A volumetric method for estimation of breast density on digitized screen-film mammograms

A volumetric method for estimation of breast densityon digitized screen-film mammograms

Olga Pawluczyk, Bindu J. Augustine, Martin J. Yaffe,a) Dan Rico, Jiwei Yang,and Gordon E. MawdsleyImaging/Bioengineering Research, Sunnybrook and Women’s College Health Sciences Centre andDepartment of Medical Biophysics, 2075 Bayview Avenue, Toronto, Ontario M4N 3M5, Canada

Norman F. BoydDivision of Epidemiology and Statistics, Ontario Cancer Institute, 610 University Avenue, Toronto,Ontario M4G 1K9, Canada

~Received 3 May 2002; accepted for publication 26 November 2002; published 6 February 2003!

A method is described for the quantitative volumetric analysis of the mammographic density~VBD!from digitized screen-film mammograms. The method is based on initial calibration of the imagingsystem with a tissue-equivalent plastic device and the subsequent correction for variations in ex-posure factors and film processing characteristics through images of an aluminum step wedgeplaced adjacent to the breast during imaging. From information about the compressed breast thick-ness and technique factors used for taking the mammogram as well as the information from thecalibration device, VBD is calculated. First, optical sensitometry is used to convert images to Logrelative exposure. Second, the images are corrected for x-ray field inhomogeneity using a sphericalsection PMMA phantom image. The effectiveness of using the aluminum step wedge in trackingdown the variations in exposure factors and film processing was tested by taking test images of thecalibration device, aluminum step wedge and known density phantoms at various exposure condi-tions and also at different times over one year. Results obtained on known density phantoms showthat VBD can be estimated to within 5% accuracy from the actual value. A first order thicknesscorrection is employed to correct for inaccuracy in the compression thickness indicator of themammography units. Clinical studies are ongoing to evaluate whether VBD can be a better indi-cator for breast cancer risk. ©2003 American Association of Physicists in Medicine.@DOI: 10.1118/1.1539038#

Key words: mammography, volumetric breast density, breast cancer, risk prediction, x-ray

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I. INTRODUCTION

Breast density as characterized from the mammogrambeen linked to the increased risk of breast cancer in mstudies.1–11 Women with high mammographic densities~i.e.,a high proportion of radiographically-opaque stroma andrenchyma! have been shown to be at an increased riskbreast cancer, when compared with women whose breastcomposed mostly of fatty or adipose tissue. Early studiesWolfe1,2 suggested that the classification of radiological apearance of mammograms on the basis of the general dbution of parenchyma, stroma and fat can yield very stroestimates of breast cancer risk. Since then, other group3–11

have reported similar findings, with estimated risk factoranging between 4.3 and 6.

Byng et al.12,13 developed a computer-aided system thquantifies mammographic density in terms of the fractionthe projected breast area that is occupied by radiographicdense tissue. They demonstrated that the method can prbreast cancer risk, with similar risk factors to the earlier sties, but with a continuous quantitative scale and with lpotential for intra- and inter-observer variability. Despite tsuccess of this method as a tool in several epidemiologstudies, it suffers from at least two limitations. First, it donot use information about the three dimensional conform

352 Med. Phys. 30 „3…, March 2003 0094-2405 Õ2003Õ30„

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tion of the breast. A simple area measurement may provan erroneous measure of the actual amount of fibroglandtissue in the breast. Second, results may be affected byexposure conditions on the appearance of the image. Becthe operating factors of the mammography system are vain an attempt to provide the best possible film image, itpossible to obtain mammograms of similar appearancebreasts of very different thickness and composition. Welieve that the risk of breast cancer is more likely relatedthe volume of dense tissue rather than the projected aremeasured by the method of Bynget al. Highnamet al. useda physics-model-based approach to estimate the thickne‘‘interesting’’ ~dense! tissue in the breast.14 We have at-tempted to develop a more simplified technique for bredensity quantification based completely on measured datobtain information about the composition of the breast.

The method described here uses the optical density inmation at each pixel in a digitized film mammogram to esmate the exposure transmitted by the breast and fromthe tissue composition that gave rise to this transmissThis allows an estimation of the volume of dense tissue,total volume of the breast and their ratio or ‘‘volumetrbreast density’’~VBD!.

The determination of VBD requires precise x-ray sensi

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353 Pawluczyk et al. : A volumetric method for estimation of breast density 353

metry and this level of quantitative imaging does not exisroutine mammographic practice. Furthermore, each mamgram is produced with individual exposure factors and, wautomatic exposure control, these may not even be knowthe technologist who produced the image. Therefore, ourproach is to calibrate the imaging system by exposingspecially-designed tissue-equivalent step wedge over a rof exposure parameters employed in mammography. Suquent variations due to the technique factors, film emulsand film processing are monitored using an aluminum swedge, placed on the breast support table of the mammophy machine.

The development of the calibration procedure andmethodology required for theVBD estimation will be ex-plored here. Results obtained with phantoms will be psented and the underlying assumptions and problems inent in the methodology will be discussed.

II. PRINCIPLE OF THE METHOD

Most of the x-ray attenuation of the breast is due to ttissue components. The first is the radiographically densefibroglandular tissues which include the stroma and parchyma. The second component is adipose or fatty tissuenote that the breast is also composed of skin and bloodsels and, in our work, their attenuation is included in tfibroglandular component. In addition, there may be calciin the breast. Where the calcium produces a detectible viimage, these areas, usually only a very small fraction ofarea of the mammogram, are eliminated from the calcutions. To determine theVBD, we attempt to calculate thfraction of the total breast volume comprised of fibroglandlar tissue.

