Interlaboratory Comparison ofUltrasonic Backscatter CoefficientMeasurements From 2 to 9 MHz

Keith A. Wear, PhD, Timothy A. Stiles, PhD, Gary R. Frank, Ernest L. Madsen, PhD,Francis Cheng, PhD, Ernest J. Feleppa, PhD, Christopher S. Hall, PhD, Beom SooKim, BS, Paul Lee, MS, William D. O’Brien, Jr, PhD, Michael L. Oelze, PhD,Balasundar I. Raju, PhD, K. Kirk Shung, PhD, Thaddeus A. Wilson, PhD, Jian R. Yuan, PhD

Objective. As are the attenuation coefficient and sound speed, the backscattercoefficient is a fundamental ultrasonic property that has been used to character-ize many tissues. Unfortunately, there is currently far less standardization for theultrasonic backscatter measurement than for the other two, as evidenced by aprevious American Institute of Ultrasound in Medicine (AIUM)–sponsored inter-laboratory comparison of ultrasonic backscatter, attenuation, and speed mea-surements (J Ultrasound Med 1999; 18:615–631). To explore reasons for thesedisparities, the AIUM Endowment for Education and Research recently supportedthis second interlaboratory comparison, which extends the upper limit of the fre-quency range from 7 to 9 MHz. Methods. Eleven laboratories were provided withstandard test objects designed and manufactured at the University of Wisconsin(Madison, WI). Each laboratory was asked to perform ultrasonic measurements ofsound speed, attenuation coefficients, and backscatter coefficients. Each labora-tory was blinded to the values of the ultrasonic properties of the test objects atthe time the measurements were performed. Results. Eight of the 11 laborato-ries submitted results. The range of variation of absolute magnitude of backscat-ter coefficient measurements was about 2 orders of magnitude. If the results of1 outlier laboratory are excluded, then the range is reduced to about 1 order ofmagnitude. Agreement regarding frequency dependence of backscatter was bet-ter than reported in the previous interlaboratory comparison. For example, whenscatterers were small compared with the ultrasonic wavelength, experimental fre-quency-dependent backscatter coefficient data obtained by the participating lab-oratories were usually consistent with the expected Rayleigh scattering behavior(proportional to frequency to the fourth power). Conclusions. Greater standard-ization of backscatter measurement methods is needed. Measurements of fre-quency dependence of backscatter are more consistent than measurements ofabsolute magnitude. Key words: backscatter; interlaboratory comparison; tissuecharacterization.

Received September 21, 2004, from the Center forDevices and Radiological Health, US Food and DrugAdministration, Rockville, Maryland USA (K.A.W.);University of Wisconsin, Madison, Wisconsin USA(T.A.S., G.R.F., E.L.M.); Boston Scientific, Fremont,California USA (F.C., J.R.Y.); Philips Research,Briarcliff Manor, New York USA (C.S.H., B.I.R.);Riverside Research Institute, New York, New YorkUSA (E.J.F., P.L.); University of Southern California,Los Angeles, California (B.S.K., K.K.S.); University ofIllinois at Urbana-Champaign, Urbana, Illinois USA(W.D.O., M.L.O.); and University of Tennessee,Memphis, Tennessee USA (T.A.W.). Revision request-ed November 18, 2004. Revised manuscript accept-ed for publication April 19. 2005.

The financial support of the American Instituteof Ultrasound in Medicine’s Endowment forEducation and Research is gratefully acknowl-edged. The mention of commercial products, theirsources, or their use in connection with materialreported herein is not to be construed as either anactual or implied endorsement of such products bythe Food and Drug Administration.

Address correspondence to Keith A. Wear, PhD,Center for Devices and Radiological Health, Foodand Drug Administration, 12720 Twinbrook Pkwy,Rockville, MD 20852 USA.

E-mail: kaw@cdrh.fda.gov

AbbreviationsAIUM, American Institute of Ultrasound in Medicine;MS, megasamples; RF, radio frequency; SNR, signal-to-noise ratio

ttenuation, sound speed, and the backscattercoefficient have been used to characterize manytissues, including blood, heart, eye, liver, kidney,prostate, and bone.1–18 In 1998, the American

Institute of Ultrasound in Medicine (AIUM) sponsored aninterlaboratory comparison of methods for measure-

© 2005 by the American Institute of Ultrasound in Medicine • J Ultrasound Med 2005; 24:1235–1250 • 0278-4297/05/$3.50

A

Article

ment of attenuation, sound speed, and back-scatter.19 Ernest L. Madsen, PhD (University ofWisconsin, Madison, WI), oversaw the design,fabrication, and distribution of phantoms to 10laboratories. Investigators performed measure-ments and submitted their results to ProfessorMadsen. The main conclusion of this effort wasthat there was broad agreement among the 10laboratories regarding attenuation and soundspeed measurements but considerable disparityregarding backscatter coefficient measure-ments.19

There are several factors that may contribute tothe increased variance for backscatter measure-ments. First, attenuation and sound speedmeasurements are usually performed in thethrough-transmission mode. Because of the rela-tively low attenuation coefficients of biologicaltissues and tissue-mimicking media, the acquiredradio frequency (RF) data (from which parameterestimates are derived) generally have a relativelyhigh signal-to-noise ratio (SNR). Backscattercoefficient measurements, on the other hand, areperformed in the pulse-echo mode. Because ofthe weak scattering properties of soft biologicaltissues and speckle noise, the SNR for backscat-tered RF data is comparatively low. A lower SNRcontributes to increased variance of measure-ments. Second, there is a greater variety of mea-surement procedures and algorithms forassessment of the backscatter coefficient20–29 thanfor the attenuation coefficient and sound speed.Third, the mathematical complexity of algo-rithms for computing the backscatter coefficientgenerally exceeds that for the attenuation coeffi-cient and sound speed. Finally, attenuation andsound speed measurement techniques may bethoroughly tested by performing measurementson standard objects (eg, plastics, liquids, and rub-bers) for which the true values are known.References for backscatter coefficients on sucheasily attainable test objects are comparativelyrare (if they exist at all).

To further investigate disparities in backscattercoefficient measurements, the AIUM sponsoreda second interlaboratory comparison study. Theresults of that study are reported herein.

Materials and Methods

PhantomsAs in the previous AIUM-sponsored interlabora-tory comparison project,19 Professor Madsen

oversaw the design, fabrication, and distributionof test phantoms to participating laboratories. Allmaterials were produced at the University ofWisconsin by methods reported previously.30–32

Three batches of phantoms were produced,labeled A, B, and C. Each of the 11 participatinglaboratories received 3 phantoms, 1 from eachbatch. As in the previous interlaboratory com-parison, each laboratory performed backscattermeasurements (usually at multiple frequencies,depending on which transducers they had avail-able) on each of the phantoms in their set.Because it is necessary to know the attenuationcoefficient and sound speed to estimate thebackscatter coefficient, participating laborato-ries measured and reported these parametersalso.

