Lesion characterization using spectral mammography
Bjorn Norell, Erik Fredenberg, Karin Leifland, Mats Lundqvist, Bjorn Cederstrom
This is the submitted manuscript of:
Norell, B., Fredenberg, E., Leifland, K., Lundqvist, M. and Cederström, B. , “
Lesion characterization using spectral mammography ,” Proc. SPIE
The published version of the manuscript is available at: https://doi.org/10.1117/12.913032 See also:
Fredenberg, E., Dance, D.R., Willsher, P., Moa, E., von Tiedemann, M., Young, K.C. and Wallis, M.G., 2013. Measurement of breast-tissue x-ray attenuation by spectral mammography: first results on cyst fluid. Physics in Medicine & Biology, 58(24), p.8609. https://doi.org/10.1088/0031-9155/58/24/8609
Erhard, K., Kilburn-Toppin, F., Willsher, P., Moa, E., Fredenberg, E., Wieberneit, N., Buelow, T. and Wallis, M.G., 2016. Characterization of cystic lesions by spectral mammography: results of a clinical pilot study. Investigative radiology, 51(5), pp.340-347. https://doi.org/10.1097/RLI.0000000000000246 All publications by Erik Fredenberg: https://scholar.google.com/citations?hl=en&user=5tUe2P0AAAAJ esion characterization using spectral mammography
B. Norell, a E. Fredenberg, a,b
K. Leifland, c M. Lundqvist, a and B. Cederstr¨om a,ba Philips Women’s Healthcare, Smidesv¨agen 5, 171 41 Solna, Sweden; b Department of Physics, Royal Institute of Technology (KTH), 106 91 Stockholm, Sweden; c Department of Mammography, Capio S:t G¨orans Hospital, 112 81 Stockholm, Sweden;
ABSTRACT
We present a novel method for characterizing mammographic findings using spectral imaging without the useof contrast agent. Within a statistical framework, suspicious findings are analyzed to determine if they arelikely to be benign cystic lesions or malignant tissue. To evaluate the method, we have designed a phantomwhere combinations of different tissue types are realized by decomposition into the material bases aluminum andpolyethylene. The results indicate that the lesion size limit for reliable characterization is below 10 mm diameter,when quantum noise is the only considered source of uncertainty. Furthermore, preliminary results using clinicalimages are encouraging, but allow no conclusions with significance.
Keywords: mammography; spectral imaging; photon counting; cyst; lesion
1. INTRODUCTION
In breast-cancer screening, the most important task of the radiologist is early detection of breast cancer. Thesecond most important task is to avoid recalling healthy women and exposing them to follow-up examinations,which may involve additional radiation or needle biopsy. Circular and oval lesions are, as opposed to stellatelesions, relatively easy to detect but difficult to characterize, and most suspicious findings of this type aretherefore called back and characterized using needle biopsy. A majority of these lesions are, however, benigncysts, and a method to characterize circular lesions as benign or malignant already at screening would have thepotential to aid the radiologist in the latter task and reduce recall rates substantially.Spectral imaging can be used to extract information about an object’s constituents using the x-ray attenuationenergy dependence, which is material specific.
2, 3
The technology has been used in the past to improve onthe signal-difference-to-noise ratio, to improve lesion conspicuity by reducing overlying anatomical structure,and to measure breast density. We have developed a method that employs spectral imaging to characterizecircular lesions as benign or malignant. Similarly to computer aided detection (CAD), the presented methodcan be used during screening examinations. The spectral mammogram is acquired as in conventional screeningmammography; no additional time or dose is needed. In contrast to CAD, however, which primarily is used fordetection and operates on the same image data as the radiologist, the method analyzes the constituents of afinding using information that is not available in a conventional mammogram.The radiologist performs the analysis by marking a region of interest around the detected lesion as well asa reference region of normal tissue surrounding the lesion. Spectral information from the marked regions ofinterests is used to determine if the finding is likely to consist of water or cancerous tissue, with the underlyingassumption that the contents of cystic benign lesions are similar to water.
