The detection of breast microcalcifications with medical ultrasound

Redistrib

The detection of breast microcalcifications with medicalultrasounda)

Martin E. AndersonDepartment of Biomedical Engineering, Duke University, Room 136 Engineering Building, Durham,North Carolina 27708

Mary S. Soo and Rex C. BentleyDuke University Medical Center, Durham, North Carolina 27708

Gregg E. TraheyDepartment of Biomedical Engineering, Duke University, Room 136 Engineering Building, Durham,North Carolina 27708

~Received 19 February 1996; accepted for publication 14 June 1996!

Microcalcifications are small crystals of calcium apatites which form in human tissue through anumber of mechanisms. The size, morphology, and distribution of microcalcifications are importantindicators in the mammographic screening for and diagnosis of various carcinomas in the breast.Although x-ray mammography is currently the only accepted method for detectingmicrocalcifications, its efficacy in this regard can be reduced in the presence of dense parenchyma.Current ultrasound scanners do not reliably detect microcalcifications in the size range of clinicalinterest. The results of theoretical, simulation, and experimental studies focused on the improvementof the ultrasonic visualization of microcalcifications are presented. Methods for estimating thechanges in microcalcification detection performance which result from changes in aperturegeometry or the presence of an aberrator are presented. An analysis of the relative efficacy of spatialcompounding and synthetic receive aperture geometries in the detection of microcalcifications isdescribed. The impact of log compression of the detected image on visualization is discussed.Registered high resolution ultrasound and digital spot mammography images of microcalcificationsin excised breast carcinoma tissue and results from the imaging of suspected microcalcificationsinvivo are presented. ©1997 Acoustical Society of America.@S0001-4966~97!02612-X#

PACS numbers: 43.10.Ln, 43.80.Qf, 43.80.Jz, 43.80.Vj@FD#

theer-oarnseangttees

a

n-and

as.k-n-k-theAsseast.ays,ex-asese-thatarlyast.ich

rre-the

itost,.

INTRODUCTION

A. The significance of microcalcifications inmammography

The primary object of screening mammography isearly detection of breast cancer. Such detection can decrthe mortality and morbidity associated with breast canc1

Microcalcifications~MCs! are small crystals of calcium apatites which form in human tissue through a numbermechanisms. Their size, morphology, and distributionimportant indicators in the mammographic screening for adiagnosis of various carcinomas in the breast. MCs prein approximately 40% of cancers, and in some cases theythe only indication of malignancy at mammography, makitheir detection and interpretation critical.1–4MCs can presenacross a broad continuum of sizes, from several millimedown to the resolution limit of mammography. Not all typare associated with cancer.5 Currently, x-ray mammographyis the gold standard for such screening mammographythe only accepted method for screening for MCs.1

a!‘‘Selected research articles’’ are ones chosen occasionally by the Edin-Chief, that are judged~a! to have a subject of wide acoustical intereand ~b! to be written for understanding by broad acoustical readership

29 J. Acoust. Soc. Am. 101 (1), January 1997 0001-4966/97/10

ution subject to ASA license or copyright; see http://acousticalsociety.org/c

ease.

fedntre

rs

nd

B. The radiologically dense breast

The natural radiological density of certain types of gladular or fibrous breast tissue can reduce the sensitivityspecificity of mammography.~Note that in this context‘‘density’’ refers to the attenuative character of the tissue,opposed to the optical density of the mammography film!One way in which it does this is by raising the local bacground density of the image, thus lowering the effective cotrast of lesion~s! and/or microcalcifications against that bacground. Another is by extending the dynamic range ofimage, which can then exceed that of the x-ray film used.a consequence it can be difficult for the clinician to chooan exposure which optimally images all regions of the breDense parenchyma also increases scattering of the x rfurther reducing the image contrast. Finally, the longerposure time which dense parenchyma necessitates increthe likelihood that the mammography image will be dgraded by patient motion artifact. It has been suggestedone of the primary causes of false negatives in the edetection of cancer is inadequate imaging of the dense breApproximately one in four women have dense breasts, whgives a measure of the magnitude of the problem.6,7

It has been shown that breast density is inversely colated with age, such that the efficacy of mammography inyoung breast is reduced.8–10 Brekelmanset al. propose this

r-

291(1)/29/11/$10.00 © 1997 Acoustical Society of America

ontent/terms. Download to IP: 130.63.180.147 On: Wed, 13 Aug 2014 16:37:04

tin

asItmnsesary

re

le

isetioyucor

or

atnucooinCra

lytoectzauhith

rteetoec

er-and-mitt beeffi-vedicheeni-

%a

ns. Inns-

totemced

eralit,per-m aonly.

msbytech-kleof

ckle.of

ndaseamve-e-Astis-areectstiontheesegersticEd-toill

Redistrib

as one probable cause of reduced sensitivity in detecearly cancers.7

C. The current role of ultrasound in mammography

Medical ultrasound plays an important role in the breclinic as an adjunct to conventional x-ray mammography.primary uses include the differentiation of solid lesions frobenign cysts, the examination of the matrix of solid lesioand guiding needle biopsy.6 Other important applications arin the examinations of young women, women with denbreasts, and women with breast implants, whichradio-opaque.11,12 It is important to note that a radiologicalldense breast may image well under ultrasound.

D. Microcalcifications under ultrasound

Current ultrasound technology and protocol does notliably detect MCs.13,14Microcalcifications which lie within ahypoechoic region, such as the interior of a hypoechoicsion, are more easily detected.11,15Their visualization is lim-ited by a number of factors which may include speckle nophase aberration, the system spatial resolution, attenuadisplay parameters, and human perception of the displaimage. Estimates of the relative impact of these effects copotentially guide attempts to improve detection performan

The analysis of MC detectability is limited by the pocharacterization of their acoustic propertiesin vivo. Filipc-zynskiet al.present an analysis of MC detectability basedthe theoretical radiation patterns of rigid and elastic spheand clinically measured speckle noise levels.16–18This analy-sis was based on a 5-MHz system center frequency andsumed that the acoustic properties of MCs are similarthose for bone. As a consequence, this analysis doesreflect the capabilities of modern 7.5- and 10-MHz transders and may underestimate the reflectivity of MCs. Basedthe acoustic impedance of hydroxyapatite, the most commconstituent of MCs, their amplitude reflection coefficienttissue is close to 0.9.5,19 For this reason, a subresolution Mis modeled below as a bright point reflector under ultsound.

