IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 66, NO. 5, MAY 2019 867

System-Independent Ultrasound AttenuationCoefficient Estimation Using

Spectra NormalizationPing Gong , Pengfei Song, Member, IEEE, Chengwu Huang , Joshua Trzasko, Senior Member, IEEE,

and Shigao Chen , Member, IEEE

Abstract— Ultrasound attenuation coefficient estimation (ACE)has diagnostic potential for clinical applications such as differ-entiating tumors and quantifying fat content in the liver. Thetwo commonly used ACE methods in the ultrasound arrayimaging system are the spectral shift method and the reference-phantom-based methods. The spectra shift method estimates thecentral frequency downshift along depth, whereas the reference-phantom-based methods use a well-calibrated phantom to cancelsystem dependent effects in attenuation estimation. In this study,we propose a novel system-independent ACE technique basedon spectra normalization of different frequencies. This techniquedoes not require a reference phantom for normalization. Thepower of each frequency component is normalized by thepower of an adjacent frequency component in the spectrumto cancel system-dependent effects, such as focusing and timegain compensation (TGC). This method is referred to as thereference frequency method (RFM), and its performance hasbeen evaluated in phantoms and in vivo liver studies. TheRFM technique can be applied to various transducer geometries(e.g., linear or curved arrays) with different beam patterns(e.g., focused or unfocused).

Index Terms— Frequency power spectra decay, least squaresmethod (LSM), system independent, ultrasound attenuation coef-ficient estimation (ACE).

I. INTRODUCTION

ULTRASOUND attenuation coefficient estimation (ACE)has diagnostic potential for many clinical applications

such as differentiating tumors and quantifying fat content inthe liver [1]–[5]. One example is for breast tissue classification.It was reported that fibrosis has higher acoustic attenuationthan normal tissue, which provides the clinical potentialfor breast cancer diagnosis [6]. Another example of ACEapplications is fatty liver quantification. The accumulation offatty droplets in the liver can lead to steatosis, which mayprogress to fibrosis, cirrhosis, liver failure, or hepatocellularcarcinoma [7]. Therefore, the measurement of fat contentin the liver has high clinical significance to avoid progres-sion of steatosis to fibrosis or worse conditions. Previous

Manuscript received December 31, 2018; accepted March 1, 2019. Date ofpublication March 5, 2019; date of current version April 24, 2019. This workwas supported in part by the National Institute of Diabetes and Digestive andKidney Diseases, National Institutes of Health under Award R01DK106957.(Corresponding author: Shigao Chen.)

The authors are with the Department of Radiology, Mayo Clinic College ofMedicine, Rochester, MN 55905 USA (e-mail: chen.shigao@mayo.edu).

Digital Object Identifier 10.1109/TUFFC.2019.2903010

studies have reported that elevated fat content in the liveris associated with increased ultrasound attenuation [2]–[5].Therefore, by measuring ultrasound ACE, one can potentiallyquantify liver fat [2]–[5], [8]. Compared with the clinical goldstandard, liver biopsy, ACE is a noninvasive measurement,which is more suitable for frequent follow-up exams [9].Hence, accurate ACE in the liver has clinical promises infatty liver detection and assessment. In addition, accurate ACEis the prerequisite for measuring other acoustic parameters,such as the backscatter coefficient [10], [11], effective scattererdiameter, and effective acoustic concentration [12]. Therefore,robust ACE is important for many other ultrasound clinicalapplications.

At present, the two commonly used ACE methods inultrasound array imaging systems are the spectral shiftmethod [13]–[15] and the reference phantom-based meth-ods [10], [16]–[21], with many efforts on improving themethods’ stability [22]–[25]. The spectral shift method esti-mates the attenuation coefficient through the downshift of theultrasound center frequency with increasing depth [21]. Forthe reference phantom-based methods, such as the spectradifference method [10], [17], [18], spectra log differencemethod [19], [20], and the hybrid method [21], [25], a well-calibrated phantom is used to normalize system-dependenteffects such as focusing, diffraction, and time gain compensa-tion (TGC). However, in practice, a well-calibrated phantom isnot always available and its ultrasound properties may changeover time [12].

Herein, we propose a new ACE method: the referencefrequency method (RFM). RFM does not require a well-calibrated reference phantom. System-dependent effects canbe canceled out by spectral normalization using adjacentultrasound frequency components, which allows RFM to beimplemented with various transducer geometries (e.g., lin-ear or curved arrays) and beam patterns (e.g., focused orunfocused).

This paper is organized as follows. Section II introducesbackscattered ultrasound signal modeling and derives the the-oretical basis for RFM. Experimental configurations are alsodescribed, including those used in the phantom and in vivoliver studies. Section III describes the results acquired in thephantom and in vivo liver studies and demonstrates the RFMperformance. Section IV discusses the advantages and futuredirections of RFM. Section V presents the conclusion.

