. It is important to note that thesupersonic regime here is capable of generating plane-shear waves of enough amplitude to propagate across thewhole image medium, even in highly attenuating media

like breasts. The resulting elasticity map shows a meanelasticity of 1 kPa with a 14% variance (Fig. 14).

The typical mean value for shear elasticity in this set ofin vivo measurements was about 1 kPa. This correspondsto a typical Young’s modulus of 3 kPa in the breast. Theseresults are in total agreement with the results on patientsof Lorenzen et al. in MR elastography [16].

This first set of in vivo measurements gave relevant re-sults on healthy breasts. Such experiments validate the


robustness of the technique and show its potential appli-cability for clinical applications and lesion detection. Thenext step is the clinical evaluation of the technique byscanning a set of women presenting benign lesions, carci-nomas, and microcalcifications. This work is planned to bedone in the next months in collaboration with the InstitutCurie in Paris. Such collaboration has been established al-ready in the past for transient elastography validation [3].Furthermore, as elasticity is not a crucial parameter for le-sion characterization, studies are currently being realizedto demonstrate that SSI also can provide viscosity mapsof the studied organ.

VII. Conclusions

A new technique for inducing and simultaneously ultra-fast imaging shear waves in soft tissues was studied andsuccessfully applied in vitro and in vivo. Quantitative elas-ticity maps have been achieved, particularly in heteroge-neous medium containing hard inclusions and on healthybreasts. Based on the acoustic radiation force, SSI relieson the generation of a supersonic moving source radiat-ing shear waves in the body. Such a supersonic regimeenables the computation of a quantitative elasticity mapof an organ in a few milliseconds, even in strongly viscousmedia. Insensitive to patient motion or boundary condi-tions, this technique requires only a classical ultrasonictransducer array and should be able to provide elasticitymaps of the scanned regions without any technical addi-tion. As SSI meets FDA requirements, the first in vivoresults presented in this work will be extended to clinicalstudies on women presenting tumors or microcalcifications.Future works also will focus on providing viscosity mapsof the medium, giving the physician a complete cartogra-phy of the viscoelastic properties of human tissues. Thevalidation of SSI for breast cancer detection should repre-sent a significant step for the future introduction of thistechnique to the medical community.

References

[1] J. Ophir, E. I. Cespedes, H. Ponnekanti, Y. Yazdi, and X. Li,“Elastography: A method for imaging the elasticity in biologicaltissues,” Ultrason. Imag., vol. 13, pp. 111–134, 1991.

[2] R. Muthupillai, D. J. Lomas, P. J. Rossman, J. F. Greenleaf,A. Manduca, and R. L. Ehman, “Magnetic resonance elastog-raphy by direct vizualization of propagating acoustic strainwaves,” Science, vol. 269, pp. 1854–1855, 1995.

[3] J. Bercoff, S. Chaffaı, M. Tanter, L. Sandrin, S. Catheline, M.Fink, J. L. Gennisson, and M. Meunier, “In vivo breast cancerdetection,” Ultrasound Med. Biol., vol. 29, no. 10, pp. 1387–1396, 2003.

[4] M. Fatemi and J. F. Greenleaf, “Ultrasound-stimulated vibro-acoustic spectrography,” Science, vol. 280, pp. 82–85, 1998.

[5] A. P. Sarvazyan, O. V. Rudenko, S. D. Swanson, J. B. Fowlkes,and S. Y. Emelianov, “Shear wave elasticity imaging—A newultrasonic technology of medical diagnostic,” Ultrasound Med.Biol., vol. 20, pp. 1419–1436, 1998.

[6] K. Nightingale, M. S. Soo, R. Nightingale, and G. Trahey,“Acoustic radiation force impulse imaging: in vivo demonstra-tion of clinical feasibility,” Ultrasound Med. Biol., vol. 28, pp.227–235, Feb. 2002.

[7] G. R. Torr, “The acoustic radiation force,” Amer. J. Phys., vol.52, pp. 402–408, 1984.

[8] L. Aki and P. G. Richards, Quantitative Seismology, Theory andMethods. vol. 1, ch. 4, New York: W. H. Freeman and Co., 1980.

[9] J. Bercoff, M. Muller, M. Tanter, and M. Fink, “Study of vis-cous and elastic properties of soft tissues using supersonic shearimaging,” in Proc. IEEE Ultrason. Symp., 2003, pp. 925–928.

[10] J. Bercoff, M. Muller, M. Tanter, and M. Fink, “Mechanicalresponse of viscoelastic soft solids to the acoustic radiationforce: Analytical Green’s formalism and experimental valida-tion,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., to bepublished.

