Optimization of mammography with respect to anatomical noise
Erik Fredenberg, Bjorn Svensson, Mats Danielsson, Barbara Lazzari, Bjorn Cederstrom
This is the submitted manuscript of:
Fredenberg, E., Svensson, B., Danielsson, M., Lazzari,
B. and Cederström, B., “Optimization of mammography with respect to anatomical noise,” Proc. SPIE 7961, Medical Imaging 2011: Physics of Medical Imaging, 796112 (2011).
The published version of the manuscript is available at: https://doi.org/10.1117/12.877985 See also:
Cederström, B. and Fredenberg, E., 2014. The influence of anatomical noise on optimal beam quality in mammography. Medical physics, 41(12), p.121903. https://doi.org/10.1118/1.4900611 All publications by Erik Fredenberg: https://scholar.google.com/citations?hl=en&user=5tUe2P0AAAAJ ptimization of mammographywith respect to anatomical noise
E. Fredenberg, a B. Svensson, b M. Danielsson, a B. Lazzari, c and B. Cederstr(cid:127)om aa Department of Physics, Royal Institute of Technology (KTH), AlbaNova University Center,106 91 Stockholm, Sweden; b Sectra Mamea AB, Smidesv(cid:127)agen 5, 171 41 Solna, Sweden; c Medical Physics Unit, General Hospital of Pistoia, Via Pertini, 708 - 51100 Pistoia, Italy
ABSTRACT
Beam quality optimization in mammography traditionally considers detection of a target obscured by quan-tum noise on a homogenous background. It can be argued that this scheme does not correspond well to theclinical imaging task because real mammographic images contain a complex superposition of anatomical struc-tures, resulting in anatomical noise that may dominate over quantum noise. Using a newly developed spectralmammography system, we measured the correlation and magnitude of the anatomical noise in a set of mammo-grams. The results from these measurements were used as input to an observer-model optimization that includedquantum noise as well as anatomical noise. We found that, within this framework, the detectability of tumorsand microcalcifications behaved very differently with respect to beam quality and dose. The results for smallmicrocalcifications were similar to what traditional optimization methods would yield, which is to be expectedsince quantum noise dominates over anatomical noise at high spatial frequencies. For larger tumors, however,low-frequency anatomical noise was the limiting factor. Because anatomical structure has similar energy depen-dence as tumor contrast, optimal x-ray energy was significantly higher and the useful energy region wider thantraditional methods suggest. Measurements on a tissue phantom confirmed these theoretical results. Further-more, since quantum noise constitutes only a small fraction of the noise, the dose could be reduced substantiallywithout sacrificing tumor detectability. Exposure settings used clinically are therefore not necessarily optimalfor this imaging task. The impact of these findings on the mammographic imaging task as a whole is, however,at this stage unclear.
Keywords: mammography; optimization; beam quality; observer model; anatomical noise; quantum noise;spectral imaging; glandularity;
1. INTRODUCTION
Beam-quality optimization of x-ray imaging systems is crucial to minimize the dose to the patient.
1, 2
This isparticularly so in mammography, where a large number of women are exposed to radiation through screeningprograms.
In traditional optimization of mammography, a target on a flat background is usually considered,and the ratio between target contrast and quantum noise is used as a figure of merit. Contrast and quantumnoise are both reduced by a harder spectrum due to higher transmission at higher energies, and there exists anoptimal energy at which the ratio is maximized at a constant dose to the breast.Nevertheless, the dominant source of distraction for many imaging tasks in mammography is not quantumnoise, but the variability of the anatomical background.
7, 8
The so-called anatomical noise has similar energydependence as the contrast, and when it is taken into account, we can expect a shift in the optimum towardshigher energies. In addition, when anatomical noise dominates, the dose may be reduced with little loss inimage quality, because, contrary to quantum noise, the anatomical noise has the same dose dependence as thesignal difference between target and background.The purpose of the present study is to investigate the effect of anatomical noise on beam-quality optimizationin mammography using an observer model. The methodology is similar to what we have previously employed forphoton-counting spectral imaging,
10, 11 but here we consider a conventional detector without energy resolution.
