Method of measuring NEQ as a quality control metric for digital mammography Aili K. Bloomquist, James G. Mainprize, Gordon E. Mawdsley, and Martin J. Yaffe Citation: Medical Physics 41, 031905 (2014); doi: 10.1118/1.4865175 View online: http://dx.doi.org/10.1118/1.4865175 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/41/3?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Characterization of scatter in digital mammography from use of Monte Carlo simulations and comparison to physical measurements Med. Phys. 41, 111914 (2014); 10.1118/1.4894808 Anatomical noise in contrast-enhanced digital mammography. Part I. Single-energy imaging Med. Phys. 40, 051910 (2013); 10.1118/1.4801905 Effect of image quality on calcification detection in digital mammography Med. Phys. 39, 3202 (2012); 10.1118/1.4718571 Quality control for digital mammography in the ACRIN DMIST trial: Part I Med. Phys. 33, 719 (2006); 10.1118/1.2163407 Validation of MTF measurement for digital mammography quality control Med. Phys. 32, 1684 (2005); 10.1118/1.1921667

Method of measuring NEQ as a quality control metric for digital mammography Aili K. Bloomquist,a) James G. Mainprize, and Gordon E. Mawdsley Sunnybrook Research Institute, 2075 Bayview Avenue, Toronto, Ontario M4N 3M5, Canada

Martin J. Yaffe Sunnybrook Research Institute, 2075 Bayview Avenue, Toronto, Ontario M4N 3M5, Canada and Department of Medical Biophysics, University of Toronto, 2075 Bayview Avenue, Toronto, Ontario M4N 3M5, Canada

(Received 3 October 2013; revised 20 December 2013; accepted for publication 28 January 2014; published 19 February 2014) Purpose: Current quality control protocols for digital mammography rely on subjective assessments of image quality or simple measures that are not comparable between vendor platforms. The noiseequivalent quanta (NEQ) can be expressed in units of image quanta (fluence) for the spatial frequency range of interest, enabling comparisons between systems and x-ray spectra. The purpose of this work is to explore use of a simple phantom to measure the components of the noise-equivalent quanta of digital mammography systems for use in routine quality control. Methods: A simple phantom is imaged on six mammography systems from different vendors. The phantom contains uniform regions for measurement of noise power spectrum (NPS), slanted edges for measurement of modulation transfer function (MTF), and objects of various thicknesses for measurement of contrast. Images were acquired at a range of dose levels on each system to examine how measurements scale with dose, and multiple images were taken at a single dose point to examine measurement reproducibility. Results: The phantom and measurement methods show good reproducibility, with average coefficient of variation values of less than or equal to 15% on all systems evaluated. Measured MTF and NPS values are comparable to other published results when the increase in scattered radiation generated by placing the phantom on the breast support is accounted for. Conclusions: Measurement of the parameters required to calculate NEQ from a single image of a simple phantom is practical, and shows promise as a method of evaluating image quality for routine quality control of digital mammography systems. © 2014 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4865175] Key words: digital mammography, noise equivalent quanta, noise power spectrum, modulation transfer function 1. INTRODUCTION Current quality control (QC) protocols for digital mammography are often reliant on subjective assessments of phantom images for overall image quality, or rely on overly simplistic measures that may not reflect clinical image quality or may not reliably capture all modes of failure. Some of the QC tests for screen-film mammography require the scoring of images of phantoms (e.g., RMI/Gammex 156) and these tests tend to be highly subjective and not particularly sensitive to changes in the image quality of digital systems.1 The European Reference Organisation for Quality Assured Breast Screening and Diagnostic Services’ (EUREF) QC program for digital mammography2 makes use of a contrast detail phantom. The procedures for evaluation of images of this phantom by a human observer are too time-consuming to be practical for routine QC,3 and the phantom is expensive, due to the use of gold for the contrast objects. An automated procedure for “reading” the contrast-detail images has been suggested, but this approach seems to be unnecessarily cumbersome.4 Measurement of signal to noise ratio (SNR) or signal difference to noise ratio (SDNR) may not 031905-1

