Ultrasound in Med. & Biol., Vol. 37, No. 11, pp. 1884–1892, 2011Copyright � 2011 World Federation for Ultrasound in Medicine & Biology

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asmedbio.2011.07.012

doi:10.1016/j.ultr

d Original Contribution

BIAS OBSERVED IN TIME-OF-FLIGHT SHEARWAVE SPEED MEASUREMENTSUSING RADIATION FORCE OFA FOCUSED ULTRASOUND BEAM

HENG ZHAO,* PENGFEI SONG,* MATTHEW W. URBAN,* RANDALL R. KINNICK,*MENG YIN,y JAMES F. GREENLEAF,* and SHIGAO CHEN*

*Department of Physiology and Biomedical Engineering; and yDepartment of Radiology, Mayo Clinic College of Medicine,Rochester, MN, USA

(Received 25 February 2011; revised 3 June 2011; in final form 23 July 2011)

Aology a200 Fishigao

Abstract—Measurement of shear wave propagation speed has important clinical applications because it is relatedto tissue stiffness and health state. Shear waves can be generated in tissues by the radiation force of a focused ultra-sound beam (push beam). Shear wave speed can be measured by tracking its propagation laterally from the pushbeam focus using the time-of-flight principle. This study shows that shear wave speed measurements with suchmethods can be transducer, depth and lateral tracking range dependent. Three homogeneous phantoms withdifferent stiffness were studied using curvilinear and linear array transducer. Shear wave speed measurementswere made at different depths, using different aperture sizes for push and at different lateral distance rangesfrom the push beam. The curvilinear transducer shows a relatively large measurement bias that is depth depen-dent. The possible causes of the bias and options for correction are discussed. These bias errors must be taken intoaccount to provide accurate and precise time-of-flight shear wave speed measurements for clinical use. (E-mail:chen.shigao@mayo.edu) � 2011 World Federation for Ultrasound in Medicine & Biology.

Key Words: Shear wave speed, Liver fibrosis, Bias, ARFI.

INTRODUCTION

Mechanical properties of tissues such as shear modulus(elasticity) are related to the state of tissue health(Sarvazyan et al. 1998). Therefore, noninvasive methodsfor measuring tissue elasticity have important clinicalapplications. Assuming isotropy, incompressibility andlinearity, the shear modulus m of a soft tissue is relatedto its shear wave propagation speed cs by eqn (1)

m5 rc2s ; (1)

where r is density, which can be assumed to be 1000kg/m3 for all soft tissues (Yamakoshi et al. 1990). Equa-tion (1) neglects tissue viscosity and frequency effects butgenerally is considered valid when the frequency of theshear wave is low and narrowband. Therefore, measure-ments of shear wave propagation speed can be used toestimate tissue elasticity for that bandwidth present inthe shear wave.

ddress correspondence to: Shigao Chen, Department of Physi-nd Biomedical Engineering, Mayo Clinic College of Medicine,rst Street, S.W., Rochester, MN 55905, USA. E-mail: chen.@mayo.edu

1884

Acoustic radiation force from a focused ultrasoundbeam can be used to generate shear waves within tissues.If a single focused ultrasound beam is used for pushing, itis commonly assumed that the shear waves generated bythe ultrasound radiation force at the focal region propa-gate within the transducer imaging plane in a directionperpendicular to the ultrasound beam axis (Parker et al.2011). Therefore, tissuemotion at several lateral positionsalong the shear wave propagation path at the push beamfocal depth can be measured using pulse-echo ultrasoundto calculate shear wave propagation speed based on time-of-flight principle. This approach was first proposed inshear wave elasticity imaging (SWEI) and later used byseveral groups with various modifications to measuretissue elasticity (Chen et al. 2009; Deffieux et al. 2009;Palmeri et al. 2008; Sarvazyan et al. 1998). Amongthese methods, supersonic shear imaging (SSI) andacoustic radiation force impulse imaging (ARFI) havebeen implemented on commercial ultrasound scannersand used for human studies (D’Onofrio et al. 2010;Deffieux et al. 2009; Muller et al. 2009; Palmeri et al.2008; Tanter et al. 2008).