Electronic mail: [email protected] . MATERIAL AND METHODS2.1. Observer modeling
The noise equivalent number of quanta (NEQ) is an efficient and wide-spread metric for system optimization.
12, 13
While the standard NEQ only takes quantum and detector noise into account, the dominant source of distractionfor many imaging tasks in mammography is the variability of the anatomical background, which is fractal.
7, 8
Richard and Siewerdsen
14, 15 proposed the generalized NEQ (GNEQ) framework as a way to include the anatom-ical noise in optimization of imaging systems:GNEQ( ! ) = ⟨ I ⟩ T ( ! ) S Q ( ! ) + S A ( ! ) ; (1)where ! is the spatial frequency in the radial direction, ⟨ I ⟩ is the expected image signal, and T is the modulationtransfer function (MTF). S Q and S A are the power spectra (NPS) of quantum and anatomical noise respectively.For uncorrelated pixels, S Q is flat. S A can be described by a power law, (cid:11)=! (cid:12) , where (cid:11) and (cid:12) are empir-ically determined constants, representing the magnitude and correlation of the noise, respectively.
7, 8
Hence,anatomical and quantum noise have completely different frequency distributions; for large targets (e.g. tumors)the anatomical noise is of relatively large importance whereas for smaller objects (e.g. microcalcifications) thequantum noise dominates. It should be noted that the anatomical background of breast tissue in reality is notpurely random, but has a deterministic component that reduces the magnitude of S A . This effect is not takeninto account in the present study.To take into account the frequency dependence and contrast of a specific task, we use an ideal-observerdetectability index as a figure of merit:
13, 14 d ′ = 2 (cid:25) ∫ Ny GNEQ( ! ) × C × F ( ! ) × ! d !; (2)where the integral is taken over the Nyqvist region. C = ∆ s= ⟨ I ⟩ is the target-to-background contrast in the imagefor signal difference ∆ s = ⟨| I background − I target |⟩ , where the angle brackets denote the expectation value. F isthe signal template, i.e. a spatial-frequency dependent task function, which integrates to the area of the targetfor unit contrast. Polar coordinates have been used for notational convenience, but all calculations were done inCartesian coordinates where appropriate, i.e. rotational symmetry was not assumed in general. More advancedobserver models, as well as inclusion of an eye filter and internal noise, have shown better correspondence withreal observers in some cases, but are not included in the present study.In traditional optimization of mammography, where anatomical noise is disregarded, there exists an optimalenergy for which the quotient ∆ s =S Q and detectability is maximized. S A , however, has similar energy depen-dence as ∆ s , and when it is taken into account, we can expect a flatter optimum and a shift towards higherenergies, in particular for large objects. In addition, when S A dominates the dose may be reduced with no lossin image quality because ∆ s =S A is dose independent as opposed to ∆ s =S Q . For a more formal derivation ofnoise and signal transfer in imaging systems we refer to our previous publications. The Sectra MicroDose Mammography system forms a basis for our study and it is briefly described here. Thesystem consists of a tungsten-target x-ray tube with 0.5 mm aluminum filtration, a pre-collimator, and an imagereceptor, all mounted on a common arm (Fig. 1, Left). The image receptor consists of several modules ofphoton-counting silicon strip detectors with corresponding slits in the pre-collimator (Fig. 1, Right). To acquirean image, the arm is rotated around the center of the source so that the detector modules and pre-collimatorare scanned across the object. The multi-slit geometry rejects virtually all scattered radiation. A bias voltage is applied over the silicon strip detector, so that when a photon interacts, charge is releasedand drifts as electron-hole pairs towards the anode and cathode respectively (Fig. 1, Right). Each strip is wirebonded to a preamplifier and shaper, which are fast enough to allow for single photon-counting. The preamplifierand shaper collect the charge and convert it to a pulse with a height that is proportional to the charge and thus reastx-ray beam Si-strip detector linespre-collimatorcompression platebreast support _ +
HV rejectionhighlowASICpre-collimatorbreastx-ray tube detector yzx scanscan
Figure 1. Left:
Photograph and schematic of the Sectra MicroDose Mammography system [image courtesy SectraMamea AB].