With this simple two-component model, and if beam dvergence and scattering in the breast are temporarily ignothe number of x-ray quanta,I tr(E) at energy,E, transmittedby the breast is

I tr~E!5I ent~E!e2„mfib~E!tfib1m fat~E!t fat…, ~1!

whereI ent(E) is the number of quanta at the entrance surfof the breast andmfib , m fat , tfib andt fat are the linear attenuation coefficients and thicknesses of fibroglandular tissuefat.

For a breast of known compressed thickness,tT ,

I tr~E!5I ent~E!e2@~mfib~E!m1m fat~E!~12m!#tT, ~2!

wherem is the fraction of each path through the breast,tT ,that is composed of fibroglandular tissue.

For a monoenergetic beam, the solution form is simple.However, because mammography is performed using a strum of x rays, we employed an empirical approach to ematem. This is accomplished by calibrating the attenuatiproperties of the x-ray beam by imaging a breast tissequivalent step wedge shown in Fig. 1. In principle, thcalibration device could be placed adjacent to the breaseach mammogram. The step wedge is composed of pladesigned to closely simulate the x-ray attenuation properof breast fibroglandular tissue and fat.15–17It ranges in thick-

Medical Physics, Vol. 30, No. 3, March 2003

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ness from 1–8 cm with tissue-equivalent attenuation comsitions~fibroglandular/adipose! of 0/100%, 30/70%, 50/50%70/30% and 100/0%.

For a given x-ray spectrum, the image of the step wedcan be used to construct a relationship betweenI tr , m andtT , as illustrated by the surface in Fig. 2. Then, if the breis imaged under the identical conditions used to imagecalibration wedge andtT is known at each location in thebreast, the value ofm can be determined by interpolatinalong this surface. This allows the calculation of the volumof dense tissue, the total volume of breast tissue andVBD.

III. MATERIALS AND METHODS

All mammograms and images of calibration and testvices were obtained on mammographic screen-film imreceptors using modern mammography machines. Thecessed films were digitized using a Lumisys 85 digital lafilm scanner, at 12 bits and a spatial resolution of 260mm.The digitizer signal was proportional~with a negative slope!to the optical density of the image at each pixel. Opticsensitometry was performed using the same mammografilm and processing employed for clinical use. A typical sesitometric curve is shown in Fig. 3 where the log relatilight exposure to the film by the sensitometer is plotted vsus the digitizer signal. In the formation of a radiograph

FIG. 1. Plastic device used for the calibration of VBD. The device is coposed of breast tissue-equivalent plastic whose x-ray attenuation propevary from adipose (m50) to fibroglandular (m5100%) equivalence. Thesteps vary in thickness from 0–8 cm. They are surrounded by a 1 cm w‘‘cladding’’ strip to minimize the effects of discontinuity of the scattereradiation field at the edges, particularly in thicker regions of the device

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image, the light exposure to the film is proportional to tx-ray energy absorbed in the screen. Therefore, Fig. 3provides an estimate of the log relative x-ray absorptionthe image receptor~LRXA !. LRXA is related toI tr(E) by

LRXA5 logF E0

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I tr~E!h~E!g~E!dEG , ~3!

where h(E) is the x-ray quantum interaction efficiency othe screen andg(E) is the number of light quanta that arrivat the film, produced per x-ray of energyE interacting in thescreen. Over the relatively narrow x-ray spectrum usedmammography,h andg are fairly constant. For example, fox-ray spectra at 24 kV~Mo/Mo! and 32 kV~Mo/Rh!, for aGd2O2S screen with phosphor loading of 34 mg/cm2, h isapproximately 92% and 85%, respectively. The value ogscales with the effective beam energy, which only variestween 13.8 and 15.3 keV. The screen sensitivity scales asproduct of these factors, which, even over this large rangexposure technique, varies by only about 10%. Theref

FIG. 2. Sample three-dimensional surface relating log relative x-ray abstion ~LRXA ! by the image receptor to the % densitym, and thickness,tT .

FIG. 3. Log relative light exposure as a surrogate for LRXA, from opticsensitometry on film.


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LRXA is a reasonable surrogate for the log transmittedposure. Using the sensitometric curve shown in Fig. 3,digitized images are all converted to LRXA.

The accuracy of determination of VBD is dependentthe system having an isoplanatic response, i.e., for unifoattenuation of the breast, the signal recorded by the imreceptor, LRXA, would be constant, independent of thecation in the image. This is not the case for mammograpsystems because of the heel effect associated with the xtube and the spatial dependence of the path length throthe beam filter, the compression plate, the grid and the insifying screen. As well, even for a breast of constanttT , theobliquity of the x-ray beam passing through the breast wresult in spatial variation in LRXA.

We have previously described a method for the correctof field nonuniformity effects,18 and when this correction habeen made, for specified exposure conditions~tube target,filter, kV and mAs!, the resultant estimate of LRXA will varyonly with breast composition and thickness.

Several concerns had to be addressed in consideringdesign of the calibration device. First, breast tissue isarranged as distinct layers of adipose and fibroglandularsue. Instead, the tissue is distributed in a complex manthroughout the breast. The geometry of tissue distributwill affect the propagation of scattered radiation throughbreast. Otherwise, we expect that, the number of x-raystected beneath the breast will be independent of howattenuators are distributed with respect to each other athe x-ray path through the breast, as shown in Fig. 4.performed an experiment to test the validity of this assumtion by examining the influence of varying the layeringthe simulated fat and fibroglandular materials on the recoing of the transmitted beam. The experiment was performfor various arrangements of 1 cm and 2 cm thick slabsfat-equivalent and fibroglandular-equivalent plastic mateals, ranging in total thickness from 2 cm to 8 cm. For aparticular total thickness of the two types of materials, t

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TABLE I. The mean in LRXA and standard error~SE! of the difference between means for each thickness wdifferent arrangements of breast-tissue-like slabs imaged under automatic exposure control mode. Mments are made over a region of interest, containing 50350 square pixels, each 260mm on a side. ‘‘fg’’5fibroglandular tissue.

