Large-transducer measurements of wavefront distortion in the female breast

ULTRASONIC IMAGING 14, 276-299

(1992)

LARGE-TRANSDUCER MEASUREMENTS OF WAVEFRONT DISTORTION IN THE FEMALE BREAST

Qing Zhu andBernardD. Steinberg

Valley ForgeResearchCenter The Moore Schoolof ElectricalEngineering University of Pennsylvania Philadelphia,PA 19104

Ultrasonic wavespropagatingthrough soft tissueexperiencewavefront distortion. Refraction occurs at boundariesbetween tissue beds having different sound speeds; scatteringoccurs within a tissuebed, causedby local impedancevariations. This paper describesmeasurements of wavefront distortion in the humanfemale breastthat indicate that refraction is the dominantdistortion mechanismwhen the ultrasonic phasedarray is very large. The determinationthat refraction dominatesthe wavefront distortion is basedupon studiesof multiple imageartifacts that result from a singlesourceradiatedthrough in vivo breastsand breastphantoms. The receiving aperturesusedwere 4.65 and 9.6 cm. Such imageartifacts arerepeatedlyobservedin the 10 young subjectsreportedin this paper,and also in older subjects. An understandingof the in vivo observations is obtained by phantomstudies. FI 1992 Academic Press, Inc. Key words: Femalebreast; imageartifact; refraction; wavefront aberration.

1 INTRODUCTION Ultrasonic waves propagatingthrough soft tissueexperiencewavefront distortion. The lateralresolutionof an ultrasoundsystem(or any other coherentimagingsystem,e.g., radar, sonar)is, in radians,the wavelength divided by the aperturesize, provided that the aperturedoesnot exceedthe scaleof the distortion. Every commercial ultrasoundinstrumentcurrently available assumesa constant speedof soundthroughout the field of view, typically 1540m/s. In reality, the velocities range from 1410m/s in fat to above 1600m/s in tissuesrich in collagen. In an attempt to achieve higher lateral resolution,transducerapertureshave becomelarger. However, the larger the aperturethe more likely that a wavefront radiating from or to a transducerarray would intercept the diverse tissuetypes and therefore develop more severe wavefront distortion. Thus, propagationanomaliesin the mediumsetthe limit to lateralresolution. Adaptive beamforming(self-calibrating,self-coheringand self-focusingor ABF) of a phasedarray for the purposeof compensatingfor wavefront aberrationis a valuable tool in severalfields [l-l 11. Over the past20 years, the Valley Forge ResearchCenter (VFRC) hasdevelopeda groupof ABF algorithmsto self-calibrationlarge, distributedanddistorted phasedarrays in microwaveimaging [3-5,9,11]. In ultrasound,a time domaincorrelationbasedtechniquefor phaseaberrationcorrection wasproposedby Flax and O’Donnell [6]. The algorithm aligns array element phasingvia calculations of the cross correlations 0161-7346/92

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Copyrighr 0 1992 by Academic Press, Inc. All rights of reproducrion in any form reserved.

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between radio frequency signals from all pairs of adjacent elements. Trahey et al demonstrated the use of image brightness from diffuse or point-like targets over a region of interest as a quality factor to compensate for phase aberration [lo]. In the published self-calibration algorithms mentioned above it is assumed (often implicitly) that phase aberrations dominate, implying that scattering induces more prominent effects on the wavefront than does refraction. Refraction occurs at boundaries between tissue beds having different sound speeds; scattering occurs within a tissue bed, caused by local impedance variations. However single source (single transmitter element) wavefront measurements in the female breast with a 4.65-cm receiving aperture at 3 MHz, which are reported in this paper, show severe amplitude distortion of the wavefront as well. Refraction is shown to be the primary cause of the amplitude distortion. Refraction causes beamsplitting and multiple arrivals from different directions at the receiving aperture. This effect is weak with a small transducer but is pronounced when the array is large enough to “see” the multiple arrivals. The objective of the reported experiment was to study the fundamental causes of wavefront distortion in the female breast viewed by a large phased array and to assess the potential applicability of ABF algorithms. This paper reports results of a single source radiated through in vivo female breasts and breast phantoms. In the in vivo measurements, the received wavefront is severely distorted, showing jagged amplitude and phase profiles. A single source imaged through tissue often appears as multiple sources. Subarray analysis demonstrates that multiple arrivals due to refraction can result in this multiple image artifact. Phantom studies support in vivo analysis. The evidence that refraction dominates wavefront distortion is obtained from studies of multiple image artifacts, of a single source, in vivo and in phantoms. Measurements are made in transmission mode with a transducer large enough to experience multiple arrivals A water path assembly was chosen for our experimental from different directions. system because of the huge transducer assembly (12 cm, 80 elements) employed and the difficulty to keep good contact between the linear transducers and the cylindrically shaped breast. Narrowband waveforms (long pulses) were used so as to avoid a possible frequency selective effect upon wavefront distortion measurement. Section 2 describes the image formation process. Section 3 briefly describes the in vivo wavefront measurement setup and procedure. Section 4 reports in vivo and phantom studies. Relevance of this narrowband water-path study to wideband contact measurement is discussed in section 5. Section 6 summarizes the paper. 2 SOURCE IMAGE FORMATION A one-way beam plot of a single transducer in the focal zone is a means to access the beam distortion after the wave propagated through inhomogeneous tissue [ 12-131. The image of a single source located in the focal zone of the receiving array (Fig. 1) is similar to the one-way beam plot, and hence can be used to study the wavefront distortion caused by tissue. The image is a 1-D line image and is the absolute value of the complex estimate of the source distribution. Without medium-induced wavefront distortion the complex estimate of the source distribution is the source distribution convolved with the radiation pattern of the receiving array. Otherwise, the complex estimate is the source distribution convolved with the angular impulse response of the medium and the radiation pattern of the receiving array. Since the source distribution and the radiation pattern of the receiving array are known, the differences in images obtained through the homogeneous medium (water in the following experiments) and the inhomogeneous breast disclose the nature of the wavefront distortion due to tissue. The word “image” throughout the paper always refers to the image of the source and not to a tissue image. The following notation and most derivations are largely followed from [14]. Mathematically, let s(u) represent the source distribution, where u = sin(@and 8 is the angle from the array normal (Fig. 1). Its radiation field in the plane of the receiving array in water after correcting for near-field curvature based on array geometry, is the inverse Fouier

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Fig. 1 Illustration of single source image formation. The source is located at the focal zoneof the receiving array.