I. THEORETICAL FRAMEWORK FOR DETECTIONPERFORMANCE OPTIMIZATION

The detectability of MCs under ultrasound is most likeaffected by a number of factors, including, but not limitedthe spatial resolution of the imaging system, speckle noisthe image, and phase aberration. An analysis of the impathese factors on MC visualization could guide the optimition of imaging systems for this task. We present a discsion of these factors and a theoretical framework for tanalysis below. The ultimate goal of such investigation isimproved visualization of MCs in the clinic.

A. Spatial resolution

While MCs are most likely to be bright reflectors, fodetection their small size would require the use of a syswith a small resolution volume focused on the MCs in ordfor them to return sufficient signal for detection relativethe surrounding diffuse scatterers. The design factors aff

30 J. Acoust. Soc. Am., Vol. 101, No. 1, January 1997


g

ts

,

ee

-

-

,n,edlde.

nes

s-oot-nn

-

,inof-s-se

mr

t-

ing the resolution of an ultrasound system are well undstood. Primary among these are the center frequency, bwidth, and aperture size of the transducer used to transand receive the ultrasound signal. System resolution mustraded against depth of penetration as the attenuation cocient of tissue also increases with frequency. The improsensitivity of ultrasound in cancerous lesion detection whaccrues with an increase of system resolution has bdemonstrated.11,20–22In a study of 14 lesions presenting mcrocalcifications at mammography, Jacksonet al. found thatthe visualization of microcalcifications was improved in 57of the patients on changing from a 4-MHz transducer to7.5-MHz transducer. In four patients the microcalcificatiowere visible only under the higher-frequency transducerthe two patients with no accompanying mass, neither traducer allowed them to be imaged.22

B. Synthetic receive aperture imaging

One means to improve the resolution of the system isincrease its aperture size. The additional imaging syscomplexity associated with a larger aperture can be reduthrough synthetic receive aperture~SRA! imaging. An SRAsystem transmits into the same region of interest sevtimes from a single transmit aperture. After each transmthe echo signals are received on a different receive subature. These signals are then coherently summed to forlarge effective receive aperture. Such a system requiressufficient channels to populate each receive subaperture23

C. Speckle reduction

Another probable cause of the failure of clinical systeto detect MCs is that their bright signals are obscuredspeckle noise. One means to reduce speckle noise is thenique of spatial compounding, through which the specpatterns received on discrete apertures from the regioninterest are averaged, reducing the variance of the speThis in turn increases the effective signal-to-noise ratiothe coherent MC echo to the speckle noise.24

D. Phase aberration

The spatial and contrast resolution of medical ultrasoucan be severely limited by a phenomenon known as phaberration. The steering and focusing of an ultrasound beusing a phased array relies on an approximation of thelocity of sound in tissue, usually 1540 m/s. In fact, the vlocity of sound through different tissues can vary greatly.an acoustic wavefront passes through inhomogeneoussues, it can become distorted as portions of its surfaceadvanced or retarded. On transmit this phenomenon affthe focusing and steering of the system point spread func~PSF!. The returning echoes incident on the elements oftransducer array are also misaligned such that when thsignals are summed to form a single echo line they no lonsum coherently. In a comprehensive study of the acouproperties of both healthy and cancerous breast tissues,mondset al.measured a range sound velocities from 1400over 1600 m/s.25 This suggests that imaging in the breast wvery likely be affected by phase aberration.

30Anderson et al.: Ultrasound detection of breast calcification


dtufodc-ndo

obhestdforo

sin

orealutena

a

ck

roon

enconanlethn

tri

ri-

i-ig-

st

hanemofhestheyer-memmt-

-the

he

mtts,

edesd.

Redistrib

E. Visualization as a detection problem

It is assumed that a subresolution MC can be modelea point target, and is to be detected on the basis of ampliby an ideal observer. In detection theory, the probability ocorrect decision is described in terms of the probabilitiestheH1 andH0 hypotheses, which in this context corresponto the ‘‘MC present’’ and ‘‘MC absent’’ hypotheses, respetively. If an amplitude threshold is applied to the ultrasousignal to decide whether a MC is present, the probabilitiesa correct detection~Pd! and that of a false alarm~Pf! arepredicted by the integrals above that threshold of the prability density functions of amplitude corresponding to tH1 and H0 hypotheses. Receiver operating characteri~ROC! curves plot Pd versus Pf as the amplitude thresholallowed to vary. Such curves thus indicate detection permance as the stringency of the decision criterion ranges flow sensitivity and high specificity~low Pd, low Pf! to highsensitivity and low specificity~high Pd, high Pf!. The rela-tive performance of different systems can be compared uthe corresponding ROC curves.

A ROC analysis comparing the relative detection perfmance of four imaging systems is presented below. Thinclude a spatial compounding system, an SRA system,two conventional systems having different spatial resotions. An ROC analysis demonstrating the impact on detion of phase aberration modeled as a thin phase screealso presented below. It is important to note that these anses are presented solely as a means to compare systemformance and do not reflect the performance of a humobserver.

F. Theoretical probability density functions ofamplitude

The statistics used here to describe ultrasound speare drawn from the literature of laser optics.26 In fully devel-oped speckle, the complex radio-frequency echo signal fdiffuse scatterers alone has a zero mean, two-dimensiGaussian probability density function~PDF! in the complexplane. Envelope detection removes the phase componcreating a signal with a Rayleigh amplitude distributioWhen a bright target, such as a subresolution microcalcifition, is introduced to the speckle, it adds a constant strphasor to the diffuse scatterers echoes and shifts the methe complex echo signal away from the origin in the compplane. Upon detection, this has the effect of changingRayleigh distribution into a Rician distribution. The RiciaPDF is defined by the following equation:

pA~a!5a

s2 expS 2a21s2

2s2 D I 0S ass2D . ~1!