The purpose of this study is to evaluate if shearwave speed measured by radiation force of a focused

Bias observed in time-of-flight shear wave speed measurements d H. ZHAO et al. 1885

ultrasound beam and time-of-flight method is affected bymeasurement conditions such as the transducer used andmeasurement location. A systematic phantom studyreveals that measured shear wave speeds can be trans-ducer dependent, depth dependent and lateral trackingrange dependent. Measurement bias is large enough topotentially change diagnosis, for example, in liverfibrosis staging. Findings in this study have importantimplications on clinical applications of shear wave speedmeasurements using ultrasound radiation force producedby a focused ultrasound beam.

METHODS

Phantom study designThe phantom study was designed to determine

whether shearwave speedmeasurements are depth depen-dent, transducer dependent or lateral tracking rangedependent, even in homogenous phantoms. Three homog-enous elasticity phantoms (custom made by CIRS, Inc.Norfolk, VA, USA) with different elasticity values wereused in this study. Each phantom had a dimension of103 103 8 cm3 (width, depth, height). Shear wave speedmeasurements were made using a curvilinear transducerC4-2 and a linear array transducer L7-4 (Philips Health-care, Andover, MA, USA) in each phantom. The focalpoint of push beam in this studywas positioned at differentdepths without any steering. For the C4-2 transducer,measurements were made with the transducer focusingat depths of 30, 40, 50, 60 and 70mm away from the trans-ducer surface. For the L7-4 transducer, measurementswere made at focal depths of 20, 25, 30, 35 and 40 mm.A shallower depth rangewas chosen for the L7-4 to reflecttypical measurement depths expected for this higherfrequency transducer. Three different transmit aperturesizes (32, 64 and 96 elements) were used to produce shearwaves at each focal depth. At each of the setup combina-tions mentioned above, five repeated measurements weremade by positioning the transducer at five different loca-tions on the phantom surface. The locations were selectedrandomly near the center of each phantom to avoid poten-tial influence of the boundaries for measurements (noreflection of shear waves from boundaries were observedin this study using flash imaging described in the nextparagraph). Therefore, we have a total of 450 shearwave measurements in this study (three phantoms bytwo transducers by five depths by three aperture sizes byfive repetitions). To determine whether shear wave speedmeasurements depend on lateral range, shear wave speedwas also calculated from two different lateral distanceranges from the push beam: 0�7.7 mm and 7.7�15.4 mmfor the C4-2 and 0�9.2 mm and 9.2�18.5 mm for theL7-4. Therefore, a total of 450 3 2 5 900 shear wavespeed estimates are reported in this study.

Shear wave speed measurementA Verasonics ultrasound system (Verasonics Inc.,

Redmond, WA, USA) was used in this study to makeshear wave speed measurements. For the C4-2 transducer,the push beam for shear wave generation had a centerfrequency of 3 MHz and duration of 331 ms. For theL7-4 transducer, the push beam for shear wave generationhad a center frequency of 5 MHz and duration of 128 ms.The push pulse duration was selected such that sufficientshear wave motion (at least several microns) could beproduced without exceeding the capacity of the transmis-sion circuit of the Verasonics system. Propagation ofshear waves was monitored for 20 ms at a frequency of4 kHz using ‘‘flash’’ imaging. In flash imaging mode,the Verasonics ultrasound system transmitted an unfo-cused ultrasound pulse (a ‘‘plane wave’’ compared witha traditional focused ultrasound ‘‘beam’’) into the imagedmedium and used parallel channel processing to generateone complete two-dimensional (2-D) ultrasound imagefrom one transmission (Bercoff et al. 2004a). The centerfrequencies used for imaging pulses were 3 MHz for theC4-2 and 5 MHz for the L7-4. Therefore, shear wavemotion can be detected within a 2-D region (with a pixelresolution of one ultrasound wavelength, which was0.51 mm for the C-2 and 0.31 mm for the L7-4) at highpulse repetition frequency (PRF), which was 4 kHz inthis study. Shear wave displacement was calculatedfrom in-phase/quadrature (IQ) data usingone-dimensional(1-D) autocorrelation method (Kasai et al. 1985). Shearwave displacement at the focal depth of the push beamwas averaged over 10 wavelengths (corresponding to anaxial range of 5mm for C4-2 and 3mm for the L7-4) alongthe beam axis to improve signal-to-noise ratio (SNR).Shear wave speed (group velocity) was then estimatedfrom the arrival time (using time-to-peak) of the shearwave at different lateral distance from the push beamcenter through linear regression (Palmeri et al. 2008).