Electronic mail: [email protected] . MATERIAL AND METHODS2.1. Description of the system
A spectral photon-counting mammography system has been developed based on the Philips MicroDose Mam-mography system. It is a scanning full-field digital mammography system with a tungsten-target x-ray tube thatacquires high- and low-energy images, i.e. a spectral mammogram, with energy-sensitive silicon-strip detectorunits. All photons below a low-energy threshold at a few keV are rejected as noise. The remaining photonsare separated by a high-energy threshold and contribute to either the low-energy or the high-energy image. Aschematic of the system is shown in Fig. 1. Detailed descriptions of the system and detector can be foundelsewhere. breastx-ray beam Si-stripdetector linespre-collimatorcompressionplatebreastsupport _ +
HV rejectionhighlowASICpre-collimatorbreastx-raytube detector yzx scanscan
Figure 1. Left:
Schematic of the Philips MicroDose Mammography system.
Right:
The image receptor and electronics.
The spectral mammogram is acquired with only one exposure and at no additional exposure time or ra-diation dose compared to a conventional mammogram. Nevertheless, a conventional mammogram is readilygenerated from the spectral data as the sum of the high- and low-energy images, and the system can thereforebe used in regular screening. Whenever needed, the spectral information can be extracted and used for lesioncharacterization or other purposes.The detected photon counts follow Poisson statistics, which makes statistical modeling fairly straightforward.However, a precise system model and careful calibration is required to predict system outcome.
4, 8–10
Material decomposition between any two materials is achieved by solving the non-linear system of equationscomprising high- and low-energy photon counts, the effective attenuation coefficients and the unknown thicknessof each material. In the context of mammography, it is customary to assume a breast composition of adipose andfibro-glandular tissue and we solve the system of equations for the two unknown parameters breast thickness h nd breast glandularity g , i.e. the percentage of fibro-glandular tissue. A glandularity map and a thickness mapare obtained by solving the system of equations for each image pixel.However, when analyzing a suspicious lesion there are three unknowns for each pixel: breast thickness, breastglandularity, and lesion thickness, where the latter is a third material assumed to be either a malignant lesion ora cystic benign lesion. Therefore, a reference region of normal tissue around the detected lesion is used along withthe region of interest that covers the lesion itself. We use this additional information to form a statistical model,i.e. the joint likelihood function, for whether the lesion is likely to be cystic (benign) or cancerous (malignant): L ( θ | x, y ) = L ( h, g, t | x, y ) = L ( h, g | x ) L ( h, g, t | y ) , (1)where the model parameter vector θ can be expressed in terms of breast thickness h , glandularity g and lesionthickness t . In other words, θ is a vector of input parameters to the system model that gives high- and low-energyphoton counts as output. The observed data x and y are the high- and low-energy photons for the surroundingtissue and the lesion, respectively. These photon counts are Poisson distributed and are well approximated bythe normal distribution N ( n i , √ n i ), and the likelihood L for the statistical model with parameters θ given theobservation x is defined by the product L ( θ | x ) = (cid:89) k f ( x k | θ ) , where f ( x | n i ) ∝ x exp (cid:18) − ( x − n i ) n i (cid:19) . (2)The joint likelihood is higher the closer the fit between the observed data and the statistical model. Equation (1)assumes that the breast thickness and glandularity is equal where the lesion is located as for surrounding tissue.The thickness t is kept fixed to zero for the surrounding tissue, whereas t for the lesion is a free variable.Given the observed lesion and its surroundings, maximization of Eq. (1) for a cyst yields a figure of merit forthe likelihood that the lesion is benign. The likelihood for a malignant tumor is computed in the same way. Thetwo hypotheses are compared using the likelihood ratio λ ( x, y ) = max θ c L ( θ c | x, y )max θ t L ( θ t | x, y ) , (3)where λ is a confidence measure. For convenience, we study the log likelihood log( λ ), i.e. for a likelihood ratiolarger than one (log( λ ) > λ ) <