Right:
The image receptor and electronics. to the energy of the impinging photon. Pulses below a few keV are regarded as noise and are rejected by alow-energy threshold in a discriminator. All remaining pulses are registered by counters. A preamplifier, shaper,and discriminator with counters are referred to as a channel, and all channels are implemented in an applicationspecific integrated circuit (ASIC). Detailed descriptions of the system and detector can be found elsewhere.
5, 16
As we have reported previously, an energy sensitive MicroDose system has been developed for spectral imagingwithin the EU-funded HighReX project.
The main difference compared to the conventional system isan additional high-energy threshold of the detector, which sorts the detected pulses into two bins according toenergy.We have designed a system model in the past that accurately predicts performance of both the conventionaland spectral-imaging MicroDose systems.
The model is based on detailed knowledge of the specific systemgeometry and published x-ray spectra, attenuation coefficients,
20, 21 and average glandular dose (AGD) coeffi-cients. It was developed using the MATLAB software package (The MathWorks Inc., Natick, Massachusetts).
Measured values on the anatomical noise exponent, (cid:12) , can be found in the literature and range between 1.5and 4 for projection images of breast tissue ( (cid:12) = 1 : − : (cid:12) = 2 : (cid:12) = 2 : (cid:12) = 2 : − : (cid:12) = 3, (cid:12) = 3 : − : ), with mean value close to 3. It is clear that (cid:12) is affected by the system MTF, but, even if notcorrected for, the MTF of most systems are close to unity at the low spatial frequencies where anatomical noisedominates. System parameters related to the x-ray spectrum, such as incident spectrum and detector efficiency,have no effect on the noise correlation at a first-order approximation. Hence, (cid:12) can be regarded fairly systemindependent and the published values should be applicable to most mammography system.Values on the anatomical noise magnitude, (cid:11) , are more difficult to deduce from published data, at least partlybecause (cid:11) is to a larger degree system specific and does depend on, for instance, incident x-ray spectrum anddetector efficiency. Nevertheless, knowledge of (cid:11) is necessary to investigate the relative effect of quantum andanatomical noise, i.e. to find the crossing between the two. We have therefore measured the anatomical noisein a set of mammograms, acquired with a spectral MicroDose system at The Health Unit number 3 of Pistoia(Azienda USL3), Pistoia, Italy, as part of a clinical study within the HighReX project. A number of womenfrom the screening program in the age group 50-69 were asked to participate. A set of images in CC view wereused for the present study.ssuming that the breast contains a mixture of adipose and glandular tissue within skin of constant thickness,contrast variation in a mammogram is caused by a variability in the glandular fraction superimposed on athickness gradient. In a conventional non-energy-resolved mammogram there is no way of separating these twocontrast mechanisms without using prior knowledge of, for instance, a slowly varying thickness gradient towardsthe breast border together with the mean glandularity. In addition, the thickness gradient interferes with low-frequency anatomical noise. Previous investigations have therefore been restricted to measurements in a centralregion where the compression paddle can be assumed to keep the breast at constant thickness. The accuracy ofthis thickness measurement also limits the accuracy of the glandularity estimation, while the proposed methoddoes not rely on a physical measurement of the breast thickness.Using spectral information and the system model, however, we are able to separate thickness from glandularity.The model generates pixel values as a function of thickness and glandular fraction which are used to produceglandularity and thickness maps for the breast. For verification, the height of the compression paddle wasregistered for each image and compared to the 90% percentile of the thickness map.Any other material in the breast that does not fit the breast model, such as skin at the breast border ormicrocalcifications, may generate outlier points. The continuous occurrence of such outlier points at the breastborder was used as a starting point for the inner limit of the skin, given that it was at least 1 mm from the outerskin limit, which was determined by thresholding. Hence, a skin map could be removed from the glandularitymap, and the remaining glandularity map was further eroded by a 2 mm-radius disc. Outlier points within theglandularity map were regarded as microcalcifications if the connected area was larger than one pixel. Isolatedpixels were assumed to be statistical noise and were assigned values extrapolated from the neighboring pixels.The glandularity maps were segmented into 256 ×
