Tailoring automatic exposure control toward constant detectability in digital mammography

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1 Tailoring automatic exposure control toward constant detectability in digital mammography Elena Salvagnini a) Department of Imaging and Pathology, Medical Physics and Quality Assessment, KUL, Herestraat 49, Leuven B-3000, Belgium and SCK CEN, Boeretang 200, Mol 2400, Belgium Hilde Bosmans Department of Imaging and Pathology, Medical Physics and Quality Assessment, KUL, Herestraat 49, Leuven B-3000, Belgium and Department of Radiology, UZ Gasthuisberg, Herestraat 49, Leuven B-3000, Belgium Lara Struelens SCK CEN, Boeretang 200, Mol 2400, Belgium Nicholas W. Marshall Department of Radiology, UZ Gasthuisberg, Herestraat 49, Leuven B-3000, Belgium (Received 2 December 2014; revised 30 March 2015; accepted for publication 10 May 2015; published 9 June 2015) Purpose: The automatic exposure control (AEC) modes of most full field digital mammography (FFDM) systems are set up to hold pixel value (PV) constant as breast thickness changes. This paper proposes an alternative AEC mode, set up to maintain some minimum detectability level, with the ultimate goal of improving object detectability at larger breast thicknesses. Methods: The default OPDOSE AEC mode of a Siemens MAMMOMAT Inspiration FFDM system was assessed using poly(methyl methacrylate) (PMMA) of thickness 20, 30, 40, 50, 60, and 70 mm to find the tube voltage and anode/filter combination programmed for each thickness; these beam quality settings were used for the modified AEC mode. Detectability index (d ), in terms of a non-prewhitened model observer with eye filter, was then calculated as a function of tube current-time product (mas) for each thickness. A modified AEC could then be designed in which detectability never fell below some minimum setting for any thickness in the operating range. In this study, the value was chosen such that the system met the achievable threshold gold thickness (T t ) in the European guidelines for the 0.1 mm diameter disc (i.e., T t 1.10 µm gold). The default and modified AEC modes were compared in terms of contrast-detail performance (T t ), calculated detectability (d ), signal-difference-to-noise ratio (SDNR), and mean glandular dose (MGD). The influence of a structured background on object detectability for both AEC modes was examined using a CIRS BR3D phantom. Computer-based CDMAM reading was used for the homogeneous case, while the images with the BR3D background were scored by human observers. Results: The default OPDOSE AEC mode maintained PV constant as PMMA thickness increased, leading to a reduction in SDNR for the homogeneous background 39% and d 37% in going from 20 to 70 mm; introduction of the structured BR3D plate changed these figures to 22% (SDNR) and 6% (d ), respectively. Threshold gold thickness (0.1 mm diameter disc) for the default AEC mode in the homogeneous background increased by 62% in going from 20 to 70 mm PMMA thickness; in the structured background, the increase was 39%. Implementation of the modified mode entailed an increase in mas at PMMA thicknesses > 40 mm; the modified AEC held threshold gold thickness constant above 40 mm PMMA with a maximum deviation of 5% in the homogeneous background and 3% in structured background. SDNR was also held constant with a maximum deviation of 4% and 2% for the homogeneous and the structured background, respectively. These results were obtained with an increase of MGD between 15% and 73% going from 40 to 70 mm PMMA thickness. Conclusions: This work has proposed and implemented a modified AEC mode, tailored toward constant detectability at larger breast thickness, i.e., above 40 mm PMMA equivalent. The desired improvement in object detectability could be obtained while maintaining MGD within the European guidelines achievable dose limit. (A study designed to verify the performance of the modified mode using more clinically realistic data is currently underway.) C 2015 American Association of Physicists in Medicine. [ Key words: FFDM, image quality, automatic exposure control (AEC), detectability index (d ), contrast-details 3834 Med. Phys. 42 (7), July /2015/42(7)/3834/14/$ Am. Assoc. Phys. Med. 3834