The 3 types of tissue-mimicking materials wereproduced to provide variety in ultrasonic proper-ties while still being representative of soft tissues.The properties of these materials were measuredat the University of Wisconsin. Phantom A, whichmimicked human liver, had an attenuation coef-ficient slope approximately equal to 0.4 dB ⋅ cm–1

⋅ MHz–1. Its frequency (f ) dependence ofbackscatter was about f 2.1 over the frequencyrange of 2.5 to 5 MHz. Phantom B had an attenu-ation coefficient slope approximately equal to 0.7dB ⋅ cm–1 ⋅ MHz–1. Its frequency dependence wasabout f 3.2 over the frequency range of 2.5 to 5MHz. Phantom C included millimeter-scale scat-terers that sometimes occur in soft tissue. Itsattenuation coefficient was in the range of valuesdetermined for in vitro human breast parenchy-ma reported by D’Astous and Foster.33 Itsbackscatter coefficient (in the range of 2.5–5MHz) was near the bottom of the range for invitro human breast parenchyma. Its frequencydependence of backscatter was about f 0.55.(Average frequency dependences are f 1.3 forhuman breast parenchyma and f 0.8 for infiltrat-ing duct carcinoma.33)

Phantom properties are summarized in Table 1.The materials for phantoms A and B were pro-duced according to the method of Madsen et al.31

They were “macroscopically uniform,” meaningthat the only nonuniformity in either materialresulted from the random positioning of micro-scopic glass bead scatterers. The scatterer num-ber densities were about 5 scatterers/mm3 (A)and 800 scatterers/mm3 (B). The componentmaterials (and relative amounts by weight) forthe type A phantoms were agarose (3.5%),

1236 J Ultrasound Med 2005; 24:1235–1250

Ultrasonic Backscatter Coefficient Measurements From 2 to 9 MHz

n-propanol (3.4%), 75- to 90-µm-diameter glassbeads (0.38%), bovine milk concentrated 3 timesby reverse osmosis (24.5%), liquid Germall Pluspreservative (International Specialty Products,Wayne, NJ) (1.88%), and 18-MΩ-cm deionizedwater (66.3%). The component materials forthe type B phantoms were agarose (2.34%), n-propanol (2.92%), Potters 3000E glass beads(Potters Industries, Valley Forge, PA) (volume-weighted mean diameter of 26 µm with 90%having diameters <43 µm and 10% having diam-eters <9 µm) (1.87%), bovine milk concentrated3 times by reverse osmosis (47.9%), liquidGermall Plus preservative (1.87%), and 18-MΩ-cm deionized water (43.1%).

The type C material consisted of gelatin-basedspheres suspended in an oil-in-gelatin dispersionand was produced according to the method ofChin et al.31,32,34 Before (random) suspension inthe oil-in-gelatin dispersion, the spheres weresieved so that their diameters ranged between 0.6and 1.7 mm. Fifty percent of the volume of thefinal type C material consisted of spheres, and50% consisted of the oil-in-gelatin dispersion.The component materials (and relative amountsby weight) of the type C phantom spheres weregelatin (11.2%), n-propanol (4.06%), p-toluic acidpreservative (0.073%), powdered graphite(16.3%), formalin (0.89%), and 18-MΩ-cm deion-ized water (67.4%). The mixture surrounding thespheres in the type C material consisted of gelatin(9.8%), n-propanol (5.07%), p-toluic acid preser-vative (0.063%), formalin (0.77%), 18-MΩ-cmdeionized water (57.1%), detergent (0.93%),kerosene (12.2%), and safflower (14.0%).

The participating laboratories (except theUniversity of Wisconsin) did not have knowledgeof the phantom properties when they performedtheir measurements.

Phantom Boundary Layer TransmissionEach phantom was wrapped in a thin layer ofplastic film (Saran Wrap; Dow Chemical, Midland,MI). It was necessary to know the ultrasonic trans-mission properties of the Saran layer to makeaccurate estimates of attenuation and backscat-ter coefficients. Experimental measurementsand numerical computations of ultrasonic trans-mission coefficients of the Saran layers were con-ducted at the University of Wisconsin. A table ofamplitude transmission coefficients for eachsample was provided to each participating labo-ratory. The values presented in these tables were

based on considering each of the 2 Saran Wraplayers separately and multiplying the entrancetransmission coefficient (from water throughSaran Wrap and into the sample) by the exittransmission coefficient (from the samplethrough Saran Wrap and into water). In general,the entrance and exit transmission coefficientsare different from each other.

Ignoring attenuation in any of the media, thecomplex transmission coefficient for perpendic-ular incidence through a single, thin layer ofSaran is given by

(1)

where j = √–1 ; Zi is the acoustic impedance of theincident material; Zsaran is the acousticimpedance of the Saran layer; Z f is the acousticmaterial of the final material; ksaran is the wavenumber in the layer; and l is the thickness of thelayer.35 If attenuation in the 3 media is consid-ered, the acoustic impedances and wave num-ber become complex. However, except forsample materials with unrealistically large atten-uation coefficients, the dominant contribution isdue to the complex wave number in the argu-ment of the trigonometric functions. Therefore,attenuation effects can be included in Equation1 by setting

(2)

where csaran is the speed of sound, and α is the fre-quency-dependent attenuation coefficient ofSaran Wrap.

In both through-transmission and pulse-echoexperiments, the sound beam first enters fromwater through the Saran layer and into the sam-

J Ultrasound Med 2005; 24:1235–1250 1237

Wear et al

Table 1. Phantom Properties

PhantomProperty A B C

Scatterer Glass beads Glass beads Gelatin-basedspheres

Embedded in: Agarose/n-propanol/ Agarose/n-propanol/ Oil-in-gelatinmilk/H2O milk/H2O dispersion

Scatterer 75–90 µm 9–43 µm 0.6–1.7 mmdiameter

Concentration 5/mm3 800/mm3 50% by volume(0.035% by volume) (0.7% by volume)

1238 J Ultrasound Med 2005; 24:1235–1250

Ultrasonic Backscatter Coefficient Measurements From 2 to 9 MHz

where Zwater, Zsample, and Zsaran are the acousticimpedances of water, the sample, and SaranWrap, respectively; csaran is the speed of sound inSaran Wrap; f is the frequency (in Hertz); α(f) isthe frequency-dependent attenuation coefficientof Saran Wrap (in nepers per meter); and l is thethickness of the Saran Wrap. Note that all vari-ables in this expression are real numbers.

The thickness of the Saran Wrap used for thesesamples was measured with a micrometer tomeasure the thickness of 32 layers of the materialand found to be 25.1 ± 0.5 µm (mean ± SD). Theacoustic impedance of a material is equal to itsdensity multiplied by its speed of sound. The den-sity of Saran Wrap was measured by computingthe ratio of the mass and volume of a large sheetof Saran Wrap and found to be 1.69 ± 0.02 g/cm3.