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be suitably sensitive to changes in spatial resolution of the imaging system, as blurring can reduce the apparent noise in images, causing an increase in these quality metrics for images whose spatial resolution is diminished. Measurements of detective quantum efficiency (DQE) are laborious and challenging to do away from the laboratory environment. It is particularly difficult to accurately measure the fluence (or quanta) incident on the detector. In addition, evaluation of the DQE measures performance of the detector, not the image quality per se, i.e., it does not indicate if the detector, as it is being used in the imaging system, is receiving enough quanta (dose) to create images of clinically acceptable quality. Measurement of the noise equivalent quanta (NEQ) may provide a practical, robust way to assess the image quality of a system objectively. The concept of a “generalized NEQ” has been proposed which extends the standard analysis to include systematic effects such as x-ray scatter, magnification, and antiscatter grids.5–7 This can make it a more realistic metric that bears a closer relation to actual system performance. Generalized NEQ measurements thus differ from the more common “Detector NEQ” evaluations which rely on standardized

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© 2014 Am. Assoc. Phys. Med.

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measurements of MTF and NPS (Refs. 8–10) usually at the detector without grid. We present here a simple way of estimating the twodimensional (2D), generalized NEQ. It is practical, robust, applicable to any digital mammography system, sensitive to changes in image quality, uses inexpensive materials and is amenable to automation. It should be suitable for QC of the system by tracking changes in image quality over time. The NEQ of an image expresses the “worth” of an image in terms of the number of quanta that appear to be used by the detector in forming the image, as determined from the signalto-noise ratio. In this sense, it is defined as the input quanta (or fluence) , scaled by DQE, NEQ = DQE.

(1)

The system DQE can be calculated as DQE =

(S · MTF)2 , NPS

(2)

where S is the signal level, measured as the mean image pixel value (after zero offset correction), MTF is the presampled modulation transfer function, and NPS is the Weiner or noisepower spectrum. Therefore, the 2D NEQ can calculated as NEQ(u, v) =

(S · MTF(u, v))2 . NPS(u, v)

(3)

Because the spatial frequency-dependent NEQ is expressed in terms of quanta (or more precisely quanta per unit area), this metric makes it possible to objectively compare the quality of images acquired on different systems—as used clinically (with scatter, and the antiscatter grid, where present, included)—with different detector element (del) sizes, and using different beam qualities and exposure levels. As will be shown, the materials required to perform the measurements are relatively inexpensive, and the method proposed is rapid and reproducible.

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2. MATERIALS AND METHODS For QC purposes, the measurement of NEQ must be a simple technique that can be readily adapted to a variety of digital mammography systems and clinically relevant imaging configurations. For the measurement of NEQ, we propose imaging a uniform block of PMMA, on which a brass square has been positioned (see Fig. 1). The uniform region of the PMMA is used to evaluate the noise power spectrum (NPS) and the slanted edges of the brass square are used to calculate the presampled modulation transfer function (MTF). Wells of known depths and a contrast disk are used to evaluate how the signal difference (contrast) varies with object thickness which can be used for detectability measurements. A 12 mm diameter lead disk one mm thick can be used to provide an estimate of the fraction of scattered radiation in the measured image signal. The phantom is placed on the tabletop and an image is acquired at a clinically relevant technique. The phantom as manufactured has a total thickness of 45.55 mm, which provides similar attenuation conditions to a 55 mm thick breast with 29% fibro-glandular tissue, which is close to the median breast.11 The 50 × 50 mm brass square is 0.127 mm thick. It has ground edges and its side is angulated by ∼7.5◦ with respect to the pixel rows of the image. It is positioned at a height of 42.38 mm above the breast support plate (on top of 42.38 mm PMMA) and covered with a protective acrylic cover plate 3.175 mm (0.125 in) thick. The contrast wells have depths of 0.991, 0.424, and 0.089 mm. The thickness of the contrast disk is 1 mm. 2.A. Detector offset and scatter measurement

The mean signal in a region of interest (ROI), S, can be corrected for detector offset. Detector offset can be estimated by performing a linear fit between pixel value and mAs (detector offset is simply the y intercept), or can be based on a priori knowledge of the unit being tested. The fraction of the

NPS region contrast wells

contrast disc brass MTF tool

not used lead disc protecve cover plate

(a)

(b)