Independent measurement of phantom elasticityShear wave speed in all three elasticity phantoms

used in this study were measured by magnetic resonanceelastography (MRE) (Muthupillai et al. 1995) and 1-Dtransient elastography (TE) (Sandrin et al. 2002) for inde-pendent comparison. MRE measurements were madeusing a 3.0T whole-body magnetic resonance imagingsystem (GE Medical System, Milwaukee, WI, USA) ata shear wave frequency of 100 Hz. A multislice spinecho based echo planar MRE sequence with four phaseoffsets was used to collect three-dimensional (3-D) shearwave data with three orthogonal motion sensitizing direc-tions. After curl filtering to remove the undesired bulkmotion, 3-D local frequency estimation (LFE) inversionwas performed to calculate shear wave speed (Manducaet al. 2001). Shear wave speeds measured at three

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8Depth (cm)

c (m

/s)

Phantom 1 Phantom 2 Phantom 3

Fig. 1. Shear wave speed measured by magnetic resonanceelastography (MRE) in three phantoms.

1886 Ultrasound in Medicine and Biology Volume 37, Number 11, 2011

orthogonal directions were averaged at each voxel to givea single estimate of speed at each spatial location.

For the 1-D transient elastography (TE) experiments,a 6.4 mm diameter, weakly focused (nominal focal range:1�7 cm), 7.5 MHz single-element transducer (ECHOUltrasound, Lewistown, PA, USA) was attached toa mechanical vibrator (V203; Ling Dynamic SystemsLimited, Hertfordshire, UK), so that the transducer canvibrate on the phantom surface during pulse-echo motiondetection. A single-cycle 100 Hz sinusoidal pulse wasused to drive the vibrator for shear wave generationthrough the transducer into the phantom under test. Trans-ducermotionwas removed from shear wave displacementdemodulated from radio-frequency (RF) ultrasound echosignals (Sandrin et al. 2002). Shear wave propagationfrom 5 mm to 35 mm in depth away from the transducersurface was used to calculate shear wave speed. Measure-ments were repeated five times at different locationsacross the surface of each elasticity phantom.

Measurement of transducer intensity fieldTo evaluate the influence on shear wave speed

measurements due to the force field of the push beamused for shear wave generation, the pressure field of thepush beam was measured using a calibrated needlehydrophone (HGL0200; ONDA Corporation, Sunnyvale,CA, USA) and the intensity was derived by using theequation I 5 p2/rc, where p is the pressure and r and care the density and sound speed of the medium, respec-tively. Two-dimensional scans were performed witha spatial resolution of 0.5 mm in the mid-elevationalplane (x-z plane) and mid-lateral plane (y-z) of the C4-2and L7-4 transducers, where x, y and z represent thelateral, elevational and axial directions of the ultrasoundtransducer, respectively. Measurements were performedin a water tank where the transducer repeatedly trans-mitted the push pulse while the hydrophone was trans-lated by step motors to scan the pressure field. Toprotect the Verasonics system and tested transducers,each transmitted pulse consisted of 32 cycles of ultra-sound (10.7 ms for C4-2 and 6.4 ms for L7-4). No appre-ciable difference of pressure field was found byincreasing the pulse durations to those used in shearwave speed measurements. Scans were obtained for theC4-2 focusing at 30 and 50 mm and for the L7-4 focusingat 20 and 30 mm from the transducer surface. Allmeasurements were made with 64 transducer elementsused for push beam transmission.

Statistical analysisPaired t-test was used to evaluate for each transducer

if there was a significant difference between shear wavespeed measurements made at different depths, differentlateral ranges from the push beam or using different

aperture sizes for push beam transmission. Because theshear wave speeds of five repeated measurements madeat each setup combination had small variation (standarddeviation around 0.01 m/s), the mean value was treatedas a single sample for that combination in the paired t-test. To test the difference between two lateral rangesusing the C4-2 transducer, we paired samples from allfocus depths, all aperture sizes and all phantoms. Asimilar pairing strategy was used to test the differencebetween focus depths and the difference between aperturesizes. The same analysis was repeated for the L7-4. Ap value less than 0.05 indicated that the measurementswere statistically significantly different.