This distribution is nonzero fora.0 only. The parameters isthe strength of the bright scatterer, whiles is the standarddeviation of the complex Gaussian described above.I 0 is theincomplete Bessel function of zero order. The Rician disbution is parameterized by the variablek, which is defined ass/s.26 The Rician distribution reduces to the Rayleigh distbution for the special cases50. A family of Rician distribu-tions for various values ofk is shown in Fig. 1. Note that the



asdeafs

f

-

icisr-m

g

-send-c-is

ly-per-n

le

mal

nt,.a-gofxe

-

curve for k50 corresponds to the Rayleigh distribution. Inthis discussion it is assumed that a subresolution microcalcfication contributes a constant strong phasor to the echo snal, although it is not possible at this time to predict thekparameter corresponding to a particular size MC in breatissue.

While the development of the Rician statistic in opticsimplies monochromicity, one can generalize the Rayleigand the Rician statistics to the broadband case, such asultrasound system. If acoustic propagation is limited to thlinear regime, the broadband signal of an ultrasound systecan be represented as the linear combination of a seriesmonochromatic systems, each at a different frequency. Tinsonification of diffuse scatterers with each of these systemproduces a Gaussian echo signal as described above. Byprinciple of the orthogonality, these signals are statisticallindependent. The broadband signal produced by their supposition is the summation of independent Gaussian randovariables, and is thus also Gaussian. For a broadband systthe constant phasor which distinguishes the Rayleigh frothe Rician correctly describes the signal from a strong scaterer provided this scatterer is at the focus.

G. ROC comparison of aperture geometries

In this context the differences between the imaging systems described manifest themselves in the parameters ofRician @Eq. ~1!#. For the analysis of aperture geometry, thesvalue was constant for theH1 case and equal to zero for theH0 case. The geometries used are shown in Fig. 2, where tf number~f /#! refers to the ratio of the focal range to aper-ture size. Thef /2 control used the center half of the apertureelements to transmit and receive, while thef /1 control usedthe entire aperture to transmit and receive. The SRA systetransmitted twice from the center of the array, receiving firson the center elements and then on the flanking elemenforming an effectivef /2 on transmit,f /1 on receive system.The spatial compounding geometry transmitted and receivon each half of the array separately, summing the echofrom the two halves after they had been envelope detecte

FIG. 1. Family of Rician probability density functions, parameterized bykvalue for as value of 1.26



h

u

u

ig.un-se

nds

--he0.ingttertofis

are. 3,eo-rvederat itealded

n atof aatedr isrray.de--tionlf-dst isof

orsncer aicu-naofs toe infor

Redistrib

The PDFs used to generate the theoretical ROC curvare summarized in Table I, wherepA(a,s,s) is the Riciandistribution shown above with parametersa, s, ands, and*represents the convolution operation. Thes parameter was aconstant in theH1 case and zero in theH0 case. The deriva-tion of theses values is described in the Appendix.

H. Methods

To simulate the imaging process described above for tpurpose of creating data for ROC analysis, fields of randonumbers with Gaussian amplitude distribution of zero meaand unit variance were created. A central point in each fiewas set to either zero~H0 case! or ten~H1 case!. This strongpoint scatterer surrounded by a field of randomly weightescatterers models the presence of a MC in an environmentweaker diffuse scatterers. The PSFs of the various apertconfigurations were also created using an acoustic fiesimulation program.27 The input field was convolved withthe PSF of each system under evaluation for bothH1 andH0cases, including the controls. This convolution definedscattering grid of 15-mm, spacing laterally by 15.4-mm spac-ing axially, resulting in a scatterer density of over 100 scaterers per resolution cell for all the systems simulated. Fnally, the resulting echo patterns were envelope detectusing the Hilbert transform and the amplitude was recordeat the target location for each imaging system and the cotrols. After a series of 1000 trials, histogram PDFs for eacsystem were created from which ROC curves were calclated.

FIG. 2. Geometries of apertures of simulated imaging systems used, wactive portions of aperture shown in black.

TABLE I. Summary of PDFs used to generate theoretical ROC curves.

System PDF

f /2 control pAuH1(a,s,s)

f /1 control pAuH1(a,s,0.707s)

SRA pAuH1(a,s,0.791s)

Spatial compounding pAuH1(a,s,1.03s)* pAuH1

(a,s,1.03s)



es

emnld

dofreld

a

t-i-eddn-h-

I. Theoretical/simulation results for aperturegeometries

The theoretical results are shown as solid curves in F3~a!–~d!. These curves represent the system performanceder relatively difficult detection conditions, i.e., for the cawhere the MC has a relatively low strength ofk51.265. Thek value is a function both of the original scatterer field athe system point spread function. For these simulationkwas estimated from the first order statistics of theH1 andH0

histograms for thef /2 control, following the theoretical expressions given by Goodman.26 This k value was also calculated using the simulated point spread function following tmethod described in the Appendix, giving a value of 1.28The curves for the SRA system and the spatial compoundsystem are almost identical. Both systems perform bethan thef /2 control case, while thef /1 control performs besof all. If based on these results alone, the better choiceimaging method between SRA and spatial compoundingnot indicated.

The simulation results for the same set of parameterssuperimposed on the respective theoretical curves in Fig~a!–~d!. These results are in good agreement with the thretical results. A common method of reducing a ROC cuto a single index of performance is to integrate the area unthe curve.28 This parameter ranges from 0.5 to 1, withgreater area indicating better performance. In this contexis also the expected fraction of correct diagnosis by an idobserver. The areas under the theoretical curves are inclufor comparison in Fig. 3~a!–~d!.