Thickness~cm! kV mAs, Filter Arrangement LRXA SE

2 25 18, Mo 1 cm fat/1 cm fg 1.837 0.00072 25 18, Mo 1 cm fg/1 cm fat 1.829 9 93 25 60, Mo 1 cm fat/1 cm fg/1 cm fg 1.881 0.00073 25 60, Mo 1 cm fg/1 cm fat/1 cm fg 1.883 9 93 25 58, Mo 1 cm fg/1 cm fg/1 cm fat 1.861 9 94 25 97, Mo 1 cm fat/1 cm fg/1 cm fat/1 cm fg 1.853 0.00084 25 98, Mo 1 cm fat/1 cm fg/1 cm fg/1 cm fat 1.854 9 94 25 98, Mo 1 cm fg/1 cm fat/1 cm fat/1 cm fg 1.859 9 95 27 156, Mo 1 cm fat/1 cm fg/1 cm fat/2 cm fg 1.866 0.00085 27 151, Mo 1 cm fat/2 cm fg/1 cm fg/1 cm fat 1.881 9 95 27 150, Mo 2 cm fg/1 cm fat/1 cm fat/1 cm fg 1.849 9 96 29 162, Mo 2 cm fat/1 cm fg/1 cm fat/2 cm fg 1.861 0.00086 30 136, Rh 2 cm fat/2 cm fg/1 cm fg/1 cm fat 1.857 9 96 30 137, Rh 1 cm fg/2 cm fat/1 cm fat/2 cm fg 1.864 9 97 32 200, Rh 2 cm fat/2 cm fg/1 cm fat/2 cm fg 1.863 0.00087 32 201, Rh 1 cm fat/2 cm fg/2 cm fg/2 cm fat 1.859 9 97 32 201, Rh 2 cm fg/1 cm fat/2 cm fat/2 cm fg 1.875 9 98 32 349, Rh 2 cm fat/2 cm fg/2 cm fat/2 cm fg 1.899 0.00078 32 338, Rh 2 cm fat/2 cm fg/2 cm fg/2 cm fat 1.877 9 98 32 338, Rh 2 cm fg/2 cm fat/2 cm fat/2 cm fg 1.878 9 9

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registered image LRXA varied only slightly over the diffeent configurations as shown in Table I.

The calibration device, made of breast-equivalent matals must be thick enough to cover the range of thicknessebreasts that would be imaged clinically~2–8 cm!. Further-more, it was desirable that the scatter conditions withinwedge were similar to those in the breast. Also, placemensuch a large calibration object had to be considered. Toserve scatter conditions similar to those in a breast, theof each step was 1 cm2 and an additional 1 cm border obreast tissue-like material, which we refer to as ‘‘claddingwas used to surround the calibration steps. With this desthe area of each step of material was sufficiently largethe step produced an image with the same brightness vathat would be produced if a slab of the same material twas much greater in area were imaged. It was found thathe area of the steps was reduced, or if the steps weresurrounded by ‘‘cladding,’’ the transmitted exposure whigher than would be the case with a larger-area slab ofmaterial.

To estimate operating parameters for breasts of diffeaverage thickness and composition, slabs of breast tisequivalent plastics16 of different thicknesses were imagedthe automatic exposure mode typically used for that typeequipment ~e.g., auto-time or auto-target/filter/kV/time!.Then, the calibration phantom was imaged in the normposition of the breast using the same exposure factorsmanual mode. This approach was chosen so that the diffethicknesses and compositions of the plastic step deviceered by a single AEC cell would not influence the techniqfactors as would be the case in an automatic exposure mThe image of the calibration device is indicated by ‘‘A’’ ithe radiograph of Fig. 5.

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For each target/filter/kV combination, the image of tplastic calibration device at a fixed mAs value is digitizand converted to LRXA using the optical sensitometry dobtained on the same day as the image was acquired.resultant LRXA image is then corrected for field nonunifomity using data from the image of a ‘‘bowl’’ phantom, constructed of PMMA as a section of an annular sphere.18 Themean LRXA is then determined for each of the 40 steps~5compositions and 8 thicknesses!. Calibration data are alsoacquired at additional mAs values. A surface relating

FIG. 5. Radiograph on 24330 cm image receptor illustrating the plastcalibration device~a!, two aluminum step wedges, located in positions cresponding to the edge of the image on the large~b! and small~c! receptors,a ‘‘hole’’ phantom~d! used for volumetric density estimation and a uniforplastic block~e!.

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percent density,m, total thickness,tT , and LRXA is thenconstructed. Using the known compressed breast thickt(x,y) and LRXA at each pixel location in the mammogramthe percent densitym(x,y) can be calculated from this suface. Finally, the volumetric breast density is calculated a

VBD5(breastApixelm~x,y!t~x,y!

(breastApixelt~x,y!* 100%, ~4!

whereApixel is the area of a pixel in the image. In the absenof further information on variations in breast thicknest(x,y) is assumed to have the constant valuetT .