2 3835 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability INTRODUCTION The automatic exposure control (AEC) system plays a fundamental role in setting the balance between patient dose and image quality in mammography imaging. For screen/film (S/F) mammography, the task of the AEC was relatively straightforward, namely, the selection of the optimal tube voltage and anode/filter (A/F) combination 1 while maintaining film optical density (OD) constant for the range of breast thicknesses examined. With the introduction of full field digital mammography (FFDM) and the absence of OD as a controlling parameter, the situation has obviously changed. While there has been considerable interest in the optimal selection of beam quality in general radiography 2 and FFDM, 3 6 the problem of choosing the correct operating point and how the radiation exposure at the detector should be controlled as a function of patient thickness has received relatively little attention. 7,8 Two factors encourage a deeper examination of the AEC operating point for FFDM systems: the increased dynamic range of both flat panel and computed radiography type digital detectors compared to S/F detectors and the removal of target OD as a constraint with regards to operating point. The notion of a target OD is linked to the Hurter and Driffield (H&D) curve for S/F systems. It was well known that the use of ODs and hence exposures outside the region of high point gamma on the H&D curve would result in reduced contrast. For this reason, radiography performed using S/F detectors is referred to contrast-limited imaging: exposure and contrast are linked. The exposure level dependency of contrast no longer applies to images generated by digital detectors; instead, the relevant parameter governing image quality is something closer to the signal-to-noise ratio (SNR) as conceived by Wagner and Brown. 9 This SNR is based around the noise equivalent quanta spectrum weighted by an observer task and is related to observer task performance. Practically, however, the SNR as defined by Wagner and Brown 9 is difficult to measure and control directly from the digital detector, and hence, most digital mammography AEC systems are designed to maintain the signal produced by the x-ray detector [i.e., pixel value (PV)] constant as a function of beam quality. Pixel values taken from For Processing images will therefore be approximately constant as beam load and beam quality change and in this sense, PV for digital detectors is analogous to OD for S/F systems. Maintaining PV constant as a function of thickness however does not guarantee constant object detectability at different thicknesses. 8 This paper proposes an alternative scheme of controlling the exposure at the detector as a function of thickness, one in which the system is required to reach some minimum target value of object detectability at all PMMA thicknesses, with the aim of improving object detectability at larger breast thicknesses. The work begins with a discussion of AEC set up for seven current mammographic systems and the means of AEC assessment followed by the motivation for a change in AEC design. A scheme is then described that enables an AEC to be set up to give constant detectability as a function of PMMA thickness and beam quality. This involves the use of the current image quality standards specified in the European guidelines for quality assurance in mammography screening 10 in conjunction with detectability calculations 11 that ensure this level of object detectability is reached over a range of equivalent breast thicknesses. Finally, the modified AEC method is applied to a flat panel-based FFDM system and then compared to the default constant PV AEC in terms of measured contrast-detail (c-d) performance, calculated detectability, signal-difference-to-noise ratio (SDNR), and mean glandular dose (MGD). 2. BACKGROUND This section gives the motivation for a change in AEC design and describes the new scheme. 2.A. AEC in current FFDM systems A number of parameters can be used to characterize the performance of an AEC used with digital detectors, including exposure at the detector, 2,12 mean signal from the detector, 13 SDNR, 10 the threshold detectability measured with a contrastdetail test object, 14 or using a detectability index. 15,16 In the European guidelines, SDNR is measured using a 0.2 mm thick Al square, imaged in combination with homogeneous poly(methyl methacrylate) (PMMA) plates, a surrogate material for breast tissue, covering a thickness range between 20 and 70 mm. Figure 1(a) shows SDNR measurements taken from our database of routine QC measurements; these data are for seven current FFDM systems that have typical setup and no reported technical problems. SDNR has been normalized to SDNR at 45 mm and Fig. 1(a) shows that the AECs of most FFDM systems do not keep SDNR constant as PMMA thickness is increased. Instead, a general trend of a falling SDNR is seen; the SDNR at 70 mm is on average 25% lower than the SDNR at 45 mm. The exception is the Hologic Selenia Dimensions, where SDNR at 70 mm is held within 5% of SDNR at 45 mm. Some aspects of the SDNR performance can be explained by examining the PV and the simple pixel SNR (i.e., mean pixel value divided by standard deviation) data in Figs. 1(b) and 1(c). It can be seen that for most systems, the PV is held approximately constant (within ±20% relative to the value at 45 mm). Two exceptions to this are the Philips Microdose and the Hologic Selenia Dimensions units, where the PV is high at 20 and 30 mm PMMA for the Philips, while PV increases at 60 and 70 mm for the Hologic Selenia Dimensions. A consequence of the approximately constant PV is that SNR is held approximately constant, as expected for quantum noise limited images [Fig. 1(c)]. Hence, the principal reason for the reduction in SDNR is the fall in measured contrast for the 0.2 mm thick Al target. This reduction is due to the increasing beam energy selected by the AEC and to scattered radiation associated with higher PMMA thicknesses. 