RESULTS

Shear wave speeds measured by MRE and 1-D TEFigure 1 shows the shear wave speed measured by

MRE in three phantoms. Within each phantom, themean and standard deviation of the shear wave speedwas calculated from a 6 3 6 cm2 region at the center ofthe phantom for each depth. Results at the top 1 cm andbottom 1 cm were not given here because these may beaffected by boundary effects. Small variation of shearwave speed measured along depth may be due to reso-nance of the phantom. The mean and standard deviationsof shear wave speed mean values along all depthsshown in Figure 1 are 1.24 6 0.01 m/s, 1.47 6 0.02 m/sand 1.806 0.02m/s for phantoms 1, 2 and 3, respectively.These results suggest that all phantoms are indeedspatially homogenous in terms of shear wave speed.Results obtained from 1-D TE are very close to those ofthe MRE tests: 1.23 6 0.02 m/s, 1.48 6 0.03 m/s and1.89 6 0.07 m/s for phantom 1, 2 and 3, respectively.These results are summarized in Table 1. No significantdifference was found by Student’s t-test between MREand 1-D TE results for phantoms 1 and 2 (p . 0.05).Phantom 3 showed a significant difference (p , 0.01).

Table 1. Phantom shear wave speeds measured by MREand 1-D TE (m/s)

MRE 1-D TE

Phantom 1 1.24 6 0.01 1.23 6 0.02Phantom 2 1.47 6 0.02 1.48 6 0.03Phantom 3 1.80 6 0.02 1.89 6 0.07

MRE 5 magnetic resonance elastography; 1-D 5 one-dimensional;TE 5 transient elastography.

Bias observed in time-of-flight shear wave speed measurements d H. ZHAO et al. 1887

Shear wave speed measured using ultrasound radiationforce

Shear wave speeds measured by the C4-2 transducerat different depths using different transmit aperture sizesare shown in Figure 2. Shear wave speeds were measured

Fig. 2. Shear wave speeds measured by C4-2 (elevational focus:70 mm) in phantom 1 (a), phantom 2 (b) and phantom 3 (c). Ateach measurement depth, three different aperture sizes (32, 64and 96 elements) were used for push beam transmission. Resultsfrommagnetic resonance elastography (MRE) and 1-D transient

elastography (TE) are also displayed for comparison.

Fig. 3. Shear wave speeds measured by L7-4 (elevational focus:25 mm) in phantom 1 (a), phantom 2 (b) and phantom 3 (c). Ateach measurement depth, three different aperture sizes (32, 64and 96 elements) were used for push beam transmission. Resultsfrom resonance elastography (MRE) and 1-D transient elastog-

raphy (TE) are also displayed for comparison.

using a lateral range of 0�15.4 mm from the push beamfocus. Different vertical scales are chosen for eachphantom to better show the differences in data. Shearwave speeds measured at different depths are signifi-cantly different (p , 0.01 for any two different depths).There are no significant differences using different pushaperture sizes for measurements (p . 0.05).

Shear wave speeds measured by the L7-4 transducerat different depths and with different transmit aperturesize are shown in Figure 3. Shear wave speeds weremeasured using a lateral range of 0�18.48 mm fromthe push beam focus. Shear wave speeds measured withdifferent aperture sizes are significantly different (p ,0.01 for any two different aperture sizes). Results aremixed for different focal depths: some are significant

Table 2. p values of paired t-test for depth

25 mm 30 mm 35 mm 40 mm

20 mm 0.39 ,0.01 ,0.01 ,0.0125 mm ,0.01 ,0.01 ,0.0130 mm ,0.01 0.0635 mm 0.83

Nonsignificant values are shown in bold.

1888 Ultrasound in Medicine and Biology Volume 37, Number 11, 2011

and some are not. The p values of paired t-test for depthare shown in Table 2.

Shear wave speeds measured by the C4-2 transducerusing two different lateral ranges (0�7.7 mm and7.7�15.4 mm) from the push beam are shown inFigure 4. Measurement differences due to different lateralranges are statistically significant (p, 0.01). Shear wavespeeds measured by the L7-4 transducer using twodifferent lateral ranges (0�9.24 mm and 9.24�18.48mm) from the push beam are shown in Figure 5. Measure-ment differences due to different lateral ranges are alsostatistically significant (p , 0.01) for this transducer.

Fig. 5. Shear wave speed measured by L7-4 using two differentlateral ranges (near: 0�9.24 mm, far: 9.24�18.48 mm) from thepush beam in phantom 1 (a), phantom 2 (b) and phantom 3 (c).At each measurement depth, three different aperture sizes (32,64 and 96 elements) were used for push beam transmission.