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868 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 66, NO. 5, MAY 2019

II. METHODS

A. Backscattered Ultrasound Signal Modeling

In ultrasound imaging, the power spectrum of the backscat-tered radio frequency (RF) signals S( fi , zk) is a function ofbackscatter location and the frequency of ultrasound, whichcan be modeled as [10], [26]

S( fi , zk) = G( fi ) · TGC(zk) · D( fi , zk) · BSC( fi ) · A( fi , zk)

(1)

where G( fi ) accounts for the transmit and receive transducerresponses at frequency fi (i is the frequency componentindex); TGC(zk) is the time gain compensation (TGC), whichvaries as a function of depth zk (k is the depth index);D( fi , zk) is the combined effects of focusing, beamforming,and diffraction; BSC( fi ) is the backscatter coefficient whichis assumed to be uniform in the local region of interest (ROI);and A( fi , zk) is the frequency-dependent attenuation definedas [10], [26]

A( fi , zk) = exp(−4a fi zk) (2)

where a is the frequency-dependent ultrasound attenuationcoefficient. A( fi , zk) is also assumed to be uniform in the ROIand has linear frequency dependence. This model generallyfits ultrasound systems with different beam patterns (e.g.,focused or unfocused) [10], [26].

B. Linear Decay of Frequency Power Ratio

To estimate the attenuation coefficient a, certain multiplica-tive terms shown in (1) need to be canceled first. This canbe accomplished by regarding the adjacent frequency in thepower spectrum fi−1 as the reference frequency and calculat-ing the power ratio (Rs( fi , zk)) between adjacent frequencycomponents S( fi , zk) and S( fi−1, zk) as

Rs( fi , zk)

= S( fi , zk)

S( fi−1, zk)

= G( fi ) · TGC(zk) · D( fi , zk) · BSC( fi ) · A( fi , zk)

G( fi−1)·TGC(zk)·D( fi−1, zk)·BSC( fi−1)· A( fi−1, zk).

(3)

We assume that the differences of beamforming and diffrac-tion effects between fi and fi−1 (i.e., two adjacent frequencycomponents) are negligible in the imaging regions where beampatterns change slowly, such as in-plane wave imaging or inthe post-focal zone of focused beam imaging. We then obtainthe following relationship:

D( fi , zk) = D( fi−1, zk). (4)

In addition, TGC(zk) is assumed to be independent of fi .Hence, these two terms (i.e., D and TGC) can be canceled afterdetermining the ratio as in (3), and we obtain the followingrelationship:

Rs( fi , zk) = G( fi ) · BSC( fi ) · A( fi , zk)

G( fi−1) · BSC( fi−1) · A( fi−1, zk). (5)

(a)

(b)

Fig. 1. (a) Frequency power after natural logarithm conversion (i.e., ln[S( fi ,zk)]) as a function of depth at three example frequencies (i.e., fi =5, 6, and 7 MHz). (b) Frequency power ratio after natural logarithm conversion(i.e., ln[RS ( fi , zk )], � f = fi − fi−1 = 0.06 MHz) as a function of depthcalculated with the same frequency components and their adjacent frequencies.The frequency power ratio decay curves for 6 and 7 MHz were shifted upwardby 2 and 4 dB/MHz, respectively, for better visualization. The linear fittingsfor each frequency are shown by the red dashed lines with the attenuationcoefficient values shown in the left upper corner of (b). The data were acquiredfrom a Fibroscan-calibrated tissue-mimicking phantom (0.68 dB/cm/MHz).The phantom was imaged with unfocused plane wave imaging at 5 MHzcenter frequency using a Verasonics Vantage system.

After taking the natural logarithm on both sides of (5),we obtain the following linear relationship between frequencypower ratio (ln[Rs( fi , zk)]) and imaging depth (zk):

ln[Rs( fi , zk)]= ln[G( fi )] − ln[G( fi−1)]

+ ln[BSC( fi )] − ln[BSC( fi−1)]− 4a( fi − fi−1)zk . (6)

Equation (6) shows that the frequency power ratio(ln[Rs( fi , zk)]) decays with increasing depth (zk) at a linearrate of [−4a( fi − fi−1)]. Therefore, the attenuation coefficientcan be estimated from the slope of the decay curve withrespect to each frequency component. The term {ln[G( fi )] −ln[G( fi−1)] + ln[BSC( fi )] − ln[BSC( fi−1)]} is the interceptof the decay curve (independent of zk) which does notaffect the slope of the curve (i.e., attenuation coefficient).Fig. 1(a) shows the frequency power after natural logarithm