J. ROC analysis of the impact of aberration

The model of phase aberration as a thin phase screethe aperture can be used to compare the performancesystem with an aberrator present to that of the unaberrcontrol. In the simulations discussed below, the aberratoapplied as a random phase error on the elements of the aThis random error is described in terms of its standardviation ~rms phase error! and its spatial autocorrelation function across the aperture. This spatial autocorrelation funcis assumed to be Gaussian with a known full-width-hamaximum ~FWHM!. The choice of appropriate first- ansecond-order statistics to describe aberration in the breahindered by the lack of comprehensive measurementssuch aberratorsin vivo.

Assuming aberrators of random structure, the authfind it most meaningful to characterize system performafor a statistically defined class of aberrators, rather than fosingle realization. Over an ensemble of aberrators of partlar statistics, thes ands parameters for each realization cavary considerably, defining a family of ROC curves forparticular target strength. In order to compare the familiesROC curves produced over different classes of aberratoreach other and to the control, the area under every curvthe ensemble was calculated and the statistics of areaeach class of aberrator is reported.

ith



t aperture

Redistrib

FIG. 3. ~a! f /1 control, ROC area50.775.~b! f /2 control, ROC area50.665.~c! Synthetic receive aperture, ROC area50.736.~d! Spatial compounding, ROCarea50.720. Given the model of microcalcification detection described in the text, these ROC curves show the relative performance of four differengeometries, described in the text and Fig. 2. Simulation results with error bars~61 standard deviation! are plotted on theoretical curves.

ndimoerFtiop

dop

eers-a

e-

e

yan-of

tionsed amnd

s of

K. Methods

Random aberrator profiles having the first- and secoorder statistics of interest were created and applied to a slated ultrasound transducer in the form of a timing erroreach element on both transmit and receive. For each abtor and for the unaberrated control the corresponding PSthe focus was created using an acoustic field simulaprogram.27 The energy of each PSF over the region of suport was calculated and used to estimate the Ricians param-eter for each realization. Each PSF was then envelopetected using the Hilbert transform, and the peak envelamplitude used to estimate the corresponding Ricians pa-rameter. Specifically, to form eachk estimate the enveloppeak value was divided by the square root of the PSF enfor each trial. This ratio was then scaled by a constant choto produce the desiredk~k5s/s! parameter for the unaberrated control. This constant is equivalent to the original scterer strength, as opposed to the strengths of the echo signalreturned from it. The justification for this method is prsented in the Appendix.

For each realization, the area under the ROC curve g



-u-nra-atn-

e-e

gyen

t-

n-

erated using the correspondingk estimate was calculated bnumerical integration. After 1000 trials the mean and stdard deviation of the area was found for each ensembleROC curves, and hence for each class of aberrator.

L. Simulation results

The mean ROC areas and associated standard deviafor three classes of aberrators are listed in Table II. Thkvalue for the control was 1.5. The aberrators used all haGaussian spatial autocorrelation function with a 6-mFWHM. The severity of the aberrators were 10-, 20-, a

TABLE II. Mean ROC areas and standard deviations for three classeaberrators.

rms phase error~ns! Mean ROC area Standard dev.

0 ~control! 0.714 NA10 0.690 0.01920 0.632 0.04530 0.594 0.045



Hator

aeanasea

thwaa

angeeoemon

enltre

wgeaalw3-

mte

isnida

eot

ufootodklisa

pa-ral

e.ion.o-di-

hyin

r

Redistrib

30-ns rms phase error. The simulated system was a 10-Mf /1 system with 100% bandwidth. For this system theseerrators are weak relative to aberrators measured inbreast.24,31The results show a significant decrease in perfmance with the increase in aberrator severity.

II. EMPIRICAL DATA ACQUISITION

Ultrasound data from excised tissue samples of brecarcinoma which contain MCs have also been collectThese samples were obtained from excisional biopsymastectomy specimens. For some samples digital spot mmography was also used to test whether MCs were preand to determine their location if found. Suspected microccifications have also been imagedin vivo.

A. Methods for and images of excised tissues

In this procedure, upon excision and transport toultrasound laboratory on ice the unfixed tissue sampleimmobilized in the center of a polystyrene Petri dish withthin layer of 10% gelatin in lactated Ringer’s solution,iso-osmotic buffer. Two small lead beads placed in theserved as position markers. The specimen underwent spmen digital spot mammography. All views were acquireda LORAD StereoGuide digital spot mammography systwith a CCD device having just over 10 lines/mm resoluti~512 lines/5 cm on each axis!.

The disk of gelatin holding the specimen was immersin lactated Ringer’s solution at room temperature ascanned using ultrasound. The lead beads reflected usound well and served as reference points for specimenistration. These scans were carried out using anf /1.3 10-MHz Panametrics piston transducer. The transducerdriven using a Tektronix PG501 pulse generator triggerinMetrotek MP215 ultrasound pulser. The echo signals wreceived using a Metrotek MR101 receiver and digitized100 MHz at 8-bit resolution using a Lecroy 9424E digitoscilloscope and stored on a computer. The transducertranslated using a computer-controlled NTR Systemspositioning system. By digitizing echo lines at 100-mm in-crements in the two dimensions perpendicular to the beavolume of echo data was acquired over each region of inest.

A pair of images of a cluster of MCs scanned in thmanner are shown in Fig. 4~a! and~b!. Each image has beeinterpolated to a finer grid using bicubic interpolation, andshown in inverted grayscale such that MCs appear asregions. Each image represents a region 2.5 mm2 in area.Figure 4~a! is the digital spot mammography image of thcluster. This image has been enhanced by the removalplanar intensity component which was a consequence oflocal variation in specimen thickness. Figure 4~b! is the de-tected ultrasound image, here presented as the maximvalue projection along the axis of acoustic propagationthe sake of comparison. The peak amplitude of their echis a function of their size and their axial position relativethe focus of the transducer, and is on the order of 20higher than the mean amplitude of the surrounding specSome differences between the images can be seen, andbe expected considering the differences between the m



zb-he-

std.dm-ntl-

es

lci-n

ddra-g-

asaret

asD

, ar-

srk

f ahe

mres

Be.to

m-

mography and ultrasound systems as well as the tissuerameters imaged by them. The theoretical FWHM lateresolution of the transducer used is just under 200mm, ap-proximately the size of the MCs in the ultrasound imagThus, the MCs shown in Fig. 4 appear to be subresolutThis high resolution, highly focused imaging system prvides good visualization of MCs under what are ideal contions relative toin vivo imaging.