0. A log likelihood ratio close to zero means that nothing can be said aboutmalignancy or benignity.In all calculations, normal breast tissue and malignant cancerous tissue were represented by published attenu-ation coefficients, and benign cysts were assumed to contain pure water. It is clearly a simplification to assumecircular lesions to be either solid tumors or cysts with fluid contents; benign cysts may be viscous rather thanfluent, benign fibroadenomas are solid, and malignant mucinous carcinomas are viscous. These exceptions allappear with some frequency, but solid tumor versus liquid cyst remains a common and important differentiationproblem. A tissue-equivalent phantom comprising normal breast tissue, malignant lesions and cystic benign lesions wasdesigned to experimentally evaluate spectral lesion characterization. Tissue equivalence was achieved by findingthe combination of polyethylene and aluminum with the closest fit to the energy-dependent attenuation coeffi-cients for the target material. Published attenuation coefficients for normal and cancerous tissue was used, and cysts were assumed to contain pure water. The lesions were 0, 10, 20, and 30 mm thick, embedded in normalbreast tissue, and covered an area of 10 ×
10 mm ; see Fig. 2 for a schematic of the phantom. The design wasvalidated by comparing the attenuation of simulated cysts (water) to compartments with actual water that wereembedded in the phantom.A flat-fielding algorithm was applied to each image but did not fully compensate for the heel effect, whichresulted in a slight thickness gradient within ±
3% perpendicular to the scan direction. To compensate for thiseffect, the low- and high-energy photon counts were rescaled with the same factor to get a thickness that wasconstant on average. issue Polyethylene Alglandular adipose skin tumor cyst
Material bases
100 90 80 70 60 504.925 4.918 4.910 4.902 4.894 4.8860.196 0.181 0.167 0.152 0.137 0.12350 40 30 20 10 04.886 4.878 4.871 4.863 4.855 4.8470.123 0.108 0.094 0.079 0.064 0.0504.859 4.833 4.894 4.868 4.928 4.9030.068 0.067 0.133 0.132 0.198 0.1974.871 4.820 4.901 4.850 4.931 4.8810.086 0.085 0.143 0.142 0.200 0.1984.894 4.792 4.916 4.814 4.937 4.8360.122 0.120 0.163 0.160 0.204 0.2014.917 4.765 4.930 4.778 4.943 4.7910.159 0.155 0.183 0.179 0.207 0.204cysts, gland. (a)(b) (c) tumors, 0% gland. cysts, 0% gland. tumors, 50% gland. cysts, 50% gland. tumors, 100% gland.0.5 cm1 cm2 cm3 cm range: lesionthickness:gladularity cysts, 100% gland. % gland.Al (cm)poly-ethylene(cm)
Figure 2.
Phantom design. (a)
Schematic of the tissue-equivalent phantom that consists of polyethylene and aluminum indifferent proportions. (b)
Material basis decomposition data used for the phantom design. (c)
Matrix showing phantomdesign.
A pilot study to clinically evaluate spectral imaging was performed at Unilabs Mammography Department, CapioS:t G¨orans Hospital, Stockholm, Sweden in 2010. Women with suspicious findings were asked to take part in thestudy and undergo examination with the spectral mammography system. A total of 12 women were examinedduring the course of the study.All lesions were indicated by experienced radiologists, and pathological examination provided ground truth.The spectral analysis according to above, including marking of lesion and surrounding tissue and calculation ofthe likelihood ratio, was performed by medical physicists.The clinical study was conducted with an early prototype system that differed slightly from the system usedfor the more recent phantom measurements. In particular, the energy resolution of the prototype was coarserand it is expected that the results would improve with the current system.
3. RESULTS3.1. Phantom measurements
The measured contrast between simulated water (i.e. decomposed into Al and polyethylene) and actual wateracquired at a range of energy spectra (26–38 kV) was within 0.1%–1.7% for both low- and high-energy photoncounts. For the ratio low-energy photons to high-energy photons, the difference between simulated and actualwater was even smaller ( < . y -axis in Fig. 3 shows a weightedifference between high- and low-energy photons rather than just the high-energy photons. This weighting wasconvenient to enhance differences and visualize the results, but was not used in any calculations.
450 500 550 600 650 700 750400405410415420425430 low-energy photon counts: n lo pho t on c oun t d i ff . : n h i − w n l o benign cystic lesionmalignant lesionnormal breast tissue (a) (b) Figure 3.
Phantom measurements. (a)
X-ray image of the phantom. (b)
Photon-count difference between cystic benignlesions (green, dashed) and malignant tumors (red, solid) as a function of low-energy counts. Expected counts (i.e. modelpredictions, lines) are compared to measurements on lesions (error bars) and the reference measurement (blue cross witherror bar).
