Characterization of tissue microstructure using ultrasonic ...

Characterization of tissue microstructure using ultrasonicbackscatter: Theory and technique for optimization usinga Gaussian form factor

Michael L. Oelzea)

Bioacoustics Research Laboratory, Department of Electrical and Computer Engineering,University of Illinois, 405 North Mathews, Urbana, Illinois 61801

James F. ZacharyBioengineering Program, University of Illinois, 1406 West Green Street, Urbana, Illinois 61801

William D. O’Brien, Jr.Bioacoustics Research Laboratory, Department of Electrical and Computer Engineering,University of Illinois, 405 North Mathews, Urbana, Illinois and Bioengineering Program,University of Illinois, 1406 West Green Street, Urbana, Illinois 61801

~Received 13 December 2001; revised 14 June 2002; accepted 20 June 2002!

Characterization of tissue microstructure through ultrasonic backscatter is hypothesized to aid indetection and classification of diseased tissues. Radio frequency signals backscattered from tissuescan be modeled according to the assumed shape, size, and distribution of scatterers in tissues. Powerspectra of rf backscattered signals describe the frequency dependence of scatterers. Experimentalmeasurements of ultrasonic backscatter from spontaneous mammary tumors in rats are obtainedover the frequency range of 4 to 12 MHz. The power spectra measured from rat tumors arecompared to theoretical power spectra derived from a 3D spatial autocorrelation function assuminga Gaussian distribution. Independent values of average scatterer diameter and acoustic concentrationare obtained by approximating the measured power spectrum with a best-fit line. Enhanced B-modeimages are made of the rat tumors and surrounding tissues with superimposed regions of interestquantified by estimated average scatterer sizes and acoustic concentrations. Scattering propertiesestimated inside the tumors and in surrounding tissues are shown to be distinct. Overall, estimatesshowed a 44.8% increase of average scatterer diameter inside the tumor as compared to tissuesoutside the tumor. With the exception of one rat, all estimates of the scatterers’ average acousticconcentration inside the tumor were less than outside the tumors. ©2002 Acoustical Society ofAmerica. @DOI: 10.1121/1.1501278#

PACS numbers: 43.80.Qf, 43.80.Vj@FD#

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I. INTRODUCTION

Conventional B-mode images of living tissues creawith a clinical ultrasound scanning system are made frradio frequency~rf! envelope-detected echo signals. Theecho signals are created by reflections from interfacestween acoustically different regions and by incoherent stering from tissue microstructures. The rf echoes are hypesized to contain frequency-dependent details aboutsmaller-scale structures~less than the wavelength! in the tis-sues. Generally, processing of conventional B-mode imaremoves the frequency-dependent information. ConventioB-mode images relate the envelope of the backscattereechoes to a gray scale. The conventional B-mode scan~bandwidths of 1 to 10 MHz! can resolve structures on thorder of hundreds of micrometers to centimeters in scale.1 Inorder to display and quantify the smaller-scale structurestissues, the frequency-dependent information must belized.

The frequency dependence of scattering from smstructures~compared to wavelength! has been used to extra

a!Electronic mail: [email protected]

1202 J. Acoust. Soc. Am. 112 (3), Pt. 1, Sep. 2002 0001-4966/2002/1

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details about the structures of different materials and meAs noted by Insana,2 light scattering from lasers has beeused to characterize the internal structure of glassespolymers,3 and x rays have been used to characterizestructure of atoms.4 In acoustics, low-frequency sound wave~below 1 kHz! have been used to measure the size andtribution of turbulence in the atmosphere.5

In a statistical sense, the frequency dependence of usound backscatter can be used to extend the resolutioconventional B-mode imaging to tens of micrometers. Ultsonic backscattering techniques have been used to charaize different aspects of microstructure in biological tissuSpecifically, backscatter has been used to extract the avescatterer sizes and acoustic concentrations~product of thenumber concentration of scatterers times the relative impance difference between the scatterers and surroundingsues! from biological tissues. Feleppaet al.6 used frequency-dependent backscatter to quantify the scatterer sizesacoustic concentration of ocular tumors. Lizziet al.7 used thesame techniques to examine the structure of the liver, wInsanaet al.8 used these techniques to parametrize renalsues. Numerous other experiments and detailed scatte

12(3)/1202/10/$19.00 © 2002 Acoustical Society of America

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models have been developed and used to describe backtered ultrasound from biological tissues.9

Acoustic scattering theories for biological tissuessume that the tissues can be modeled as inhomogenfluids.2 Scattering occurs when an acoustic wave propagacross a region that has a different density and/or compribility relative to the surrounding tissue or fluid. In mocases, a sphere, a cylinder, or some simple geometricfiguration has been used to approximate the scatteringticle shape. If the size~diameter! of the scatterer is on thesame order or smaller than the wavelength of sound, thenpattern of the scattered signal is well known for simple gmetric shapes.10 In addition, the size and shape of the sctering region determine the magnitude at which a specfrequency of sound will be scattered.