To quantify the speed of sound and attenuationcoefficient of Saran Wrap, the amplitude trans-mission coefficient of a single layer of Saran Wrapin water was measured by a narrow-band tech-nique. The experimental setup consisted of awater tank, a Wavetek (now Fluke Corporation,Everett, WA) model 81 function generator, anAmplifier Research (Souderton, PA) model75A250 RF power amplifier, a LeCroy (ChestnutRidge, NY) model 9410 digital storage oscillo-scope, and several pairs of unfocused transducers(Panametrics, Waltham, MA; and Aerotech,Lewistown, PA) with various center frequencies.The function generator created a low-amplitudevoltage signal of 30 cycles at a specific frequency,which was amplified and sent to a transmittingtransducer. The signal detected by the receiving

transducer was displayed directly on the oscillo-scope, which was triggered with a pulse from thefunction generator that was synchronous with thestart of the output voltage pulse. Received wave-forms with and without the Saran film in theultrasound path were acquired. Ten measure-ments in 1-MHz steps were made between 1 and10 MHz with the use of several pairs of transduc-ers with common nominal center frequencies.Thirty-one measurements were conductedbetween 15 and 50 MHz with 1 pair of 30-MHzbroadband transducers. Table 2 provides detailson each pair of transducers used for these mea-surements. The amplitude transmission coeffi-cient was obtained by dividing the amplitude withthe Saran present by the amplitude without theSaran present.

The results of these measurements and a fit ofthe amplitude transmission coefficient given byEquation 1 are shown in Figure 1. The fit parame-ters correspond to a speed of sound of 2400 m/sand an attenuation coefficient of 5.0 nepers ⋅ m–1 ⋅MHz–1.5 ⋅ f 1.5. The results of this fit for the speed ofsound and attenuation coefficient of Saran Wrapwere used in Equation 3 to produce a table oftransmission coefficients using Equation 3 foreach sample that was sent to each participatinglaboratory over the range of 1 to 50 MHz.

Data Acquisition and AnalysisThe laboratory numbers in the following sectionshave been assigned randomly and do not corre-spond to the order of institutions listed on the firstpage of the article.

ple and then exits from the sample through the Saran layer and into water. Therefore, the total effecton the magnitude of the ultrasound signal is equal to the product of the absolute value of Equation 1with Zi = Zwater and Zf = Zsample and the absolute value of Equation 1 with Zi = Zsample and Zf = Zwater,namely,

(3)

Laboratory 1Samples were interrogated in a tank containingdistilled water at room temperature. APanametrics model 5800 pulser/receiver and 3matched pairs of circular (19.1-mm-diameter)focused transducers were used. The center fre-quencies were 2.25, 3.5, and 5 MHz, respectively.The focal lengths were 50.8, 50.8, and 38.1 mm.Samples were placed in the focal plane. Receivedsignals were digitized (8 bit, 10 MHz) with aLeCroy model 9310C dual 400-MHz oscilloscopeand stored on computer (via a General PurposeInterface Bus) for offline analysis.

To measure sound speed, arrival times ofreceived broadband pulses were measured withand without the sample in the water path. Groupvelocity, cg, was computed from

(4)

where d is the thickness of the sample (measuredwith calipers), ∆t is the difference in arrival times,and cw is the temperature-dependent speed ofsound in distilled water given by Kaye andLaby36:

(5)

where T is the temperature in degrees Celsius.Temperature was measured with a digital ther-mometer and ranged between 21°C and 23°C.

Each arrival time was computed as follows. Thesignal envelope was computed with the use ofthe Hilbert transform. The arrival time was com-puted from the maximum in the signal enve-lope. Using the envelope maximum rather thanthe leading edge of the pulse or zero crossingsminimizes errors in estimates of sound speeddue to frequency-dependent attenuation.37

A through-transmission method was used tomeasure attenuation. With 2 opposing coaxiallyaligned transducers (1 transmitter and 1 receiv-er), transmitted signals were recorded both withand without the sample in the acoustic path. Theattenuation coefficient was estimated by a log

J Ultrasound Med 2005; 24:1235–1250 1239

Wear et al

Table 2. Transducers Used in Measurement of Saran Wrap Amplitude Transmission Coefficient

Freq Transmitter ReceiverUsed, Manufacturer/ Center Diameter, Manufacturer/ Center Diameter,MHz Part No. Freq, MHz in Part No. Freq, MHz in

1.0 Aerotech/ 1.0 1.125 Aerotech/ 1.0 0.50 Delta PN2797 Delta PN2792

2.0 Panametrics/ 2.25 0.5 Aerotech/ 2.25 0.25V306 Delta PN2794-1

3, 4 Panametrics/ 3.5 0.5 Aerotech/ 3.5 0.25V382 Delta PN2794-2

4, 5, 6 Panametrics/ 5.0 0.5 Aerotech/ 5.0 0.25V309 Delta PN2794-3

7, 8 Panametrics/ 7.5 0.5 Aerotech/ 7.0 0.25V320 Delta PN 2794-4

9, 10 Panametrics/ 10.0 0.5 Krautkramer/ 10.0 0.25V311 Delta COJWM4

15–45 Panametrics/ 30.0 0.5 Panametrics 30.0 0.5V356 V356

Figure 1. Modulus of the amplitude transmission coefficient for a single layer ofSaran Wrap with water on both sides as a function of frequency. Measured valuesare filled circles, and the solid line represents Equation 1, where a speed of soundof 2400 m/s and an attenuation coefficient of 5.0 nepers ⋅ m–1 ⋅ MHz–1.5 ⋅ f 1.5

were used to obtain the best fit to the experiment.

spectral difference technique.38 Potential diffrac-tion-related errors in this insertion techniquemay be ignored, provided that the speed ofsound in the phantoms is close to that of water.39

Backscatter coefficients were measured by areference phantom method.28 Approximately25 echoes were acquired from each phantomby translating the transducer laterallybetween acquisitions. The front surface of thephantom was aligned with the transducerfocal plane. Radio frequency data were gatedto isolate the interior of the phantom and toexclude specular echoes. The range gate was1.8 cm long and began 2 mm beyond the spec-ular echo. The ratios of the squared moduli ofthe fast Fourier transforms of the test phantomRF data to reference phantom data were com-puted. Compensation for attenuation was per-formed with Equation 17 from O’Donnell andMiller.21

All measurements were compensated for loss-es due to transmission through the Saran Wraplayer.

Laboratory 2All measurements were performed in distilled,highly degassed (PO2 = 1.3 mg/L) water at 22 ±0.2°C. All measurements were compensated forthe transmission coefficient through the sam-ples’ surfaces.

Source transducers were driven by a Panametricsmodel 5800 pulser/receiver. Three sphericallyfocused transducers were used as sources formeasurements of sound speed, attenuation, andbackscatter: (1) Panametrics model V380 (diam-eter of 25.4 mm, center frequency of 3.9 MHz,fractional bandwidth [–3 dB] of 42%, focal lengthof 90 mm, –6-dB focal beam width of 1.5 mm,and –6-dB depth of focus of 25 mm), (2)Panametrics model V321 (diameter of 19.1 mm,center frequency of 8.4 MHz, fractional band-width of 34%, focal length of 95 mm, –6-dBfocal beam width of 1.1 mm, and –6-dB depthof focus of 38 mm), and (3) ValpeyFisherCorporation (Hopkinton, MA) model IS1004HR(diameter of 12.7 mm, center frequency of 10MHz, fractional bandwidth of 42%, focal lengthof 38 mm, –6-dB focal beam width of 0.8 mm,and –6-dB depth of focus of 25 mm).