The phantom lesions were characterized at 29 kV and with the 0-mm lesion as reference. All lesions werecorrectly characterized with likelihood ratios log( λ ) = − − −
240 for respectively 10-, 20-, and 30-mmtumors (red dots in the figure), and log( λ ) = 3, 54 and 140 for the cysts (green dots).Quantum noise sets a lower limit on lesion size that can be accurately characterized. A log likelihood | log( λ ) | = 4 is equivalent to a separation of two standard deviations between the most likely malignant lesionand the most likely cystic lesion. For spherical lesions at clinical dose levels, this typically occurs at lesiondiameters less than 10 mm. However, the situation improves for elliptical lesions if the area cross-sectional tothe x-ray path is larger than the lesion thickness. Figure 4 shows the graphical user interface for the software tool and the results for a 13-mm benign cystic lesion.The best fit to the observed data that maximizes the likelihood function was obtained for a 6 mm thick cystembedded in 39 mm breast tissue with 28% glandularity. A positive likelihood ratio of λ = 30 indicated that thelesion was likely to contain water and therefore probably benign. The compression height (40 mm in this case)serves as a sanity check, but is a too coarse measure to be trusted as ground truth.Figure 5 illustrates calculation of the likelihood ratio for the case in Fig. 4. The 2D histogram in the left-hand panel shows the distribution of high- and low-energy counts over the marked lesion and reference area. Inqualitative accordance with Fig. 3, the red and green solid lines in Fig. 5 represent model predictions of benignand malignant lesions with increasing thickness from 0 to t . The right-hand panel of Fig. 5 shows a closeup ofthe model predictions with the mean of the measurements indicated. This case is clearly characterized as a cyst.In total, 9 circular lesions (7 benign and 2 malignant ones) were observed during the study. Out of these, 7were correctly characterized with a decision boundary at log( λ ) = 0. One lesion was incorrectly characterizedand the remaining one could not be characterized at all because of non-constant breast thickness. Moreover, ofthe correctly characterized lesions, two were very close to the decision boundary. igure 4. Overview (left) and closeup (right) of the user interface with a marked benign cystic lesion (red), the surroundingregion that is used for reference (blue), and the resulting analysis: log likelihood, thickness, glandularity, and cyst thickness. benign cystic lesionmalignant lesionnormal breast tissuelesionlow-energy photon counts: log n lo pho t on c oun t d i ff e r e n ce :l og n h i − w l og n l o low-energy photon counts: log n lo pho t on c oun t d i ff e r e n ce :l og n h i − w l og n l o Figure 5.
Photon-count difference between cystic benign lesions and malignant tumors as a function of low-energy counts.
Left:
Histograms over the marked lesion and reference area with superimposed solid lines that represent expected counts(model predictions).
Right:
Closeup of the expected counts compared to the mean of the histograms. [Color imageavailable online.] . DISCUSSION
It must be emphasized that the likelihood function that was used is an approximation and does not includeseveral systematic and statistical uncertainties. Therefore, the likelihood ratios ( λ ) given in Sec. 3.1 are expectedto be reduced if additional uncertainties are included, and some preliminary findings are presented here. Theassumption that both glandularity and thickness are equal for the lesion and surrounding region can be ques-tioned. Fig. 3 shows that the gridlines for equal breast thickness are nearly parallel to the lines with varyinglesion thickness. Thus, a difference in glandularity between the two regions should not affect the separation ofcysts from solid tumors substantially, but only change the estimated lesion thickness.A thickness difference between the lesion and background region, however, shifts a point almost perpendic-ularly to the lesion lines, thus seriously affecting the discrimination task. For a 1-cm lesion in a 5-cm breast,a gaussian uncertainty of the thickness difference of about a quarter of a mm, translates to half the separationbetween the cyst and solid tumor curves. The method is also sensitive to unknown inhomogeneities in the in-coming x-ray field, such as a heel effect. We need to know the fluence ratio of the two regions to about 0.5%precision to have a two sigma separation.A more detailed analysis of these uncertainties, as well as additional ones, such as threshold accuracy andstability, must be performed to fully evaluate the confidence of the lesion classification.
5. CONCLUSIONS
Measurements on a tissue-equivalent phantom showed that a significant difference between cysts with fluidcontents and cancerous tissue can be detected with spectral lesion characterization at imaging conditions thatare standard for screening. This result indicates that the specificity of mammographic screening could beincreased. The amount of clinical data is too small to draw any final conclusions, but the results on clinicalimages are encouraging. Future work should include compensation for thickness gradients, accurate attenuationcharacterization of cyst fluid, and studies of the model accuracy.
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