GONG et al.: SYSTEM-INDEPENDENT ULTRASOUND ACE 869

calculation (i.e., ln[S( fi , zk)]) as a function of depth withthree example frequency components ( fi = 5, 6, and 7 MHz)in a calibrated tissue-mimicking phantom (Fibroscan-calibrated value: 0.68 dB/cm/MHz). Fig. 1(b) shows thefrequency power ratio after natural logarithm conversion(i.e., ln[Rs( fi , zk)]) as a function of depth calculated at thesame frequency components with their adjacent frequencies( fi = 5, 6, and 7 MHz, and � f = fi − fi−1 = 0.06 MHz).In Fig. 1(b), the frequency curves decay with similar linearslopes for different frequencies at zk ≤ 4 cm. However, the6-MHz frequency curve starts to deviate from the linear decaytrend at a depth of approximately 6 cm, and the 7-MHzfrequency curve starts at approximately 4 cm. The deviationis caused by the higher ultrasound attenuation experiencedby the higher frequency signals, which results in significantlylowered signal-to-noise-ratio (SNR) and, consequently, falselyelevated frequency power ratio. The higher the ultrasoundfrequency, the shallower the depth that the deviation wouldstart to occur. The falsely elevated decay curve may lead tounderestimation of the attenuation coefficient and limit thepenetration of the method. In practice, the assumption ofuniform tissue acoustic attenuation may be violated by nonuni-form tissue structures, which leads to significant oscillationsof the frequency power ratio decay curves. In such cases,directly fitting a linear slope to the frequency power ratiodecay curve at each frequency and averaging the results maybe suboptimal for obtaining robust attenuation measurement.Therefore, here we adopted the least squares method (LSM)to mitigate these issues (i.e., noise and oscillations on thedecay curve) and improve the estimation accuracy. In LSM,the power spectra ratio after natural logarithm calculation(i.e., ln[Rs( fi , zk)]) at all frequencies can be fit to a one-parameter model [27]. The model can automatically searchfor the best solution to minimize estimation errors over allfrequencies.

C. Attenuation Coefficient Estimation With theLeast Squares Method

After calculating the spectra ratio (5), two unknown termsremain in the expression: the transducer frequency response[G( fi )] and backscatter coefficient [BSC( fi )]. To completeACE with the LSM model, these two terms need to becanceled. Cancelation can be accomplished by normalizing thefrequency power ratio [Rs( fi , zk)] using the value obtainedat a reference depth, zr [i.e., Rs( fi , zr ), r is the referencedepth index]. Afterward, both G( fi ) and BSC( fi ) in (5) can becanceled because of depth independency. Estimations obtainedusing different zr values can be averaged to reduce errorsdue to electric noise (as shown in Fig. 1) [28], oscillationsdue to small nonuniform structures in the tissue, and spatialvariation noise due to constructive and destructive interfer-ences from the backscattered signals [29]. Uncorrelated zr

values with at least one-pulselength interval are preferred foreffective averaging. The normalization step can be describedas

Rsnor( fi , zk , zr ) = Rs( fi , zk)

Rs( fi , zr )= A( fi , zk)

A( fi , zr )

A( fi−1, zr )

A( fi−1, zk). (7)

Taking the natural logarithm on both sides of (7), we obtainthe following linear relationship of the LSM model:

ln[Rsnor( fi , zk, zr )]= −4a fi zk + 4a fi zr − 4a fi−1zr + 4a fi−1zk

= −4a( fi − fi−1)(zk − zr ) (8)

when zk �= zr .There is only one unknown variable, a, that needs to be

solved in the LSM model

[�a] = arg min

a

R∑

r=1

K∑

k=1

I∑

i=1

{ln[Rsnor( fi , zk , zr )]

+ 4a( fi − fi−1)(zk − zr )}2 (9)

when zk �= zr .R is the total number of reference depths used in the LSM

fitting.

D. Defining Constraints for LSM

To further stabilize the estimates determined using LSM,constraints can be added to the model

amin ≤ a ≤ amax. (10)

Then the solution of the LSM in (9) subject to the above-mentioned bound constraints can be solved via proximal gradi-ent iteration [30]. The maximum and minimum constraints canbe determined in an adaptive way according to the acquireddata. Because one measurement of the frequency power ratio,ln[Rsnor( fi , zk , zr )], can generate one estimation of a, we canfirst calculate all possible a values using all measurements asfollows:

ai,k,r = ln[Rsnor( fi , zk , zr )]−4( fi − fi−1)(zk − zr )

. (11)