focused beam pattern

transformof s(u) denotedas V,(X) = F-‘(s(u)) = ls(u)exp(-jkm)du

(1)

where k = z, il is the wavelength and x representsposition in the array. The induced a signal i,(x) = w(x)v,(x), where w(x) is an aperture weighting function. The weighting function describesthe array in terms of its length, the amplitude taper introduced for sidelobecontrol, and the number of array elementsand their spacings. The complex estimateof the sourcedistributionis the Fourier transformof i,(x), that is SW(u)= F[i,(x)] = F[w(x)v,(x)]

= F[w(x)]*F[v,(x)]

= f(u)*s(u)

(2)

where f(u) = F[w(x)] = Iw(x)exp(jkux)dr is the radiation pattern of the array and * denotesconvolution. If the sourceapproximatesa point source,the complex imagecan be equatedto the radiationpatternof the array. In the breast,the radiationfield at the receiving array is (xL’,+(x)~(x), where m(x) is the mediuminduceddistortion and a is a constantto reflect any signal loss. The induced singleis then

ib(xl = w(x)1m, (x)m(x) I

(3

The complex estimateof the sourceis

kJ(u,= aF[w(x)v,(x)m(x)] = af(u)*s(u)*p(u)

(4)

where p(u) = F[m(x)] is the angular impulseresponseof the medium. For a point-like source,the compleximageapproximatesthe convolution of the radiationpatternof the array and the angularimpulseresponseof the medium. In our transmissionmeasurement,any transmitting array elementcan be usedas a source (Fig.2). Since the sourceis located in the near field of the receiving aperture, a focusing vector w/(x) needsto be calculated to account for near-field curvature of the wavefront. Let w(n)= 1, for n=l,2,......N, in the following analysis, where Nd = L, d

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Cross-Section of Breast Transmitter Array

Receiver Array

, Distorted

Radiated Wavefront Single Bhent 3 -

Z

t

Fig. 2 Experimental3 MHz systemfor in vivo measurement of ultrasonicwavefront distortionin the breast. Z is the wave propagationdirection, X is the transducerdirection andY is perpendicularto X and Z.

is the elementspacingandL is the length of the receiving array. Let v,(n) denote sampled radiation field at the nth receiving element obtained through water alone and then v,(n) = w,(n)v,(n). The inducedsignal i,(n) through water is i,(n) = w(n)v,(n) = w,(n)v,od

(5)

The weight vector w/(n) can be chosenas exp(-jarg(v,(n))), which accountsfor nearfield curvature of the wavefront, elementpositionerrorsandcircuitry errors. The complex estimateof the sourcedistribution is i&4) = F[w,(n)v,(n)]

= ~~w,(n)v,(n)exp[jk(fuf)u] n=O

(6)

When imaging through tissue,the sameapertureweighting function w,(n) is used to focus the array on the sourceand also to remove systemerrors due to elementposition error andcircuitry error. The inducedsignal ib (n) is

k,(n)= w(4[qv(4m(~)l = ay,(n>dn) = aw,(n>v,(nMn) = w,(n)v,(n)

(7)

where v,(n) = m,(n)m(n) is the sampledradiation field at the nth receiving element through breastin water. The complexestimateof the sourcedistribution is h(u)= F[wf(n)v,(n)] = ‘iw,(n)v,(n)exp[jk(nd)u]

(8)

"=O

h

Comparisonbetween ib(u) S*(U) allows us to assessthe image degradation causedby mediuminduceddistortion. The aboveequationsare for CW transmissioncorrespondingto wavelength il.

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3 WAVEFRONT

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The experimental system for measuring the received complex envelopes of single source wavefronts propagated through female breasts is described in detail in [15]. Basically it is composed of two, parallel go-element linear arrays facing each other in a transmission mode (Fig.2). The center to center element spacing is 1.494 mm. Each element consists of 6 subelements which are electrically connected. Their centers are separated by 0.2489 mm. The height of the element is 10 mm and it is focused at 7 cm in the elevation plane. Under computer control, a long, 16 its burst of 3 MHz ultrasound is launched from a single element of the transmitter array. After propagation through the breast (78 ps), which is immersed in a reservoir of water, the received signal at the first receiver element is coherently demodulated by multiplication with an internal oscillator. The analog inphase and quadrature values are measured relative to the transmitted pulse and integrated for 18 l.ts. The analog data are digitized by using two high speed 8 bit A/D converters (MAX- 150 10) and stored. About 200 its later, a second identical waveform is launched from the same transmitter element and the complex envelope at the second receiver element is recorded. This process continues until 31 receiver elements are incremented and 31 complex envelopes recorded, which corresponds to a 4.65cm receiving aperture. This collection of data from 31 receiver elements is the sampled radiation field vb = (v,(l),v,(2),......v,(N)] in equation 7 and called one single-source profile. To measure the spatial inhomogeneities through various portions of the breast, the transmitter element is incremented after each complete single-source profile recording. Vertical arrows in figure I indicate translation directions of the transmitting transducer and the receiver subarray. A total of 38 single-source profiles are recorded for each sequence of source transducer positions within 31 x38 x200 ps = 0.2356 s. The transducers are selected from the middle of the transmitting array. (Because of the possibility that patient motion could distort the data, particularly during systole, multiple measurements were made for each experiment and the one with the least evidence motion artifact was selected. The procedure is discussed in section 5.5.) After data acquisition, the transducer platform is raised (or lowered) 1 cm to expose the breast at a different level, relative to the chest wall, to the ultrasound wave. An average of three such slices are taken through each breast. The slices are taken from the region of the nipple to within 2 cm of the chest wall. The elevation increment of 1 cm is automatically controlled by a stepping motor. The size of the elevation step corresponds to the vertical dimension of the linear arrays. After each such trial, the breast is removed and the same sequence of single-source profiles is recorded through the water for calibration and focusing purposes. The 10 subjects reported upon in this paper were volunteer students and office workers. Their average age was 28 years, ranging from 23 to 33 years. All were healthy, premenopausal women. Similar wavefront distortion measurements have been conducted at the Hospital of the University of Pennsylvania (HUP). A total of 43 volunteers have participated in the in vivo experiments. Their average age is 45 years, ranging from 27 to 68 years. The HUP results are discussed in [16] and will be reported in the future. 4 MULTIPLE

IMAGE ARTIFACTS

4.1 In Vivo Studies 4.1.1 In vivo observations

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Fig. 3 Images of single transducers with a 4.65 cm receiving transducer array. 3 MHz narrowband waveform. Abscissa is lateral position in image in mm. Ordinate is amplitude. Source direction is indicated by dotted line. (a) Image of the source transducer element ##41through water alone. (b) Image of the same source through breast ID#lOR immersed in water. Propagation path is approximately 2 cm from chest wall. (c) Image of the adjacent source transducer element #42 (separation 1.5 mm) through the same breast slice.