17 Overall, SDNR drops with increasing PMMA thickness and hence, we expect a corresponding fall in object detectability. The AEC test in the European guidelines uses a combination of SDNR and the threshold gold thickness (i.e., small detail detectability) when specifying minimum or

3 3836 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability 3836 FIG. 1. (a) SDNR normalized to SDNR at 45 mm PMMA, (b) PV normalized to PV at 45 mm, and (c) (pixel) SNR normalized to SNR at 45 mm, shown for seven FFDM systems. recommended AEC performance. The prediction of the SDNR value corresponding to a given contrast threshold thickness T t can be done given that we expect a simple linear relationship between SDNR and 1/T t. Briefly, data from a previous study are used 11 in order to illustrate this relationship. Figure 2 plots the reciprocal of threshold gold thickness for the 0.1 mm diameter disc measured using CDMAM as a function of detector air kerma against SDNR for three FFDM systems. For these data, CDMAM was imaged with 40 mm PMMA for detector air kerma values ranging between approximately 25 and 200 µgy. SDNR was measured using the standard method 10 for a 50 mm PMMA block imaged using AEC settings for tube voltage and A/F, while T t was estimated using the processing described by Young et al. 18 The figure confirms the expected linear relationship as both 1/T t and SDNR have a square root dependency with detector air kerma for a quantum limited x-ray detector. An explicit measurement of threshold gold thickness is made at 50 mm PMMA equivalence (CDMAM with 40 mm PMMA) in the EUREF protocol, and SDNR is used to infer image quality at other PMMA thicknesses. If we assume the simple linear relation between SDNR and 1/T t also holds between different PMMA thicknesses, then we can estimate threshold gold thickness at 70 mm from measured T t at 50 mm and the relative SDNR. Table I shows the measured T t value at 50 mm PMMA for the seven FFDM systems discussed above, along with the value of T t at other PMMA thickness predicted using relative SDNR. These data show an average threshold gold thickness for the seven systems of 1.18 µm gold, a result considerably below the minimum acceptable value of 1.68 µm gold and within 7% of the achievable value, 1.10 µm. Table I shows low values of T t for PMMA <40 mm and high values of T t at 60 and 70 mm PMMA, respectively, indicating high image quality at low PMMA thickness and reduced image quality at higher PMMA thickness. The average value of T t at 70 mm is 1.42 µm, indicating an increase in T t of 20% compared to the value at 50 mm. The one exception in Table I is the Hologic Selenia Dimensions, where T t at 70 mm is predicted to be within 1% of the value at 50 mm PMMA (associated SDNR behaviour discussed above). Given this fall in SDNR as PMMA thickness increases from 45 to 70 mm (with one exception), one would expect reduced object detectability at larger breast thicknesses. FIG. 2. Reciprocal of threshold gold thickness for 0.1 mm disc plotted against SDNR for three FFDM systems; a first order linear fit is applied (r 2 value was 0.98 for all three curves). Detector air kerma was varied between approximately 25 and 200 µgy. 2.B. An alternative AEC setup We now define a modified AEC scheme, designed to prevent a drop in object detectability at PMMA thicknesses greater than 40 mm. The required image quality level for PMMA thickness 40 mm is taken from the European guidelines, 10 as this is a recognized international standard. Regarding the actual target image quality value, the current acceptable value of 1.68 µm for a 0.1 mm disc would clearly not improve image quality over current typical settings and hence we have adopted the current achievable value of 1.1 µm gold for a 0.1 mm diameter disc. 19 While such a regime would not improve image quality for the Hologic Selenia Dimensions, image quality for all six remaining systems in Table I would be improved at PMMA thicknesses of 50 mm and above. There would be little or no change for 40 and 45 mm PMMA for most units. Section 3 details how the modified detectability regime was implemented for a Siemens MAMMOMAT Inspiration FFDM system.