One attenuation value ai,k,r can be generated from eachfrequency component fi at each depth zk using each refer-ence depth zr . The distribution of all estimated attenuationvalues can then be obtained by estimating the histogramof ai,k,r . Fig. 2 shows a histogram example obtained froma Fibroscan-calibrated tissue-mimicking phantom (calibratedvalue: 0.68 dB/cm/MHz). The histogram presented a relativelywide range of attenuation distribution. This is caused bythe oscillations of the frequency power ratio decay curves[Fig. 1(b)] due to noise and the constructive and destructiveinterferences from the backscattered signals [29]. In addition,when zk gets close to zr , it is equivalent to using a small-sized ROI for attenuation estimation. The estimation accuracywith small-sized ROI would be lowered and errors couldoccur (e.g., negative estimations in Fig. 2) [23]. An extremecondition is when zk = zr , which makes the denominatorof (11) zero. Consequently, constraints would be necessary forLSM to stabilize the attenuation estimation. In the exampleof Fig. 2, the bin width of the histogram was set to be0.1 dB/cm/MHz. The cutoff limits were selected at 75% ofthe most frequent value (the cutoff limits were empiricallydetermined and indicated by the red dashed line) on both sides.Then, we calculate the constraints in this example as

amin = 0.5 ≤ a(dB/cm/MHz) ≤ amax = 0.9. (12)

870 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 66, NO. 5, MAY 2019

Fig. 2. Histogram of all estimated attenuation without any constraints (ai,k,r ).The data were acquired from a Fibroscan-calibrated tissue-mimicking phantomwith calibrated value of 0.68 dB/cm/MHz. The phantom was imaged withunfocused plane wave imaging at 5 MHz center frequency using a Vantagesystem. fi range: 4–6 MHz, � f = fi − fi−1 = 0.06 MHz, a total numberof 34 fi was used; zk range: 3 cm, �zk = zk − zk−1 = 0.0055 cm, a totalnumber of 550 zk was used; zr range: 3 cm, �zr = zr − zr−1 = 0.1 cm,a total number of 30 zr was used; a total number of 34×550×30 = 5.6×105

attenuation values were estimated.

E. Experimental Configurations

1) Through-Transmission Calibration: The proposed RFMwas first validated using the through-transmission (T–T) cali-bration method [31]. A tissue-mimicking phantom was fabri-cated following the procedure as described in [31] (cylinderphantom, diameter: 5 cm, height: 4 cm). A 50%–50% evapo-rated milk-to-water ratio was tested in the study using a pairof identical unfocused single-element transducers (Olympus,Center Valley, PA, USA), transmitted at a 5-MHz centerfrequency.

RFM was then applied to estimate the attenuation coefficientof the fabricated tissue-mimicking phantom. The estimatedvalue was then compared with the T–T calibrated value. RFMdata were acquired using unfocused plane wave compoundingwith a Verasonics Vantage system (Verasonics Inc., Kirkland,WA, USA), equipped with a linear array transducer L11-4v(4.5–10.5 MHz, Verasonics Inc., Kirkland, WA, USA). Forcompounding plane wave imaging, 16 compounding angleswere selected, which ranged from −15◦ to +15◦ at 2◦ interval.The pulse repetition frequency (PRF) was 4 kHz, leading toa 250-Hz postcompounding PRF. The center frequency of thetransmit pulse was 5 MHz.

We then selected an ROI on the beamformed IQ image.The ROI was set from 1 to 3.5 cm, both laterally and axially(i.e., size of 2.5 cm × 2.5 cm). Then, the selected ROIwas divided into ten wavelength long data blocks along theaxial direction (i.e., size of 0.3 cm × 2.5 cm). The axialoverlap between data blocks were around 98%. Each A-linesegment (i.e., 0.3 cm long) in a given data block was first zero-padded to calculate sufficiently close fi and fi−1 values in thespectrum (� f = fi − fi−1 = 0.06 MHz in Fig. 1). Then, the

Welch technique [32] was applied to the zero-padded A-linesegment (0.3 cm long) to obtain a single power spectrum.The power spectra of all A-line segments in the given datablock were averaged laterally to obtain the mean powerspectrum at a certain depth (zk), which is denoted as S( f, zk).A total number of 450 mean power spectra were obtainedin a 2.5-cm-long ROI with 98% axial overlap between datablocks (�zk = zk − zk−1 = 0.0055 cm). The frequency powerratio between adjacent frequencies was calculated using (3).Then, the normalization step, as shown in (7), was applied bydividing the power ratio [Rs( fi , zk)] by the ratio acquired atthe reference depth zr [Rs( fi , zr )]. Multiple zr values wereselected from the top to the bottom of the ROI along theaxial direction at 1-mm intervals, resulting in 25 differentzr in a 25-mm-long ROI. The frequency range ( fi ) usedfor ACE was 4–6 MHz. The normalized power spectra ratio[Rsnor( fi , zk , zr )] at all fi , zk , and zr values were then passedto the LSM model for the final ACE shown in (9).