For example, in tumor pathology these scatteringgions as viewed by a pathologist using an optical microscinclude typical macrostructures such as tumor nodules,microstructures such as epithelial cells. Tumor nodules corange in size from millimeters to centimeters in diametEpithelia cells measuring 10–20mm in diameter could bearranged as individual cells in supporting stroma. In adtion, epithelial cells could also be arranged in tubulesglands that measure 50–150mm in diameter. These epitheliacells are supported by a stroma composed of connectivesue and blood vessels that have a unique tissue densitycan also encapsulate the mass and form a tumor no~macrostructure!.

Enhanced B-mode images can be constructed by relascattering information~estimated average scatterer size aacoustic concentration in this study! about the tissue microstructure obtained from the backscattered rf signals tolected pixels or regions of interest~ROIs!. Enhanced imagesare formed by superimposing the quantified estimatesconventional B-mode images.11 An enhanced imaging technique that could be adapted for real-timein situ clinical di-agnosis ~classification! of cancerous tissues would havenormous medical significance.

This study examines the estimation of scattering propties like the average scatterer size and acoustic concentrin order to construct enhanced B-mode images. Sectiooutlines the theory used to model the tissue microstructuSection III outlines a novel estimation scheme used to invthe model from the measured data and obtain the avescatterer parameters. The new estimation scheme doeassume that the scattered power spectrum has linearquency dependence. Instead, the new estimation schemea least-squares procedure to fit a line to a measured ffactor and relates the slope and intercept of that line toerage scatterer properties. Section IV discusses the expevariance inherent in the estimation scheme used. Sectioshows enhanced B-mode images of four rats with spontaous mammary tumors and compares scattering propefrom ROIs inside the tumors and in surrounding tissues. Tfinal section gives some concluding remarks and futurerections for this work.

J. Acoust. Soc. Am., Vol. 112, No. 3, Pt. 1, Sep. 2002 O

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II. THEORETICAL DESCRIPTION

Scattering in tissues arises from spatial changes inacoustic impedance about the local mean value. If the walength of ultrasound is larger than or on the same order assize of a scattering region, some of the incident acouenergy will be scattered in all directions. The amount of eergy scattered in any one direction will depend on the sshape, and orientation of the scatterer relative to the walength and propagation direction of sound.12 Backscatter re-fers to that portion of the scattered field directed back tosource aperture. The frequency content of the backscattpulse will also depend on the size and shape of the scatt

The tissue model used in this study assumes a spcollection of randomly distributed, weakly scattering paticles ~Born approximation!. Under the assumption of weascattering, multiple scattering is assumed to be negligiBecause the scatterers are randomly distributed, the rf bscattered signal will be due to incoherent scattering. Inspecific case of the rat tumors, it is expected that there mexist distinct regions of homogeneous scattering. The hogeneous regions could lead to a coherent scattering comnent. If the homogeneous regions were several wavelenin size, then the effects of coherent scatter from these regwould be outside the analysis bandwidth. The effects ofcoherent scatter were assumed negligible and thus wignored.8,13The exact location and size of each scatterer cnot be determined, but rather a statistical description oferage properties within a certain volume of interest maydeduced.13–15

The size, shape, distribution, and elastic properties ofscatterers in the medium will determine the frequency depdence of the backscattered signals. In the tissue modelspatial autocorrelation functions can be used to describesize, shape, elastic properties, and distributionscatterers.13–16 Instead of calculating the correlation functions directly for the scattering medium, some authors hfound it convenient to calculate the acoustic intensity fofactor F.14,15 The form factor is proportional to the Fourietransform of the autocorrelation function and describesfrequency dependence of the scattering in terms of the sshape, and elastic properties of the scatterers. The Fotransform of the autocorrelation function for statistically stionary scattering is defined as the power spectrum andcorporates the form factor. Insanaet al. showed that in thespecial case of randomly positioned, spherical scatterersform factor is a function of the average effective scattesize ~diameter! and the frequency.14

For the present study the Gaussian form factor is usemodel the soft tissue scattering from spontaneous mammtumors in rats. The Gaussian form factor has been usemodel the scattering properties of many soft tissues.7,17,18

The choice of the Gaussian form factor over other form ftors ~exponential and spherical shell! was made because thaverage chi-square value between the measured form faand the theoretical form factors was smallest with the Gauian. The Gaussian form factor, as derived by Insanaet al., isgiven by14

FGauss~2k!5e20.827k2aeff2

, ~1!