The hydrophone used for sound speed andattenuation coefficient measurements was a 1-mm2 bilaminar membrane hydrophone (model804; Perceptron, Plymouth Meeting, PA). Sound

speed was determined by Equation 4. The refer-ence sound speed for water was taken to be 1488m/s. Transit time difference (∆t) was measuredvia a correlation integral technique40 betweenthe water path and through-tissue signals col-lected at the hydrophone. Sample thickness wasmeasured with a ruler. The attenuation coeffi-cient was measured by the same log spectral dif-ference method used by laboratory 1.

Backscatter coefficients were estimated by a cal-ibrated pulse-echo technique.26 The power spec-trum was determined for regions of interest (20wavelengths axially by 5 beam widths laterally) bytaking the squared magnitude of the Fouriertransform of gated sections from the backscat-tered time signal. A Hamming window was usedto gate the time signals. The effects of the equip-ment on the power spectrum measurement werefactored out by dividing by the reference spec-trum from a planar acrylic surface with knownreflectivity. Also, the medium’s attenuation wascompensated for.

Laboratory 3A Panametrics model 5900PR pulser/receiverwas used. Two different single-element Panametricstransducers were used to scan the phantoms.The 3.5-MHz transducer had an aperture of 9.5mm and a focal length of 42 mm; the 5.0-MHztransducer had an aperture of 9.5 mm and a focallength of 50 mm.

The phantoms were scanned in 10 planes sepa-rated by 0.5 mm. Each scan plane consisted of 40scan lines separated by 0.5 mm. Data were digi-tized by an Acqiris (Monroe, NY) analog-to-digi-tal board operating at a 50 megasamples (MS)/ssampling rate. Each scan line was digitized with3400 eight-bit samples. Data were acquired withthe transducer focus placed at the front (near)surface of the phantom, that is, at a depth of 0mm, then at depths of 5, 10, 15, 20, 25, 30, 35, and40 mm, that is, at the rear (far) surface of thephantom.

The speed of sound was calculated by measur-ing the phantom thickness and then determiningthe time between zero-crossing of the RF echosignal at the front (near) and rear (far) surfaces ofthe phantom. Time was determined by countingthe number of samples between the zero-cross-ings. (At 50 MS/s, the duration of 1 sample is 0.02microseconds.) The transducer was focused mid-way into the phantom. Phantom thickness wasmeasured with a mechanical vernier caliper

1240 J Ultrasound Med 2005; 24:1235–1250

Ultrasonic Backscatter Coefficient Measurements From 2 to 9 MHz

with a digital readout. The speed of sound wascomputed as c = 2 * thickness/(0.02 * samples),where the factor of 2 takes into account theround-trip distance for echoes to propagate.

Attenuation was determined by plotting spec-tral midband values (expressed in decibels rela-tive to reflections from a glass plate) as afunction of depth into the phantom. The com-putations were made for each depth with thefocus at the given depth. Midband values werecomputed for the bandwidth that provided anadequate SNR at all usable focal lengths. Signal-to-noise considerations limited us to 4 depthsfor phantoms A and C and to 5 depths for phan-tom B. The sound speed differences betweenimmersion bath water and the phantoms weretaken into account in determining the actualfocal zone depths, which in all phantoms werecloser to the near surface of the phantom thanthe depths corresponding to transducer dis-placements of 5, 10, 15, 20, and 25 mm. The aver-age of midband values computed in all planesfor each transducer-phantom combination wasused to determine the slope of midband as afunction of true depth into the tissue.Attenuation, α, was computed as

(6)

where fc is the center midband frequency; thefactor 2 accounts for the round-trip distance tothe actual depth; and ∆M/∆d is the slope of thelinear regression of midband versus true depth.

The backscatter coefficient, BSC, was comput-ed as

(7)

where PBS is the power of signals backscatteredfrom the phantom; P0 is the power of signalsbackscattered from a perfect reflector (glassplate); Ω is the solid angle subtended by thetransducer; and D is the depth of the insonatedvolume (0.3969 L, where L is the length of theHamming window used in these studies). PBS/P0is equivalent to the midband value; the relation-ship is PBS/P0 = 10 exp (M/10), where M is thenormalized or system-corrected midband value(expressed in decibels relative to the referencevalue).

Laboratory 4A reference phantom method was applied tomeasure backscatter and attenuation coeffi-cients using an Acuson 128XP scanner equippedwith L7 and V4 array transducers (SiemensMedical Solutions, Mountain View, CA) andmodified to provide intermediate frequencydata. Echo signals were digitized at 64 MS/s with8-bit precision.

For sound speed measurements, the transittime from the front interface to the back inter-face of the cylinder was averaged over 20 nonad-jacent beam lines. The thickness of the cylinderwas measured with calipers. Sound speed wasestimated with the use of the range equation.

A 4-microsecond Blackman-Harris window wasmodulated by cos (ωot) and sin (ωot), where ωo isthe analysis frequency, and t is the echo arrivaltime. Signals from the test cylinders were con-volved by each set of quadrature bandpass coeffi-cients, the bandwidth of which was determinedby the window duration.28 The filtered echo sig-nals in each quadrature channel were thensquared, and the 2 waveforms were added, pro-ducing a single time-dependent waveform.Averaging over all the independent waveformsresulted in an averaged and filtered signal inten-sity versus depth for each test cylinder at the anal-ysis frequency. The analysis for both transducerswas performed in 0.25-MHz steps over the usefulbandwidth. The same analysis was applied to thesignals from the reference phantom.

Depth-dependent ratios of filtered echo signalintensities from the test cylinders to intensitiesfrom the reference phantom then were obtained.The logarithm of the intensity ratio plottedversus depth was quasilinear. The slope of a linefitted to these data was proportional to the dif-ference between the attenuation coefficient ofthe test cylinder and that of the reference phan-tom. Because the latter was known, the attenua-tion in the test cylinder could be deduced. Theratio was compensated for attenuation lossesversus depth. The average of this compensatedratio versus depth was multiplied by thebackscatter coefficient of the reference phantomto yield the backscatter coefficient for the testcylinder.

Laboratory 5 The experimental setup consisted of a watertank, a Wavetek model 81 function generator, anAmplifier Research model 75A250 RF power

J Ultrasound Med 2005; 24:1235–1250 1241

Wear et al

amplifier, a LeCroy model 9410 digital storageoscilloscope, and several pairs of unfocusedtransducers (Panametrics and KB Aerotech [nowGE Inspection Technologies], Lewistown, PA)with various center frequencies. The functiongenerator created a 30-cycle low-amplitude volt-age signal, which was amplified and sent to atransmitting transducer. The received signal wasdisplayed on an oscilloscope, which was trig-gered with a pulse from the function generatorthat was synchronous with the onset of the out-put voltage pulse. Received waveforms with andwithout the sample in the ultrasound path wereacquired.

Sound speed was computed from Equation 4with cw =1488.4 m/s (22.0°C).41 Sample thicknesswas measured with calipers. A zero-crossing wasused as a marker for arrival time measurement.Attenuation was measured by a log spectral dif-ference method as discussed in the section forlaboratory 1.