2) System Independency Phantom Study: The proposedRFM was also tested on two tissue-mimicking phantomscalibrated using Fibroscan 502 Touch system (Echosens, Paris,France), whose accuracy was validated in simulation, tissue-mimicking phantoms, and in vivo livers as in [5]. Fibroscanacquisitions were performed using the M-probe (3.5 MHz)following regular acquisition procedures [33]. The mediancontrolled attenuation parameters (CAP) measured from thetwo phantoms were: Phantom 1 (cuboid shape, surface area:6.5 cm × 18 cm, depth: 18 cm): 0.68 dB/cm/MHz (CAP =238 dB/m), and Phantom 2 (cuboid shape, surface area:6.5 cm × 18 cm, depth: 18 cm): 0.95 dB/cm/MHz (CAP =332 dB/m), respectively, from ten repeated valid measure-ments (interquartile range/median < 20%). To demonstratethat RFM is system independent, in addition to the Van-tage system tests, both phantoms were also imaged with aGeneral Electric LOGIQ E9 (LE9) system (General ElectricHealthcare, Wauwatosa, WI, USA) with conventional line-by-line focused beam scanning and a linear array transducer9L-D (2–8 MHz, General Electric Healthcare, Wauwatosa, WI,USA). For the LE9 focused-beam imaging, 176 A-lines werebeamformed with focal depth of 2.5 cm ( f -number = 5).The imaging frame rate was 25 Hz. The center frequencyof the transmit pulse was 5 MHz. Five repeated acquisitionswere conducted on each phantom using each imaging system(Vantage-unfocused or LE9-focused).

For post-IQ processing, the lateral size of the ROI was2.5 cm wide and was positioned around the center of theimage. Axially, the ROI was selected from 3- to 6-cm-depthrange to coincide with the postfocal zone of the focusedbeams using the LE9 system. This is because the focus beampattern varies slowly in the postfocal zone, which reducesthe diffraction differences between adjacent frequency com-ponents as assumed in (4). The frequency range used for ACEwas 4–6 MHz. The rest of the IQ data postprocessing stepsare the same as those in T–T calibration. In addition, thedetailed focusing effect on ACE was analyzed as functionsof different depth ranges selected for ACE and differentf -numbers during focused beam transmissions. The f -numbertesting was accomplished with the Vantage system and L11-4v

GONG et al.: SYSTEM-INDEPENDENT ULTRASOUND ACE 871

probe since the f -number can be flexibly adjusted in Vantagerather than LE9. The focus was set at 2.5 cm with ROI rangedfrom 3 to 6 cm axially. All other parameters were the sameas for Vantage-plane wave imaging configurations.

3) In Vivo Liver Attenuation Coefficient Estimation: Theproposed method was also tested on five patients goingthrough clinically indicated magnetic resonance imaging(MRI) of liver (all males; age: 53 ± 17 years; body massindices: 29 ± 3.9 kg/m2). The study was approved by Insti-tutional Review Board (IRB) of Mayo Clinic. A writteninformed consent was obtained at the time of enrolment fromeach participant. All patients underwent overnight fasting.Proton density fat fraction (PDFF) acquired with MRI wasused as reference standard. PDFF is a standardized and objec-tive measure of mobile proton density proportion attributableto fat in the liver which has been shown to have highmeasurement accuracy in phantoms, human liver samples, andanimal and human studies [34]. Thus, PDFF is consideredas a reliable quantification metric of liver fat content andwas often used as reference standard in literatures [35], [36].The elevated fat content in the liver is also associated withincreased ultrasound attenuation [2]–[5]. Therefore, the cor-relation between PDFF and ACE values was calculated toevaluate the performance of proposed ACE method. The PDFFwas measured with MRI scanner GE Optima 450 (GeneralElectric Healthcare, Wauwatosa, WI, USA) using IDEALIQ sequence. The in vivo liver ACE was performed usingunfocused plane wave compounding mode on the VerasonicsVantage system. The unfocused mode could avoid the focusingeffects on ACE and ensure a more flexible ROI selection range.The focusing effects on the ACE accuracy will be shown inSection III-B. The Vantage system was equipped with a curvedarray transducer C1-6D (1–6 MHz, General Electric Health-care, Wauwatosa, WI, USA). The transmit center frequencywas 3.5 MHz. Other parameter settings were identical to theones used in the phantom studies (Section II-E2).