F IG . 1. (a) Schematic and (b) radiograph of phantom used for measuring NEQ. In the schematic, a view from above is on the top and a cross section is below. The schematic is not to scale. Medical Physics, Vol. 41, No. 3, March 2014

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signal in the images due to x-ray scatter, SF can be estimated (crudely) by comparing the signal behind the lead disk Sd with the signal, Sv , in the immediate vicinity of the lead disk in the image, Sd SF = . (4) Sv 2.B. Modulation transfer function

The presampled MTF is calculated in both the x and y directions using an oversampled edge and the standard algorithm described by Fujita et al.12 The edge-spread function was constrained to be monotonic to reduce the noise in the final curve, similar to Maidment’s method.13 The relatively wide (50 mm) brass square is used to obtain a profile that is long enough to allow accurate assessment of any lowfrequency drop14 in MTF due to off-focal radiation, scatter and/or glare in the detector system.15–17 Because of the noisiness/uncertainty at high spatial frequencies, the MTF was truncated at the spatial frequency where it dropped below 0.05, and the MTF at all frequencies beyond this cut-off were set to zero for the purposes of subsequent calculation of NEQ. The estimate of the low spatial frequency component of the MTF due to scatter and other effects is highly sensitive to the width of the (ROI) for the measurement. However, excessively wide ROIs will contribute increasing noise in the measurement at higher spatial frequencies, reducing the confidence there. The size of the ROI was increased interactively until the low-spatial frequency drop appeared to stabilize without increasing high spatial frequency noise. From a heuristic examination of results for both phosphor and selenium based detectors, a distance of 16 mm on either side of the edge was selected to be the optimal length of line-spread function. To obtain the 2D MTF(u, v) from orthogonal measures of MTF(u) and MTF((v) is not straightforward. Some sources of unsharpness are rotationally symmetric and others are not. A complete examination of MTF((u, v) would likely require either a full measurement of a two-dimensional point-spread function [PSF(x,y)] which is prone to poor SNR or would require extensive modeling to convert MTF((u) and MTF((v) to MTF((u, v) for each system. Nevertheless, it is reasonable to assume that most systems are governed by a MTF of the form (5) MTF(u, v) = To (ρ)Tx (u)Ty (v),

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where To (ρ) is a rotationally symmetric component and Tx and Ty are the separable components. For nonscanned systems such as flat-panel detectors, the biggest separable component is the sensitivity profile of the discrete detector elements, which for a rectangular detector element, can be expressed as a sinc function in each dimension. For a detector, whose elements have an active region with side lengths p and q in the x and y directions, respectively, we have Tx (u) = sinc(up) and Ty (v) = sinc(vq).

(6)

For measurements of “system” or “generalized” MTF, there is generally a difference in performance along the x and y axes. In this case, it is assumed that the 2D MTF is constructed as MTF(u, v) = To (ρ)Textra (u)Tx (u)Ty (v),

(7)

assuming that the more blurred direction is along x. The degradation, Textra (u) referring to the additional blur seen in one direction, is extracted as the ratio between the two MTF measurements as MTFx (u) . (8) Textra (u) = MTFy (u) Note that depending on system design, the higher blur may occur in either direction. Hence, the rotationally symmetric component is   MTFy (ρ) MTFx (ρ) 1 + . (9) To (ρ) ≈ 2 Textra (ρ)sinc(ρp) sinc(ρq)

2.C. Noise power spectrum

The two dimensional NPS is calculated using the multitaper method (MTM), with adaptive weighting.18 Using the MTM method results in a “cleaner” NPS, at the cost of some broadening (loss of spectral resolution) of any peaks (i.e., grid artefact) in the spectrum. Regions of interest are selected from the portions of the image where only PMMA was present in the beam. The ROIs are chosen such that the maximum angle of the x-ray beam (θ ) subtended is less than 4.7◦ , so changes in beam intensity across the ROI [proportional to cos3 (θ )] are kept to less than 2%. The ROIs used for NPS calculation were 512 pixels square. This results in a maximum cos3 correction error of 1.8%. S is the mean signal in the regions of interest used

TABLE I. Digital mammography systems used for evaluating NEQ as an image quality metric. System