Transducer intensity field measurementsThe measured intensity fields of the C4-2 focused at

30 and 50 mm in depth are shown in Figure 6. Two-dimensional images of the intensity field are presented

Fig. 4. Shear wave speed measured by C4-2 using two differentlateral ranges (near: 0�7.7 mm, far: 7.7�15.4 mm) from thepush beam in phantom 1 (a), phantom 2 (b) and phantom 3(c). At each measurement depth, three different aperture sizes(32, 64 and 96 elements) were used for push beam transmission.

here for the mid-elevational plane (x-z plane) and mid-lateral plane (y-z plane). When the transducer is focusedat 30 mm, focusing in the lateral direction is good.However, there are two split peaks in the elevationaldirection of the transducer, which can be seen clearly inthe y-z plane scan. Computer simulation with Field II(Jensen and Svendsen 1992) confirms the presence ofthe split peaks but these simulation results are not shownhere for the sake of succinctness. The C4-2 has a fixed el-evational focus at about 70 mm in depth. Focusing theC4-2 too close to the transducer surface may cause unde-sired features in the elevational direction such as the splitpeaks at 30 mm focal depth. Note that these measure-ments were made with relatively long transmission tone-bursts required in SWEI measurements. Focusing inelevational direction is better for short transmissionpulses used for imaging. The split peaks produce shearwaves that travel out-of-plane to the shear wave detectionplane (x-z plane in Fig. 6). Implications of split peaks inshear wave speed measurements will be discussed inthe next section. Referring to Figure 6b, focusing is betterin both lateral and elevational direction when the C4-2 isfocused at 50 mm in depth.

The measured intensity fields of the L7-4 focusing at20 and 30 mm in depth are shown in Figure 7. Two-dimensional images of the intensity field are presented

Fig. 6. Normalized intensity field of the C4-2 measured exper-imentally in the mid-elevational plane (x-z plane) and mid-lateral plane (y-z plane) when the transducer was focused at

30 mm (a) or 50 mm (b).

Fig. 7. Normalized intensity field of the L7-4 measured exper-imentally in the mid-elevational plane (x-z plane) and mid-lateral plane (y-z plane) when the transducer was focused at

20 mm (a) or 30 mm (b).

Bias observed in time-of-flight shear wave speed measurements d H. ZHAO et al. 1889

here for the mid-elevational plane (x-z plane) and mid-lateral plane (y-z plane). Focusing is good in both lateraland elevational directions. The L7-4 has a fixed eleva-tional focus at about 25 mm in depth.

DISCUSSION

Data in this study show that shear wave speedsproduced with radiation force of a focused ultrasoundbeam and time-of-flight can be transducer dependent,depth dependent and lateral range dependent. It wasfound that shear wave speed measured by the C4-2 trans-ducer increased when measurements were made closer tothe transducer surface. This finding is consistent withresults reported by D’Onofrio et al. (D’Onofrio et al.

2010), where ARFI with a different curvilinear trans-ducer was used to measure liver shear wave speed in 20healthy volunteers. They reported that the mean shearwave speed was 1.56 m/s in deep portion vs. 1.90 m/sin shallow portion of the right lobe. Another study inhealthy volunteers reported similar findings (Kaminumaet al. 2011). However, this difference was thought to bedue to inherent liver ‘‘stiffness’’ variation or compressionfrom transducer or cardiovascular system. Results fromthis study suggest that this difference might instead bedue to depth dependent measurement bias. Referring toeqn (1), a small bias in shear wave speed can result ina bigger bias in elasticity because the shear modulus isproportional to square of shear wave speed. For example,the shear wave speed measured by the C4-2 in phantom 2was about 1.7 m/s at 30 mm depth and 1.5 m/s at 70 mm

Ele

vati

onal

Source 1

Source 2

ab

d

Transverse direction

Fig. 8. Schematic plot of bias caused by shear wave propa-gating from the split peaks in elevational direction.

1890 Ultrasound in Medicine and Biology Volume 37, Number 11, 2011

depth, giving values of m of 2.3 kPa and 2.9 kPa from eqn(1). Using the cutoff values from a MRE study with 133liver biopsy patients (Huwart et al. 2008), this can leadto a difference between F0 (no fibrosis) and F $ 2 (stage2 fibrosis or higher). Therefore, bias occurring in clini-cally relevant measurement conditions can be largeenough to change diagnosis results and clinical decisionmaking.