A. Compensation for shifts in sensitometry orexposure technique

The characteristics of the system will vary from the initcalibration conditions, both due to the use of different expsure factors for different breasts and shifts in film emulscharacteristics and film processing. For example, an increin the kV would increase the slope of the calibration surfawhile varying the mAs from that used for the calibratiowould shift the surface upward or downward with a minvariation in slope. Therefore, the calibration shouldchecked routinely, preferably with every image. It is impratical, however, to image the plastic calibration device besthe breast during mammography. Because the device is 8thick, it would be necessary to place it on the upper surfof the compression plate, rather than on the breast suptable to avoid interference with compression of the breaswould have to be placed away from the chest wall beyothe projected image of the breast and would have to be tito ensure that x rays would impinge orthogonally on eastep. In addition, the device is fairly large in area and wooccasionally interfere with imaging. For these reasons,calibration was performed initially with the plastic devicalone in the beam. To track variations in the operating cditions or system characteristics from those used for inisystem calibration, a thin aluminum step wedge was imaalongside the breast during every mammogram.

The aluminum wedge consists of 7 steps, increasingthickness by 1.5 mm, each with an area of 6313 mm. Be-cause the wedge is only 10.5 mm thick, it can be attachethe tabletop, and does not have to be tilted toward the fospot. The area of each step is adequate to provide a regioapproximately uniform optical density for calibration puposes. The aluminum wedge is placed on the breast suptable in the corner distal to the chest wall edge of the imand is included in each image of the plastic calibration phtom @~b! and ~c! in Fig. 5#.

For a given target/filter/kV combination, a shift in thpixel value of the image of a particular aluminum step aparticular time indicates either that the mAs is different frothat used for calibration~i.e., the LRXA has changed! or thatthe film emulsion characteristics or processing has variedeither case, the shift of apparent LRXA from the calibratipoint is determined from the image of the aluminum swedge, and a correcting shift is applied to the calibratdata previously determined with the plastic wedge. Thus


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shifts in the real or apparent quantity ofx rays used for theexposure are compensated.

In the compensation procedure, first, the digitized imaof the plastic calibration device and the aluminum stwedge is converted to LRXA using the optical sensitomedata obtained on the same day as the image was obtaWhen this procedure is initially performed, the resulting sface is referred to as the ‘‘reference’’ calibration. Compention is then achieved by using the LRXA value for a particlar step in the aluminum wedge~Fig. 6! to quantify thevariation and then shift the reference surface appropriatelconform to the current imaging characteristics.

Because of the nonlinear sensitometric characteristicthe mammographic film~Fig. 3!, the determination of LRXAis only linear with thickness over a limited range of thicnesses of the plastic calibration device. In addition, behardening causes the relationship between thicknessLRXA to depart slightly from linearity. The thickness rangover which there is essentially a linear relationship willreferred to as the ‘‘useful thickness range’’ and this will vafor various exposure conditions. To facilitate the shifting prcess used to compensate for technique factor changesvariations in film processing, it is useful to perform lineextrapolation of the LRXA from this region to include thentire thickness range of the calibration device.

B. Testing the compensation method

To evaluate the performance of the compensation methwe produced a set of images that included both the placalibration device and the aluminum step wedge on the sfilm. The LRXA under each aluminum step is recorded onimages produced on the mammography system. Typicasteps that occur within the mid range of optical densitiesthe mammography film are used. The use of the alumin

FIG. 6. Mean LRXA is measured on a particular step of aluminum, whgives a value in the linear part of the sensitometry curve of the film.

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step wedge to correct for variations in exposure, film pcessing, film emulsion and filter was evaluated experimtally.

In the first experiment, the mAs was varied from the rerence condition. Three images were taken. The firstacquired at Mo/Mo 25 kV/120 mAs, defined here as the rerence calibration condition. The calibration curves~LRXAvs tT for 100% gland and 100% fat! obtained from this imageof the plastic step phantom are called reference calibracurves~denoted bygr and f r , respectively!. The other twoimages, obtained using 25 kV/170 mAs~Case ‘‘m1’’! and 25kV/24 mAs ~Case ‘‘m2’’!, were treated as the test imageThe calibration curves obtained using the data from the ptic calibration device on the m1 and m2 test images willreferred to as the ‘‘actual’’ calibration curves (ga and f a).

The shift in the LRXA due to the mAs variation is calculated on a particular step of aluminum~Fig. 6! and this shift

FIG. 7. The ‘‘hole’’ phantom made of various compositions of breaequivalent material, used in testing the VBD method.

FIG. 8. Digitized mammogram represented by gray levels. Minimum den~maximum LRXA, ‘‘Ã’’ and maximum density~minimum LRXA, ‘‘ 1’’ ! areindicated.


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is applied to the reference calibration curves to matchactual calibration curves for these cases~the shifted calibra-tion curves are denoted bygs and f s , respectively!.

The performance of the method over time was evaluaby producing three sets of images~one image for each targefilter/kV combination! at six-month intervals. Only one combination will be discussed here. The reference image~25 kV,120 mAs! was considered to have been obtained at time ‘‘The second set at 6 months, with technique factors 25 kVmAs will be referred to as Case ‘‘p1’’ and the one-year image, obtained at 25 kV, 80 mAs will be referred to as Ca‘‘p2.’’

An experiment was performed to verify the validity ousing data from only one optical sensitometry curve~ob-tained at the same time as the reference image! to correct for

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FIG. 9. The calibration curve obtained with the plastic device at Mo/MokV/120 mAs. The mean LRXA values for square areas of 535 mm of eachstep (m5100% and 0%! are shown. The actual experimental data pointsshown with a* . The region of linear behavior is indicated by the solid linextrapolation is shown by the dashed line.