B. In vivo methods and observations

A 66-year-old volunteer presenting at mammograpwith a cluster of MCs approximately 1.5 cm from the sk

FIG. 4. Cluster of microcalcifications in excised breast carcinoma unde~a!digital spot mammography and~b! high-resolution ultrasound, shown ininverted grayscale.



uouicreudinap

maarr d

urthadaaurutee

alopst

xa

heetiivsinsis

hee ofam-dich

un-cted

ch-ent

ity, to

theeo-uredheforuldsticoreig.

oseri-ereuldDif-tedni-.9.7ingan-get

lyin a, auetheforted

r ad as

re-

talss

Redistrib

surface was recruited and underwent a localized ultrasoexam. The MC cluster had been the object of a previneedle core biopsy which did not remove the MCs and whleft a small scar on the skin. An Elegra scanner manufactuby the Siemens Medical Systems Ultrasound Groequipped with a 7.5-MHz linear array transducer was usescan the breast in the region of this scar. In this imagmode the scanner provided FWHM spatial resolution ofproximately 200mm axially and 220mm laterally. After ad-justment of the B-mode image gain and logarithmic copression, a pair of bright targets were identifiedapproximately 13 and 16 mm depth. These targets appeas isolated points rather than extended structures undenamic scanning. The unfocused radio frequency~rf! data oneach channel of the transducer were simultaneously captfor the transmit scan line passing through the centers oftargets. These data were captured several times over a rof system gain settings and stored on a computer. Theset found to have the maximum gain without saturation wselected for further analysis. One data set was also captat the same gain settings within the same scan plane throthe tissue approximately 6 mm away from the targets laally. This data set was used to calculate a rough estimatthe echogenicity of the surrounding tissue.

The mammogram films on which this cluster were locized were also examined using a binocular microscequipped with a measurement reticule. The cluster consiof 6 MCs ranging approximately 200–550mm in diameter.The poor contrast of some of the targets prevented emeasurement.

One rf data set is shown in Fig. 5. The deviation in techo arrival time profile in this data from the geometric dlay profile is used below as an estimate of phase aberradue to tissue inhomogenaities. In order to estimate the arrtime profile across the array, segments of the echo datarounding each target were upsampled by a factor of 8 usinterpolation and aligned on a channel-to-channel basis unormalized cross-correlation. This method of alignment i

FIG. 5. rf echoes from a pair of suspected microcalcificationsin vivo.



ndshdptog-

-tedy-

edengetasedghr-of

-eed

ct

-onalur-gnga

refinement of that described by Flax and O’Donnell.29 Thesignal amplitude is progressively diminished away from tcenter of the aperture due to the limited angular responsthe array elements, which each have a lateral FWHM bewidth of approximately623°. Further analysis was restricteto the group of channels at the center of the aperture whhad interelement correlation values of>0.5. As the exactlocation of the targets relative to the transducer wasknown, the respective local peaks of the envelope-detesignal were used as range estimates.

For a linear array of transducer elements receiving eoes from a point target, the geometric delay at each elemte is defined by the equation

te5A~xe2xt!

21yt21zt

2

c, ~2!

where~xe ,0,0! is the element location, (xt ,yt ,zt) is the tar-get location, andc is the speed of sound. Once this quantis squared it becomes a second-order polynomial. Thusfind the best-fit geometric delays for thein vivo data, asecond-order polynomial was fit~by least-mean-squared! tothe square of the measured arrival time profiles, andsquare root of this best-fit curve was taken to find the gmetric delays. These were then subtracted from the measarrival time profiles to achieve focusing. After focusing, tarrival time profiles have a residual phase error of 7.1 nsthe proximal target and 8.5 ns for the distal target. It shobe noted that the distal target may be subject to acoushadowing by the proximal target. The phase profiles befand after focusing for the proximal target are shown in F6~a! and ~b!.

The patterns of echoes seen in Fig. 5 are similar to thobserved from wire and point targets in water tank expements. Some pulse distortion was evident. If the echoes win fact from the MCs observed at mammography, it shobe noted that these were not truly subresolution targets.fraction, resonance, and ‘‘creeping-wave’’ effects associawith reflection from elastic targets on the order of the insofication wavelength may be contributing to this distortion30

As a control for phase error, a wire target at a depth of 1mm in a Radiation Measurements, Inc. tissue mimickphantom was also imaged and the data analyzed in the mner described above. After geometric focusing the wire tarechoes had a residual r.m.s phase error of 5.6 ns.

The targets are also highly echogenic, making it unlikethat these targets were merely bright speckles. To obtacrude estimate of the background speckle echogenicitycontrol data set for an rf line through the surrounding tiss~described above! was used. Both the target data set andcontrol data set were synthetically focused and summedeach target in turn. The local peak of the envelope detecsignal was used as an estimate of the Ricians parameter foreach target. The standard deviation of the control rf ove2.5-mm window centered on these peak values was usean estimate of the Ricians parameter. Thek parameter es-timates for the targets was found by calculating the corspondings/s ratio. The approximatek values found by thismethod were 17 for the proximal target and 44 for the distarget. Technical limitations of the data acquisition proce



hedthnsuet

ubetfrocerantaetnho

cr

rentents.ne

ct ailityndofcur-odetionofal-thecan-sibleet-inal

bleza-tiont oflden-o-ishea-on

ofares inurethinodsper-res-ss thetionvi-t an ineed

gler-ue.

ero

Redistrib

prevent estimation of the error in these measurements. Thigh k values suggest that these targets could be easilytected by an ideal observer in uniform tissue. However,clinical detection problem is complicated by the limitatioof the human observer, the nonuniformity of breast tissand the presence of other echogenic structures withinbreast, among other effects.