Figure 3a shows the image i,(u) of the source (transducer element #41) when the I I propagation medium is water alone. The receiving aperture is 4.65 cm. The ordinate is amplitude and the abscissa is the distance in the transmitting array measured from the left end (bottom in figure 2) and is proportional to 120x u (Fig. 1). The transmitting frequency is 3 MHz. The image shows the expected diffraction pattern of the transducer element convolved with the radiation pattern of the receiving array. Sidelobes are A vanishingly smaI1. Figure 3b shows the image sb(a)of the same source with the same I I transmitting frequency when the propagation medium includes a breast. The image properties change dramatically. Figure 3c is the image of the adjacent source (transducer element #42) imaged through the same breast slice and obtained 0.0062 s later. The distance between two sources is only 1.5 mm, which is approximately 3 wavelengths. The propagation paths lay in a plane parallel to the chest wall and approximately 2 cm from it.

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These images are typical of most single source images through breast. In general, images exhibit some or all of the distortion-induced characteristics shown here. These characteristics are: (a) The image of a single source looks like multiple sources. (b) Images of two almost identical sources are totally uncorrelated when the sources are only slightly separated, in this case by as little as 1.5 mm, which is 3 wavelengths. (c) No main lobe is seen. (d) The largest lobes are far from the source direction (dotted line). Closely related phenomena were reported by Moshfeghi and Waag [ 171 who imaged a small reflector through laterally compressed breasts in vivo and also through water (two way) by using f/l and f/2.6 transducers with wideband pulses centered at 3 MHz. They reported unusually high sidelobe levels (greater than -10 dB) in many of the subjects but none as high as is evident in figure 3b and c. There were three major differences between the Moshfeghi and Waag experiments and ours that can account for the difference. About half the difference (5 dB) is accounted for by their two-way propagation as compared to our one-way propagation. Next is the frequency diversity effect of their wideband transducer, which lowers large sidelobes and tends to fill in the valleys between them. In addition, compressing the breast down to approximately 3 cm in thickness reduces the ray bending at the skin surface caused by refraction because the ultrasound beam enters the breast normal to the surface. The authors also reported that the beam was steered off-axis at random by as much as 10 mm in some cases, which is also seen in our experiment in figure 3b and c. In our experiments, sources imaged through different breasts, at different distances from the chest wall and at different locations in the slice, have some or all of the characteristics described in (a)-(d) above. One common phenomenon in particular is frequently observed; it is the lobe splitting seen within the dotted rectangles in figure 4a and b. Lobe splitting results from coherent destructive interference of waves arriving at an array from different directions. The evidence is a deep null in a region of high energy in the image. Refraction, which causes ray bending, can induce this phenomenon. It requires multipath or multiple arrivals at the receiving array from more than one directions. Refraction occurs at interfaces that separate local volumes having different propagation speeds. Their sizes must be large compared to wavelength to induce ray bending; otherwise, the coherent effect of refraction upon the wavefront is lost and the energy is broadly scattered instead. Thus, the interface between the subcutaneous fat layer, in which the speed is significantly lower than water at room temperature, and glandular tissue (1437 m/s as compared to 1494 m/s and 1540 m/s), is likely to be one candidate source of refraction. Another is any isolated body the order of 1 cm or larger having propagation speed different from the glandular tissue in which it embedded (examples are intramammary fat lobules, cysts and tumors). 4.1.2 Subarray analysis In order to examine the phenomenon seen in figure 4, we begin with the simple case from the nipple region shown in figure Sa. Such images are often seen when the propagation paths are close to the nipple region. The amplitude and phase profiles obtained from the measured complex single-source profile are shown in figures 5b and 5c (solid). The amplitude profile indicates two lobes. The amplitude drop between the highest peak and the deep null, which are marked by arrows, is 21 dB, which is far too much to be accounted for by attenuation alone. The differential path length, estimated from the geometry, is about the same as the lateral distance between the highest peak and the null, which is 1.1 cm. Thus, attenuation at 3 MHz can account for approximately 3 dB change at most. Figure 5c also shows the phase profile of water alone (dotted). The difference between the two phase profiles is the phase profile attributed to tissue only because it is corrected for near-field curvature and system errors. It is shown in figure 5d. The left half portion, which may be identified with the left lobe of the amplitude profile (Fig. 5b), shows an approximately zero-slope linear phasefront. A subarray half the size of the receiving transducer receiving this portion of the field images a single, narrow beam focused to broadside. This is shown in the solid curve of figure 5e. The right half of figure Sd shows a nonlinear, nonzero slope phasefront. The nonlinearity implies defocusing and the nonzero slope implies beam displacement from the axis. A subarray

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Image in mm

Image in mm

Fig. 4 Images of a single transducer through breasts immersed in water. 4.65 cm receiving array. 3 MHz narrowband waveform. Propagation path is parallel to chest wall. Abscissa is lateral position in image in mm. Ordinate is amplitude. Source direction is indicated by dotted vertical line. Lobe splitting is evident in dotted rectangles. (a) Image of source transducer element #39 through breast ID#lOR approximately 2 cm from chest wall. (b) Image of source transducer element #38 through breast ID#16R approximately 4 cm from chest wall.

half the size of the receiving defocused beam off-broadside images gives the double image array appears to come from two

array receiving this portion of the field images a single (Fig. 5e (dashed)). The coherent summation of these of figure 5a. In effect, the energy arriving at the receiving directions.