4 3837 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability 3837 TABLE I. Threshold gold thickness (T t ) for 0.1 mm diameter disc measured explicitly at 50 mm PMMA equivalence using CDMAM (bold values). Figures in italics show T t predicted at other PMMA thicknesses using relative SDNR. The acceptable and achievable values in the European guidelines are 1.68 and 1.10 µm, respectively. GE essential Siemens MAMMOMAT Inspiration Hologic Selenia Hologic Selenia Dimensions PMMA (mm) T t (µm) T t (µm) T t (µm) T t (µm) IMS Giotto T t (µm) Fuji Amulet T t Philips Microdose Average (µm) T t (µm) T t (µm) MATERIALS AND METHODS 3.A. Digital mammography system The FFDM system used in this work was a Siemens MAM- MOMAT Inspiration (Siemens AG Healthcare, Erlangen, Germany). This unit has an a-se detector with 85 µm pitch and a selenium layer thickness of 200 µm. Three different A/F combinations (Mo/Mo, Mo/Rh, and W/Rh) are available. Nominal focal spot dimension is 0.3 mm, the source-to-image receptor distance (SID) is mm while source-to-breast support table distance (STD) is 637 mm. The system uses a linear grid, with a ratio of 5:1, lead septa, and strip density of 31 lines/cm. 3.B. Evaluation of the default AEC The starting point for the modified scheme was the OPDOSE mode. This is the default clinical AEC program on this system and is designed to maintain PV constant as a function of imaged object thickness. A standard protocol 10 was used for the assessment: PMMA thicknesses ranged from 20 to 70 mm and a 0.2 mm thick mm Al square was positioned 60 mm from the chest wall edge. Following the protocol described in the European guidelines, the Al square was positioned on top of the 2 cm PMMA; additional PMMA blocks were then added on top of the 2 cm PMMA with the Al in an unchanged position. The Siemens MAMMO- MAT Inspiration AEC segmentation was disabled for these tests and the antiscatter grid was in place. From these images, the PV, standard deviation, and SDNR were calculated. This evaluation of the default AEC mode also served as a baseline against which the modified AEC could be compared. 3.C. Detector response Detector response curves are required for linearization of the DICOM grayscale images prior to calculation; 20 although the Inspiration has a linear response, linearization has to be performed in order to remove any offset that may be present. Detector response was measured for PMMA thicknesses of 20, 30, 40, 50, 60, and 70 mm, with the PMMA supported at the x-ray tube exit port and antiscatter grid removed. For a given PMMA thickness, tube voltage and the A/F combination were set by the OPDOSE program. Air kerma at the detector was measured with a calibrated Barracuda MPD dosimeter. Pixel values were taken from DICOM For Processing type images using a 5 5 mm region of interest (ROI) placed 60 mm from the chest wall edge and centered left right. Plots of PV versus air kerma at the detector (DAK) for the different beam qualities gave six detector response curves. An additional response curve, measured with 2 mm Al filtration placed at the x-ray tube and a beam quality of 28 kv W/Rh, was used to linearize the images required for the MTF calculations. This measurement was performed following the standard method described in the IEC D. Derivation of modified AEC settings using a detectability index For a given PMMA thickness, the proposed constant detectability modified AEC scheme uses the default tube voltage and A/F settings programmed as function of thickness for the OP- DOSE, which were already used with the default AEC, as these settings have been shown to be optimal for this system. 3,4,15 Maintaining these settings means that any change in object detectability comes from a change (reduction) in image noise. This entails an increase in tube current-time product (mas) at a given PMMA thickness. In order to calculate the new mas settings, one could assume that the images are quantum noise limited and threshold gold thickness is related to some set beam load (i.e., mas) as 1 T m L 1/2 m, (1) where T m is the measure threshold gold thickness and L m is the mas value selected by the default AEC mode, and therefore, the target mas could be calculated as T 2 m L target = L m. (2) Ttarget 2 Here, T target is the threshold gold thickness value chosen as target and L target is the mas value obtained by inserting this threshold gold thickness target value in the equation.