1203elze et al.: Ultrasonic characterization of tissue microstructure

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wherek is the acoustic wave number andaeff is the averageeffective scatterer radius. The Gaussian form factor repsents a spherical scatterer that varies continuously withsurrounding tissues and has a uniform particle radius~seeRef. 9, Chap. 4, Appendix B!. Instead of a sharp discontinuity with the impedance like a solid or fluid-filled spherespherical shell, the Gaussian scattering particle is represeby a gradual change in the impedance from the surroundtissues. Instead of having a definite radius like the sphershell or a solid or fluid-filled sphere, the Gaussian functhas an effective radius,aeff , that is related to particle shapor impedance distribution. In the tumor model~rat fibroad-enoma! used in this study, tubules and glands formedneoplastic epithelial cells ranged between 50–150mm in di-ameter. These structures were distributed at random in aporting matrix composed principally of well-collagenizedbrous connective tissue.

Typical backscatter measurements from tissue volumare made by choosing a region of interest~ROI! and gatingthe backscattered rf time signal corresponding to the RThe measured power spectrum is the magnitude squarethe Fourier transform of the gated, rf time signal. The effeof the gating function~windowing function! and beam func-tion of the transducer~weakly focused piston transducer nethe focal plane! are needed to properly model the bacscattering measurement. Lizziet al. incorporated the gatingfunction ~Hanning window! and beam pattern effects in thdevelopment of the model to normalize the theoretical bascattered power spectrum.16 In the frequency domain, thenormalized, theoretical power spectrum is given by

W~ f !5185Lq2aeff

6 rzvar2 f 4

@112.66~ f qaeff!2#

e212.159f 2aeff2

, ~2!

with L the gate length~mm!, q the ratio of aperture radius tdistance from the region of interest, andf is the frequency~MHz!. The quantity,rzvar

2 , is termed the acoustic concentrtion and is the product of the number of scattering particper unit volume~mm23!, r, and the fractional change in thimpedance between the scattering particles and the surroing medium,zvar5(Z2Z0)/Z0 , whereZ is the acoustic im-pedance of the scatterers andZ0 is the acoustic impedance othe surrounding medium. The exponential term is the Gauian form factor term in the frequency domain.

The measured power spectrum is the magnitude squof the Fourier transform of the gated time signal. The effeof the equipment on the power spectrum measurementfactored out by dividing by a calibration spectrum.13,15 Toobtain the calibration~reference! spectrum, a pulse is reflected from a planar surface with known reflectivity areceived by the emitting transducer. The transducer isingle element, piston style, and weakly focused. The satransducer, equipment, and settings are used to send anceive the reflected pulses that are used to obtain the bscattered signals from a selected ROI in the tissue. Thenar surface is located at the same axial distance fromtransducer as the center of the ROI selected in the tissu~inthe focal zone of the transducer!. The measured power spetrum of the signal from the gated ROI in the tissue is dividby the power spectrum of the reference signal.

1204 J. Acoust. Soc. Am., Vol. 112, No. 3, Pt. 1, Sep. 2002

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The data must be acquired from a large enough voluin order to obtain good estimates because the measpower spectrum describes statistical properties of thedium. Several authors have examined the relationshiptween the size of the ROI~gate length! and the estimation ofscattering power and scatterer statistics.16,19–22As the size ofROI is increased, the statistical estimations should convefor a random scattering medium. Two important factorskey to choosing an appropriate gate length. First, the timbandwidth product should be greater than 1. Second, a lagate length means that more scatterers will be included inspectrum. The sum of the random phase contributions frolarge amount of scatterers is more likely to cancel than fra few randomly spaced scatterers. Toppet al.19 examined thequestion of convergence and concluded that adequate estions could be obtained by taking ROIs with gate lengths10 or more wavelengths at the center frequency of interrotion. Figure 1 shows estimations of scatterer diameter mfrom a computer software phantom. The scatterer size emates were made using the estimation scheme outlineSec. III. The particles in the software phantom scatteredcording to the Gaussian form factor with an effective diaeter of 49mm. The impedance of the scattering particle,Z,was given the value of glass~density 2.38 g/cm3, longitudi-nal sound speed 5570 m/s! and the impedance of the surounding medium,Z0 , was given the value for agar~density1.0 g/cm3, longitudinal sound speed 1540 m/s!. The centerfrequency of the incident pulse and analysis bandwidth waround 7 MHz (l50.22 mm) with a 70% bandwidth defineat 26 dB ~half-power bandwidth of the pulse–echo signa!.The scattering was assumed to occur in the focal zonetransducer with an f-number of 5, where the value ofq wouldbe very small. From Fig. 1 it is seen that the estimationsscatterer diameter begin to converge to 49mm at a gatelength of about 2.5 mm, or 11 wavelengths of the cenfrequency.

Typically, a ROI is made up of a number of parallgated A lines of the same length. The power spectrum msured from an individual A line may have sharp fluctuatio~noise! due to the random nature of the scatterer spacingthe medium.23 The fluctuations represent deviations from tshape of the power spectrum modeled with the form facConsecutive parallel A lines should have similar statisti

FIG. 1. Estimated scatterer diameters from Gaussian-type particlessimulated random scattering medium versus gated length of the backtered rf signal.