Detector technology

Manufacturer

Model

Nominal pixel size (μm)

Grid type

1

Photo-stimulable phosphor (BaFBr:Eu)

Carestream (with GE gantry)

50

5:1 laminar, reciprocating (Ref. 21)

2 3 4 5

CsI on a-Si TFT array Amorphous selenium Amorphous selenium a-Si photon counting system Amorphous selenium

GE Hologic IMS Philips

CR 975 with EHRM2 screen (GE 800T gantry) Senographe DS Selenia Giotto Microdose

100 70 85 50

5:1 laminar, reciprocating (Ref. 22) Cellular 6:1 laminar, reciprocating (Ref. 23) NA

Planmed

Nuance

85

5:1 laminar, reciprocating (Ref. 24)

6

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TABLE II. Technique factors used to acquire images of the NEQ phantom and the contrast-detail phantom. The asterisk (*) indicates mAs value used for repeated images of the NEQ phantom. The plus (+) indicates the setting closest to what the AEC of the system would choose for a 42 mm thick breast. System 1 2 3 4 5 6

Target

Filter

kV

Grid present

mAs settings used

Estimated MGD (mGy)

Mo Mo W W W W

Mo Rh Rh Rh Al Ag

28 27 29 28 32 30

Yes Yes Yes Yes No Yes

28*, 56+ , 100 63*+ , 125 17, 45*+ 100 20, 45*+ , 90 7*, 13+ , 26 35*, 71+ , 140

0.41, 0.89, 1.59 0.86, 1.71 0.20, 0.53, 1.18 0.24, 0.55, 1.10 0.33, 0.61, 1.22 0.46, 0.93, 1.83

for the estimation of the normalized NPS, after correction for detector offset. 2.D. CR systems

System 1 is a CR system whose pixel values are recorded on a logarithmic scale during the digitization process. The image data from System 1 were transformed into a domain where the values become linear with exposure according to the following manufacturer-supplied equation P Vlin = 65535 × 10

P Vlog −4000 1000

,

(10)

where PVlog is the original (logarithmically transformed) pixel value and PVlin is the linearized pixel value. A “gain correction” was then applied to the image data to reduce the low spatial frequency variations due to the heel effect. The gain correction map was created by averaging together eight images of a 4 cm thick slab of PMMA which covered the entire imaging field, transforming the data using Eq. (7), normalizing to the maximum value and dividing all images by this map. 2.E. Dose calculation

To estimate the mean glandular dose, tube output, and halfvalue layer measurements from current routine physics testing reports were used with appropriate conversion factors for the phantom thickness of 45.55 mm (deemed equivalent to a 29% fibro-glandular breast 55 mm thick. The conversion factors were interpolated from published tables.19, 20 2.F. Systems measured

To assess the effectiveness of measuring the NEQ as described here, NEQ and CD phantom images were acquired on a range of digital mammography systems with varying doses and beam qualities. The systems used are described in Table I and the technique factors used are given in Table II. 2.G. Error/uncertainty analysis

To estimate the variability of this method of measurement, the acquisition of images, and analysis of NEQ was repeated 12 times at a single technique on all the mammography systems, moving the phantom slightly between images. The standard deviations (σ ) of the measured values of each component of the NEQ, as well as among the overall NEQ Medical Physics, Vol. 41, No. 3, March 2014

measurement were calculated. The coefficients of variations (σ /mean) were also calculated. For frequency-dependent parameters, these calculations were performed for all spatial frequencies (0 ≤ u ≤ 1/2d, 0 ≤ v ≤ 1/2d where d is the pixel spacing). 2.H. Comparison

The approach used here to get a “system” or generalized NEQ measure makes it difficult to compare to more conventional measurements of detector performance by other groups. Nevertheless, we can extrapolate the expected behavior from NEQ results obtained in the literature using a simple transformation model. Two effects dominate the MTF measurement, when the overall system is included, an increased low-spatial frequency scatter component and an increase in focal spot blurring. The scatter fraction can be estimated from the system response (Cooper et al.16 ). Following the approach of Salvagnini et al.,15 we can extract the scatter component and the detector component of the system MTF. Here, we assumed that the scatter was uniform (indicating a completely flat line spread function). Then the spatial frequency representation is SF δ(f) where SF is the scatter fraction (the ratio of the scattered and total quantum fluences at the detector), δ(f) is the dirac delta function, and the result is a transformed MTF (used for visual comparison) that appears like the following MTF(f ) = SF δ(f ) + (1 − SF )MTF0 (f ).