5 3838 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability 3838 This could then be repeated for each PMMA thickness, using a measurement of threshold gold thickness at that PMMA thickness; however, there are some limitations to this approach. First, if there is some deviation from quantum noise limited behaviour for the system then this simple relationship will not hold exactly. Second, the measured detectability is characterized using threshold gold thickness via the CDMAM c-d test object at each PMMA thickness. This can be time consuming as at least eight CDMAM images are required to establish a single threshold gold thickness value. 10 Furthermore, we found that using a set of eight images leads to a measured uncertainty [coefficient of variation (cov)] on this value of approximately 10% for the 0.1 mm diameter disc; using more images would reduce uncertainty but is more time consuming. An alternative detectability measure was used instead, based around the non-prewhitening with eye filter (NPWE) model observer 22 that has been validated against CDMAM results for a range of FFDM systems. 11 Once the presampling MTF has been established, detectability can be calculated from a single image, i.e., from an AEC image acquired for the estimation of SDNR. Furthermore, measured uncertainty is lower, with a typical cov of approximately 3%. Given that the target detectability level must be set using threshold gold thickness (the system is required to meet the achievable threshold gold thickness level of 1.10 µm at 50 mm and above) then a measurement of threshold gold thickness is needed at 70 mm, effectively calibrating detectability index against threshold gold thickness. The detectability index is related to threshold gold thickness as d 1/T; 11 thus, the target detectability index (d target) associated with the target threshold gold thickness (T target ) measured for a given PMMA thickness is ( ) d target = d 70mm T70mm, (3) T target where T 70mm is the measured threshold gold thickness for 70 mm phantom thickness and d 70mm is the detectability index value measured at this thickness. Equation (3) gives the target detectability index value (d target ) that corresponds to the target threshold gold thickness value we have chosen (i.e., the achievable level of 1.10 µm). We require this level to be achieved for 70 mm PMMA this target value was then used for all other thicknesses. The detectability index (and the SDNR) has a power relationship with detector air kerma, 11 and hence to find the mas required to reach this level of detectability at each given PMMA thickness, detectability index was plotted as a function of mas (i.e., L) and then fitted with a power law curve of the form, d mm(l) = A mm L B mm, (4) where L is the mas value, A mm and B mm are the fitting coefficients of the d curves. d mm(l) is the detectability index calculated as a function of mas for different thicknesses. A numerical example of A mm and B mm together with the fitting equation for 20 mm PMMA is plotted on the graph in Fig. 5(b). In this example, X = L and Y = d mm(l). Inserting the d target value obtained with Eq. (3) and the A mm and B mm values obtained for the different phantom thicknesses with Eq. (4) in the following equation: ( d ) 1/Bmm target L target (mm) = (5) A mm allow the calculation of the mas values [L target (mm)] required to obtain the same detectability index value (d target ) for all phantom thicknesses. The threshold gold thickness at 70 mm PMMA equivalent in Eq. (3) was measured using ten CDMAM images. As the CDMAM test object is approximately equivalent to 10 mm PMMA, then an additional 60 mm of PMMA blocks was used, 10 mm of which was placed between the test object and the breast support table. Automatic scoring was performed using Erica 2 software 23 and the c-d curve calculated 18 from which the threshold gold thickness for the 0.1 mm diameter disc was taken (= T 70 mm ). The same procedure was applied to the more commonly used measure of SDNR by replacing the d values with the SDNR values in equations from 3 to 5. This can be done using the same image set. 3.E. Detectability index calculation The detectability index (d ) used for these calculations is defined in Eq. (6), 2πC d 0 = S( f )MTF( f )VTF( f ) 2 f d f 0 S2 ( f )MTF 2 ( f )VTF 4 ( f )NNPS( f ), (6) f d f where C is the contrast measured using the 0.2 mm thick Al square, f is the spatial frequency, MTF( f ) is the presampling modulation transfer function, and NNPS( f ) is the normalized noise power spectrum. VTF( f ) is the visual transfer function taken from Kelly 24 for a nominal image magnification of 1.5 and viewing distance of 400 mm. 11 Given the use of the 0.1 mm disc in the image specification, the signal was defined for a disc-like object of this diameter using Eq. (7), S( f ) = d 2 J 1 (πd f ), (7) f where J 1 is a Bessel function of the first kind and d is the object diameter. A circular object of this diameter is a reasonable approximation to the smallest microcalcifications and hence represents a typical and important task for mammography imaging systems. The study of Warren et al. 19 compared clinical detection of simulated microcalcifications against imaging performance specified using the 0.1 and 0.25 mm discs in the CDMAM test and found close agreement. 3.E.1. Presampling modulation transfer function Detector presampling MTF was measured at 28 kv, W/Rh with an additional 2 mm Al at the x-ray tube exit port using the edge method. 25 Details of the implementation are given elsewhere. 26 In this study, a steel plate with machined straight edges of dimension mm and thickness 0.8 mm was positioned on the breast support platform, angled slightly ( 3 ) against the pixel matrix. A mm region of interest was extracted from the edge image and differentiated in order to