The measurement of backscatter coefficientswas performed according to the method of Chenet al.29 Echo signals from broadband source puls-es were compared with the echo from a planereflector. Data were acquired from the sample ina tank of degassed and distilled water. A functiongenerator (FG 5010; Tektronix, Inc, Beaverton,OR) created 1-cycle sinusoidal pulses with a fre-quency near the transducer center frequency (3.5MHz). The pulses were amplified with a broad-band RF power amplifier (240L; ENI, Rochester,NY) and used to drive the transducer. This result-ed in a broad-bandwidth acoustic pulse withapproximately 50% fractional bandwidth. Echosignals were received and amplified with aPanametrics 5052UA pulser/receiver. A 10-microsecond interval was digitized at 100 MS/swith a LeCroy 9310A digital storage oscilloscope.Echo signals from the samples were obtained for98 positions by translating the sample in a rasterfashion with the use of a stepper motor system.

Laboratory 6Transducers with center frequencies of 10 and 15MHz were built in-house for use in this study.The computer-controlled acoustic field scanningprogram was used to measure the beam pattern.A calibrated hydrophone, HP function generator(Hewlett-Packard Company, Palo Alto, CA), ZHL-32A amplifier (Mini-Circuits, Brooklyn, NewYork), TDS-520 oscilloscope (Tektronix, Inc), andDC power supply were used.

The speed of sound and attenuation were mea-sured by a substitution method as described bylaboratory 1. The reference speed of sound inwater was 1540 m/s. Sample thickness was mea-sured with calipers. A substitution method wasused to measure backscatter coefficient20 (alsosee laboratory 7 methods). A flat stainless steelblock was used for a reference reflector.

Laboratory 7For sound speed measurements, a Panametrics5-MHz, 12.7-mm-diameter transducer was used.The Panametrics 5052UA pulse generator wasused as a source. A LeCroy 9400A digital oscillo-scope was used to digitize RF data.

Samples were placed between the transducerand a steel reflector. The time delays for theechoes from the reflector (Tm) and from bothinterfaces of the sample (t1 and t2) were mea-sured. The sound speed (cm) was then calculatedfrom

(8)

where Tw is the propagation time measuredwhen the sample is removed. The referencespeed of sound in water, cw, was 1481 m/s.42

For attenuation and backscatter measure-ments, a pair of 7.5-MHz, 6-mm-diameter trans-ducers (Echo Ultrasound, Reedsville, PA) wasused. The source was a Wavetek 191 functiongenerator. A log spectral difference method (seemethods for laboratory 1) was used to computethe attenuation coefficient.

For backscatter measurements, a protectioncircuit (Expander, DEX-3; Matec, Northborough,MA) consisting of a series of high-frequencydiodes was placed between the source and thetransducer. Two limiters were placed between thetransducer and the oscilloscope. The backscat-tered signals were digitized by a 500-MS/s analog-to-digital converter (CS 8500; Gage AppliedTechnologies, Montreal, Quebec, Canada) at a250-MS/s sampling rate. The specimen wasplaced at the Rayleigh distance of a nonfocusedtransducer. The backscatter coefficient in a cylin-drical sample volume in the specimen was deter-mined by measuring the backscattered powerand normalizing it to the power reflected from aperfect plane reflector (to correct for incidentintensity and beam characteristics).20 Phantomthickness was measured with calipers.

1242 J Ultrasound Med 2005; 24:1235–1250

Ultrasonic Backscatter Coefficient Measurements From 2 to 9 MHz

Laboratory 8The transmitting transducer was excited with abroadband pulse generated by a fast-transitionmetal oxide semiconductor field effect transistorswitch (model PVX-4150; Directed Energy Inc,Fort Collins, CO) under the timing control of adigital delay/pulser (model DG535; StanfordResearch Systems, Sunnyvale, CA). The switchwas used to hold off a 150-V DC voltage from apower supply (model PS310; Stanford ResearchSystems). The received signal was conditionedwith an amplifier (model BR-640A; Ritec Inc,Warwick, RI) before being captured in a 12-bitdigitizer (model CS12100; Gage AppliedTechnologies) at 100 Ms/s. Each waveform (2048samples) was a temporal average of 256 acquisi-tions. The sample was moved in 1-mm steps tocollect signals from 225 independent sites in a 15× 15 grid. All experiments were performed at22°C.

The speed of sound was measured with athrough-transmission method as explained inthe methods for laboratory 7. The speed ofsound in water was taken to be 1490.8 m/s. Atransmitting transducer (5-MHz center frequen-cy, 12.7-mm diameter, and 25.4-mm focus;model A309S-SU; Panametrics) was positionedso that its focus was at the front interface of thephantom sample. A receiving transducer (5-MHz center frequency, 25.4-mm diameter, and50.8-mm focus; model V307; Panametrics) wasplaced so that its focus overlapped that of theother transducer.

To measure attenuation, a through-transmis-sion measurement was performed with the sam-ple in place and with the sample removed (waterpath only). The baseline DC offset of the signalswas then subtracted. Signals were isolated with a5.12-microsecond rectangular window. A logspectral difference method was used (see labora-tory 1). Corrections for the transmission coeffi-cient of the sample interfaces were performed.

Backscatter measurements were performedwith the same 5-MHz transmitting transducer asabove in the pulse-echo mode. The receivingelectronics were protected from the excitingpulse by cross-diode protection circuitry(Diplexer RDX-2; Ritec). The focus of the trans-ducer was placed to begin near or slightly afterthe front wall of the sample. The analysis of thebackscattered signal was performed by position-ing a 2.56-microsecond Hamming window 3.2microseconds below the first detected echo from

the front wall of the sample. The frequency-dependent power spectra were then calculatedfor each independent site and then averaged.The resulting mean apparent backscatteredpower spectrum was then referenced to the sig-nal reflected from the surface of an acrylic plate(amplitude reflection coefficient = 0.37) placed atthe focus.43

The backscatter coefficient was computed bythe formula derived by Chen et al.30

(9)

where ⟨ |Vs(f )|2⟩ is the ensemble average ofbackscattered power spectra from medium;|Vref(f)|

2 is the backscattered power spectrumfrom the planar reflector at focus; r0 is the radiusof curvature of transducer; l is the length of thewindowed backscatter signal (cτ/2); a is theradius of the active element of the transducer;and E∞ = 0.46. R is the reflection coefficient of thereference surface; T is the intensity transmissioncoefficient of the water–Saran Wrap–phantominterface; and C is the correction for the window-ing function (C = 0.63 for Hamming).29 Theattenuation correction was given by

(10)

where a(f) is frequency-dependent attenuation;x is the length of the material before start of thewindow; c is the speed of sound in the material;τ is the duration of the windowed backscattersignal.

Measurements of Uniformity and DriftMeasurements of the speed of sound, attenua-tion coefficients, and backscatter coefficientswere made at 22°C in December 2002 andJanuary 2003 on at least 9 phantoms from eachof the 3 sets (A–C) before the samples were sentfrom the University of Wisconsin to the variousparticipants. After the participants had complet-ed their measurements, each participant’s 3phantoms were returned to the University ofWisconsin, where measurements were repeatedat 22°C in January and February 2004 according

J Ultrasound Med 2005; 24:1235–1250 1243

Wear et al

to the same procedures as those used before thesamples had been sent out. Thus, any change(drift) in the material properties of the samplescould be assessed. Measurements were per-formed at multiple frequencies throughout the2- to 14-MHz range.