For the in vivo liver study, an ROI with sizes of 3.5 cm ×4.5 cm laterally and axially, respectively, was selected aroundthe most uniform area in the liver B-mode images. Largevascular structures were avoided in the ROI selection [2]. Thefrequency band used for ACE was 3.0–4.0 MHz.

III. RESULTS

A. Through-Transmission Phantom Measurements

The estimated attenuation coefficient values determinedusing the fabricated tissue-mimicking phantom with T–T cal-ibration and the proposed RFM were 0.443 ± 0.032 and0.457±0.025 dB/cm/MHz, respectively. No significant differ-ence ( p = 0.602) between these two groups of measurementswas detected using two-tailed t-test, with a significance levelof 5%. The T–T calibration validates the accuracy of RFM.

B. System Independency Phantom Study

Fig. 3 shows the frequency power spectra ratio decaycurves after natural logarithm calculation using Phantom1 (0.68 dB/cm/MHz calibrated attenuation coefficient) with

Fig. 3. Frequency power ratio decay curves after natural logarithm(i.e., ln[RS ( fi , zk)]) as a function of depth acquired from a Fibroscan-calibrated phantom (0.68 dB/cm/MHz). The curves were acquired at 4, 5, and6 MHz using Vantage-unfocused (central frequency: 5 MHz) and LE9-focused(central frequency: 5 MHz) systems, respectively. The frequency power ratiodecay curves for 5 and 6 MHz were shifted upward by 2 and 4 dB/MHz,respectively, for better visualization.

TABLE I

ACE OF PHANTOM 1 (dB/cm/MHz)

TABLE II

ACE OF PHANTOM 2 (dB/cm/MHz)

both Vantage and LE9 systems. Three sample frequen-cies are shown: 4, 5, and 6 MHz. The decay curvesobtained using different ultrasound systems and transmis-sion modes are in good agreement at these three examplefrequencies.

Tables I and II show the ACE values for the two Fibroscan-calibrated phantoms determined using Vantage and LE9systems, respectively. The ACE values with and withoutconstraints are both shown, which were consistent from both

872 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 66, NO. 5, MAY 2019

Fig. 4. Bar plots of mean ACE values acquired from two Fibroscan-calibrated phantoms using Vantage and LE9 imaging systems. Error bars:standard deviation from five repeated measurements.

imaging systems. The values also agreed well with Fibroscancalibrations. The ACE values estimated without constraintsshowed slightly higher standard deviation than those esti-mated with constraints, demonstrating the effectiveness ofthe constraints. Fig. 4 shows the bar plots of ACE withconstraints on the two phantoms using the two imagingsystems. No significant difference between these two groupsof measurements was detected using two-tailed t-test, with asignificance level of 5%. This phantom study demonstratedthe system independency of RFM—accurate ACE values canbe obtained with different imaging configurations.

The RFM was based on the assumption that the differencesof diffraction effects between two adjacent frequency com-ponents are negligible in the imaging regions where beampatterns change slowly as shown in (4). This assumption holdstrue in plane wave imaging and in the postfocal zone offocused beam imaging (with f -number = 5) as shown inphantom tests. For a more thorough investigation, the focusingeffect of the proposed method was then studied for variousdepth ranges and f -numbers.

Fig. 5(a) shows the axial beam profiles simulated inField II [37], [38] following the same transducer geometriesand the imaging conditions as in phantom studies. Fig. 5(b)shows attenuation values measured from Phantom 1 withdifferent depth ranges selected for ACE using both imagingsystems. For Vantage-unfocused system, the beam patternchanges slowly after 1 cm depth. The assumption in (4) isvalid and accurate attenuation estimations were obtained for alarge imaging region (i.e., 1–7 cm). However, for LE9-focusedsystem, the beam pattern changes more rapidly in the focalzone as compared to postfocal zone. When the ROI coincideswith the beam focal zone (i.e., 1–4 cm, focusing at 2.5 cm),the focusing effect could not be completely canceled by cal-culating the power ratio between adjacent frequencies, leadingto underestimation of the attenuation value. In deeper depthregion (i.e., 4–7 cm), the drop of attenuation value was dueto the low SNR and the resulting falsely elevated frequencypower ratio at higher frequency components (e.g., 6 MHzacquired with LE9 as shown in Fig. 3). Despite these, accurateattenuations could be obtained in the postfocal zones withadequate SNR (i.e., 2–5 cm and 3–6 cm).

(a)

(b)

Fig. 5. (a) Field II-Simulated axial beam profiles following the LE9 andVantage imaging configurations. (b) Focusing effect on different rangesof depths used for attenuation estimation. The data were acquired froma Fibroscan-calibrated tissue-mimicking phantom with calibrated value of0.68 dB/cm/MHz. The error bars show the standard deviation from fiverepeated measurements.