6 3839 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability 3839 find the edge position. A first order polynomial curve was applied to the maximum values of the differentiated edge image and the fitted coefficients were used to calculate the angle of the edge. The PV data in the extracted ROI were reprojected using a subpixel binning factor of 0.2 to form a composite edge spread function (ESF) that is sampled more finely than the native image pixel spacing. The ESF was then differentiated to form the line spread function (LSF), and the MTF was calculated by taking the modulus of the fast Fourier transform (FFT) of the LSF and normalizing to the value of the zero spatial frequency bin. Images were acquired at a DAK that was a factor 3 times the typical operating DAK for the system. 3.E.2. Normalized noise power spectrum The algorithm used to estimate the noise power spectrum is described elsewhere; 26 NPS was calculated over a region of pixels, using records of pixels extracted with an overlap of 50% in both x- and y-directions. A 2D polynomial surface was fitted to and subtracted from the region before ROI extraction. The squared modulus of each Fourier transformed ROI was added to the final ensemble and the final NPS estimate was taken from a radial average of the ensemble (including the 0 and 90 spatial frequency axes), as the NPS was found to be isotropic for both systems. Dividing by (mean PV) 2 of the linearized region from which the NPS was calculated gave the NNPS. In order to reduce uncertainty on the NNPS, two NNPS curves were estimated from two adjacent pixel regions for each image. The centre of each region was approximately 85 mm from the chest wall edge and within 50 mm of the image centre in the left right direction. The two resulting curves were then averaged to give the final NNPS curve; the same region positions were used for all images. 3.E.3. Contrast The contrast was estimated using a mm Al square object of thickness 0.2 mm. The Al square used for the contrast was placed 60 mm from the chest wall side of the detector and centered in the left right direction. Contrast was calculated as described in the European QA guidelines 10 using the mean PVs of five ROIs (each subdivided in four equal size regions): one placed on the Al region and the other four placed in the background. The measured contrast was calculated as shown in Eq. (8), C = 1 k k j=1 1 n n i=1 PV Bkg i 1 k k j=1 1 n j 1 n n i=1 PV Al i n i=1 PV, (8) Bkg i where PV Bkg refers to the pixel value of a background ROI and PV Al refers to the pixel value of a ROI positioned in the Al square. The index i indicates the four regions inside each ROI. The index j indicates the four ROIs, each a square of side 5 mm. 3.F. Verification of the modified AEC scheme The impact of the modified AEC settings was tested as a function of PMMA thickness in a homogeneous back ground j (PMMA) and in a nominal structured background. Detectability was assessed using three measures: the detectability index (d ), SDNR, and CDMAM c-d measurements. For the homogeneous background, the PMMA/Al square images for 20, 30, 40, 50, 60, and 70 mm were reacquired with the modified acquisition settings using mas values calculated from Eq. (5). CDMAM images were also acquired for these PMMA equivalences (i.e., mm PMMA equivalent). As before, 10 mm PMMA was always placed under the CDMAM test object, and ten images were acquired at each PMMA thickness. This c-d analysis made as a function of PMMA thickness was also applied to the default AEC mode described in Sec. 3.B in order to characterize the difference in AEC schemes using threshold contrast detectability. A nominal structural background was then generated by replacing 10 mm of PMMA with a 10 mm slice of the mammography BR3D phantom (CIRS, Inc., Virginia) such that detectability could be compared in images containing some structured noise. Each semicircular slice of this phantom is mm and contains materials respectively mimicking 100% adipose and glandular tissues, combined in an approximate 50/50 ratio by weight. The phantom was formed by placing a 10 mm thick PMMA plate on the breast support table, followed by one slice of the BR3D phantom. Greater thicknesses were made by adding more plates of PMMA. For each measurement performed to calculate the SDNR a 0.2 mm thick mm Al square was place at 60 mm from the chest wall edge. A picture of the phantom together with a mammographic image of this configuration is shown in Fig. 3. Measurement of noise and contrast in a homogeneous image is reasonably straightforward given that noise and contrast exhibit reasonable stationarity. 27 However, evaluation of contrast and SDNR requires careful definition in an image containing structured noise. 28 For a homogeneous background, SDNR is assessed using five equally sized ROIs, one placed over the Al object and four placed in the background adjacent to the Al object. 29 However, the nonstationarity of PV and standard deviation in the BR3D structured background results in considerable position dependence of the measurement ROIs. To overcome this, PV and standard deviation were measured using 205 ROIs of dimension 5 5 mm placed across the entire structured phantom and averaged. The structured phantom for use with CDMAM was built up as follows. Two 10 mm BR3D structured plates were arranged side by side, such that they covered most of the CD- MAM cells, and placed on the breast support table. The CD- MAM test object was placed on these structured plates, yielding a c-d test object with an approximately 20 mm PMMA equivalence. The thickness of this structured c-d phantom was increased by the addition of 10 mm PMMA plates, covering the mm PMMA equivalence. Images were reacquired for these thicknesses using the acquisition factors established for constant PV and modified AEC settings as this would allow an assessment of the imaging performance for a structured background. The CDMAM images acquired with the structured phantom were read manually by three readers using the Sara 2 software. 30 The images were displayed using Agfa display software (Agfa Healthcare, Mortsel, Belgium) on two