256 pixel regions-of-interest (ROIs) with 128 pixels overlap.ROIs containing outlier points were discarded, and the image was excluded from measurement if more than 50%of the ROIs were discarded. The NPS was calculated in Cartesian coordinates as the mean of the squared Fouriertransform of the difference in image signal from the mean in each ROI. The effect of the field of view on themeasured NPS is a convolution with the window function (spectral leakage), and due to the sharply peakedspectrum, window artifacts can be expected, in particular at low spatial frequencies. A Hann data taper wastherefore applied to each ROI prior to calculating the NPS. Rotational symmetry was assumed, and S A ( ! ) wasfound by converting from Cartesian to polar coordinates and averaging over 2 (cid:25) . The radial NPS was least-squarefitted to ln( S ) = ln( (cid:11)! − (cid:12) + Φ) ; (3)where Φ represents the quantum noise that is approximately flat. The logarithm makes the power-law NPSlinear, which provides a better fit. Spatial frequencies above 0.1 mm − were included in the fit. Φ was convertedusing the system model to an expected AGD, which was monitored to be within reasonable values in order tovalidate the fitting and conversion procedures.Except for the exclusion criteria mentioned above, images were excluded from measurement if any of thequantities glandularity mean, (cid:11) , (cid:12) , or quantum noise differed more than 50% between right and left breastimage. Finally, a set of 2 ×
56 images remained.
As an example, we have chosen to illustrate the optimization procedure on the Sectra MicroDose Mammographysystem. It should be noted, however, that the results are generally valid for any mammography system. Theanatomical noise levels were chosen in accordance with the measurement above, and the system model was usedto evaluate the system response and to calculate the GNEQ and detectability index.
For the purpose of experimental verification, we have constructed a phantom simulating tissue with differentglandularity content, as well as tumors with varying thickness embedded in tissue of 0, 50 and 100% glandularity,respectively. Since x-ray absorption to a good approximation can be described as a linear combination of only twofunctions, photo absorption and Compton scattering, which have separable energy and material dependencies,he absorption and energy dependence of any material can be simulated with a proper combination of any twomaterials.
21, 28
In our case, the material bases are aluminum and polyethylene, and the phantom is made up of25 squares with 30 mm side, where each cell contains a combination of aluminum and polyethylene representinga certain tissue type of 45 mm thickness. For example, 45 mm 50% glandular tissue is equivalent to 43.53 mmpolyethylene and 1.04 mm Al, whereas the corresponding values for a 10 mm thick tumor embedded in 50%tissue are 43.65 mm and 1.25 mm, respectively.The entrance surface air kerma (ESAK) for a fixed mAs was measured using an ion chamber (type 23344and electrometer Unidose E, PTW, Freiburg, Germany) for tube voltages between 24 and 40 kV in steps of1 kV. With knowledge of the total filtration, the AGD could be calculated, assuming a 45 mm breast with 50%glandularity. Images were then acquired for a fixed AGD of 0.70 mGy. For each kV, two images were acquiredwith the phantom rotated 180 o inbetween, in order to cancel any residual flat-fielding imperfections.The mean pixel value and standard deviation was measured for each cell, using a ROI of 20 ×
20 mm . Usingthese values, a scalar equivalent to Eq. 2 can be usedSDNR ∝ | m i − m j | (1 − (cid:31) ) (cid:27) Q;i + (cid:31)(cid:27) A ; (4)where m i and (cid:27) i is the mean and standard deviation, respectively, of the i :th ROI; (cid:31) is a parameter that showsthe relative strength of the anatomical noise; and (cid:27) A is the standard deviation of the mean for an ensembleof ROIs with varying glandularity. Assuming that T ( ! ) has no energy-dependence, the dependence on beamquality of Eq. 2 calculated for a fixed dose, can be equally calculated using Eq. 4, if the noise mixing parameter, (cid:31) , is chosen appropriately. We will make no attempt here to derive (cid:31) , but only look at the two special cases (cid:31) = 0 (statistical noise is completely dominant) and (cid:31) = 1 (anatomical noise is completely dominant).