FIG. 10. Mean LRXA plotted versus percent density~m! for various thick-nesses,tT , for 25 kV/120 mAs exposure conditions.

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Medical Physics, Vo

TABLE II. Percent density,m, estimated using ‘‘reference’’ calibration curves~25 kV/120 mAs, 4-cm holephantom!. Estimates based on use of calibration data from all material compositions~five-point! and using onlym50 andm5100% ~two-point! are shown. Means and standard deviations~SD! are given for each methodThe standard error~SE! in the difference between the two methods and the 95% confidence interval~CI! of thedifference are also given. Significant differences are indicated by boldface.

Actual ~%! 100 75 50 25 0

Two-pointestimate

100 ~0.3! 79 ~1.3! 49 ~1.3! 28 ~1! 3 ~1.2!Mean ~SD!Five-pointestimate

100 ~0.3! 79 ~1.2! 51 ~1.3! 28 ~1.3! 4 ~1!Mean ~SD!Difference inmean~SE!

0 ~0.2! À2 „0.21… 0 ~0.19! À1 „0.18…

0 ~0.049!95% CI fordifference

20.097 to10.097 20.4 to 10.4 À2.42 toÀ1.58 20.37 to10.37 À1.36 toÀ0.64

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daily processing variations on the test images or on the mmograms. First, for the p1 and p2 images, the ‘‘actual’’ cabration curves were determined from the image of the placalibration device by using the sensitometry curves~p1 andp2 sensitometric curves! obtained on the same days as trespective images.

The shift correction was then evaluated using two diffent methods. In the first, the images of the aluminum swedge were converted to LRXA using the reference sensmetric curve (sr) and the shift from the aluminum step othe reference calibration image was calculated. Then,comparison purposes the images of aluminum steps walso converted to LRXA using the p1 and p2 sensitomecurves (sp1 andsp2) and the shift from the aluminum step othe reference image was calculated again. The shifts w

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then applied to the reference calibration curves to matchactual calibration curves to those for the test images.

The reference calibration images were taken on the lasize ~24330! films with two identical aluminum stepwedges: one placed in a corner of the image distal tochest wall and the other located in a position that wocorrespond to the same location on an 18324 cm imagereceptor. This allows the calibration for both image recepsizes to be accomplished from the same film. To testvalidity of the shifting method to calibrate the small sizfilms, another calibration image was taken on the small sifilm with the same exposure conditions used for the refence image~25 kV, 120 mAs!. Sensitometry data from thesmall sized film are used to convert the test image to LRand thus produced the actual calibration curves.

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TABLE III. Accuracy of estimation of VBD on the hole phantom~4 cm thick! using actual calibration curves (f a andga) and shifted calibration curves (f s andgs) for case ‘‘m1’’ ~25 kV, 170 mAs! and on a 2 cmthick phantom for case ‘‘m2’’~25 kV 24 mAs!. The standard error in the difference and confidence inter~CI! for the difference between the actual and shifted calibration for each case is also shown.
Case Actual~%! 100 75 50 25 0

Using f a andga

100~0.2! 77~1.5! 50~1.35! 27~1.3! 0~0.3!Mean ~SD!

‘‘m1’’Using f s andgs

100~0.04! 78~1.2! 51~1.4! 29~1.4! 1~1.3!Mean ~SD!

Difference in means~SE! 0 ~0.024! À1~0.222! 21~0.225! À2~0.221! À1~0.154!CI for the difference 20.05 to10.05 À1.44 toÀ0.56 À1.44 toÀ0.55 À2.45 toÀ0.05 À1.30 toÀ0.69

Using f a andga

99~1.3! 75~3.0! 46~2.7! 20~1.9! 0~0.2!Mean ~SD!

‘‘m2’’Using f s andgs

99 ~1.04! 75~2.9! 45~2.7! 18~2.2! 0~0!Mean ~SD!

Difference in means~SE! 0 ~0.19! 0 ~0.48! 1 ~0.44! 2 ~0.26! 0 ~0.02!CI for the difference 20.38 to10.38 20.95 to10.95 0.12 to 1.87 1.48 to 2.5 20.046 to10.046

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To study the effect of filter variation on the calibratiocurves, two images were taken with similar kV and mAs, bwith different filters~30 kV, 150 mAs, Mo Filter and 30 kV,140 mAs and Rh Filter!.

C. Testing accuracy of VBD method

To test the accuracy in determination of VBD with thmethod, a breast equivalent ‘‘hole’’ phantom, shown in Figwas created. The phantom was built as a set of 1 cm thlayers of breast-equivalent plastic material representincombination of 50% by thickness of fibroglandular tissand 50% adipose tissue. Each layer had 5 cylindrical borediameter 2.54 cm. These holes could be filled with cylind

FIG. 11. Performance of the calibration shifting method, using data fromaluminum step wedge. The response to mAs variation from the refercalibration point is evaluated here.~a! For each of fat~f! and fibroglandulartissue~g!, the reference curves,f r , gr , at 25 kV/120 mAs, the actual calibration curves,f a , ga , actually obtained at 25 kv/170 mAs and the shiftreference curvesf s , gs are shown.~b! Similar results for imaging withexposure factors of 25 kv/24 mAs.


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cal plugs whose x-ray attenuation properties varied betwthose of fat and fibroglandular tissue, thus allowing boththickness and composition of the phantom to be varied. Tphantom was used in all subsequent experiments to tesaccuracy of density estimation techniques.