Results

In the results that follow, laboratories are anony-mously labeled numbers 1 through 8, assignedrandomly. The numbers in the figures corre-spond to the laboratory identification numbersin “Materials and Methods” but do not corre-spond to the order of the institutions listed on thefirst page of this article.

Figure 2 shows measurements of attenuationcoefficients for the 3 phantoms, as functions offrequency, for the 8 laboratories. Agreement waswithin 0.15 dB ⋅ cm–1 ⋅ MHz–1 for phantom A andwithin 0.2 dB ⋅ cm–1 ⋅ MHz–1 for phantom B butonly within 0.5 dB ⋅ cm–1 ⋅ MHz–1 for phantom C.

Figure 3 shows measurements of sound speedfor the 3 phantoms, as functions of frequency, forthe 8 laboratories. There was broad agreementfor most laboratories, but some measurements(laboratories 3, 4, and 6) were at times 30 to 60m/s greater than the majority.

Figure 4 shows measurements of backscattercoefficient for the 3 phantoms, as functions offrequency, for the 8 laboratories. In the case ofphantom A (Figure 4A), most measurementsshowed similar rates of increase of the backscat-ter coefficient with frequency between 2 and 5MHz. The laboratories that performed measure-ments between 5 and 9 MHz seemed to agreethat the backscatter coefficient was roughly con-stant within that frequency range. The solidcurve in Figure 4A depicts the theoreticalbackscatter coefficient, based on the theory ofFaran,44 assuming a scatterer diameter of 82.5µm (the midpoint of the range from 75 to 90 µm).The theory should not necessarily be taken to bea perfectly accurate estimate because it is basedon numerous assumptions and approximations.The beads were not perfect spheres, as the theo-ry assumes, and their true material propertieswere not known (generic values for glass wereused instead). The true scatterer number densitywas only known to within about 10%. The theoryignores coherent scattering and multiple scatter-ing, which may have been present. The true dis-tribution of scatterer sizes was not known.

Nevertheless, it is perhaps worthwhile to pointout that laboratory 2 obtained the closest agree-ment with theory. Laboratories 1, 4, and 8 agreedwith theory to within about a factor of 2.Moreover, most laboratories measured frequen-cy dependence of backscatter to be fairly consis-tent with theoretical prediction.

In the case of phantom B (Figure 4B), verygood agreement existed among the laboratories

1244

Ultrasonic Backscatter Coefficient Measurements From 2 to 9 MHz

Figure 2. Measurements of frequency-dependent attenuationcoefficients for phantom A, phantom B, and phantom C.

J Ultrasound Med 2005; 24:1235–1250

(except laboratory 7) regarding the magnitudeand frequency dependence of the backscattercoefficient. The solid curve in Figure 4B depictsthe theoretical backscatter coefficient, based onthe theory of Faran,44 assuming a scatterer diam-eter of 26 µm (the midpoint of the range from 9to 43 µm). As explained above, caution must beexercised in comparison of experimental data tothis theory. The dashed curve in Figure 4B indi-

cates the frequency dependence of backscatterfor Rayleigh scattering (frequency to the fourthpower), which is valid at frequencies less than 6MHz. Most laboratories measured frequencydependence of backscatter to be fairly consistentwith theoretical prediction.

J Ultrasound Med 2005; 24:1235–1250 1245

Wear et al

Figure 3. Measurements of sound speed (SOS) for phantom A,phantom B, and phantom C.

Figure 4. Measurements of frequency-dependent backscattercoefficient for phantom A, phantom B, and phantom C. Solidcurves correspond to the theoretical backscatter coefficients,based on the theory of Faran.44 The dashed curve in B indicatesthe frequency dependence of backscatter for Rayleigh scattering(frequency to the fourth power), which is valid at low frequencies.

Agreement in backscattering measurementsacross laboratories was poor for phantom C(Figure 4C). The laboratories generally agreed,however, that the frequency dependence of thebackscatter coefficient was much flatter forphantom C than for phantoms A and B. Thematerial properties of the scatterers for phantomC were not known sufficiently well to permit ameaningful theoretical estimate of the backscat-ter coefficient based on Faran’s theory.44 As in thecase for phantom A, the results from laboratories1, 2, 4, and 8 seemed to cluster together.

Table 3 shows measurements of phantomuniformity. The numbers in the table show with-in-batch ranges (maxima minus minima) ofmeasurements of sound speed, the attenuationcoefficient (at 5 MHz), and the backscatter coef-ficient (at 5 MHz) performed at the University ofWisconsin before distribution to the participat-ing laboratories. In all cases, the variation insound speed was no more than about 3 m/s. Thevariation for the attenuation coefficient (near 5MHz) was less than 0.1 dB/cm for phantoms Aand B and about 0.6 dB/cm for phantom C. Thevariations for the backscatter coefficient wereless than or on the order of 36% for all 3 phan-toms.

Table 4 shows changes in measurements ofacoustic properties between December 2002 andJanuary 2003 (before samples were sent to partic-ipating laboratories) and January 2004 andFebruary 2004 (after samples were returned byparticipating laboratories) assessed at theUniversity of Wisconsin. In all cases, soundspeed drifted by no more than about 2 m/s. Theattenuation coefficient at 5 MHz drifted by nomore than about 0.1 dB/cm. The backscattercoefficient drifted by no more than 10% for all 3batches.

Discussion

The range of variation of the absolute magnitudeof backscatter coefficient measurements wasabout 1 (excluding laboratory 7) or 2 (includinglaboratory 7) orders of magnitude. There wasbetter agreement among laboratories regardingmeasurements of the frequency dependence ofbackscatter, which is an indicator of scatterersize. For example, when scatterers were smallcompared with the ultrasonic wavelength, exper-imental frequency-dependent backscatter coef-ficient data obtained by the participatinglaboratories were usually consistent with theexpected Rayleigh scattering behavior (propor-tional to frequency to the fourth power).

Sound speed variations (whether due to phan-tom nonuniformity, temporal drift, or disparityof measurements among participating laborato-ries) observed in this study are not likely toexplain a substantial fraction of the disparity inbackscatter coefficient measurements. The effectof errors (or variations of any sort) of soundspeed estimates on backscatter coefficient esti-mates is as follows. Errors in sound speed mea-surement lead to inaccurate range gating ofbackscattered signals. For a gate duration ∆t, thecorresponding gate length from a pulse-echo sig-nal is d = c∆t/2. A relative error in sound speed εc(|cmeas – ctrue|/ctrue) would correspond to the samerelative error in estimated gate length εd (|dmeas –dtrue|/dtrue) and scattering volume εv. (Scatteringvolume is proportional to the product of gatelength and beam width.) The computedbackscatter coefficient is inversely proportionalto the assumed scattering volume. Therefore, therelative error in the backscatter coefficient wouldbe εBSC = εv = εd = εc. From Figures 2–4, it can be

1246 J Ultrasound Med 2005; 24:1235–1250

Ultrasonic Backscatter Coefficient Measurements From 2 to 9 MHz

Table 3. Phantom Uniformity

Parameter A B C

c, m/s 1.7 2.5 3.2α, dB/cm 0.06 0.08 0.6BSC, % 21 30 36

Shown are ranges (maximum minus minimum) for within-batch measurements of sound speed (c), attenuation coeffi-cient (α, at 5 MHz), and backscatter coefficient (BSC, at 5MHz) for phantom batches A, B, and C. The backscattercoefficient range is expressed as a percentage of the averagebackscatter coefficient for the batch. Values for attenuationand backscatter coefficients were obtained from power lawfits to measured data.