3. RESULTS AND DISCUSSION3.1. Measurement of the anatomical noise in mammograms
The process of measuring the anatomical noise is shown for a representative case in Figure 2; conventionalnon-energy-resolved absorption image, thickness map, glandularity map, skin separation, and segmentation intoROIs. The radial NPS, measured in the glandularity map from Fig. 2 and fitted to Eq. 3, is shown in Fig. 3.In this example, the breast thickness was 5.7 cm and the mean glandularity was 0.29. NPS parameters (cid:11) =1 : × − mm and (cid:12) = 2 :
75, together with a dose of approximately 0.62 mGy yielded a crossing betweenanatomical and quantum noise at 3.4 mm − . Note that the markers in the NPS plot are interpolated from theactual measurement points to generate an equidistant log vector.The results from the group of patients are summarized in Fig. 4, where (a) shows a histogram over the breastthickness that are approximately normal distributed around a mean of 5.0 cm. A scatter plot of the compressionpaddle height as a function of estimated thickness is shown in Fig. 4(b). There is a strong correlation but,irrespective of breast thickness, a systematic deviation of approximately 3 mm.A scatter plot of the mean glandularities as a function of breast thickness is shown in Fig. 4(f). There seemsto be an inverse correlation between thickness and glandularity, which is in accordance with previous studies. Note, however, that the linear least-square fits that are displayed in Fig. 4(d–f) only serve to guide the eye; anycorrelations could not be established with confidence at this point and should only be regarded as indications.The mean glandularity over the group was 16%, which is surprisingly low compared to published results, despitethe relatively high age of the participating women (age group 50-69). The mean was calculated over the entireglandularity map and hence not biased by ROI sampling. Fig. 4(c) shows the mean glandularity distributionfor the group, i.e. the average of the glandularity histograms calculated for each individual. We note that theglandularity distribution is skewed and not Gaussian.Figures 4(d, e) show results from the NPS measurement; (cid:11) and (cid:12) respectively. It seems (cid:12) is fairly invariantwith breast thickness, whereas (cid:11) exhibits anticorrelation. Note that, if the correlation observed here is a realeffect, it has nothing to do with the passage of more material since the thickness is taken out of the equation.Rather, it may be explained by the fact that thicker breasts contain more adipose tissue (c.f. Fig. 4(f)), and b r e a s t t h i c k n e ss [ c m ] g l a n d u l a r i t y f r a c t i o n Figure 2.
The process of deducing thickness and glandularity from a spectral mammogram. From left to right: 1)conventional absorption image where thickness gradient and glandular variation are superimposed, 2) thickness map, and3) glandularity map, where the skin and ROI segmentations are highlighted. Color images available online. −2 −1 −6 −4 −2 radial frequency [mm −1 ] N P S [ mm ] measured NPSfitted S A fitted S Q Figure 3.
The radial NPS measured in the glandularitymap of Fig. 2 and fitted to Eq. 3 to separate the anatom-ical ( S A ) and quantum ( S Q ) noise components. hence less structure. When the line integral through the breast is taken into account in order to calculate theimage NPS, these two effects will to some degree cancel. The mean (cid:11) was 6 : × − mm , and the mean (cid:12) was2.7 (standard deviation 0.06), which is in good agreement with previously reported values. These results can beused to calculate the NPS in breast images of virtually any imaging system, given that the system geometry isknown. n u m b e r o f p a t i e n t s (a)3 4 5 6 73456 breast thickness [cm] c o m p r e ss i o n h e i g h t [ c m ] (b)0 0.2 0.4 0.6 0.8 1glandular fraction b r e a s t a r e a [ a . u . ] (c) 3 4 5 6 70 0.10.30.40.5 breast thickness [cm] g l a n d u l a r f r a c t i o n (f)3 4 5 6 701.0 2.03.04.0 x 10 −4 breast thickness [cm] α [ mm ] (e)3 4 5 6 72.5 2.62.72.82.9 breast thickness [cm] β (d) Figure 4.