One possible cause of depth dependent bias inC4-2 measurements is the undesired intensity field ofthe push beam. The force field F, which is proportionalto the intensity field where the force per unit volume,can be written as F 5 2aI/c where a and c are the ultra-sound attenuation and sound speed of the medium.According to Figure 6a, the push beam generating theradiation force has two peaks with equal distance fromthemid-elevational plane. Figure 8 is a simplified illustra-tion of the force field in the transducer focal plane. Thebroken line rectangular box represents the transducerwith its ultrasound beamdirecting into plane of this figure.The two peaks are represented by source 1 and source 2that are confined within this figure but have longer axialextension out of the figure plane. Shear wave speed is esti-mated from the arrival time along the mid-elevational linerepresented by the solid horizontal line in Figure 8. Attime t1 and t2, the shear wave travels distance a and b tointersect with the horizontal line where shear wave detec-tions aremade. If the real shear wave speed of themediumis c0, then a5 c0t1 and b5 c0t2 (the shear waves fromsource 2 are not shown in Figure 8 for clarity of presenta-tion). However, the apparent shear wave speed bymeasuring the arrival time along the mid-elevationalline is:

~c5d

t22t15

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

a21b222ab cosqp

t22t1$

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

a21b222abp

t22t1

5b2a

t22t15

c0t22c0t1t22t1

5 c0:

(2)

Therefore, the measured shear wave speed is alwaysgreater than the true wave speed. When the C4-2 isfocused deeper, sources 1 and 2 will be closer to themid-elevational plane and the bias will be smaller.Figure 6b shows a single peak in elevational direction

when the transducer is focused at 50 mm in depth.However, a relatively wide beam width in the elevationaldirection can still generate significant out-of-plane shearwaves that introduce bias (though smaller) to speedmeasurements.

The bias in shear wave speed measurement alsodepends on the lateral range used for speed measurement:bias is smaller when the measurement range d in Figure 8is farther away from the sources (smaller q and thereforesmaller ~c). This is consistent with the results in Figure 4.

Figure 6 also shows non-zero intensity before andbeyond the transducer focus, which has an ‘‘X’’ shapein the x-z plane. Therefore, additional shear waves gener-ated from these non-focal regions can propagate to thefocal plane and interfere with the shear wave comingfrom the focal zone. The apparent speed of these addi-tional shear waves will be different from the true shearwave speed if measured along the lateral direction atthe focal plane because the lateral measurement directionis not parallel with the propagation direction of theseadditional shear waves. Different aperture sizes (32, 64and 96 elements) for push beam transmission used inthis study will change the angle of the ‘‘X’’ shape.Figure 2 indicates that different aperture size does notchange shear wave speed measured by the C4-2 signifi-cantly at any given depth. This seems to suggest thatfor the C4-2, bias in shear wave speed measurementmay be influenced more by the push beam shape in they-z plane than that in the x-z plane.

Focusing of the L7-4 is good in both lateral andelevational direction at a focal depth as small as 20 mmand the shear wave speed measured with the L7-4 showslittle dependence with focal depth. Compared with theC4-2, the L7-4 shows more obvious change with differentaperture size. This is not surprising because wider aper-ture size should not change the X beam shape too muchfor the C4-2 (outer elements contribute little to thefocused beam because they are oriented away from thefocus due to the curvature of the transducer). Similar tothe C4-2, the L7-4 consistently shows higher shearwave speed at lateral range close to the push beam.

The potential sources of error discussed above areassociated with time-of-flight based estimators relyingon a priori information about the shear wave propagationdirection from a focused beam. More advanced inversionalgorithms that do not make such assumptions will not beaffected by this source of error. However, it is notuncommon for ultrasound based direct inversion methods(Bercoff et al. 2004a) to assume negligible out-of-planepropagations, the validity of which may require furtherinvestigations.

Other than the push beam shape, dispersion isanother possible reason for the measurement biasesobserved in this study. Equation (1) assumes a pure elastic

0 100 200 300 400-20

-15

-10

-5

0

Frequency (Hz)

Nor

mal

ized

spe

ctra

l res

pons

e (d

B) 30 mm50 mm70 mm

Fig. 9. Power spectra of shear waves (recorded 5 mm awayfrom the push beam) generated by the C4-2 with different focal

depths in phantom 1.