The result is the well-known double-image artifact frequently observed in cardiac and abdominal echo imaging 11g-211.. Another way to view the phenomenon is that the two wavefronts arriving at the large receiving array add destructively in the direction of the deep null in the image of figure 5a. This phenomenon is pronounced when the receiving aperture is large enough to measure the interference of the arrival energy from the two (or more) directions. 4.1.3 Further considerations

in the nipple region

Figure 6 showshow coherent interference of direct and refracted rays can cause double image artifacts. A set of imagesof single transducersis obtained from the same

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Recking Amy in mm

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Rec&agAttayittmm

so

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Fig. 5 Simplecaseof lobe splitting. 4.65 cm receiving array. 3 MHz narrowbandwave propagatingthrough breastID#l 1L. Sourcedirection is indicatedby dotted line. Propagationpath is approximately4 cm from chestwall and closeto the nipple. (a) Image of a singlesourcetransducerelement#5. (b) Measuredamplitudeprofile at the receiver array showingtwo lobes. Abscissais lateralposition in mm in the receiving subarray. (c) Measuredphaseprofiles at the receiver array through water (dotted) and breast(solid). (d) Phaseprofile of breastalonecorrectedfor near-fieldcurvatureand systemerrors. This curve is the difference betweenthe curvesin c. (e) Subarrayimagesshowingnarrow, focusedbroadsideimage(solid) obtainedfrom left half of the receiveddataset, and defocussed,off-broadsideimage(dashed)obtainedfrom the right half of the receiveddata set.

breastslice ID#l IL usedin figure 5. The crosssectionof the breastsliceis approximately 3 cm and the location of the slice is approximately midway between transmitting and receiving arrays. The propagationpath is closeto the nipple region where,for at leastthree reasons,the breastslicecan bemodeledasa simple,homogeneous circle for examiningthe effects of refraction. First, there is lesssubcutaneous fat closeto the nipple region and no subcutaneous fat immediately beneaththe nipple and areola. Second,thereis insufficient room for large bodiesof diverse speedsto fill in the small cross-sectionnear the nipple.

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+ ------- 1.5cm-------) e---e-

I

... . .. .. .. c

1136#37#38#39w40#41#42#43#44y45Y46

111111111111 transmitters Water

1494 m/s

b

i Breast Slice In

Receiving Array

#36

#37

#38

#39

#40

#41

#42

#43

#44

#45

#46

Fig. 6 Refraction in nipple region. (a) Transmittingelements.(b) Breastslice(EMIlL) approximately 4 cm from the chestwall. Two propagationpaths. (c) Normalizedimages of transmittingelements#36 to 46.

Third, much of the spaceis occupied by the network of ducts which radiate from the nipple. Becausethe duct cross-sectionis at mosta few mm in the non lactating breast[22], ducts scatter energy and cannot induce the coherent wavefront bending required for the multipath phenomenon. Figure 6 showsimages(part c) and sourcelocations(part a) of 11 singletransmitter elements. Source#41 is centrally locatedrelative to the breastslice, and consequentlyits entire beamis interceptedby the breast. Beamspreadingresultsfrom the velocity changeat the interfaces, but no splitting occurs. The beamwidth of the image is wider than that through water due to the slight defocusingbut no multiple imageartifact is observed. For

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source #45, on the other hand, which is located laterally, a partial beam is intercepted by the breast and refracted at the two water-tissue interfaces. This energy arrives at the section of the receiving array indicated as portion 1. Another partial beam passes through water alone and arrives at portion 2 which is overlapped with the portion receiving rays through tissue. Cancellation occurs in the overlapping portion and results in the two lobes in the amplitude pattern shown earlier in figure 5b. 4.1.4 Image correlation study The above study showed how the interface between two media can cause a multiple image artifact. The situation is more severe when the rays pass many boundaries. For example, in the upper part of the breast (1.5 to 2 cm above the nipple), an incident wave can easily encounter several types of tissues with different refractive indexes, such as irregularly shaped subcutaneous layer, glandular tissue, large deposit of intramammary fat and sometimes cysts and tumors. The propagating rays can experience considerable interference as they pass through these tissues and produce complicated multiple images seen in figures 3 and 4. The image correlation coefficients obtained from each breast slice at different levels allows us to observe how the complexity of the propagation medium varies with distance from the nipple region. Figure 7 shows the normalized correlation between complex images as a function of distance from the nipple, obtained from two breasts that were large (210 cm) both in cross section and length and almost filled the entire reservoir. A complex image sequence is formed from a set of single-source profiles at each slice, which is obtained as described in section 2. Successive images, therefore, correspond to transmissions spaced by 1S mm. The kth image correlation coefficient is defined as

p[kl=C where C normalizes p to unity at the origin, K is the total number of sources used, kcn)(rn) is the nth complex estimate of the source in the sequence, m is the FFT bin number (proportional to lateral position in the image) and M = 256. For both sets of data, the 50% correlation distance is about 1 mm when the measurements are made 2 or more cm

Transmitter

Arr

Speed of sound close

Receiver

mm receiving v 120mm

Fig. 7 Normalized image correlation coefficient of single source images at different distances from the nipple for two subjects.

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from the nipple. It increases dramatically in the nipple region, rising to 2.5 mm at a distance of 1 cm. These data show how quickly the image decorrelates in the upper part of the breast due to the multiple refractive index changes of the medium. In figure 7, correlation distance is estimated by linear interpolation of data points spaced by 1.5 mm. It is possible that the precipitous drop at the origin is caused by uncorrelated noise, in which case the lag 0 value would be the sum of the signal power and the noise power. If the noise was not removed from the correlation function, a serious error could result in the estimation of the correlation distance. This was not the case, however. Figure 7a shows a correlation curve without breast (labeled water) in which the correlation is close to unity for the entire curve. If noise had contaminated the correlation estimation, this curve, too, would show it. Since the correlation remained high for nearly 30 mm, we can assume that linear interpolation is satisfactory. Very interesting direct rime-of flight measurements in the neighborhood of 4 MHz have been reported in in vivo studies of breast by Trahey et al (261. They reported an average FWHM (twice what we define as the 50% correlation distance) of correlation curves of arrival time profiles for a group consisting of both premenopausal and poslmenopausal women to be the order of 2.1 mm with standard deviation of 0.74 mm when a single source radiatedthrough the breast. Unfortunately it is not possibleto relate the two experimentsbecausethe linearslopesin arrival time profiles were removedin their study (for the purposeof evaluatingresolution effect) and their transducersize wasabout onethird the sizeof ours (4.65 cm). 4.2 PhantomStudies In the phantom studies described below, we used two types of phantoms to demonstrate that refraction between interfaces of large structures comparable to the wavelengthcan producesimplemultiple imageartifacts. The measuredcorrelationdistance is shownto be approximatelythe scalesize of the structures. Thesephantomsare simpleandinclude only oneor two refractive index changesat most. In vivo breast is much more complicated than these simple phantomsregarding refractive index changes. Multiple refraction betweenfat and glandulartissueaswell as scatteringwithin glandulartissuecan give rise to complicatedimageartifacts and dramatic decorrelationof the imageseenin figure 7. 4.2.1 Castor oil model To study the refractive effect of the subcutaneous fat layer, which is believed to be one important sourceof refraction becauseof the 7% speedmismatch with the interior glandular tissue, we set up a scatter-freecastor oil model. The model consistedof two concentriccastoroil bagsat different temperatures(Fig. 8) to emulatea simplebreastmodel consistingof an outer circular annulusof subcutaneousfat surroundingan inner circle of glandulartissue. The phantomis locatedcloseto the receiving array. The scangeometryis changedfrom a 4.65cm moving receiving subapertureto a fixed 9.6-cm aperture,because rays can be steeredout of the 4.65 cm subaperture.Double-bagcastoroil model is scatterfree because the temperatureand density within each bagis constantand, therefore, there are no local velocity perturbations. The data were taken immediately after the cold bag wasinsertedinto the warm bag: thustemperaturegradientswere likely to be avoided within each bag. The reasonto chosecastor oil with different temperaturesasa simplebreast modelis that it hasa well documentedspeedof soundvs. temperatureandits attenuationis closeto tissue. Experimentally, a sticky cold castoroil bagcan be easily deformedand will keepits deformedshapefor many minutes. Castor oil is an interesting liquid; at 10°C its acoustic speed(1536 m/s) is very closeto that of glandulartissue,while at 30°C its acousticspeed(1452m/s) is closeto that