[11] L. Sandrin, M. Tanter, S. Catheline, and M. Fink, “Shear mod-ulus imaging with time resolved 2D pulsed elastography,” IEEETrans. Ultrason., Ferroelect., Freq. Contr., vol. 49, pp. 426–435,Apr. 2002.

[12] T. E. Oliphant, R. R. Kinnick, A. Manduca, R. L. Ehman, andJ. F. Greenleaf, “An error analysis of helmholtz inversion forincompressible shear vibration elastography with application tofilter design for tissue characterization,” in Proc. IEEE Ultrason.Symp., 2000, pp. 1795–1798.

[13] S. K. Jespersen, “Tools for improving the diagnosis of atheroscle-rotic plaque using ultrasound,” Ph.D. dissertation, CADUS,Dept. of Information Technology, Technical University of Den-mark, Lyngby, Denmark, Nov. 1997.

[14] M. Tanter, J. Bercoff, L. Sandrin, and M. Fink, “Ultrafast com-pound imaging for 2-D motion vector estimation: Applicationto transient elastography,” IEEE Trans. Ultrason., Ferroelect.,Freq. Contr., vol. 49, pp. 1363–1374, Oct. 2002.

[15] Food and Drug Administration, “Information for ManufacturersSeeking Marketing Clearance of Diagnostic Ultrasound Systemsand Transducer,” U. S. Dept. Health and Human Services, Foodand Drug Administration, Center for Devices and RadiologicalHealth., 1997.

[16] L. Lorenzen, R. Sinkus, and G. Adam, Elastography: Quan-titative Imaging Modality of the Elastic Tissue Properties.Stuttgart-New York: Rofo Fortschr. Geb. Rontgenstr., ThiemeVerlag, 2003, pp. 623–630.

Jeremy Bercoff was born in August 1977in Paris, France. In 2001 he received theengineer degree from the Ecole Superieurede Physique et de Chimie Industrielle de laVille de Paris (ESPCI) with a specializationin physics. In 1999, he worked at AdvancedTechnology Laboratories (ATL) Ultrasound,a Philips Medical System company based inSeattle, WA, on the development of echo-graphic systems. In 2000, he received his mas-ter degree at the Laboratoire Ondes et Acous-tique in Paris. He is now achieving his Ph.D.

degree at the Laboratoire Ondes et Acoustique, working on shearwave propagation in soft tissues for cancer detection, ultrafast imag-ing, and flow measurements.

Mickael Tanter was born in December 1970in Paimpol, France. He received the engineerdegree in electronics from Ecole Superieured’Electricite (SUPELEC) in 1994. In 1999, hereceived the Ph.D. degree in physics (acous-tics) from the University of Paris VII for hiswork on the application of time reversal toultrasonic brain hyperthermia. He is now aresearcher in the National French Center ofScience (C.N.R.S) and joined the laboratoryOndes et Acoustique at the Ecole Superieurede Physique et de Chimie Industrielle de la

Ville de Paris (ESPCI) in 2000.His current research interests include wave focusing techniques in

heterogeneous media, medical ultrasonic imaging, ultrasonic brain


imaging, shear-wave propagation in soft tissues for cancer detection,ultrasonic therapy, nonlinear acoustics, and active noise control.

Mathias Fink received the diplome de Doc-torat de 3ieme cycle in solid state physicsin 1970 and the Doctorat es-Sciences degreein acoustics in 1978 from University of ParisVII, Paris, France. From 1981 to 1984, hewas a professor of acoustics at StrasbourgUniversity, Strasbourg, France. Since 1984,he has been a professor of physics at Uni-versity of Paris VII (Denis Diderot), Paris,France. In 1990, he founded the LaboratoireOndes et Acoustique at the Ecole Superieurede Physique et de Chimie Industrielle

de la Ville de Paris (ESPCI). In 1994, he was elected at the Insti-tut Universitaire de France. In 2002, he was elected to the FrenchAcademy of Technology. In 2003, he was elected to the FrenchAcademy of Science.

His current research interests include medical ultrasonic imagingultrasonic therapy, nondestructive testing, underwater acoustics, ac-tive control of sound and vibration, analogies between optics andacoustics, wave coherence in multiple scattering media, and time re-versal in physics. He has developed different techniques in specklereduction, wave focusing in inhomogeneous media, and in ultrasoniclaser generation. He holds 28 patents, and he has published morethan 300 articles.

Supersonic shear imaging: a new technique for soft tissue elasticity mapping

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