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properties if located near each other. The difference betwrf echoes from the consecutive A lines will be the differenin random spacings of the scatterers. If the statistical proties of consecutive A lines can be assumed the same,averaging the consecutive A lines should reduce the ranfluctuations seen in a single A-line spectrum. Averaging wyield a better overall description of the scatterer statistproperties. The average measured power spectrum is gby

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whereR is the reflection coefficient of the planar reflectopn( f ) is the gated rf time signal of thenth A line, N is thenumber of gated A lines, andWref( f ) is the reference powespectrum.

The measured power spectrum describes the frequedependence of the scatterers in the medium. Frequedependent attenuation will affect the measured power strum and, if not compensated for, give rise to inaccurestimates of scattering properties. Typically, attenuationcreases with frequency. The slope of the power spectrumbe more negative if the frequency-dependent losses aretaken into account. In order to give optimal estimationsscattering properties, the frequency-dependent attenuamust be compensated. If the gate size were infinitesimsmall, the frequency-dependent attenuation losses coulcompensated, assuming constant attenuation, by simple-attenuation compensation given by14

Wcomp~ f !5Wmeas~ f !e4a~ f !x, ~4!

wherea( f ) is the frequency-dependent attenuation andx isthe propagation distance through the attenuating mediumthe center of the gated region. When the gate length issmall and the attenuation is not negligible, point compention does not correctly account for frequency-dependlosses. Figure 2 shows estimations of scatterer sizes fsoftware phantoms with large attenuation (8 dcm@7 MHz) as the gate length is increased using the poattenuation-compensation function and no attenuation cpensation. The large attenuation was used to coincide

FIG. 2. Estimated scatterer diameters from Gaussian-type particlessimulated attenuating medium~8 dB/cm @7 MHz! using attenuation com-pensation and no attenuation compensation;D, unattenuated signal;h, un-compensated attenuated signal;3, point compensated attenuated signal;L,compensated signal using Eq.~6!.


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the attenuation measured in rat intercostal tissues~1.1dB/cm/MHz!.24 Point-attenuation compensation causesunderestimation of the average scatterer diameter, whileaccounting for frequency-dependent attenuation leads tooverestimation of scatterer diameter. Attenuatiocompensation functions exist that account for frequendependent losses to the measured power spectrum obtafrom gates of finite length.25–27 The attenuation-compensation functions are represented by

Wcomp~ f !5Wmeas~ f !A~ f ,L !, ~5!

whereL is gate length. An attenuation-compensation funtion derived for gated signals was used in this study, angiven by27

A~ f ,L !5e4a0~ f !x0F 2a~ f !L

12e22a~ f !LG2

, ~6!

where a0( f ) and x0 are, respectively, the attenuation anpropagation distance of the intervening tissues anda( f ) isthe attenuation coefficient in the gated region~assumed con-stant!.

III. MODEL INVERSION

Several techniques have been used to parametrizeshape of the measured power spectrum or to estimate perties of the scatterers in a tissue from the shape of the msured power spectrum. These techniques relate the theocal models to the measured backscatter data. Enhaimages are then formed with the spectral parameters orestimated scatterer properties in order to aid in identifyand characterizing diseased tissues. Several authorssuccessfully used enhanced~parametric! images of the back-scatter coefficient and attenuation to aid in tisscharacterization.15,16,19,28–31Zagzebskiet al. used the back-scatter coefficient parametric images to classify disealiver.29 Other researchers have used the slope and intercethe measured backscattered power spectrum to createmetric images.19 Feleppaet al.30 and Lizziet al.16 have usedthe intercept, slope, and midband fit to the measured bascattered power spectrum and create parametric imagesaided in detection and classification of cancer in the eyeprostate. Insana and Hall15 created parametric images fromscatterer size estimates, scattering strength measuremchi-square images, and integrated backscatter coefficientages. The chi-square images were important to show hwell the model represented the interrogated medium forparticular ROI.

If the deduced parameters are related to actual physproperties of the tissues, i.e., the average scatterer sizeacoustic concentration, it may be possible to partially verthe particular form factor models through other means. Psible verification of the model might also be obtainthrough light microscopy. Ultrasound waves detect chanin the mechanical~compressibility, density! properties of thetissues, while light microscopy detects electromagnetic~di-electric! changes in the tissues. Scattering particles arepected to have both mechanical and electromagnetic diences with surrounding tissues. There will not be a one

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one correlation between mechanical and electromagnproperty changes in the scattering particles, but the optcharacteristics should give an approximation of shapesize that can be related to acoustic estimations and aiverification of the form factor models. Estimation of the siand acoustic concentration properties of scatterers is dable because they are hypothesized to relate directly to mphological features in the tissues examined.