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0

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Fig. 8 In vitro emulation of simple breast model: glandular tissue surrounded by subcutaneous fat.

of fat. The reference average speed of sound of glandular tissue is 1546 m/s, which is obtained from measurements of the whole breast of 13 young premenopausal women [23]. The reference speed of fat is 1437 m/s, which is reported in [24] obtained from in vitro macroscope studies at body temperature (37OC). The water temperature is 20°C in these castor oil phantom experiments, for which the acoustic speed is 1482 m/s [25]. Since castor oil does not scatter ultrasound, imaging through castor oil is affected only by refraction. Therefore, provided that the castor oil bag is large enough to intercept the entire beam on the portion of the surface facing the source, only ray-bending will occur. The image of the source will be displaced but not significantly distorted. Figure 9 explains the pertinent issues in refraction. Source A, a transducer element of width d, radiates a beam to the receiving aperture through water and a castor oil bag. The speed in the bag Cc can be lower or higher than in the water Cw. The illustration in figure 9a corresponds to Cc < 2ml Cw. The bag cross-section is large compared to 7, the approximate width of the beam between its first zero crossings at distance D1, which contains the bulk of the energy in the beam. The incoming rays are slightly convergent, indicative of a source at A’ at a distance D2 from the receiving transducer. When the receiving array is focused at the source distance D, a single somewhat defocused image is formed. When the source is moved to B (Fig. 9b) part of the beam passes directly to the receiver and part of the beam undergoes refraction as it enters and leaves the castor oil bag. The two subbeams arrive at the array from different directions and the imaging system “sees” two sources, at B and B’. The situation,is further complicated when a smaller higher speed bag is inserted into the warm bag (Fig. SC). The subbeam through the interior passes through a convergent lens (the warm bag) and a divergent lens (the cold bag). The source appears to be at c’. The outer subbeam, passing through the warm bag alone, acts like the beam in figure 9a and appears to have arrived from c”. Therefore, the image shows two sources.

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Fig. 9 Single castor oil bag experiment, Cc < Cw. (a) Source A is located opposite the center of the bag. Image is at A’. (b) Source B is located to the side of the bag. Images are at B and B’. (c) Double-bag experiment. Ccl < Cw 4~2. Images are at c’ and C”.

Figures 10 and 11 pertain to the castor-oil phantom experiments. Figures lob and c show images of transducer element #SO in single-bag castor oil experiments at 1OoC and 300C. The source is nearly centrally located with respect to the bag, corresponding to

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Fig. 10 Imagesof a singletransducer#.50. 9.6 cm receiving array. 3 MHz narrowband waveform. Abscissais lateralpositionin imagein mm. Ordinate is amplitude. Source direction is indicated by dotted line. (a) Imageof the sourcethrough water alone(2000 (b) Through warm castoroil bag (3OoC)roughly 9 cm in diameterinsertedin water. (c) Throughcold castoroil bag(1OOC)roughly 9 cm in diameterinsertedin water. (d) Through doublecastoroil bag (the diametersareroughly 11 and3.5 cm) with temperatures of the outer and inner bagsgiven in (b) and (c). All bagsareroughly conical in shape.

sourceA in figure 9a. As expected,singlesourcesareobserved. Defocusingcausedbeam broadening,asis evident by comparisonwith the samesourceimagedthrough water alone (Fig. 10a). The measured-3 dB beamwidths through water, cold castoroil bag and warm castor oil bag are 0.88 mm, 1.18 mm and 1.32 mm, respectively. The castor oil bag in eachexperimenthasthe shapeof a conewhich is similarto the shapeof the breast. When a smallercold castor oil bag is insertedinto the warm castor oil bag and the conical shapes are roughly unchanged,the image of the source, shown in figure IOd, indicates two primary sources,aspredictedby figure 9c. The above experiments

involved

three distinct

propagation

vokmes

- water, cold

castoroil andwarm castor oil - eachwith a different soundspeed.The correspondingin vivo volumes are water, subcutaneousfat and glandular tissue. The experiment demonstratesthat this refraction-only phantom can produce large image-lobe artifacts similarto the breast-in-waterimagesseenin figure 4. Wavefront distortiondueto refraction is causedby fat-glandulartissueandthe other breasttissueinterfaces (when the tissuebedsare large comparedto wavelength and the

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Fig. 11 Imagesof a singletransducerwith 9.6 cm receiving array. 3 MHz narrowbandwaveform. Abscissais lateralpositionin imagein mm. Ordinate is amplitude. Sourcedirection is indicatedby dottedline. (a) Image of the sourcethroughthe double-bag castoroil phantomwith matched acousticspeedsat water-warmcastor oil interface. No multiple lobes observed. (b) Through the double-bag castoroil phantom(inset)with inner bagdeformedby handto emulatethe irregular shapeof the glandular tissue. Multiple lobesappearbecauseof refraction at irregularinterface. (c) Imageof transducer#44 through breast ID#llR. Note similarity to (b).