To facilitate evaluation of the effect of the time intervbetween calibration and acquisition of the mammograsome of the test images of the hole phantom were obtaon the same films as used to record images of the calibraphantom. Six thicknesses of the phantom were configuFor each thickness, the composition of the plugs varied isteps from 0–100% densities in regular intervals, thus yieing 30 configurations. In addition, a uniform phantom maof 50/50 breast-equivalent material of the same thicknesthe hole phantom was placed adjacent to it, as shown in ‘of Fig. 5. The aluminum wedge was attached to the bresupport table in the corner of the image field, as it is usedthe clinical setting.

The phantoms were then imaged using the same expomode as would be employed for a breast of typical comsition ~50% fibroglandular tissue/50% fat by volume!. Theprocessed radiographs were digitized, image pixel valwere converted to LRXA using Fig. 3 and then correctedfield nonuniformity. A surface similar to that of Fig. 2 wathen created from the plastic calibration device. Usingknown thickness of the test phantoms, for each pixel ofradiograph, a calculation of the percent of fibroglanducontent was performed to create a digital volumetric denimage.

We then tested the performance of the shifted calibratin the estimation of VBD. This was done by calculating tdensities on the hole phantom images acquired at them1, m2, p1 and p2 conditions using actual calibration curand also using the shifted reference calibration curves.

D. Thickness constraints

For each machine, the compressed breast thicknesstT

and the imaging techniques~kV, mAs, anode/filter! on eachmammogram were recorded. Using information from the iage of the aluminum step wedge, the previously-obtaincalibration curves were then shifted to match the currentposure conditions and then used to estimate the volumebreast density.

Accurate knowledge of the compressed breast thicknesan important factor in the accurate estimation of VBD.constrain the error in the compressed breast thicknessidentified two parameters on each image:~1! the minimumLRXA, which corresponds to the path through the brecontaining the maximum amount of dense tissue and~2! themaximum LRXA which corresponds to the path passithrough the minimum amount of dense tissue~Fig. 8!. If thethickness information recorded by the machine was corrthe maximum and minimum LRXA values obtained from tbreast image would lie between the LRXA corresponding100% fat and 100% fibroglandular on the shifted calibratcurves for that thickness. We used these as constraints o

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TABLE IV. Performance of shifting correction on temporal drifts and variation of exposure technique Estimation of VBD on the hole phantom~3 cm thick!using actual calibration curves (f a andga) and shifted calibration curves (f s andgs). Case ‘‘p1’’ 225 kV, 87 mAs, time56 months; Case ‘‘p2’’225 kV, 80mAs, time512 months. The standard error in the difference and the confidence interval~CI! for the difference between the actual and shifted calibrationeach technique is also shown.

Case Actual~%! 100 83.3 50 33.3 0

Using f a andga

100~0.3! 85~1.6! 49~2.1! 38~2.3! 0~0.2!Mean ~SD!

‘‘p1’’Using f s andgs

100~0.03! 88~1.8! 52~1.9! 38~2.9! 0~0!Mean ~SD!

Difference in means~E! 0 ~0.035! 23 ~0.28! 23 ~0.33! 0 ~0.43! 0 ~0.02!95% CI for the difference 20.07 to10.07 À3.55 toÀ2.45 23.65 to22.35 20.85 to10.85 20.05 to10.5

Using f a andga

100~0.7! 83~.2! 46~1.5! 33~1.7! 0~0.2!Mean ~SD!

‘‘p2’’Using f s andgs

97~1.3! 82~1.7! 48~1.9! 34~1.8! 0~0.3!Mean ~SD!

Difference in means~SE! 3 ~0.17! 1 ~0.32! 22 ~0.28! 21 ~0.29! 0 ~0.04!95% CI for the difference 2.66 to 3.34 0.36 to 1.64 À2.55 toÀ1.45 À1.56 toÀ0.43 20.08 to10.08

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thickness inaccuracy. If the maximum LRXA was greathan the LRXA for 100% fat on the calibration curve, ththickness was reset to a lower value such that the maximLRXA matches the LRXA for 100% fat on the calibratiocurve. Similarly, if the minimum LRXA was lower than thLRXA for 100% gland on the calibration curve, the thicknewas increased to match the LRXA for 100% gland.

IV. RESULTS AND DISCUSSION

A. Calibration

From images of the plastic calibration device, taken othe range of x-ray target/filter/kV combinations for each tyof mammographic unit to be used for VBD measurement,digitizer signals under each step were converted to LRXTypical data for 100% fibroglandular tissue and 100%equivalent steps are shown in Fig. 9. These curves are sthrough the surface of Fig. 2. For a given step thickness, tgive the LRXA that would result if the path were throughtissue of a particular composition. Results are extrapolabeyond their region of linearity on the film to cover the entrange of thickness of the plastic device.

In Fig. 10, the same data are plotted versusm, the percentof the path composed of fibroglandular tissue, for the raof thicknesses which holds a linear relation with LRXA. Ththickness range~4 cm to 7 cm for fat and 3 cm to 5 cm fogland! is the previously discussed ‘‘useful thickness rangfor the exposure condition of 25 kv, 120 mAs. Initially, VBDwas determined using data from all five values ofm availablein the calibration device. We found, however, that LRXAquite linear withm. The accuracy of the calibration is summarized in Table II. In this example, the system was cbrated for a Mo target and Mo filter~0.025mm thick! at 25


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kV, 120 mAs. The results using all five of the material cabration conditions were compared to those from a two-polinear fit and excellent agreement is seen.