7 3840 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability 3840 F. 3. Image of the CDMAM phantom acquired with the structured background (BR3D CIRS phantom). PMMA was used to increase the thickness; as shown in the front view, the PMMA was placed always on top of the CDMAM phantom. 5 megapixel medical grade Barco monitors (Barco, Kortrijk, Belgium) which were calibrated to the DICOM GSDF standard. 3.G. MGD The modified AEC scheme entails an increase in mas and hence, it is important to confirm that the MGD remains within dose limits. MGD for both AEC schemes was thus calculated using a standard method31 MGD = Kgcs, (9) where K is the incident air kerma at the upper surface of the breast, measured without backscatter, g is the incident air kerma to mean glandular dose conversion factor, g-factors correspond to a glandularity of 50%, the factor c corrects for any difference in breast composition from 50% glandularity, and the factor s corrects for any different x-ray spectrum used. 4. RESULTS Table II presents acquisition factors (kv and A/F) for the default AEC mode as PMMA thickness is changed from 20 to 70 mm, for the homogeneous and structured back- grounds. This table shows the expected result that the system maintains PV approximately constant as thickness increases from 20 to 70 mm of PMMA (mean PV = 325 and 321 for homogeneous and structured backgrounds, respectively, maximum deviation from the mean is 3%). The 4% difference in mas selected for the two different backgrounds indicates a close match in terms of attenuation between pure PMMA and PMMA with the 10 mm BR3D plate. The change in contrast in going from 20 to 70 mm is similar for the two backgrounds, falling from 17% to 11% for the homogeneous case and from 18% to 12% for the structured case. For the homogeneous images, SDNR falls by 39%, reflecting the 35% fall in contrast. A 37% reduction was seen for the NPWE detectability index supporting the relationship derived between SDNR and detectability index in an earlier study for a 50 mm homogeneous PMMA thickness.11 A smaller reduction in SDNR (22%) is seen for the structured background geometry as PMMA equivalence changes. As might be expected, the absolute SDNR values are lower than for the homogeneous case, a reflection of the increased standard deviation present in the structured images. The largest difference between the two background types is seen for the NPWE results, where the detectability index, for the structured background, at 70 mm is only 6% lower than the value for 20 mm PMMA This difference between the two backgrounds is illustrated in Fig. 4 T II. Results for the default AEC mode versus PMMA thickness for both homogeneous (H ) and structured (S) (i.e., with 10 mm plate BR3D) backgrounds. Shown are tube potential, anode/filter combination, and contrast calculated for 0.2 mm thick Al sheet along with the tube load (mas), PV, SDNR, and detectability index. mas PV Contrast SDNR Detectability index Thickness (mm) Anode/filter Tube voltage (kv) H S H S H (%) S (%) H S H S W/Rh W/Rh W/Rh W/Rh W/Rh W/Rh

8 3841 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability 3841 FIG. 4. (a) SDNR and (b) detectability index (d ) versus PMMA equivalent thickness for the homogeneous and structured backgrounds. Tube voltage, mas, and A/F settings are given in Tables II and IV for the default and the modified AEC mode, respectively. which plots SDNR and detectability index for the default AEC mode (i.e., constant PV) for the two different backgrounds. Figure 5(a) plots the detectability index for the 0.1 mm disc as a function of offset corrected PV for different thicknesses for homogeneous background; offset corrected PV is related to the energy absorbed in the x-ray converter layer. 14 In Fig. 5(a) the detectability index follows an approximate square root response as expected for quantum noise dominated images. 11,32 There is a systematic decrease in detectability index with increasing PMMA thickness at a given energy absorption in the detector, coming principally from the reduction in contrast but also due to increased noise from the scattered radiation. The detectability index data were replotted as a function of mas [Fig. 5(b)] and fitted using the power law relationship shown in Eq. (4), yielding the coefficients needed to estimate the new mas settings via Eq. (5). These coefficients, A mm and B mm, are listed in Table III. Example fit coefficients are shown in Fig. 5(b) for the 20 mm PMMA thickness. The c-d curve for 70 mm PMMA used to estimate the target detectability index value is shown in Fig. 6(a) for the homogeneous background. Also plotted in this figure are the c-d curves for the other PMMA thicknesses, for the default AEC mode (constant PV). An increase of 62% in measured threshold gold thickness with PMMA thickness is seen, from 0.86 µm (20 mm PMMA) to 1.39 µm (70 mm PMMA) for the 0.1 mm diameter disc, an indication that small detail detectability is not held constant by this mode. The same observation holds for the c-d curves (human reading) in the structured background where the threshold gold thickness for the 0.1 mm diameter disc increases by 39%, from 0.99 to 1.37 µm as PMMA equivalence increases [Fig. 6(b)]. This is in line with the reduction in detectability index and SDNR measured for the constant PV mode (Fig. 4). Figure 6(b) also shows that the background structure has a greater influence on threshold gold thickness for larger diameter discs; the average increase in threshold gold thickness in going from homogeneous to structured backgrounds for 0.10 and 0.25 mm diameter discs is 13% and 30%, respectively. In these figures, the acceptable and the achievable curves from the quality assurance European guidelines are plotted; these curves strictly apply to the homogeneous case using 40 mm of PMMA with the CD- MAM phantom but are shown to aid visual comparison of the graphs. FIG. 5. Detectability d for a 0.1 disc object in a homogeneous background as a function of (a) offset corrected PV and (b) mas.