soundspeedis fairly constant within each bed, e.g, glandular tissue,intramammary fat lobules,tumor, cyst). In addition, refraction-induceddistortion alsoarisesat the water-fat interface and is unrelated to propagationin breasttissueitself. To reduce the refraction effect at the water-fat interface and to isolate the refraction problem at the fat-glandular tissueinterface, we changedthe distilled water temperatureto 10°C to match the speedof sound at the water-fat interface. Figure lla showsan image of the source through a double-bagcastoroil phantom,each bagroughly conical, with matchedacousticspeedat the water and warm castoroil interface. No signof multiple lobesis observedbecausethe inner bag is large enoughto capture the major portion of the beam,correspondingto the imagingof the sourceA in figure 9a. The situation changesdramatically when the inner bag is deformedby hand (Fig. 11b and inset) so as to emulatethe irregular shapeof the glandulartissue. Now, multiple sourcesare observed, which is a very realistic imageseenthrough breasttissue. Figure 1lc is an in vivo examplefrom breastID#!l IR. Thesephantommeasurements repeatedlyindicate that refraction causedby the 7% or so difference in the speedsof soundbetweenglandular tissueand subcutaneousfat,

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a tibroadenoma

tllmor

A

c3

with necrotic

core Cl I

t 8cm

I I I 4--plastic holder

b

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subcutaneous

fat

fat

Fig. 12 Configuration of compressed breast phantom. Acoustic speeds of the materials are: subcutaneous fat, 1462 m/s; glandular region, 1570 m/s; cyst, 1576 m/s; cyst wall, 1555 m/s; tumor, 1508 m/s; and fibroadenoma, 1570 m/s. (a) Top view. Propagation is downward, into the paper. Cl, C2, etc., indicate positions and cross-sections of the beam (b) Side view. Propagation is from top to bottom.

combined with the irregularly shaped boundary between them, is an important cause of multiple image formation. 4.2.2 Compressed breast phantom Refraction is more severe in our experiment than in a compressed breast because breast curvature is preserved when the breast is freely suspended in water and is eliminated in the phantom. Nevertheless, irregular boundaries between tissue beds and relatively large bodies such as intramammary fat lobules, cysts and tumors still exist in the compressed breast and refraction-induced multiple image artifacts can be anticipated. Supporting evidence is obtained from studies of a compressed breast phantom. The phantom is a sandwich of subcutaneous fat, glandular tissue and subcutaneous fat, with flat and parallel faces, as shown in figure 12. The fat layers are 1.5 cm thick and have undulating interfaces with the glandular tissue. The radii of the curvatures of the undulations are approximately 1.6 cm. The glandular tissue layer is roughly 1.5 cm thick. Imbedded in it are a 0.9 cm diameter walled cyst and a roughly 1 cm diameter irregularly shaped tumor, each large enough to induce refraction effects. Other smaller bodies are also shown in the figure. The acoustic speeds of materials are given in the legend of figure 11.

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lmageinmm

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Image in mm Fig. 13 Images of a single source through compressed breast phantom immersed in water. 9.6 cm receiving array. 3 h4Hz narrowband waveform. Abscissa is lateral position in image in mm. Ordinate is amplitude. Source direction is indicated by dotted line. Water speed matched to fat speed. (a) Propagation path Cl (Fig. 12a) contains glandular tissue alone. (b) Propagation path C5 contains glandular tissue alone. (c) Propagation path C2 contains glandular tissue and irregularly shaped tumor.

The distilled water temperature into which the phantom is placed is controlled so that the acoustic speed matches that of the subcutaneous fat, thereby eliminating refraction from the water-fat interface. The experimental configuration is similar to that shown in figure 8. Figure 13 shows single transducer images through three paths in the phantom. Cl and Cg are free of cysts and tumors and encounter only the subcutaneous fat-glandular tissue interfaces. C2 includes an irregularly shaped tumor with necrotic core. The three images are in parts a, b and c. They all show image artifacts. The path through the tumor (part c) is most severe, notwithstanding the fact that the speed of sound difference between glandular tissue and tumor (62m/s) is much less than the difference between glandular tissue and fat (108/s). The further implication is that sharp refractive index change can induce more severe ray bending to different directions than smooth refractive index change does, and the resulting subbeams interfere, which is the case when the irregularly shaped tumor is included in the propagation path.

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Fig. 14 Normalized image correlation coefficient of point source images of a single slice. Curve A (solid) is image correlation coefficient of compressed breast phantom at slice indicated by C3 in figure 1 la. Curve B (*) is correlation coefficient of compressed breast phantom at slice indicated by C4 in figure 12a. Curve C (x) is correlation coefficient of two-bag castor oil phantom with inner bag deformed as shown in figure 1 lb (inset).

4.2.3 Correlation comparison Image correlation experiments, as described at the end of the section 4.1, were also conducted for the two bag castor oil model and the compressed breast phantom. Two slices through the phantom include the 0.9 cm diameter walled cyst and the toughly lcm diameter irregularly shaped tumor; their propagation paths are indicated in figure 12a by C3 and C4, respectively. From the sizes of these objects and the geometry seen in figure 12a, the expected correlation distance is the order of 1.5 cm, which is approximately observed in curves A and B in figure 14. Note that the correlation distance in the phantom is an order of magnitude larger than that observed in the breast, except in the neighborhood of the nipple (Fig. 7). We believe that this difference is due to multiple refraction as well as scattering in vivo and simple single refraction in the phantoms. Curve C shows image correlation through the %-bag castor oil phantom. The inner bag was deformed as shown in figure 1lb. The lobes of the inner bag and their spacings are the order of 1 - 1.5 cm. This range, therefore, is the expected correlation distance, which agrees with the measurements shown in curve C. The three experiments indicate that when the propagation path includes a single body of refractive-index difference, the image correlation distance is the scale size of that body or its significant parts. In the breast, except for the irregular boundary between the subcutaneous fat and the glandular tissue, the propagating wave can easily encounter several structures of different refractive indexes. The multiple refraction as well as scattering that results dramatically reduces the image correlation distance, as is evidenced in the curves of figure 7.