Fig. 6. Focusing effect with different f -numbers. The data were acquiredfrom a Fibroscan-calibrated tissue-mimicking phantom with calibrated valueof 0.68 dB/cm/MHz. The phantom was imaged with focused beam imagingat 5-MHz center frequency using a Verasonics Vantage system. Focus: 2.5 cmdepth. Depth range for ACE: 3–6 cm. Error bars: standard deviation from fiverepeated measurements.

Fig. 6 shows the ACE values measured from focusedbeam imaging with different f -numbers using Vantage system.When the beams are tightly focused (e.g., f -number = 3),the ACE value was overestimated in the postfocal zone. This isbecause the beam energy diverged fast in this region. The rapiddecrease of the backscattered signal intensity led to an illusionof higher attenuation. When f -number was 4 or higher, validmeasurements could be achieved in focused-beam imaging(less than 10% error as compared to calibrated value).

C. In Vivo Liver Attenuation Coefficient Estimation

Fig. 7 shows the mean ACE values estimated on eachpatient from three repeated measurements. The ACE estima-tions show good correlation with PDFF values (coefficient ofdetermination, R2 = 0.93), further demonstrating the feasibil-ity and potential of the method.

GONG et al.: SYSTEM-INDEPENDENT ULTRASOUND ACE 873

Fig. 7. In vivo human liver ACE from five patients and their correlationwith PDF. The mean attenuation values from three repeated estimations areshown for each patient with the histogram-generated constraint values shownin the brackets. Error bars: standard deviation.

IV. DISCUSSION

This paper describes a new system-independent ACE tech-nique, RFM, which uses the power of the adjacent frequencyas the reference to cancel system-dependent effects such asfocusing, TGC, and diffraction. RFM does not require areference phantom and can be applied to different transducergeometries (e.g., linear or curved arrays) and different beampatterns (e.g., plane wave or focused beams).

RFM presented accurate estimations in the T–T calibrationand the Fibroscan-calibrated phantom studies. The combina-tion of the LSM with constraints could effectively suppressvariations of the spectra, leading to more robust and accu-rate ACEs. However, the data-generated constraints requirehistograms of all estimated attenuation values which mayincrease the computation load of the method. In the in vivoliver study, ACE values obtained with RFM showed goodcorrelation with clinically indicated PDFF values, furtherdemonstrating the method’s feasibility. The SNR is an impor-tant factor for robust ACE, especially for deeper imagingregions with higher imaging frequencies (as shown in Fig. 1).Extensive studies have been performed to improve the SNR ofB-mode images, such as using multiple transmit beams [39],coded excitations [40], or multiplane wave imaging [41]–[43].The robustness of the proposed RFM-ACE technique isexpected to be further improved after combination with theseSNR-improving techniques. The noise cancelation strategiesas described in [9] can also be applied to suppress the noiseinfluence on RFM-ACE analysis.

The RFM was based on the assumption that the differ-ences in diffraction effects between two adjacent frequencycomponents are negligible. This assumption was valid whenthe beam patterns changed slowly such as in-plane waveimaging and the postfocal zone of loosely focused beamimaging ( f -number ≥ 4). However, for the regions wherebeam patterns changed rapidly, this assumption was vio-lated and the method could not yield accurate estimations.In addition, performing ACE in the postfocal zone may limitthe penetration of RFM in focused-beam imaging due to

insufficient SNR as compared to focal zone. Beam profilesimulations or measurements may be needed, especially inimaging with tightly focused beams, to cancel the beamdiffraction effects more effectively for ACE.

The in vivo ACE measurements in patients had larger vari-ations (maximum STD/mean = 8.4%) than those in phantomstudies. One possible reason may be because different liversections were imaged in each trial and liver properties mayvary in different acoustic windows. In addition, the in vivoliver ACE was only performed with Vantage-unfocused systemin this study to allow more flexible ROI locations. Futurepatient studies using focused beams will be conducted toinvestigate the performance of the proposed method for in vivoapplication.

In this study, the entire ROI was assumed to have uniformattenuation coefficient. This method offers a robust solutionto estimate mean attenuation coefficient of relatively uniformtissues such as liver. For heterogeneous tissues, however,the estimation accuracy may be compromised because theuniform assumption is violated. In addition, the LSM withconstraints averages out small oscillations of the frequencypower ratio decay curves to stabilize ACEs. Correspondingly,the method may not be sensitive enough to detect localattenuation variations in heterogeneous tissues.