Table 4. Phantom Drift

Parameter A B C

c, m/s –0.1 1.1 1.5α, dB/cm 0.03 0.01 0.11BSC, % <2 <10 <5

Shown are average changes in measurements of parametersbetween January 2003 (before distribution to participatinglaboratories) and January 2004 (after participating laborato-ries performed measurements) for phantom batches A, B,and C. The maximum minus minimum backscatter coeffi-cient (BSC) is expressed as a percentage of the averagebackscatter coefficient for the batch. Values for attenuation(α) and backscatter coefficients were obtained from powerlaw fits to measured data; c indicates sound speed.

seen that in the worst case (phantom C), mea-surements varied by as much as about 70 m/s orabout 5%. This is a high variability for a relativelyeasy measurement. However, it would only pro-duce 5% variations in backscatter coefficientmeasurements, a negligible fraction of the totalobserved (1–2 orders of magnitude). The within-batch nonuniformity (Table 3) and temporaldrift (Table 4) of sound speed of the phantomswere less than or on the order of 3 m/s, again cor-responding to negligible variations of backscat-ter coefficient estimates.

It is also unlikely that attenuation coefficientvariations (whether due to phantom nonunifor-mity, temporal drift, or disparity of measure-ments among participating laboratories)observed in this study could explain a significantfraction of the disparity in backscatter coefficientmeasurements. Errors in attenuation coefficientestimates lead to inaccurate compensation ofbackscatter data for the effects of attenuation. Ifattenuation coefficient variation were a primarydeterminant of backscatter coefficient variation,then those laboratories underestimating attenu-ation coefficients would be expected to under-compensate their backscatter data and reportlow backscatter coefficients. Similarly, those lab-oratories overestimating attenuation coefficientswould be expected to report high backscattercoefficients. Thus, one might expect a positivecorrelation between estimates of attenuationand backscatter coefficients. However, as indi-cated in Figure 5, no such positive correlationwas observed in this study. In addition, the with-in-batch nonuniformity (Table 3) and temporaldrift (Table 4) of attenuation coefficients for thephantoms were less than or on the order of 0.6dB/cm at 5 MHz. Because the phantoms wereabout 4 cm thick, this would lead to a range ofattenuation of less than or on the order of 1.5 dBat 5 MHz. This is far too small to produce any-where near the 1 or 2 order(s) of magnitude (ie,10–20 dB) variation in the backscatter coefficientestimate that was observed.

Within-batch nonuniformity and temporaldrift of backscatter coefficients were less than36%. Again, this variability is small comparedwith the 1 to 2 orders of magnitude variation ofmeasurements reported by the participating lab-oratories.

One possible source of disparity that remains isthat different data reduction algorithms, even ifimplemented correctly, may yield substantially

different values. Some methods use focusedtransducers, whereas others use unfocusedtransducers. Under some conditions, focusedand unfocused transducers may yield disparateresults.45 For calibration, some methods use aplanar reflector, whereas others use a phantomthat contains distributed pointlike scatterers.The model for the backscattering object may be

J Ultrasound Med 2005; 24:1235–1250 1247

Wear et al

Figure 5. Scatterplots of attenuation coefficient measurementsversus backscatter coefficient measurements at 5 MHz for phan-tom A, phantom B, and phantom C.

continuous or discrete. Under these circum-stances, production of different quantitative val-ues by different approaches should not besurprising.

Experimental error may also be an appreciablesource of disparity. Data acquisition issues (cor-rect positioning of transducers relative to sam-ples, correct positioning of reference reflectors,avoidance of saturation of receiving electronicsand digitizer, and optimization of transmittedpower to maximize the SNR without saturation)could contribute to errors. In addition, datareduction software errors, which may remainundetected in the absence of a reference stan-dard test, can also exacerbate inaccuracy. Forexample, although laboratories 6 and 7 bothused the same method for backscatter coefficientestimation, they obtained markedly dissimilarresults for phantoms B and C. At least one ofthese laboratories is likely to have had experi-mental or software error.

Although considerable disparity existedamong the participating laboratories regardingabsolute levels of backscatter, the level of agree-ment regarding frequency dependence of thebackscatter coefficient was fair. This establishessome promise for standardized estimation ofscatterer size.

Finally, the present study offers several im-provements over the previous AIUM-sponsoredinterlaboratory comparison.19 First, the upperrange of frequencies has been extended from 7 to9 MHz (the highest frequency for which multiplemeasurements are available for comparison).Second, the analysis of phantom uniformity anddrift has been expanded from attenuation andsound speed (in the previous study) to alsoinclude backscatter (in this study). Consequently,the candidate mechanisms for disparity inbackscatter coefficient measurements in thisstudy could be narrowed down more convincing-ly to algorithmic differences and software/exper-imental error. Third, the results in this studywere compared with theoretically expectedbackscatter coefficients, allowing independentand objective evaluation of laboratory measure-ments. Fourth, and most important, the testphantoms in this study (unlike the previousstudy) have been returned to those laboratoriesrequesting them. Now participating laboratorieshave standardized test objects, with propertiesdocumented in this article (with moderate con-sistency if not complete unambiguity), to help

them refine their backscatter coefficient mea-surement methods. It is hoped this will lead toimproved consistency in future reports of fre-quency-dependent backscatter coefficientsamong the participating laboratories.

References

1. Shung KK, Sigelmann RA, Reid JM. Scattering ofultrasound by blood. IEEE Trans Biomed Eng 1976;23:460–467.

2. Angelsen BAJ. A theoretical study of the scatteringof ultrasound from blood. IEEE Trans Biomed Eng1980; 27:61–67.

3. Madaras EI, Barzilai B, Perez JE, Sobel BE, Miller JG.Changes in myocardial backscatter throughout thecardiac cycle. Ultrason Imaging 1983; 5:229–239.

4. Campbell JA, Waag RC. Measurements of calf liverultrasonic differential and total scattering cross sec-tions. J Acoust Soc Am 1984; 75:603–611.

5. Lizzi FL, King DL, Rorke MC, et al. Comparison oftheoretical scattering results and ultrasonic datafrom clinical liver examinations, Ultrasound Med Biol1988; 14:377–385.

6. Wear KA, Milunski MR, Wickline SA, Perez JE, SobelBE, Miller JG. Differentiation between acutelyischemic myocardium and zones of completedinfarction in dogs on the basis of frequency-depen-dent backscatter. J Acoust Soc Am 1989; 85:2634–2641.

7. Turnbull DH, Wilson SR, Hine AL, Foster FS.Ultrasonic characterization of selected renal tissues.Ultrasound Med Biol 1989; 15:241–253.

8. Insana MF, Hall TJ, Fishback JL. Identifying acousticscattering sources in normal renal parenchyma fromthe anisotropy in acoustic properties. UltrasoundMed Biol 1991; 17:613–626.

9. Insana MF, Wood JG, Hall TJ. Identifying acousticscattering sources in normal renal parenchyma invivo by varying arterial and ureteral pressures.Ultrasound Med Biol 1992; 18:587–599.