5 DISCUSSION 5.1 One Dimensional Limitation of the Measurements Our measurements are one dimensional (X, in figure 2) while the wavefront distortions are in two dimensions (X and Y, both normal to 2). The cone shaped breast curvature and the irregularly shaped boundary between the two types of breast tissues in the Y direction can split the incident rays in the Y-Z plane. The split rays are likely to split

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again when they approachthe other end of the tissueinterface and the breastcurvature. Therefore, the received rays may travel above and below the breastslice being examined. Assumingthat this is the case,someof the imagecomplexity seenearliercan be ascribedto the out-of-plane energy. Without this extra energy, the wavefront distortion would reduce and simpler compensationalgorithms would suffice. Removing the out-of-plane energy, therefore, would be desirable. A two-dimensional array is necessaryfor this task. A narrow beamformed in the Y-Z planewould reject the out-of-planeenergy. However, the problem is not as simpleasit sounds. A large Y-dimension to the aperture is neededto achieve the narrow Y-Z beam, and wavefront distortion in the Y-Z plane may require a adaptive weight-vector control to form that beam. If further researchproves this to be the case,2-D adaptivecontrol algorithmsto deal with the entire problemat once will have to be developed. 5.2 Narrowbandvs. WidebandMeasurements The bandwidth of the transmittedsignalusedin the reportedexperimentswasvery narrow (about 60 kHz; the pulseduration was 16 us) so asto avoid a possiblefrequency selectiveeffect upon wavefront distortion. The mainfrequency selectivemechanismis the absorptionof energy by tissue. The long 18 us receiving window is usedto match the transmitted long pulse. Thus the overall frequency responseof the transmitter and the receiver is about 60 kHz. Refraction, however, which showedto be dominant, can induce multipath through ray-bending and, therefore, interference phenomenain the receiving aperture. It is possiblethat suchmultipath arrivals aresufficiently separatedin time sothat their energieswould not coexist in the receiving apertureif a short pulse,typical of echo scanning, were employed. If this were the case we would expect to experience significantly lower wavefront complexity with a shortpulse than we observewith our 16 t.tspulse. For this reasonwe alsoincludeda 1 PLS short pulse(about 1 MHz) and broke up the 18 ps receiving window into 1 us consecutive windows in the following in vivo experimentsat HUP. Similar to the narrowband case,severeamplitude distortion of the wavefront is observedin eachof those 1 ps receiving windows in which significant energy is received [16]. No significant late arrivals were found in most subjects. This suggeststhat multipathsor multiple arrivals developeddue to refraction arealreadyestablishedwithin a 1 l.tsperiod (approximately 3 wavelengthsat 3MHz) and are not significantly separatedin time. Therefore the long pulse and the long receiving window do not contribute significantly to the observedcomplexity reportedin this paper. The role of systembandwidthupon the focusingof an ultrasonicbeampropagating one way through humantissuewas explored by FosterandHunt [131. They measuredthe beampattern of a singletransducerin the focal region. In one in vitro breastmeasurement with both narrowbandand wideband waveforms, the narrowbandwaveform produceda beam pattern similar to figure 3b and c, while the wideband waveform showeda clear, single lobe pattern. The authors offered the tentative explanation that diffraction was responsible. Our conjectureis that weak scatteringis the primary agent. Refraction may not have been significant becausethe breastsamplewas a thin slice with parallel sides. Scattering perturbs the phasefront and is highly frequency selective. Therefore the wideband wideform would smooth the perturbations induced by each frequency component. The result would be a clearpattern, asobserved. 5.3 Contact Measurementvs. Water Path Measurement A water path assemblyhasbeenusedin our transmissionmeasurements reportedin this paper. The reasonwas briefly explained in section 1. The refraction is severein this configuration becauseof the tissue/waterinterfaceand the intact curvature of the breast. In subsequentmeasurementsmadeat HUP, we usedbaby oil (speed1430m/s) rather than water to match the speedof subcutaneous fat (1437m/s). To further reducerefraction due to the oblique incident angle at the subcutaneousfat-glandular tissue interface, we instructedall volunteersto pushtheir breastslaterally againstthe transmittingarray, which partially flattenedone sideof the breast. Furthermore,largebreastswhich filled almostthe

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entire reservoir were selected for analysis; in these cases the breasts were partially flattened against both transducer arrays. However, severe wavefront amplitude distortion and multiple image artifacts reported in this paper still exist [ 161. Therefore, we believe that our measurement results are similar to what would be obtained with contact measurements. 5.4 Implication for Next Generation System Design To achieve higher lateral resolution than provided by commercial equipment today, a large transducer aperture is required. However, the paper shows that the breast induces severe wavefront distortion over an array of 4-5 cm and that refraction is the primary cause. Adaptive weight-vector controlled algorithms being studied in this and other fields respond primarily to scattering and not to refraction, and therefore their utility is questionable. Newer and stronger algorithms are probably needed to solve the one-dimensional array problem. In the event that one-dimensional control proves inadequate, it will be necessary to develop two-dimensional adaptively controlled transducers. To minimize refraction at the skin surface, a transducer compressing the breast against the chest wall is needed. Such a transducer also flattens the interface between subcutaneous fat and glandular tissue to some degree and reduces refraction at this interface [27-281. But when a large transducer comparable to the size of the breast is employed, it is difficult to keep good contact between the transducer and the examined breast. The result may be that only a portion of the transducer is effectively used see ]17]. Under extreme compression, a contact area may be increased but the geometric relationships between different tissue types in the interior may be distorted. This makes locating exact positions of suspicious findings difficult [29]. Thus the dual need is for a large transducer array suitable to achieve high lateral resolution and with a geometry that minimizes the refractive effect. A concave transducer conformal to the breast surface is such a compromise. With such an array, and with more powerful ABF algorithms, the problem of achieving high lateral resolution should be solved. A r- 8 - z concave cup array conformal to the breast is worthy of investigation (Fig. 15). 5.5 Possible Effect of Subject Motion Upon Image Correlation Measurements The experimental procedure was designed to minimize the effect of patient motion during the systole period by taking three sets of 38 single-source profiles in rapid succession and choosing the one with the least evidence of motion. Since the systole period lasts only a fraction of a second, one of the three sets is likely to avoid the systole period and provide relatively stationary data. To determine which profile set was best, a reduced set of 16 profiles also was taken immediately following each 38-profiie set. These were compared with the corresponding 16 profiles from the full set, and the pair with the best match determined which 38-profile set was chosen for analysis. For the selected pairs, the averages and the standard deviations of the amplitude and phase profile differences were calculated. The average amplitude difference is less than 0.5% of the mean amplitude with standard deviation less than 5% of the mean value. The average phase difference is less than 0.0005 radians with standard deviation less than 0.1 radians. These numbers are sufficiently small to ensure that motion did not contribute significant decorrelation in the correlation measurements. Therefore, the dramatic decorrelation as seen in figure 7 is caused by tissue.