(11)

If the differences in magnification are small, the effect of the focal spot blur can be ignored. We compared our MTF method with the results of Marshall et al.,25 , Monnin et al.,26, 27 and Ghetti et al.28 From data reported in these papers we extracted the frequencies at which the MTF dropped to 50% and 10% in the x and y direction. Marshall et al.25 evaluated a CR system using TABLE III. Measured detector offsets and estimated scatter fractions. System 1 2 3 4 5 6

Detector offset in ADU (std. dev.)

Estimated scatter fraction

− 4.16 (18.27) − 5.7 (NA) 54.70 (4.35) − 1.78 (0.90) − 63.46 (17.55) − 1.21 (6.16)

0.16 0.10 0.01 0.12 0.03 0.10

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F IG . 2. The measured modulation transfer functions. Systems 1–3 are shown on the left graph, and systems 4–6 are shown at right.

EHRM3 plates rather than the EHRM2 plates tested in our work. It should be noted that because the EHRM3 plate has a thicker phosphor than the EHRM2 plate, the resolution is slightly lower. Marshall et al.25 measured MTF on a Siemens Inspiration, which is believed to use the same detector technology (85 μm selenium detector elements, Anrad, St. Laurent QC, Canada) as Systems 3 and 6. Adapting a method used by Salvagnini et al.,15 our measured values were adjusted to remove the low-frequency drop due to scatter by dividing the MTF by (1-SF), in an attempt to make the measurements more comparable to the other works, where scatter is not included. We applied a similar analysis for the noise power spectrum. Provided that the x-ray spectra are similar, the major

difference between our technique and others is the change in the scatter conditions. Others have measured the “normalized NPS” (NNPS) of the detector performance by removing the grid and acquiring the image in such a manner as to minimize the scatter (i.e., absorber placed near the x-ray source). The system NNPS as evaluated here was measured with the grid (where available) in place and attenuator placed on the breast support plate, explicitly including any induced scatter. The NNPS is NNPS(u, v) =

NPS(u, v) , k2

(12)

F IG . 3. Two-dimensional relative log(NNPS). Grayscale spans from the minimum to maximum value (adjusted to exclude spikes from gridlines). The x and y axis scales are the same for all systems. Medical Physics, Vol. 41, No. 3, March 2014

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F IG . 4. Normalized NPS. Averages of 15 columns of data in the x and y directions are shown. Systems 1–3 are shown on the left graph, and systems 4–6 are shown at right.

where k is the open-field, offset-corrected mean signal of the image on which the NPS is calculated. If the system is largely dominated by quantum noise, then NPS(u, v) is proportional to the fluence, , but k is also proportional to fluence, such that NNPS(u, v) ∝ 1/, thus for the same x-ray spectra conditions, a predictive NNPS can be obtained quite simply NNPS(u, v, 2 ) ≈

1 NNPS(u, v, 1 ), 2

(13)

which provides an estimate of the NNPS when the fluence is 2 from a measured NNPS at fluence 1 . Comparing a scatter-free NNPS measurement to an NNPS measurement that includes scatter is more difficult. Nevertheless, if it is assumed that the scatter component is uniform, it will increase the fluence. In this case, the fluence reaching   the detector will TS 0 be approximately, 2 ≈ 2 TP + TP SP R , where 02 is the scatter-free, grid-free fluence, TP is the primary transmission of the grid, TS is the scatter transmission of the grid, and SPR is the grid-free scatter-to-primary ratio. Here, energy effects have been ignored. The values for TP , TS , and SPR were obtained from literature15, 29 and 1 / 2 ≈ D1 / D2 where D1 is the reported dose used in the measurement of NNPS in the literature reference and D2 is estimated from our measured kerma in air and simulated transmission spectrum of the phantom. The spectrum was estimated based on a model presented by Boone et al.30 for the desired anode and filter combination. The filter thickness was originally set to the nominal filter thickness quoted for each system and then adjusted such that the simulated half-value layer (HVL) matched the HVL that we measured on that system. Additional filtration was added to account for the compression paddle (polycarbonate) and the phantom (PMMA). Corrections for inverse square law were used to estimate the kerma at the plane of the detector. Again, if the system is largely quantum noise limited, then comparing NNPS for different x-ray spectra will be relatively Medical Physics, Vol. 41, No. 3, March 2014