Bias observed in time-of-flight shear wave speed measurements d H. ZHAO et al. 1891

medium. For viscoelastic materials, shear wave speed isdispersive and frequency dependent (Chen et al. 2009).Therefore, if the frequency band of the shear wavechanges with focus depth, aperture size or lateral range,the measured shear wave speed can also change due todispersion caused by material viscosity. Figure 9 showsthe power spectra of shear waves (recorded 5 mm awayfrom the push beam) generated by the C4-2 with differentfocal depths in phantom 1. The spectra are similar to eachother. These results seem to suggest that viscous disper-sion is not the main cause of the depth dependent biasfor C4-2. Note that these experiments were performedin phantoms made with Zerdine� (ComputerizedImaging Reference Systems Inc., Norfolk, VA, USA),which has low viscosity (Havre et al. 2008). Tissue hashigher viscosity and therefore the impact of dispersioneffects requires further investigations.

There are several possible options to correct for theshear wave speed measurement bias. One can use homog-enous phantoms with known viscoelasticity to calibratemeasurements made at different depth and steered angle.The transducer, its aperture size used for the push beamand the lateral range used in shear wave speed measure-ment are usually fixed for a given clinical application.The calibration would only need to cover the viscoelasticrange and measurement locations expected in a particularclinical application. For a curvilinear array, the activeaperture can be translated along the curved surface ofthe transducer to produce push beams at different angleswithout real ‘‘steering’’. Therefore, the correction factorprobably will be insensitive to ‘‘steering angle’’ in thiscase because the push beam shape and frequency contentof the shear wave should not change significantly fordifferent push beam angles. The shear wave speed wasmeasured in phantom 2 using five different push beamangles (0�, 4.7�, 9.5�, 14.2� and 18.9�) when focusing

at 30 mm with the C4-2. Variation of shear wave speedmeasurements among these five angles were less than0.06 m/s (data not shown). A calibration table can begenerated and used to correct for measurements in realtissues. Interpolation may be needed to increase the‘‘resolution’’ of such a calibration table.

Another correction option is through simulation.The intensity field of the push beam can be calculatedand used to compute the force field of the push beam.Shear waves generated by the push beam can be simu-lated with finite element method (Palmeri et al. 2005)or Green’s function (Bercoff et al. 2004b). Measurementbias along the lateral direction at the focal depth can thenbe estimated from these simulations and used to correctreal tissue measurements. A correction table similar tothe phantom calibration approach can be generated bythe simulation method. The 3-D beam shape for pulse-echo detection can also introduce averaging to shearwave motion detection (Palmeri et al. 2006) and, there-fore, should also be accounted for in the simulationcorrection approach.

This study has some limitations. First, the possiblereasons for these observed biases in shear wave speedmeasurement are hypothetical and not confirmed. Thisstudy is intended as a ‘‘case report’’ to alert investigatorsin this field of a potential problem in these measurements.Further investigations are required to understand andconfirm the mechanism causing this phenomenon. Thesimulation approach outlined abovemay provide valuableinsights into this investigation. Second, the MRE and 1-DTE utilized different excitation sources, shear wavefrequencies, reconstruction algorithms and regions-of-interest that introduce additional unknowns for thecomparison with shear wave speed measured by time-of-flight with radiation force, making them not idealcontrol experiments. Third, shear wave detection in thisstudy used flash imaging, which is different from thetypical focused ‘‘beam’’ detection in other methods suchas ARFI. Therefore, results in this study may be differentfrom other methods where beam detection is used. SNRof echoes from flash imaging may not be as high as thatfrom the focused beam detection schemes. Displacementtracking errors associated with scatterer shearing withinthe tracking point spread function (Palmeri et al. 2006)is also different for flash imaging. However, shear wavesdetected by flash imaging matched simulation by Green’sfunction very well in viscoelastic phantom studies, sug-gesting that flash imaging can provide reliable trackingof shear waves (Bercoff et al. 2004b).

CONCLUSION

It is shown with a systematic phantom study thattime-of-flight shear wave speed measurements using

1892 Ultrasound in Medicine and Biology Volume 37, Number 11, 2011

radiation force produced by a focused ultrasound beamcan be dependent on transducer geometry, focusing depthand lateral tracking range used. Measurement bias can belarge in terms of clinical relevance and, therefore, requirecareful monitoring or correction.

Acknowledgments—This workwas supported byNIH grantsDK082408,EB02640 and EB001981. The authors thank Dr. Richard Ehman forhis support of MRE measurements on phantoms used in this study.

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