Thus it is reasonable to use simple linear interpolatfrom Fig. 2 to estimate behavior between calibration steand, for a given value of LRXA in the mammogram, to dterminem for any path through the breast, provided that tthickness of the breast at that location is known.

B. Effect of calibration shift with the aluminum wedge

1. Changes in exposure

Table III demonstrates the performance of the aluminstep wedge method in correcting for a change of mAs frthe initial calibration or reference condition. The shiftinprocedure is also illustrated in Figs. 11~a! and 11~b! for casesm1 and m2, respectively. Here, for both 100% fat and 10fibroglandular tissue, three curves are shown:r—the refer-ence calibration curves;a—the curve for calibrations performed at the actual exposure conditions; ands—the refer-ence curve shifted according to the shift in LRXA due to tmAs variation, determined on a particular step of aluminu~Fig. 6!.

It is seen that the shifted reference calibration curvmatch well with the actual calibration curves over the usethickness range for both test images, although some discancy between the slope of the shifted and actual calibracurves is observed for large thicknesses. This is due toferences in the degree of beam hardening present inthickness region where the data for each of the curvesobtained. The above experiments suggest that the calibrais independent of mAs changes. Therefore calibration canperformed for each kV used clinically, by acquiring dataonly one mAs setting.

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2. Temporal changes—Sensitometry and Õorexposure factors

Table IV describes how well the aluminum step wedmethod performs in compensating for variations over timemAs or film processing from the reference calibration coditions. The film contrast and speed obtained from each ssitometric curve for the above three cases are shown in TV. It is apparent that the speed is elevated considerablycontrast is slightly elevated for case p1 compared to thosethe reference condition and case p2. The p2 images wacquired when the site switched to a new processor.

Figures 12~a! and 12~b! illustrate the effect on performance of shifting the reference calibration curves to mathe actual calibration curves obtained for case p1 when uthe sr sensitometric data to obtain LRXA, rather than tmore currentsp1 on the p1 image to find the shift. Thshifted reference calibration curve usingsp1 closely matchedthe actual calibration curves for the p1 image. Althoughshifted reference calibration curves usingsr did not match aswell with the actual calibration curves for p1 as whensp1

was used. Figure 13 illustrates the performance of shiftthe reference calibration curves for case p2 using thesr onthe p2 image to find the shift. The shifted reference calibtion curves match well with the actual calibration curvesthe p2 image.

The above experiments suggest that using only the reence sensitometry data (sr) to convert the test images omammograms to LRXA is feasible and can still produce dsity estimates over the useful thickness range for a givenof exposure factors with reasonable~;5%! accuracy as seein Table IV. But, the accuracy can be improved by usingsensitometry image obtained on the same day as the mmogram was produced to convert optical densities to LRX

3. Effect of change of image receptor size

Figure 14~a! shows that the calibration curves obtainfrom 18324 and 24330 image receptors match closely fsimilar imaging conditions. Therefore, the calibration is retively insensitive to the size of the image receptor.

4. Effect of change of filter

Figure 14~b! shows that the calibration curves obtainusing similar kV and mAs, but with different filters matcvery closely in the useful thickness range; i.e., in this cause of the Rh filter did not cause any change in the contr

TABLE V. Film speed and contrast indices obtained from the sensitomdata obtained at times 0, 6 months and 12 months. The speed inddefined as the optical density measured at Step 12 on the image of an osensitometry strip, while the contrast index is obtained as the differencoptical density between Step 10 and Step 14.

Time Contrast Speed

0 2.46 1.396 months 2.57 1.62

12 months 2.37 1.48


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This suggests that at least for the combinations tested,bration needs to be performed for only one anode/filter cobination.

C. Determining volumetric breast density

1. Phantom studies

The accuracy of the VBD method and the shift correctioon the hole phantom images acquired at 25 kV/170 mAs

FIG. 12. Calibration curves shifted using data from the aluminum swedge to correct for processing and/or mAs variations~p1 test case!. ~a! Thereference calibration curvesf r , gr , obtained at Time50 ~25 kv, 120 mAs!were shifted to match the actual curves,f a , ga , obtained for the p1 testimage obtained at Time56 months~25 kv, 87 mAs!. The p1 test image wasconverted to LRXA using the reference sensitometry data,sr , in order tofind the shift. ~b! The p1 test image was converted to LRXA using thsensitometry data,sp1 , obtained at the same day the image was taken. Tshift in the LRXA from the reference calibration image was then calculaand applied to the reference calibration curves,f r , gr , to match the actualcalibration curves,f a , ga .

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25 kV/24 mAs, using the actual calibration curves and ausing the shifted reference calibration curves, is shownTable III. The table gives estimates ofm and the differencefrom the true value when calibration is performed at the iage acquisition conditions~i.e., using the actual calibratiocurves! or with the shifted reference calibration curves. Tdensity map of the hole phantom imaged at the caseexposure condition, obtained using the shifted reference cbration curves is shown in Fig. 15~a!. The density profileacross one vertical line in the image is shown in Fig. 15~b!.It was found thatm can be estimated with an absolute errof 5%.

Figure 16 illustrates the effect of the nonuniformity corections on density estimates. The plot represents the msignal along the centerline of the image. As can be seen fthe figure, the uncorrected image varies by more than 20%density in areas of the phantom that are distant from the fospot. When careful precalibration of the system is employso that field nonuniformity is corrected, the difference btween the estimated VBD and the actual value is less t5%.