Measurement results from the set of mammograms: (a) histogram over breast thicknesses, (b) compressionheight as a function of estimated breast thickness, (c) mean glandularity distribution, (d{f ) anatomical noise exponent( (cid:12) ), anatomical noise magnitude ( (cid:11) ), and glandularity, respectively, as functions of thickness. Measurement points areindicated by circles. The straight line in plot (b) shows the measured height in order to visualize the deviation. Linearleast-square fits are provided in (d–f) in order to guide the eye to the trend.
Figure 5 shows detectability ( d ′ ) as a function of x-ray tube acceleration voltage for a 5 mm tumor and a100 (cid:22) m microcalcification in quantum and anatomical noise. The targets were embedded in an average breastaccording to the previous section; 5.0 cm thickness, 20% glandularity, and a glandularity distribution accordingto Fig. 4(c). The mA was adjusted at each kV in order to keep AGD and exposure time constant. All threeplots have equal axes and are directly comparable.Figure 5(a) plots detectability for the tumor and microcalcification at an AGD of 0.5 mGy and in anatomicalnoise corresponding to (cid:11) = 6 : × − mm and (cid:12) = 2 :
7, i.e. the mean values from the group of patients. Thedashed lines represent detectability for pure anatomical noise and pure quantum noise. These extreme caseswere normalized to the first data point for each target in order to show the trend over the kV range. The shaded
20 30 40 50 60 0 5 10 15 tube voltage [kV] d e t e c t a b i l i t y − d ’ tumorMC noise type:pure S A − pure S Q (a) pure S A pure S Q pure S A pure S Q S A + S Q S A + S Q Figure 5.
Detectability ( d ′ ) as a function of x-ray tubeacceleration voltage for a 5 mm tumor and a 100 (cid:22) mmicrocalcification (MC) in quantum S Q and anatomical S A noise. (a) Tumor and microcalcification at an AGDof 0.5 mGy and in an average level of anatomical noise.The dashed lines correspond to pure anatomical and purequantum noise, normalized to the first data point. Foreach imaging task, the position of the solid line in theshaded area indicate the relative influence of the two noisesources. (b)
Quantum noise dependence. The AGD overa range of dose levels in the shaded area, which yields avarying influence of quantum noise. For the tumor, thefull range falls on the solid line and is therefore not visible. (c)
Dependence on the anatomical noise magnitude with (cid:11) ranging in the shaded area from the first ( Q ) to thethird ( Q ) quartile of the measured values. Color imagesavailable online.
20 40 50 0 10 S Q range: 0.25 − 0.75 mGytumorMC30 5 tube voltage [kV] d e t e c t a b i l i t y − d ’
20 40 50 0 10 S A range: Q and Q of α tumorMC30 60 515 tube voltage [kV] d e t e c t a b i l i t y − d ’ (c) low S A high S A low S A high S A mean S A mean S A areas represent the range where target detectability may fall depending on the relation between quantum andanatomical noise. We make the following observations: • The pure-quantum-noise lines correspond to targets on flat backgrounds, i.e. similar to traditional opti-mization that only takes quantum noise into account. There is a maximum at 22 kV for both targets.Optima that are independent of target material is in line with previous research when quantum noise aloneis considered. • The pure-anatomical-noise case has a less distinct maximum, which is shifted to a substantially higher kVcompared to the quantum-noise case. Again, the optimum seems fairly independent of target material andis rather a function of target size. • Detectability of the microcalcification is influenced by anatomical noise, but quantum noise dominates andthe maximum is found at 24 kV, i.e. fairly close to traditional optimization. • Tumor detectability is completely dominated by anatomical noise for this case, and the tube voltagedependence is significantly different from the outcome of traditional optimization methods.Quantum noise dependence of the two targets is illustrated in Fig. 5(b); detectability is plotted for dose levels0.25–0.75 mGy, where the solid line in the center corresponds to the case in Fig. 5(a). Tumor detectability isirtually unaffected by dose and the three cases coincide. Detectability of the microcalcification, however, isclearly affected. For pure quantum noise, d ′ would be proportional to dose, but because of the anatomical noisecomponent in the microcalcification case there