Insana and Hall15 estimated the average scatterer sizeminimizing the average squared difference~MASD! betweenthe theory and measurements over a range of scatterervalues. The MASD between the theoretical normalizpower spectrum and the measured power spectrum is calated by14

MASD5minS 1

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m

~Xi2X̄!2D , ~7!

with

Xi510 log@Wmeas~ f i !A~ f i ,L !FGauss~aeff , f i !/ f i4#, ~8!

and

X̄51

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whereA is the attenuation-compensation term andm is thenumber of points in the frequency data bandwidth. The emate of the average scatterer diameter is the argumentminimizes Eq.~7!.

Typically, the measured power spectrum is in termsthe scatter strength, a decibel scale

Smeas~ f !510 log@Wcomp~ f !#. ~10!

Inverting the measurement of the backscattered power strum with the theoretical spectrum enables scattering pareters to be estimated. Relating Eq.~10! to Eq. ~2! gives

Smeas~ f !510 logH 185Lq2aeff6 rzvar

2 f 4

@112.66~ f qaeff!2#

e212.159f 2aeff2 J .

~11!

Expanding the logarithm in Eq.~11! yields

Smeas~ f !510 log@185Lq2aeff6 rzvar

2 #

210 [email protected]~ f qaeff!2#

210~12.159f 2aeff2 !loge110 logf 4. ~12!

Typically, the ratio of transducer radius to distance frotransducer to ROI is small (q!1), which allows the secondterm on the right-hand side to be approximated by

log~11x!'x loge ~ for small x!, ~13!

because the value 2.66(f qaeff)2!1. Subtracting thef 4 term

from the right-hand side gives

Smeas~ f !210 logf 4'M ~aeff2 ! f 21I ~aeff

6 ,rzvar2 !, ~14!

where

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Comparing Eq.~14! to that of a line (y5mx1b), wherex5 f 2, it is seen that the intercept,I, is a function of theeffective average radius~diameter! of the scatterers and thacoustic concentration of scatterers. The slope,M, is a func-tion of the average effective diameter of scatterers only. Tslope and intercept of the line can be found by using lesquares to fit a line to the measured data~left side! of Eq.~14!. From the slope value, the average scatterer diametestimated. Once the average effective scatterer diametestimated, the average acoustic concentration of scattecan be estimated from the intercept value and the estimvalue of the scatterer diameter. The best-fit line paramederived in Eqs.~15! and ~16! differ from the linear param-eters used in the estimation scheme by Lizziet al. in thatEqs.~15! and~16! represent the best-fit line to the measurform factor ~with some constants related to the gating abeam functions!.32 The linear parameters estimated from tapproach by Lizziet al. are deduced from the scatterepower spectrum, which is not linear over a large rangefrequencies.32

The estimation scheme described here has a distinctvantage over the MASD estimation scheme in the numbecalculations needed to derive the estimates. In the MAestimation scheme, different values for the average scattdiameter are chosen until a minimum average squared dience is found. The summation of the squared differenceues is done every time a different average scatterer diamis tried. Several choices of scatterer diameter may be tbefore the average squared difference is minimized. For escatterer diameter tried, the squared difference must beculated at each data point in the analysis bandwidth. Inbest-fit line estimation scheme the summation of the bawidth values is done only once and the estimated averscatterer diameter is obtained.

IV. EXPECTED VARIANCE OF ESTIMATION SCHEME

The expected variance of the estimation scheme deoped in this work was calculated in order to optimize tmeasurement for inverting the scatterer parameters. FChaturvedi and Insana,33 the expected variance of the aveage scatterer diameter from measurement of the Gausform factor is given by

varD̂'(j 51

N H varF̂Gauss~ f j !S ]D

]F̂Gauss~ f j !D 2J , ~17!

whereD̂ is the estimated average scatterer diameter andN isthe number of data points used in the analysis bandwidthevaluate the variance ofD̂, the relationship between the average scatterer diameterD and the measured form factomust be determined. Using the best-fit line technique,small q, Eq. ~14! can be rewritten as

Smeas~ f !210 logf 4'10 log@ F̂Gauss~ f ,D !•C~D,rzvar2 !#,

~18!

so that


10 log@ F̂Gauss~ f ,D !•C~D,rzvar2 !#5M ~D ! f 21I ~D,rzvar

2 !. ~19!

The slopeM can be determined using regression to find the best-fit slope

M ~D !5N( j 51

N f j2 10 log@ F̂~ f j !•C#2( j 51

N f j2( j 51

N 10 log@ F̂~ f j !•C#

N( j 51N f j

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M ~D !'213.2D2, ~21!

which gives, after simplification

213.2D2

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N f j2( j 51

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N( j 51N f j

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~22!

where the factors involving 10 logC subtract out. Defining

s f 25N2(j 51

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f j42NS (

j 51

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f j2D 2

, ~23!

and rearranging yields

(j 51

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s f 2G50, ~24!

which is of the form( j 51N Yj50. The chain rule of differen-

tiation is used

]Yj

]F̂~ f j !5

]Yj

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]D

]F̂~ f j !, ~25!

with

]Yj

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j 51

N26.4D

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N, ~26!

and

]Yj

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s f 2F̂~ f j !. ~27!