10. Sehgal CM. Quantitative relationship between tissuecomposition and scattering of ultrasound. J AcoustSoc Am 1993; 94:1944–1952.

11. Wear KA, Garra BS, Hall TJ. Measurements of ultra-sonic backscatter coefficients in human liver andkidney in vivo. J Acoust Soc Am 1995; 98:1852–1857.

1248 J Ultrasound Med 2005; 24:1235–1250

Ultrasonic Backscatter Coefficient Measurements From 2 to 9 MHz

12. Feleppa EJ, Kalisz A, Sokil-Melgar JB, et al. Typing ofprostate tissue by ultrasonic spectrum analysis. IEEETrans Ultrason Ferroelectr Freq Control 1996;43:609–619.

13. Silverman RH, Folberg R, Boldt HC, et al. Correlationof ultrasound parameter imaging with microcircula-tory patterns in uveal melanomas. Ultrasound MedBiol 1997; 23:573–581.

14. Russell MD, Sun H, Wicks ML, et al. Ultrasonic non-destructive evaluation applied to prostate cancerdetection. Nondestr Test Eval 1998; 14:237–256.

15. Wear KA. Frequency dependence of ultrasonicbackscatter from human trabecular bone: theoryand experiment. J Acoust Soc Am 1999; 106:3659–3664.

16. Hall CS, Scott MJ, Lanza GM, et al. The extracellularmatrix is an important source of ultrasoundbackscatter from myocardium. J Acoust Soc Am2000; 107:612–619.

17. Oelze ML, Zachary JF, O’Brien WD Jr.Characterization of tissue microstructure using ultra-sonic backscatter: theory and technique for opti-mization using a Gaussian form factor. J Acoust SocAm 2002; 112:1202–1211.

18. Oelze ML, O’Brien WD, Blue JP, Zachary JF.Differentiation and characterization of rat mamma-ry fibroadenomas and 4T1 mouse carcinomas usingquantitative ultrasound imaging. IEEE Trans MedImaging 2004; 23:764–771.

19. Madsen EL, Dong F, Frank GR, et al. Interlaboratorycomparison of ultrasonic backscatter, attenuation,and speed measurements. J Ultrasound Med 1999;18:615–631.

20. Sigelmann RA, Reid JM. Analysis and measurementof ultrasound backscattering from an ensemble ofscatterers excited by sine-wave bursts. J Acoust SocAm 1973; 53:1351–1355.

21. O’Donnell M, Miller JG. Quantitative broadbandultrasonic backscatter: an approach to nondestruc-tive evaluation in acoustically inhomogeneous mate-rials. J Appl Phys 1981; 52:1056–1065.

22. Nicholas D, Hill CR, Nassiri DK. Evaluation ofbackscattering coefficients for excised human tis-sues: principles and techniques. Ultrasound MedBiol 1982; 8:7–15.

23. Lizzi FL, Greenebaum M, Feleppa EJ, et al.Theoretical framework for spectrum analysis in

ultrasonic tissue characterization. J Acoust Soc Am1983; 73:1366–1373.

24. Campbell JA, Waag RC. Normalization of ultrasonicscattering measurements to obtain average differ-ential scattering cross sections for tissues. J AcoustSoc Am 1983; 74:393–399.

25. Madsen EL, Insana MF, Zagzebski JA. Method ofdata reduction for accurate determination of acous-tic backscatter coefficients. J Acoust Soc Am 1984;76:913–923.

26. Insana MF, Hall TJ. Parametric ultrasound imagingfrom backscatter coefficient measurements: imageformation and interpretation. Ultrason Imaging1990; 12:245–267.

27. Yao LZ, Zagzebski JA, Madsen EL. Backscatter coef-ficient measurements using a reference phantom toextract depth-dependent instrumentation factors.Ultrason Imaging 1990; 12:58–70.

28. Zagzebski JA, Yao LX, Boote EJ, Lu ZF. Quantitativebackscatter imaging. In: Shung KK, Thieme GA(eds). Ultrasonic Scattering in Biological Tissues.Boca Raton, FL: CRC Press Inc; 1993:451–486.

29. Chen JF, Zagzebski JA, Madsen EL. Tests of backscat-ter coefficient measurement using broadband puls-es. IEEE Trans Ultrason Ferroelectr Freq Control1993; 40:603–607.

30. Chen X, Phillips D, Schwarz KQ, Mottley JG, ParkerKJ. The measurement of backscatter coefficientfrom a broadband pulse-echo system: a new for-mulation. IEEE Trans Ultrason Ferroelectr FreqControl 1997; 44:515–525.

31. Madsen EL, Frank GR, Dong F. Liquid or solid ultra-sonically tissue-mimicking materials with very lowscatter. Ultrasound Med Biol 1998; 24:535–542.

32. Chin RB, Madsen EL, Zagzebski JA, Jadvar H, Wu X-K, Frank GR. A reusable perfusion supporting tissue-mimicking material for ultrasound hyperthermiaphantoms. Med Phys 1990; 17:380–390.

33. D’Astous FT, Foster FS. Frequency dependence ofultrasonic attenuation and backscatter in breast tis-sue. Ultrasound Med Biol 1986; 12:795–808.

34. Madsen EL, Zagzebski JA, Frank GR. Oil-in-gelatindispersions for use as ultrasonically tissue-mimickingmaterials. Ultrasound Med Biol 1982; 8:277–287.

35. Ford RD. Introduction to Acoustics. Amsterdam, theNetherlands: Elsevier; 1970:77.

J Ultrasound Med 2005; 24:1235–1250 1249

Wear et al

36. Kaye GWC, Laby TH. Table of Physical and ChemicalConstants. London, England: Longman; 1973.

37. Ragozzino M. Analysis of the error in measurementof ultrasound speed in tissue due to waveformdeformation by frequency-dependent attenuation.Ultrasonics 1981; 19:135–138.

38. Kuc R, Schwartz M. Estimating the acoustic attenu-ation coefficient slope for liver from reflected ultra-sound signals. IEEE Trans Son Ultrason 1979; 26:353–362.

39. Xu W, Kaufman JJ. Diffraction correction methodsfor insertion ultrasound attenuation estimation. IEEETrans Biomed Eng 1993; 40:563–570.

40. Devries P. Computational Physics. New York, NY:John Wiley & Sons; 1994.

41. Marczak W. Water as a standard in the measure-ment of speed of sound in liquids. J Acoust Soc Am1997; 102:2776–2779.

42. Dunn F, Edmonds PD, Fry WJ. Absorption and dis-persion of ultrasound in biological media. In:Schwan HP (ed). Biological Engineering. New York,NY: McGraw-Hill; 1969:205–332.

43. Selfridge A. Approximate material properties inisotropic materials. IEEE Trans Son Ultrason 1985;32:381–394.

44. Faran JJ. Sound scattering by solid cylinders andspheres. J Acoust Soc Am 1951; 23:405–418.

45. Yuan YW, Shung KK. The effect of focusing on ultra-sonic backscatter measurements. Ultrason Imaging1986; 8:121–130.

1250 J Ultrasound Med 2005; 24:1235–1250

Ultrasonic Backscatter Coefficient Measurements From 2 to 9 MHz