similar, as both the NPS((u, v) and the k (Ref. 2) terms in Eq. (9) are proportional to the square of the absorbed energy terms, so that their effects largely cancel one another. Secondorder effects such as changes in the Swank factor or changes related to the depth of interaction are expected to be small, unless the compared x-ray spectra straddle a K-edge of the detector.31 3. RESULTS 3.A. Detector offset and scatter

The measured detector offset and scatter fractions are given in Table III. 3.B. MTF

The measured MTF values are shown in Fig. 2. 3.C. NPS

The normalized noise power spectra are shown in 2D form in Fig. 3 and plotted along the x and y directions in Fig. 4. TABLE IV. Summary NEQ values. NEQ 2.5 cycles/mm System 1 2 3 4 5 6

5 cycles/mm

x

y

x

y

1.58 × 104 9.05 × 104 1.74 × 105 2.94 × 104 1.26 × 105 7.54 × 104

1.99 × 104 9.11 × 104 1.79 × 105 2.98 × 104 9.86 × 104 5.58 × 104

3.73 × 103 2.09 × 104 1.10 × 105 1.21 × 104 6.05 × 104 2.71 × 104

6.63 × 103 3.61 × 104 1.04 × 105 1.24 × 104 1.35 × 104 2.63 × 104

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F IG . 5. Radially averaged NEQ for all systems, calculated for images of the test phantom acquired at different mAs. As expected, once the signal becomes large enough to be above the electronic noise threshold, the NEQ scales with exposures to the detector (mAs). Each system is shown in the graph labeled with the corresponding number.

The average of the central 15 rows (or columns) of the spectrum data is shown for the x and y directions, similar to the approach of Marshall et al.25

3.D. NEQ

The NEQs at 2.5 and 5.0 cycles/mm are summarized in Table IV. For nominally isotropic systems the radial average of the 2D NEQ was used. For the nonisotropic systems the averages of the central 15 rows (or columns) of the NEQ data are given for the x and y directions similar to Marshall et al.25

The radially averaged NEQs for all systems as measured at different mAs settings are shown in Fig. 5. As expected, NEQ scales with exposure to the detector (mAs) once the signal is above the electronic noise threshold. The NEQ for all systems measured at the most clinically relevant dose settings and normalized by mean glandular dose are shown in Fig. 6. 3.E. Error/uncertainty analysis

The results of the repeatability analysis are summarized in Table V. The first value for each system reports the standard

F IG . 6. NEQ for different imaging systems, normalized by the estimated mean glandular dose to a 4 cm thick breast composed of 29% fibro-glandular tissue and 71% adipose tissue. Averages of 15 columns of data in the x and y directions are shown. Systems 1–3 are shown on the left graph, and Systems 4–6 are shown at right. Medical Physics, Vol. 41, No. 3, March 2014

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TABLE V. Standard deviations (σ ) and coefficient of variations (COV, σ /mean) among repeated measurements of the NEQ parameters. The σ and COV were calculated at each frequency. The standard deviations and COVs averaged across all frequency bins and the maximum values are reported. System 1 2 3 4 5 6

σ MTF avg., max

COVMTF avg., max.

σ NNPS avg., max

COVNNPS avg., max.

COVNEQ avg., max.