Combining Eqs.~26! and ~27! with Eq. ~25! yields

]D

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4.34N

26.4D

~ f j22 f 2!

s f 2F̂~ f j !. ~28!

Substituting Eq.~28! into Eq. ~17! gives

varD̂5(j 51

N

varF̂~ f j !S 4.34N

26.4D

~ f j22 f 2!

s f 2F̂~ f j !D 2

. ~29!

From Chaturvedi and Insana33

varF̂~ f j !'@FGauss~ f j !#2g~ f j !, ~30!

with


g~ f !5F11S sin~2p f NpDt !

Np sin~2p f Dt ! D2G , ~31!

whereDt is the sampling interval of the time signal andNp

is the number of points in the time signal. ApproximatingF̂by FGaussyields the result

varD̂52.0931022N2

D2s f 22 (

j 51

N

g~ f j !~ f j22 f 2!2. ~32!

For a long time signal,g( f j )'1, which gives

varD̂52.0931022

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N

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Calculation of the variance of the average diametertimation for the MASD technique gives the same valuethe best-fit line estimation technique. Simulations andperiments by Chaturvedi and Insana showed that thepected variance derived for the MASD estimation schewas valid for a Gaussian form factor.33 The reason that theexpected variance of the estimated scatterer diameter issame for the best-fit line estimation scheme and the MAscheme is that both techniques minimize the squared difence. The MASD finds the value of the scatterer diamethat minimizes the squared difference between the measdata and the theoretical. The best-fit line is a least-squareof the theoretical spectrum to the experimental spectrum.stead of trying different values for the average scattererameter until the average squared difference is minimized,best-fit line automatically minimizes the average squaredference and consequently yields the best estimate of theerage scatterer diameter.

For the estimation scheme, the variance is inversely pportional to the average scatterer diameter squared.larger the average scatterer diameter the more precisescatterer estimation should be. However, as the relativeof the wavelength becomes smaller, the theory may notrectly describe the scattering. Likewise, estimating the sterer parameters at higher center frequencies over a labandwidth also decreases the expected variance in thesurement ofD. The analysis bandwidth needs to be choswith consideration of the expected scatterer properties.sana and Hall15 discussed the importance of keeping thekaeff

value within the range of 0.5 and 1.2. Using frequenciesfar below the range~larger wavelength compared to scattersize! means the signal scattered from the microstructumay be too small to be discerned from the noise. Usingquencies too far above the range~smaller wavelength compared to the scatterer size! means that the size and shapethe scatterer no longer dictates the frequency dependenc


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a certain average size of the scatterer is expected, the asis frequency bandwidth needs to be chosen accordingly.calculation of the expected variance in the estimation tenique exhibits the trade-off between larger bandwidth acenter operating frequency and the restrictions on thekaeff

value. The calculation of the expected variance is importto optimizing the measurement technique. The measuremtechnique is optimized for the variance by choosing the laest bandwidth and largest center frequency that fit withinacceptablekaeff range. The dependence of the expected vance directly ong( f ) also shows that a better estimatiomay be made from a longer gated signal.

V. ENHANCED IMAGES OF RAT MAMMARY TUMORS

The least-squares best-fit line estimation scheme uting the Gaussian form factor model was applied to B-moimage rf data obtained from mammary tumors that hadveloped spontaneously in rats. The average scatterer sizeacoustic concentration~physical concentration of scatteretimes the average relative impedance difference betwscatterers and surrounding tissues! were estimated from therf signals used to construct the B-mode images. The expmental protocol was approved by the Laboratory AnimCare Advisory Committee at the University of Illinois aUrbana-Champaign and satisfied all campus and NIH rufor the humane use of laboratory animals. Four SpragDawley rats~Harlan, Indianapolis! that had developed spontaneous mammary tumors were evaluated. Each rat wasthanized with CO2, and the tumor and surrounding area weimmediately shaved and depilated. The rat was then plaon a holder in a tank of degassed water at 37 °C for scanwith an ultrasonic transducer. A single-element broadbtransducer was used to scan laterally across the tumorssurrounding tissues. The transducer was moved laterallymicropositioning system with step size of 100mm betweeneach scan. The transducer had a center frequency of abMHz with an 80%–90% frequency bandwidth~Gaussianspectrum defined at26 dB!. The transducer had a diametof 12 mm and a focal length of 50 mm. Measurements wtaken within or near the focal zone. The frequency and bawidth were chosen based on the expected values of theerage scatterer sizes in the rat tissues. The frequencybandwidth were chosen so that the variance in the measment would be minimized while keeping within the optimkaeff range. The transducer was operated in pulse/echo mthrough a Panametrics 5800 pulser/receiver~Waltham, MA!.The signals were recorded and digitized on an oscillosc~Lecroy 9354 TM; Chestnut Ridge, NY! and downloaded toa PC for postprocessing. The sampling rate of the recesignals was 50 MHz. Figure 3 shows a picture of the rat iholder ready to be scanned. The mammary tumor is locaon the upper left portion of the chest. The black line acrthe tumor and chest represents the direction and the lengthe lateral scan.