The authors are also interested in the potential of sresolution MCs as echogenic point targets to aid in the msurement and characterization of phase aberration inbreast. The authors expect the phase profile of echoessuch targets to reflect the presence of an aberrator. Therelation between the measured profile and the actual abtor will be limited by system parameters such as noiseaperture geometry as well as assumptions made aboustructure of the aberrator. No significant phase error wfound in the profiles after geometric focusing for the targdescribed above. While conclusions regarding aberratiothe breast cannot be drawn from this single case, the autfind it interesting that this result differs significantly fromother reported breast aberrator measurements which desrms phase errors on the order of 60 ns.24,31 However, the

FIG. 6. Arrival time profile of echoes from proximal suspectedin vivomicrocalcification~a! before and~b! after geometric focusing. The aperturused has been limited to those elements with nearest-neighbor ccorrelation coefficients of 0.5 or greater.



see-e

,he

-a-hemor-ra-dthessinrs

ibe

experimental procedure described above is also diffefrom those used to make these other aberrator measurem

As described in the theoretical discussion above, ofactor which prevents the reliable visualization ofin vivoMCs is speckle noise in the detected image. We expesubresolution MC to appear as a bright speckle. The abof the clinician to discern such a target from the backgrouspeckle noise will be profoundly affected by the degreebrightness compression applied to the B-mode image. Inrent ultrasound scanners, the dynamic range of the B-msignal can be compressed, often using a logarithmic funccontrolled by the operator, to fit within the dynamic rangethe display. As MC detection is not the object of typicclinical scanning protocols, it is unlikely the imaging parameters used are optimized in this regard. For example,targets described above were not visible on the initial swith the scanner configured with typical logarithmic compression and mean brightness. The targets became vionly after the compression was reduced to its minimum sting and the gain adjusted to return the image to the origmean brightness.

III. CONCLUSION

Medical ultrasound is not currently considered a reliameans to visualize MCs in the breast. While such visualition has been discussed in the literature, closer examinaof this issue is necessary in light of the rapid advancemenimaging systems. Improvements in MC visualization wouextend the capability of medical ultrasound and be of pottial clinical benefit, particularly to the young and/or radigraphically challenging patient. The work described in thpaper is ultimately directed towards quantifying both tphysical factors which we believe currently limit visualiztion and the relative impact of system design parametersvisualization.

We have begun this examination by posing the taskMC visualization as a detection problem. The methodsbased on theory and simulations for analyzing the changethe Rician statistic which result from changes in apertgeometry or the presence of an aberrator modeled as aphase screen. Examples of the application of these methare presented to show the expected changes in detectionformance due to changes in aperture geometry and the pence of an aberrator. These methods can be used to asserelative performance of ultrasound systems in the detecof subresolution MCs modeled as point targets in an enronment of diffuse scatterers. Initial results indicate thalarge imaging aperture is best used coherently rather thathe spatial compounding configuration considered. Wpresent observations from the imaging of MCs in excistissue and suspected MCsin vivo, demonstrating the highechogenicity of MCs and their potential to serve asin vivopoint targets. In order to improve modeling of this imagintask in the interest of improving visualization, considerabexperimental and clinical work is still required to characteize the typical scattering properties of MCs and breast tiss

ss-



.rarom

-rinceagca

hetucrinthmdiF

t

,rri

dihatit

e-

al:

nian

cermsovetionthe:

ies,

thegrees

thimu-ithe

tainSFthe

thens.redSFin

sys-d in

ency

Redistrib

ACKNOWLEDGMENTS

This work was supported by NIH Grant No7R01CA43334 and NSF Engineering Research Center GNo. CDR-8622201. Technical support for this work was pvided by the Ultrasound Group of Siemens Medical SysteInc.

APPENDIX

For a givens value the Rician distribution is parametrized by thes parameter. In comparing the detection peformance of different apertures or of the same aperture wdifferent aberrators, it has been assumed that the differeamong them can be described solely in terms of scaling thparameters appropriately. The resulting speckle statisticsthen used to describe relative performance at detectinstrong coherent scatterer in a volume of weaker diffuse sterers.

A method is required to calculate the variance of techo signal using an arbitrary aperture geometry or aperaberrator. The output of the ultrasound system at the focan be described in terms of the convolution of the scattefunction with the point spread function of the system atfocus. We model the scattering function as a field or voluof random numbers with zero-mean Gaussian amplitudetribution. The PSF has zero mean and is deterministic.clarity a vector notation to represent locations in spaceadopted. Hence the echo signal received from a point atfocus is written as a convolution integral:

e~x!5EAllh

s~h!p~x2h! dh, ~A1!

wheree~x! is the echo signal,s~x! is the scattering functionp~x! is the PSF, andx is a location in space. For a particulascattering function this will be a constant. To find the vaance of the echo signal one must find

se25^~e~x!!2&2ê~x!&2, ~A2!

where^ & represents the expectation operator over manyferent scattering functions. Noting that the echo signalzero mean, the second term can be dropped. We subs~A1! into the first term:

^~e~x!!2&5K S EAllh

s~h!p~x2h! dhD 2L . ~A3!

Introduce dummy variables to simplify the product of intgrals:

^~e~x!!2&5K EAllh1

s~h1!p~x2h1!dh1

3EAllh2

s~h2!p~x2h2!dh2L ,5K E

Allh1EAllh2

s~h1!s~h2!p~x2h1!

3p~x2h2!dh1 dh2L . ~A4!



nt-s,

-thessereat-

reusgees-orishe

-

f-sute

The expectation operator can be moved within the integr

^~e~x!!2&5EAllh1

EAllh2

^s~h1!s~h2!&^p~x2h1!

3p~x2h2!&dh1 dh2 . ~A5!

The term ^s~h1!s~h2!& is recognized as the autocorrelatiofunction. For a scattering function modeled as a Gausswhite random process with variancess

2, this simplifies to adelta function at the origin. Also, the functionp~x! is deter-ministic. This allows the simplification of the integral:

^~e~x!!2&5EAllh1

EAllh2

d~h12h2!p~x2h1!