is a slightly weaker dependence, in particular at higher doseswhere anatomical noise becomes more important.Figure 5(c) illustrates anatomical noise dependence in the range (cid:11) ∈ (2 : ; : × − mm , which corre-sponded to the first and third quartile of the measured (cid:11) . The solid line is for the mean (cid:11) and equals thecorresponding lines in Fig. 5(a, b). Microcalcification detectability is slightly affected by the anatomical noiselevel, and the optimum is shifted in the order of 1 kV. The dependence is, however, substantially higher for thetumor case because if its larger size. We chose a background of 50% glandular tissue and as target a 20 mm tumor embedded in said tissue. For theanatomical noise, we used the five ROIs with glandularity equal to { } . In Fig. 6, the squaredSDNR is plotted as a function of tube voltage for (cid:31) = 0 and (cid:31) = 1, respectively. The curves are arbitrarilynormalized to be equal at the tube voltage for which the statistical noise-dominated curve has its maximum. Forcomparison, theoretical curves of detectability index based on Eq. 2 are included. Even though the agreementis not prefect, the theoretical results are corroborated by the phantom experiment. Although the imaging casesare different, these curves may be qualitatively compared to the dashed curves in Fig. 5(a).
25 30 35 4000.2 0.40.60.811.2 tube voltage [kV] S D N R [ a . u . ] Pure anatomical noise: experimentPure statistical noise: experimentPure anatomical noise: modelPure statistical noise: model
Figure 6.
Squared signal-difference to noise ratio for a20 mm tumor embedded in 50%-glandularity tissue asa function of tube voltage for pure statistical and pureanatomical noise, respectively. Also included are theoret-ical curves from Eq. 2.
4. CONCLUSIONS
Spectral information was used for advanced thickness equalization in a set of mammograms, and we were ableto measure the anatomical noise without bias from a thickness gradient. Our detailed knowledge of the imagingsystem under study allowed us to convert the measured NPS in units of incident quanta to units of glandularityvariations in the breast, which can be converted and used for virtually any mammography system. The measuredanatomical NPS served as input to calculate an ideal-observer detectability index for, which was used to evaluatethe system for a range of imaging conditions under influence of anatomical noise.Figure 7 illustrates the main conclusions of this study; detection of a tumor and a microcalcification as afunction of x-ray tube acceleration voltage. It is clear that inclusion of anatomical noise and imaging task inbeam-quality optimization may yield very different results than a traditional analysis based solely on quantumnoise. Detection of very small objects, such as small microcalcifications, is fairly unaffected by anatomical noise,and traditional optimization of the signal-to-quantum noise ratio is a reasonably good approximation. For largertargets, such as tumors, anatomical noise dominates over quantum, however, and optimum imaging conditionsare shifted to considerably higher energies. This means that 1) it is possible to reduce dose without loss in imagequality, and 2) it is also possible, or even beneficial, to increase the acceleration voltage. The latter may inurn be advantageous in order to reduce scan time or tube loading. These theoretical results were verified bymeasurements on a custom-made phantom that accurately simulates absorption of normal and cancerous tissueas a function of energy.
20 40 50 0 0.51.01.5 microcalcificationtumor30tube voltage [kV] d e t e c t a b i l i t y − d ’ Figure 7.
Detection of a tumor and a microcalcificationas a function of x-ray tube acceleration voltage, i.e. thecase in Fig. 5 but normalized to the first data point. Theoptima for these two targets are located at radically dif-ferent voltages due to the inclusion of anatomical noise.
How these findings influence the optimization of the mammographic imaging task as a whole is at this stageunclear. It should also be noted that this is a simplified theoretical study and that these results should becorroborated by clinical investigations.
ACKNOWLEDGMENTS
The authors wish to thank S. Karlsson and N. Dahlman at KTH, Stockholm, Sweden for phantom fabrication.This research was funded in part by the Swedish agency for innovation systems (VINNOVA).
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