Two-dimensional B-mode images were constructed frthe ultrasonic scan lines from each rat. Each scan linetaken from a gated portion of the rf backscattered signalrecorded for postprocessing. The axial distance ofB-mode images was associated with the time base of


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signals, and the lateral position of the images was associwith the lateral step length where the individual scan linwere recorded. From the 2D B-mode images, ROIs wdivided into regions inside and outside the tumor whereB-mode images appeared to be homogeneous~no interfacesor large echoes!. The regions scanned and analyzed outsthe tumors were intercostal tissues. The ROIs were separto determine if normal surrounding tissues could be differtiated from the tissues inside the tumors based on the sterer properties.

After scanning, the tumors were excised, fixed in 10neutral-buffered formalin, processed, and stained with hetoxylin and eosin stain for routine histologic evaluationlight microscopy. The tumors were diagnosed as fibroenomas following histopathologic evaluation. Figureshows a photomicrograph of a tissue slice through a tumusing light microscopy. The tumor consisted of wedifferentiated mammary epithelial cells arranged in tubuand glands that were distributed at random in a suppormatrix composed principally of well-collagenized fibrouconnective tissue. Tubules and glands formed by neoplaepithelial cells ranged in size between 50–150mm in diam-eter.

Scatterer estimates were made for each ROI usingbest-fit line estimation scheme. The backscattered rf sig

FIG. 3. Rat to be scanned in holder in tank of degassed water. Ultrasscans ran laterally across the chest and tumor following along the blackThe tumor is located on the upper left side of the chest.

FIG. 4. Photomicrograph of a rat mammary tumor. The specimen was fiin 10% neutral buffered formalin, dehydrated, embedded in paramounted on a glass slide, and stained with hematoxylin and eosin staimicroscopic evaluation. The tumor consists of well-differentiated epithecells arranged in acini surrounded by bands of fibrous connective tissuescale bar represents 50mm.


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was gated from each ROI using a Hanning window andmeasured power spectrum was calculated according to~3!. The average scatterer diameter and average acousticcentration were estimated from the measured power strum. The attenuation for the tissues was deduced frombackscatter according to the method listed in ShungThieme~p. 247!.9 Regions where the scattering appearedmogeneous with depth were selected in order to estimatebest attenuation value by examining the overall loss ofbackscattered signal with depth. If the region selected ismogeneous with scattering, then the only difference betwscattering from particles near and farther away is the atteation loss over the extra propagation distance. The attetion deduced from the backscatter in a particular rat was tused to estimate the scatterer properties throughout theticular rat. The average attenuation coefficient estimafrom the backscatter was 0.9 dB/cm/MHz, assuming a lindependence.

Conventional B-mode images were constructed oftumors and surrounding tissues. Following the enhancedaging model of Toppet al.19 the average scatterer propertiwere superimposed in boxes corresponding to the gROIs. In the enhanced B-mode images by Toppet al., thenumber inside the superimposed box represented the slothe measured average backscatter coefficient. In this wtwo numbers representing the average scatterer diameteaverage acoustic concentration are listed in the ROI boFigures 5–8 show enhanced B-mode images of the ratmors and surrounding tissues. The top number representaverage scatterer diameter~micrometers! in the ROI, and thebottom number represents the average acoustic concentr~mm23!. Noise is evident in the B-mode images of themammary tumors. The noise is due to the low-power sysused for imaging and not because of the large bandwidt

The average scatterer properties estimated inside thmor and outside the tumor from healthy tissues were tcompared. Figure 9 shows the mean of the average scatdiameters measured inside the tumors and outside the tuof the four rats. An examination of the average estimascatterer diameters inside and outside the tumors showed

FIG. 5. Enhanced B-mode image of rat 1 with the tumor located betwthe lateral distance of 0 to 1.8 cm. The top number in the boxes reprethe average scatterer diameter~mm! and the bottom number represents taverage acoustic concentration (10* log@mm23#).


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the scatterers inside the tumors were larger than scatterethe surrounding normal tissues. Overall, the estimashowed a 44.8% increase of average scatterer diameter inthe tumor as compared to the tissues outside the tumor. Wthe exception of the first rat, all differences of scatterer sin the tumors were outside the standard deviation of scattsize estimates outside the tumors.