3p~x2h2!dh1 dh2 ,

5ss2E

Allh1

p~x2h1!2 dh1 . ~A6!

For a givenss2, the difference between the speckle varian

of different imaging systems can be described solely in teof their respective point spread functions. The integral abrepresents the energy of the PSF, considering the funcp~x! as solely real. This can also be determined ink-space domain by the application of Parseval’s theorem

se25ss

2E2`

`

uP~k!u2 dk. ~A7!

For the ROC analysis comparing aperture geometrse2 for each system was both calculated in thek-space do-

main and estimated by directly integrating the energy ofsimulated PSF. These two methods gave results which ato within one percent. The Ricians parameter in this analysiwas also calculated for thef /2 control from the simulatedPSF by settings equal to the product of the target strengand the peak amplitude of the detected PSF. In these slations the target strength was 10. For the ROC analysis wphase aberration,se

2 was estimated by directly integrating thenergy of the simulated PSF.

The Fraunhofer approximation states that under cerconditions the lateral and elevational components of the Pcan be approximated by the spatial Fourier transform ofaperture times a quadratic phase term.32 The transform of thePSF is the system response ink space, which through theapplication of the Fraunhofer approximation amounts toconvolution of the transmit and receive aperture functioFor the comparison of the geometries, the systems diffeonly in the lateral dimension, and thus the integration of Penergy in thek-space domain was reduced to the integralthe lateral dimension only:

se25ss

2E2My

`

uP~kx!u2dkx . ~A8!

The normalized apertures used to represent the differenttems are defined as simple rectangle functions, describearbitrary units of amplitude (A) and space (x), and areshown schematically in Fig. A1~a!. The lateral transmit–receive response of these systems in the spatial frequdomain in units of magnitude (uAu) and spatial frequency



-

paaolthlvth

-

totheed.lly,

se,omof

e of

tioned.

ver

SF

ion,

ling

cer

, J.n-phy

net,ifi-sur-

C.

ntia

cy

Redistrib

(kx) are shown in Fig. A1~b!. Their respectives values areshown in Table AI. Theses values were calculated by finding the integral @Eq. ~A8!# of each of the respectivetransmit–receive responses, and normalizing these to thef /2control.

For the spatial compounding case the two speckleterns which are summed to form an average are statisticindependent, and the PDF of their sum equals the convtion of the PDFs of the two images. The PDFs for bosubapertures were defined, and these were then convoThes value used for the right and left subapertures was

FIG. A1. Aperture functions used to represent imaging systems, showarbitrary units of space.~b! Lateral transmit–receive response in the spafrequency domain, shown in arbitrary units of lateral spatial frequency.



t-llyu-

ed.at

of the f /2 control with a slight correction reflecting the decrease in their effective size due to look angle.

The scaling of thes parameter must also be taken inaccount. Changing the system aperture size will affectabsolutes value as the sensitivity of the system is changHowever, this scaling affects the diffuse scatterers equasuch that this sensitivity change does not affect thek param-eter, which determines detectability. In the aberrated cathe PSF is distorted and its peak is often shifted away frthe focus. In order to include such cases in our estimatedetection performance, the authors adopt the peak valuthe PSF envelope as an estimate of the scaling ofs, regard-less of the peak’s location. This approach regards a detecsuccessful even if the target visualization is misregisterConsider the introduction of a point scatterer of strengthA atlocationx in Eq. ~A1!:

e~x!5EAllh

@s~h!1Ad~h2x8!#p~x2h!dh,

5Ap~x2x8!1EAllh

s~h!p~x2h!dh. ~A9!

We wish to maximize ue~x!u& over many realizations of thescattering function. We apply the expectation operator omany realizations ofs~x!:

ûe~x!u&5K UAp~x2x8!1EAllh

s~h!p~x2h!dhU L .~A10!

Finally, the triangle inequality is applied. Note that the Pp~x! is deterministic:

ûe~x!u&<Aup~x2x8!u1K U EAllh

s~h!p~x2h!dhU L .~A11!

The second term simplifies to a constant in the expectatthus ûe~x!u& can only be maximized by choosingx to coin-cide with the peak of the envelope ofp~x!. This supports thechoice of the envelope peak as an estimate of the scaof s.

1L. W. Bassett and D. L. Butler, ‘‘Mammography and early breast candetection,’’ Am. Fam. Physician43, 547–557~1991!.

2D. M. Hansell, J. C. Cooke, C. A. Parsons, S. H. Evans, D. R. DanceM. Bliss, and I. Ilesley, ‘‘A quantitative analysis of the spatial relatioships of grouped microcalcifications demonstrated on xeromammograin benign and malignant breast disease,’’ Br. J. Radiol.61, 21–25~1988!.

3B. de Lafontan, J. P. Daures, B. Salicru, F. Eynius, J. Mihura, P. RouaJ. L. Lamarque, A. Naja, and H. Pujol, ‘‘Isolated clustered microcalccations: diagnostic value of mammography—series of 400 cases withgical verification,’’ Radiology190~2!, 479–483~1994!.

4E. S. de Paredes, P. L. Abbitt, S. Tabbarah, M. A. Bickers, and D.

inl

TABLE AI. s values for simulated systems calculated in the frequendomain.

System f /1 control f /2 control SRA

s values A 13 A 2

312 A 5

3

Normalized 1

&

11

A 85



a-

eriy

o

d Fe

as

ol

in

ltra

p

strCli

r,as

b

e

strc

och

y,ter.

g-assolid

ion

rk,re-

ithasic

E.

, P.east

romEE

ing

alsns.

in a

c-’ J.

Redistrib

Smith, ‘‘Mammographic and histologic correlations of microcalcifictions,’’ RadioGraphics10~4!, 577–589~1990!.

5A. Fandos-Morera, M. Prats-Esteve, J. Tura-Soteras, and A. TravCros, ‘‘Breast tumors: composition of microcalcifications,’’ Radiolog169~2!, 325–327~1988!.