Figure 17 illustrates the first-order thickness correctbeing employed on the mammograms. It shows that ifminimum LRXA which corresponds to the maximuamount of dense tissue in the uniform thickness region ofbreast is less than the LRXA corresponding to 100% fibglandular tissue at the given compressed breast thicknessthickness is reset to a higher value at which the minimLRXA from the breast matches the 100% gland LRXAgs . The drawback of this technique is that here we assuthe minimum LRXA on the breast image to be equivalent100% density and maximum LRXA to 100% fat. If the actutissue composition is otherwise, then the shift in thicknwith this method will be less than the required amount. N

FIG. 13. The reference calibration curves~25 kv, 120 mAs!, f r , gr , wereshifted to match the actual calibration curves,f a , ga , obtained for the p2test image~25 kv, 80 mAs!. The test image was converted to LRXA usinthe reference sensitometry,sr , in order to find the shift.


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ertheless, this approach will produce at least a partial cortion.

The variation in thickness in the peripheral region of tbreast can be another source of error if not corrected fothe breast is treated like a slab whose thickness is that ocenter of the breast, then the thinner peripheral region wocause the total breast volume to be overestimated andvolume of fibroglandular tissue to be underestimated, caing an underestimation of VBD. We are currently developia technique to identify the margin of the breast and to emate a thickness map of the breast.19 The changing thicknessinformation thus obtained can be used to improve the acracy of the VBD measurements.

2. Clinical implementationIn clinical use, the system is initially calibrated using th

tissue-equivalent step wedge~Fig. 1!. Calibration is re-

FIG. 14. ~a! Calibration curves obtained from taking the image of plasstep phantom on 18324 and 24330 image receptors using similar kV ansimilar mAs.~b! The calibration curves obtained using a Mo filter and a Rfilter ~30 kV, 140 mAs!.

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checked every six months. The aluminum step wedgesmounted on both the large and small sized image receptothe mammography units~as shown in Fig. 8!. They can betemporarily removed if necessary to avoid interfering wthe examination of women with very large breasts. The stem has been used in over 1000 examinations as partclinical study that is underway.

V. CONCLUSION

We have described a method for calculating volumebreast density~VBD! on digitized screen-film mammogramAn important feature of this method is that it is user indpendent, and thus does not suffer from observer bias. A ptic calibration device composed of a range of tissuequivalent materials can be used to determine breast den

FIG. 15. Volumetric density estimation for a 4 cm thickhole phantom usingthe shifted plastic calibration curves~25 kV/170 mAs!. ~a! density~VBD!map and~b! density profile atx5450.


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and the onlya priori knowledge required is the compressbreast thickness, the image acquisition conditions andsensitometry data. This should not be a problem in a modmammography clinic, where most of the machines recordexposure factors and breast compression on the mamgram, although there is a certain degree of inaccuracy aciated with the thickness measurement and the thicknesformation in the peripheral region of the breast.

Because of its thickness, it is impractical to include tplastic breast-equivalent wedge on every image and sthinner aluminum wedge is used to monitor shifts from treference calibration conditions. To obtain accurate resuthe calibration procedure should be performed over a ra

FIG. 16. Effect of nonuniformity corrections made with the use of t‘‘bowl’’ phantom on the density estimates obtained with the 4 cm thick hphantom imaged at 25 kV, 120 mAs and the profile shown is aty5650 ~260mm pixel size!.

FIG. 17. The maximum~‘‘ 3’’ ! and minimum~‘‘ 1’’ ! LRXA obtained fromthe mammogram are shown. The minimum LRXA obtained from the mamogram found to be less than the LRXA corresponding to the 100% glon the calibration curve at the given compressed breast thickness~3.1 cm!.So, in this case the thickness is increased to 3.8 cm to match the 100%LRXA on the calibration curve.

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of mammographic energies. The shift in the log transmitexposure as estimated from the image of an aluminumwedge provided an effective method to correct for variatiodue to exposure and processing from the calibration cotions. Phantom studies show that VBD can be estimatewithin 5% density of the actual value. VBD should represean improvement over the existing methods of determinbreast density, because it provides information about theume of dense tissue rather than just the projected arelarger clinical study to assess the association of VBD wactual breast cancer risk is ongoing.

ACKNOWLEDGMENTS

We received valuable assistance from the Chief Mamography Technologist, Joan Glazier, and the other tenologists at Sunnybrook & Women’s Health Sciences Cenin calibrating the mammography units. We are grateful toTerry Fox Foundation and to The Canadian Breast CanResearch Initiative for their support of this research.

a!Corresponding author. Telephone:~416! 480-5715; fax:~416! 480-5714;electronic mail: [email protected]. N. Wolfe, ‘‘Risk for breast cancer development determined by mamographic parenchymal pattern,’’ Cancer37, 2486–2492~1976!.

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9C. Byrne, C. Schairer, J. Wolfe, N. Parekh, M. Salane, L. A. Brinton,Hoover, and R. Haile, ‘‘Mammographic features and breast cancer reffects with time, age, and menopause status,’’ J. Natl. Cancer Inst87,1622–1629~1995!.

10E. Warner, G. Lockwood, M. Math, D. Tritchler, and N. F. Boyd, ‘‘Thrisk of breast cancer associated with mammographic parenchymalterns: a meta-analysis of the published literature to examine the effemethod of classification,’’ Cancer Detect. Prev.16, 67–72~1992!.

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17J. W. Byng, J. G. Mainprize, and M. J. Yaffe, ‘‘X-ray characterisationbreast phantom materials,’’ Phys. Med. Biol.43, 1367–1377~1998!.

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Documents

A volumetric method for estimation of breast density on digitized screen-film mammograms