0.010, 0.024 0.011, 0.020 0.011, 0.020 0.012, 0.024 0.004, 0.019 0.009, 0.022

0.03, 0.15 0.03, 0.15 0.03, 0.15 0.04, 0.20 0.03, 0.32 0.03, 0.11

1.2 × 10−4 , 4.0 × 10−2 2.0 × 10−4 , 7.3 × 10−3 4.6 × 10−5 , 2.8 × 10−4 1.2 × 10−4 , 2.6 × 10−3 2.9 × 10−4 , 1.5 × 10−3 1.1 × 10−4 , 5.9 × 10−3

0.13, 0.79 0.14, 0.47 0.14, 0.33 0.14, 0.31 0.14, 0.30 0.14, 0.38

0.13, 1.41 0.16, 0.77 0.15, 0.46 0.16, 0.50 0.14, 0.42 0.15, 0.45

F IG . 7. COVs for the MTF for each system type (12 repeated images). Systems 1–3 are plotted on the left, and Systems 4–6 are plotted on the right.

F IG . 8. Comparison of our system MTF measurements with estimated system MTFs derived from literature for (a) System 2 and (b) System 3. For our measurements, the average of the x-direction and y-direction is shown. Medical Physics, Vol. 41, No. 3, March 2014

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TABLE VI. MTF values compared with other published work where data are available: The spatial frequency (cycles/mm) at which the MTF drops to 50%. The values we measured have been adjusted to remove the low-frequency drop due to scatter by dividing the MTF by (1-SF), to make the measurements more comparable to other work where scatter is not included. The percent difference from our measurement is given in parenthesis. System 1 2 3 4 5 6

50%

Marshall et al. (Ref. 25)

Monnin and Verdun (Ref. 26)

x: 2.41 y: 2.66 3.25 4.53 3.78 x: 4.03 y: 3.34 4.19

2.28 (x: −5%, y: −14%) 3.29 (1%) 4.53 (0%) 4.86 (29%) x: 6.52 (62%) y: 3.48 (4%) 4.86 (16%)

x: 2.2 (−9%) y: 2.4 (−10%)

deviation and COV averaged across all spatial frequencies. The second value reports the maximum values of standard deviation and COV. The dependence of the COVMTF on spatial frequency are shown in Fig. 7. The average COV for the NEQ is modest (< =15%) for all systems. The greatest maximum COV is exhibited by System 1, which is the CR system. Here the repeated images of the NEQ phantom were taken using different imaging plates, which may add to the variability in the measured parameters. For the purpose of analysis, it was necessary for this system to perform an additional flat-fielding correction and then to transform the pixel values into a domain that is linear with exposure. Both these steps may add noise and uncertainty. The absolute variations in MTF measurements are quite small, as shown by the average and maximum σ values. Since the MTF decreases as spatial frequency increases, the coefficient of variation (COV) tends to increase with increasing spatial frequency (see Fig. 7). For the NNPS, the magnitude of the COV did not depend on the spatial frequency. 3.F. Comparison

The MTFs measured for Systems 2 and 3 are compared with other published measurements in Fig. 8 as well as in Tables VI and VII. When the previously published measurements are adjusted in an attempt to remove the effect of scatter, the resulting curves are comparable to those measured here. Where other published measurements reported a single MTF, rather than the MTF in the x and y directions, we averaged the MTF in the x and y directions before comparing our measurements with theirs. Figure 9 compares the radially averaged NNPS from this work with several NNPS reported by others for Systems 2

Monnin et al. (Ref. 27)

Ghetti et al. (Ref. 28)

3.6 (11%) 6.1 (35%)

3.7 (14%)

x: 5.8 (44%) y: 4.1 (23%)

and 3. System 2 was measured at 27 kV Mo/Rh, 63 mAs, with a HVL of 0.37 mm of Al. System 3 was measured at 29 kV W/Rh, 45 mAs, with a HVL of 0.54 mm. Following the method outlined by the IAEA,32 the air kerma at 4.2 cm above the table top was measured to be 223 and 99 μGy for the systems, respectively. For System 2, the scatter conditions and grid transmission factor were measured by Alonzo-Proulx29 to be Tp = 0.66, Ts = 0.15, and SPR = 0.47. For System 3, the scatter conditions were interpolated from measurements by Salvagnini et al.15 for 40 and 60 mm thick PMMA to our phantom of thickness 45.55 mm which yielded Tp = 0.74, Ts = 0.028, and SPR = 0.635. The energy-weighted transmission through the phantom was estimated using an x-ray spectra model.30 Filter thicknesses were adjusted to achieve the measured HVL for each system which was found to be 17 and 48 μm for Systems 2 and 3, respectively. The transmissions through the phantom were 0.032 and 0.053, and inverse square law factor was 0.82 and 0.81. The effective grid factors (Tp +Ts SPR) were 0.73 and 0.76 for Systems 2 and 3, respectively. Accounting for the transmission through the phantom, inverse square law effects, scatter and grid transmission, and the detector kerma were estimated to be 74 and 50 μGy for the two systems. Finally, the NNPS data as reported in the literature were transformed using Eq. (10) at the desired detector air kerma, to make an estimate of a system NNPS. Transformed values are depicted by the solid lines in Fig. 9 where reasonable agreement is seen with our measured curves. 4. DISCUSSION Considerable variability is seen among the measured NEQs. This reflects the variety of detector technologies and