6V. P. Jackson, R. E. Hendrick, S. A. Feig, and D. B. Kopans, ‘‘Imagingthe radiographically dense breast,’’ Radiology188, 297–301~1993!.

7C. T. M. Brekelmans, H. J. A. Collette, C. Collette, J. Fracheboud, ande Waard, ‘‘Breast cancer after a negative screen: follow-up of womparticipating in the DOM screening programme,’’ Eur. J. Cancer28A,893–895~1992!.

8I. C. Bennett, R. Freitas, Jr., and I. S. Fentiman, ‘‘Diagnosis of brecancer in young women,’’ Aust. New Zealand J. Surg.61, 284–289~1991!.

9M. L. Palmer and T. N. Tsangaris, ‘‘Breast biopsy in women 30 yearsor less,’’ Am. J. Surg.165, 708–712~1993!.

10I. R. Brand, D. A. Sapherson, and T. S. Brown, ‘‘Breast imagingwomen under 35 with symptomatic breast disease,’’ Br. J. Radiol.66,394–397~1993!.

11V. P. Jackson, ‘‘Sonography of malignant breast disease,’’ Semin. Usound, CT, MR10~2!, 119–131~1989!.

12P. B. Guyer and K. C. Dewbury, ‘‘Ultrasound of the breast in the symtomatic and X-ray dense breast,’’ Clin. Radiol.36, 69–76~1985!.

13A. J. Potterton, D. J. Peakman, and J. R. Young, ‘‘Ultrasound demontion of small breast cancers detected by mammographic screening,’’Radiol.49, 808–813~1994!.

14P. B. Guyer, K. C. Dewbury, D. Warwick, J. Smallwood, and I. Taylo‘‘Direct contact B-scan ultrasound in the diagnosis of solid bremasses,’’ Clin. Radiol.37, 451–458~1986!.

15F. Kasumi, ‘‘Can microcalcifications located within breast carcinomasdetected by ultrasound imaging?,’’ Ultrasound Med. Biol. Suppl. 114,175–182~1988!.

16L. Filipczynski, ‘‘Detectability of calcifications in breast tissues by thultrasonic echo method,’’ Arch. Acoust.8~3!, 205–222~1983!.

17L. Filipczynski, and G. Lypacewicz, ‘‘Estimation of calcification in breatissues by means of the ultrasonic echo and shadow methods,’’ AAcoust.9~1–2!, 41–50~1984!.

18L. Filipczynski, T. Kujawska, and G. Lypacewicz, ‘‘Ultrasonic echmethod in detection breast calcifications. Transient analysis,’’ ArAcoust.11~3!, 287–298~1986!.



a-

f

.n

t

d

-

-

a-n.

t

e

h.

.

19D. E. Grenoble, J. L. Katz, K. L. Dunn, R. S. Gilmore, and K. L. Murt‘‘The elastic properties of hard tissues and apatites,’’ J. Biomed. MaRes.6, 221–233~1972!.

20E. Kelly-Fry, S. T. Morris, V. P. Jackson, R. W. Holder, and N. T. Sanhvi, ‘‘Variation of transducer frequency output and receiver band-pcharacteristics for improved detection and image characterization of sbreast masses,’’ Ultrasound Med. Biol. Suppl. 114, 143–161~1988!.

21P. J. Dempsey, ‘‘The importance of resolution in the clinical applicatof breast sonography,’’ Ultrasound Med. Biol. Suppl. 114, 43–48~1988!.

22V. P. Jackson, E. Kelly-Fry, P. A. Rothschild, H. R. W. , and S. A. Cla‘‘Automated breast sonography using a 7.5 MHz PVDF transducer: pliminary clinical evaluation,’’ Radiology159~3!, 679–684~1986!.

23L. F. Nock, and G. E. Trahey, ‘‘Synthetic receive aperture imaging wphase correction for motion and for tissue inhomogeneities, part I: bprinciples,’’ IEEE Trans. Ultrason. Ferroelec. Freq. Contr.39~4!, 489–495~1992!.

24P. D. Freiburger, D. C. Sullivan, B. H. LeBlanc, S. W. Smith, and G.Trahey, ‘‘Two-dimensional ultrasonic beam distortion in the breast:invivomeasurements and effects,’’ Ultrason. Imag.14, 398–414~1992!.

25P. D. Edmonds, C. L. Mortensen, J. R. Hill, S. K. Holland, J. F. JensenSchattner, and A. D. Valdes, ‘‘Ultrasound tissue characterization of brbiopsy specimens,’’ Ultrason. Imag.13, 162–185~1991!.

26J. W. Goodman,Statistical Optics~Wiley–Interscience, New York, 1985!.27J. A. Jensen, and N. B. Svendsen, ‘‘Calculation of pressure fields farbitrarily shaped, apodized, and excited ultrasound transducers,’’ IETrans. Ultrason. Ferroelec. Freq. Control39~2!, 262–267~1992!.

28J. A. Swets, ‘‘ROC analysis applied to the evaluation of medical imagtechniques,’’ Invest. Radiol.<dbxNULL >14~2!, 109–121~1979!.

29S. W. Flax, and M. O’Donnell, ‘‘Phase aberration correction using signfrom point reflectors and diffuse scatters: basic principles,’’ IEEE TraUltrason. Ferroelec. Freq. Control<dbxNULL >35~6!, 758–767~1988!.

30A. J. Rudgers, ‘‘Acoustic pulses scattered by a rigid sphere immersedfluid,’’ J. Acoust. Soc. Am.45~4!, 900–910~1968!.

31L. M. Hinkelman, D. L. Liu, and R. C. Waag, ‘‘Measurement and corretion of ultrasonic pulse distortion produced by the human breast,’Acoust. Soc. Am.97, 1958–1969~1995!.

32J. W. Goodman,Introduction to Fourier Optics~McGraw-Hill, San Fran-cisco, 1986!.



Documents

The detection of breast microcalcifications with medical ultrasound