6 SUMMARY Wavefront distortion sets the limit to lateral resolution of ultrasonic imaging systems. In order to break this resolution limit, adaptive beamforming algorithms are needed to correct the distortion. Algorithms developed at VFRC and elsewhere, in ultrasound and in other imaging fields, primarily deal with scattering problems, in which

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b 2.

, J

Normal

of a single element

element

Fig. 15 (a) 2-D r- 8 -z Concave Cup Array. Z-axis is the wave propagation direction. The proposed transducer is pushed against breast toward the chest wall. (b) Geometry of a single element. The normal of the element is not necessarily the radial direction of the cup. A small change in p from radial direction of the cup adds a degree of freedom for expanding the field of view.

the distortion source can be modeled as a quasirandom phase screen close to the receiving array. In ultrasound, the algorithms of Flax and O’Donnell [6] and Trahey at al. [lo] are examples. One purpose of our experiment was to determine whether this model is suitable for the breast. This paper describes the experiments and their explanations that lead to the conclusion that refraction is a major cause of wavefront distortion in the breast for a large phased array. As a consequence, the earlier algorithms are too weak to solve the very large ultrasonic array problem and newer and stronger algorithms are probably required. Refraction causes beam splitting during propagation in the tissue and multiple arrivals at the transducer array. Refraction effects are not confined only to the plane of the array but at right angles to it as well. This out-of-plane energy undoubtedly contributes to the severe complexity of the received wavefront. Experience may prove that onedimensional control per se is inadequate to compensate for complicated wavefronts, in which case two-dimensional arrays with 2-D adaptive control will be required.

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ACKNOWLEDGMENTS Special thanks to Dr. Richard J. Pauls for his design and construction of the experimental system used in this report. Invaluable consultation was freely offered by Drs. Kai Thomenius, Director of Research of Interspec Inc., an ultrasound imaging firm in Ambler, Pa., and Ronald Arenson, Associate Chairman of the Dept. of Radiology of the HUP. The heart of the electronic system, a Vingmed SM-20, was donated by Interspec and the two, 80- element arrays were given by Dr. Clyde Oakley, Manager of R&D of Echo Ultrasound, Lewistown , Pa.; we are very grateful for both. The compressed breast phantom was provided by Professor Ernest L. Madsen of the University of Wisconsin. Funding was from the Commonwealth of Pennsylvania under the Ben Franklin Partnership program.

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[S] Steinberg, B. D., Microwave imaging of aircraft, Proc. IEEE 76, 1578-1592 (1988). [6] Flax, S. W. and O’Donnell, M., Phase aberration correction using signals from point reflectors and diffuse scatterers: basic principles, fEEE Trans. Ultrason. Ferroelec. Freq. Conrr. 35, 758-767 (1988). [7] Trahey, G. E. and Smith, S. W., Properties of acoustical speckle in the presence of phase aberration part I: first order statistics, Ultrasonic Imaging IO, 12-28 (1988). [8] Smith, S. W., Trahey, G. E., Hubbard, S.M. and Wagner, R. F., Properties of acoustical speckle in the presence of phase aberration part II: correlation lengths, Ultrasonic Imaging IO, 29-5 1 (1988). 191 Attia, E. H. and Steinberg, B. D., Self-cohering large antenna arrays using the spatial correlation properties of radar clutter, IEEE Trans. Antennas Prop. AP-37, 30-38 (1989). [lo] Trahey, G. E., Zhao, D., Miglin, J. A. and Smith, S. W., Experimental results with a real-time adaptive ultrasonic imaging system for viewing through distorting media, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 37,418-427 (1990). [ 1 I] Steinberg, B. D. and Subbaram, H, Microwave Imaging Techniques. Chapters 8 and 9 (John Wiley and Sons, New York, 1991). [ 121 Foster, F. S. and Hunt, J. W., The Focusing of Ultrasound Beams Through Human Tissue, in Acoustical Imaging, Vol. 8, A.F. Metherell, Ed., (plenum, New York,1979) [13] Foster, F. S. and Hunt, J. W., Transmission of ultrasound beams through human tissue - focussing and attenuation studies, Ultrasound Med. Biol. 3, 257-268 (1979). [ 141 Steinberg, B. D., Principles ofAperture and Array System Design. (John Wiley and Sons, New York, 1976).

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[15] Pauls, R. J., An experimental system for in vivo measurement of ultrasonic wavefront distortion in the breast using a 200-h, 3 MHz array. Valley Forge Research Center Report VFRC-UP-4-91 Univ. Pa., Phila. PA , (1991). [16] Zhu, Q., Large-Transducer Measurements of Ultrasonic Wavefront Distortion in the Female Breast, Ph.D. Dissertation, (Univ. of Pennsylvania, Philadelphia, PA, 1992). [17] Moshfeghi, M. and Waag, R. C., In vivo and in vitro ultrasound beam distortion measurements of a large aperture and a conventional aperture focused transducer, Ultrasound Med. Biol. 5, 415-428 (1988). [18] Sauerbrei, E.E., The split image artifact in pelvic ultrasonography: physics, J. Ultrasound Med. 4, 29-34 (1985).

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[22] Mendelson, E. B., Ultrasound secures place in breast Ca management, Diagnostic Imaging, 120-129 (1991). [23] Kossoff, G., Fry, E. K.and Jellins, J., Average velocity of ultrasound in the human female breast, J. Acousr. Sot. Am 53, 1730-1736 (1973). [24] Foster, F. S., Strban, M. and Austin, G., The ultrasound macroscope: initial studies of breast tissue, Ultrasonic Imaging 6, 243-261(1984). [25] Del Grosso, V. A. and Mader, C. W., Speedof sound in pure water, J. Acoust. Sot. Am. 52, 1442-1446(1972). [26] Trahey, G. E., Freiburger, P. D., Neck, L. F. and Sullivan, D. C, In vivo measurements of ultrasonic beamdistortion in the breast, Ultrasonic Imaging f3,71-90 (1991). [27] Kelly-Fry, E., Influenceson the developmentin the united statesof ultrasoundpulseecho breastinstrumentation, In: Ultrasound Mammography, Harper AP ed. University press,Baltimore, Maryland, (1985). [28] Madsen, E. L., Kelly-Fry, E. and Frank, G. R., Anthropomorphic phantomsfor assessingsystemsusedin ultrasound imaging of the compressedbreast, Ultrasound in Med. & Biol. 14, 183-201(1988). [29] Guyer, P. B. and Dewbury K. C., Sonomammography:An Atlas of Comparative Breast Ultrasound. (JohnWiley and Sons,New York, 1987).

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