TABLE VII. MTF values compared with other published work: The spatial frequencies at which the MTF drops to 10% are given. The values we measured have been adjusted to remove the low-frequency drop due to scatter by dividing the MTF by (1-SF), to make the measurements more comparable to other work where scatter is not included. System 1 2 3 4 5 6

10%

Marshall et al. (Ref. 25)

Monnin and Verdun (Ref. 26)

x: 6.03 y: 6.37 7.40 11.4 8.59 x: 7.47 y: 5.84 9.09

5.56 (x: −8%, y: −13%) 7.32 (−1%) 10.1 (−11%) 9.58 (12%) x: 12.3 (65%) y: 6.17 (6%) 9.58(5%)

6.0 (x: 0%, y: −6%)

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Monnin et al. (Ref. 27)

7.8 (5%) 11.6 (2%) x: 10.4 (39%) y: 7.4 (21%)

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F IG . 9. Comparison of measured NNPS with literature for (a) System 2 and (b) System 3. Dashed lines correspond to estimated NNPS curves as reported in Refs. 25, 27, and 28. Solid curves represent the transformed NNPS using Eq. (10).

beam qualities being used and the different dose operating points selected by the automatic exposure controls. The measurements made with this technique include the grid (where present in the system). Since all grids reject a significant fraction of the primary signal, as well as some greater proportion of the scattered signal, the NEQs of systems using a grid will be lower than those without a grid for comparable entrance exposures. Whether the improvements in contrast and reduction in low-spatial frequency noise gained by use of a grid outweigh the overall reduction in NEQ likely varies depending on breast thickness, density, and detection task, and could be explored in future work with task-based measures. This method of measuring the NEQ has some limitations. The two-dimensional MTF is only an approximation, and may not accurately reflect system behavior in all directions. The measurement of NPS is noisy, and repeated images are required to improve confidence in the estimated values. Future work could include determining standard NEQ thresholds for acceptable image quality, assessing the sensitivity of the NEQ measurement to changes in factors other than dose that affect image quality (such as grid efficiency, beam quality, and loss of resolution due to focal spot blur or motion inaccuracy in scanning systems) and incorporating the parameters measured to calculate NEQ into an observer model for use in task-based measures of image quality.33

5. CONCLUSIONS NEQ shows promise as an objective measure for QC that includes information related to the key factors that are thought to influence diagnostic image quality. The units of measure are not device or technology dependant, allowing intersystem comparison. The measurement of NEQ will allow the evaluaMedical Physics, Vol. 41, No. 3, March 2014

tion of a system as it is used, to ensure that the fluence delivered to the detector is sufficiently high to provide the required level of image quality while not over-irradiating the patient. The method described here for measuring NEQ is robust and practical to use in the field. The NEQ scales appropriately with exposure. Except for the case of System 5 where further investigation is necessary, the MTF and NPS values measured with the proposed phantom and method correspond with previously published results measured on similar systems by others. NEQ could be incorporated into task-based methods of evaluating image quality. ACKNOWLEDGMENTS Funding for this work was received from the Canadian Cancer Society (Grant No. 2010-700538) and from Mammographic Physics Inc. (SR&ED #1). The authors gratefully acknowledge Courtice Imaging Centre, St. ThomasElgin General Hospital, Sunnybrook Health Sciences Centre, Royal Victoria Regional Health Centre, and Radiology Associates Clarkson for allowing access to their mammography equipment. a) Author

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