The ROI size is usually a tradeoff between reduced ACEvariance and improved ACE spatial resolutions [29]. TheROI used in the study is relatively large because the nor-malization step of RFM relies on the power spectra ratiodetermined at reference depth zr . Multiple uncorrelated zr

values (i.e., with at least one pulselength interval) are neededto effectively average out spatial variations of ACE mea-surements. Future studies may focus on reducing the ROIsize while retaining the estimation precision needed to applyRFM on heterogeneous tissues. Another limitation of thisstudy is that we did not systematically compare the perfor-mance of the proposed method with those of other ACEmethods (e.g., spectra shift method and reference phantom-based methods) under the same conditions. Future study maybe needed in this area. It would also be interesting to test theaccuracy of different methods as functions of focusing effect,ROI size, SNR level, speed of sound, and phantom selection(homogeneous or inhomogeneous) [23], [44].

In this study, the attenuation frequency dependence wasassumed to be linear [as shown in (2)]

A( fi , zk) = exp( − 4a f na

i zk), where na = 1. (13)

For a more general model, tissue attenuation can be writtenin the nonlinear form as na �= 1. Modifying RFM to adapt tononlinear models will be the subject of future studies.

V. CONCLUSION

In this paper, we proposed an RFM to enable system-independent and reference-phantom-free ACE for biologicaltissues. RFM uses the adjacent frequency components of theultrasound signal to cancel system effects such as focusing andTGC. When combined with LSM, RFM demonstrated accurate

874 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 66, NO. 5, MAY 2019

ACE estimations in phantoms and in vivo livers. The proposedRFM can be potentially applied to various ultrasound imagingsystems with different transducers and imaging configurations.

ACKNOWLEDGMENT

The authors would like to thank R. R. Kinnick for hisvaluable help in performing the phantom study.

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Ping Gong received the B.Sc. degree in biomedicalengineering from Tianjin University, Tianjin, China,in 2010, the M.Sc. degree from the Departmentof Electrical and Computer Engineering, LakeheadUniversity, Thunder Bay, ON, Canada, in 2012,and the Ph.D. degree in biomedical physics fromRyerson University, Toronto, ON, Canada, in 2016.

She is currently with the Department of Radiology,Mayo Clinic College of Medicine, Rochester, MN,USA. Her research focuses on developing ultra-sound transmission and beamforming algorithms to

improve ultrasound image quality.

Pengfei Song (S’09–M’14) was born in Weihai,China, in 1986. He received the B.Eng. degree inbiomedical engineering from the Huazhong Uni-versity of Science and Technology, Wuhan, China,in 2008, the M.S. degree in biological systems engi-neering from the University of Nebraska-Lincoln,Lincoln, NE, USA, in 2010, and the Ph.D. degreein biomedical sciences-biomedical engineering fromthe Mayo Graduate School, Mayo Clinic College ofMedicine, Rochester, MN, USA, in 2014.

He is currently an Assistant Professor with theDepartment of Radiology, Mayo Clinic College of Medicine. His currentresearch interests are ultrasound microvessel imaging and ultrasound shearwave elastography.

Dr. Song is a Member of AIUM and Sigma Xi.

Chengwu Huang was born in China, in 1989.He received the B.S. degree in biomedical engi-neering from Beihang University, Beijing, China,in 2012, and the Ph.D. degree from the Departmentof Biomedical Engineering, Tsinghua University,Beijing, in 2017.

He is currently with the Department of Radiol-ogy, Mayo Clinic College of Medicine, Rochester,MN, USA. His current research interests includeultrasound microvessel imaging and ultrasoundelastography.

Joshua Trzasko (M’99–SM’14) received the B.S.degree in electrical and computer engineering fromCornell University, Ithaca, NY, USA, in 2003,and the Ph.D. degree in biomedical engineeringfrom Mayo Graduate School, Rochester, MN, USA,in 2009.

He is currently an Associate Consultant with theDivision of Medical Physics and an Assistant Pro-fessor of radiology and biomedical engineering withMayo Clinic, Rochester, MN, USA. His researchfocuses on the development and application of sta-

tistical signal processing methods for medical imaging, including quantitativeimaging, artifact correction, and limited data reconstruction in magneticresonance imaging (MRI); radiation dose reduction in X-ray computed tomog-raphy (CT); and ultrasound (US) microvasculature imaging.

Shigao Chen (M’02) received the B.S. and M.S.degrees in biomedical engineering from TsinghuaUniversity, Beijing, China, in 1995 and 1997, respec-tively, and the Ph.D. degree in biomedical imagingfrom the Mayo Graduate School, Rochester, MN,USA, in 2002.

He is currently an Associate Professor with theMayo Clinic College of Medicine, Rochester, MN,USA. His research interests are noninvasive quan-tification of the viscoelastic properties of soft tis-sue using ultrasound and ultrasound microvesselimaging.