Figure 10 shows the estimated average acoustic contration inside and outside the tumors of the four differerats. With the exception of the first rat, all estimates of avage acoustic concentration inside the tumor were lessthe average acoustic concentration outside the tumors. Ebars representing the standard deviation are not included

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FIG. 6. Enhanced B-mode image of rat 2 with the tumor located betwthe lateral distance of 0.4 to 1.8 cm. The top number in the boxes reprethe average scatterer diameter~mm! and the bottom number represents thaverage acoustic concentration (10* log@mm23#).

FIG. 7. Enhanced B-mode image of rat 3 with the tumor located betwthe lateral distance of 0 to 1.1 cm. The top number in the boxes represthe average scatterer diameter~mm! and the bottom number represents thaverage acoustic concentration (10* log@mm23#).


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cause, in most of the examined cases, the error barsactually larger than the magnitude of the acoustic concention. The large standard deviation means that the aveacoustic concentration might not be a precise estimationestimate of the average acoustic concentration was mfrom the estimated intercept of the best-fit line and the emated average scatterer radius to the sixth power. Errorthe estimate of the average scatterer radius lead to mlarger errors in the average acoustic concentration. Incase where there is definite separation~no overlap betweenthe error bars! between the average scatterer sizes~rats 2–4!,a definite difference was seen between the estimated aveacoustic concentration inside and outside the tumor. Whthe estimated average scatterer diameters inside the tuand outside the tumors were close~rat 1!, the difference be-tween the average acoustic concentration is very smallnot a good indicator of tissue structure difference.

FIG. 8. Enhanced B-mode image of rat 4 with the tumor located betwthe lateral distance of 1.6 to 3.5 cm. The top number in the boxes reprethe average scatterer diameter~mm! and the bottom number represents taverage acoustic concentration (10* log@mm23#).

FIG. 9. Mean value of average scatterer diameters inside and outsidtumors. Error bars represent one full standard deviation about the mea


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In order to verify the theory and acoustic estimates frothe tumors, a comparison with the tissue microstructthrough other means is necessary. Comparing the lightcroscopic image of Fig. 4 with the acoustic estimates oferage scatterer size shows that there are structures onsame order in size. However, relating the light microscoimages with acoustic estimates may not be a valid compson. The acoustical technique measures mechanical propchanges in the tissue structure, while the light microscomeasures electromagnetic properties of the tissues. Tmay not be a one-to-one correlation between changes intwo properties. Much work needs to be done to verify tacoustical theory and estimation scheme by relating the emates to actual tissue structures.

VI. CONCLUSION

An estimation scheme was devised to rapidly assessaverage scatterer diameter and average acoustic concetion from soft tissues using the Gaussian form factor modThe estimation scheme works by using least squares toline to the measured form factor. The precision of the emation scheme was shown to be equivalent to the MAscheme used by Insanaet al.11,12 to obtain scatterer size estimates. The best-fit line estimation scheme takes advanof the unique functional form of the Gaussian form factorreduce calculation time and give rapid estimates. Previestimation schemes assumed that the power spectrum isear with frequency.16 The best-fit line estimation scheme asumes linear dependence for the measured form factornot the power spectrum.

Four rats that had developed spontaneous mammarymors were obtained and scanned with an ultrasonic traducer. The tumors and surrounding healthy tissues wereterrogated in order to compare the average scattproperties. The rf backscattered signals were gated fROIs that were selected in each of the rats. EnhanB-mode images were constructed from conventional B-mimages superimposed with estimated scattering parameThe enhanced images were used to visually detect difences in tissue microstructure properties.

Comparisons of average scatterer diameters estiminside the tumors and in the surrounding normal tissshowed that distinctions existed between the average s

FIG. 10. Mean value of the average acoustic concentration inside andside the tumors.

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terer properties. The distinctions could be used to clastissues according to their microstructure. The distinctiocould further be used to aid in the noninvasive diagnosisdisease.

Future work needs to be done to better account forfrequency-dependent losses produced by attenuation. Thsumption that attenuation is homogeneous throughout this not necessarily true. In most cases, it is expected thaattenuation and scattering properties will deviate from oregion to the next. If the deviations are substantial, themore detailed mapping of the attenuation throughout diffent regions will be needed to correctly account for tfrequency-dependent losses to the measured power spec

This study has shown that scattering properties likeaverage scatterer diameter and average acoustic concetion can readily be estimated from rf backscattered signMeaningful analysis of the statistical properties betwescatterer parameters inside and outside the tumors is limby the spontaneous nature of the tumors. The tumors gredifferent places on each rat in an uncontrolled fashion.each comparison, different surrounding tissues were cpared with the tumor tissues. Future work will be doneimplanting solid tumor cell lines in rats and closely manaing their growth. In creating a managed line of tumors insubjects, a more meaningful comparison of the statistproperties of scatterers in healthy and diseased tissues cmade.

ACKNOWLEDGMENTS

Thanks to James P. Blue and Rita J. Miller, DVM, ftheir technical assistance. This work was supported by NGrant Nos. CA09067 and CA79179.

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