9 3842 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability 3842 TABLE III. A mm and B mm are fit coefficients used in Eq. (4) from plotting detectability index versus mas. Also given is target detectability (d ) required to reach threshold gold thickness of 1.1 µm for the 0.1 mm diameter disc in 70 mm PMMA. The calculated mas to reach constant target detectability is given, along with the actual mas for the implemented modified AEC. Anode/filter setting is W/Rh for all PMMA thicknesses. Thickness (mm) kv mas for default AEC Target (constant PV) A mm B mm d mas for target d mas programmed for modified AEC Table III shows that a target detectability index value of 1.5 is required in order for the 0.1 mm diameter disc to meet the European guidelines achievable limit of 1.1 µm. Also shown are the detectability index fit coefficients required to calculate the mas for the different PMMA thicknesses. Comparing these calculated mas values for the constant detectability scheme with those for the constant PV mode (Table II), the constant detectability mode requires lower mas for thicknesses below 40 mm and a higher mas for thicknesses above 40 mm. When implementing the modified AEC scheme, we took the decision not to decrease system detectability at thicknesses below 40 mm and just to implement the constant detectability mode for thicknesses from 40 mm and above. Table III shows the selected mas for constant detectability index. Given the limited mas stations available on the system, it was not possible to set the exact mas values predicted by Eq. (5) for the validation phase. The power coefficient term (B mm ) in Table III is close to 0.5, indicating that the images are largely quantum noise dominated, although there is an increase in B mm, suggesting some contribution from structured noise at higher PMMA thicknesses. Table IV presents acquisition factors (A/F, kv, and mas) for the modified AEC mode as PMMA thickness is changed from 20 to 70 mm, for the homogeneous and structured backgrounds. This table shows that PV is not kept constant in this mode but rather increases by 49% for PMMA thicknesses above 40 mm, for both backgrounds. This increase in PV for 50 mm PMMA increases image brightness (assuming a positive LUT is used) of the displayed For Processing images. However, there is no increase in brightness for the For Presentation images viewed and evaluated clinically by the radiologist, due to the scaling and autoranging processing applied to these images. The similar PV found for the two backgrounds again shows the close match in terms of attenuation between pure PMMA and PMMA with the 10 mm BR3D plate. The change in contrast in going from 20 to 70 mm is similar for the two backgrounds and it is equal to the contrast found for the default AEC mode, falling from 17% to 11% for the homogeneous case and from 18% to 12% for the structured case. The values for SDNR and detectability index are plotted in Fig. 4. Figure 4(b) shows that detectability index measured from the images reacquired using the modified AEC mode to maintain detectability constant (above 40 mm PMMA) is close to the target of 1.54 (maximum deviation from target is 3%) The small differences in absolute value are probably due to limitations in choosing an exact/closest mas value. As might be expected, settings that keep the detectability index constant also maintain SDNR constant in both background types at 8.1 and 6.3, respectively [Fig. 4(a)], with a maximum deviation of 4% and 2%. FIG. 6. c-d curves measured in homogeneous (on the left) and structured background (on the right) for phantoms thickness of mm for the constant PV mode. Tube potential and A/F combination for both of these graphs are given in Table II.

10 3843 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability 3843 TABLE IV. Results for the modified AEC mode versus PMMA thickness for both homogenous (H) and structured (S) (i.e., with 10 mm plate BR3D) backgrounds. Shown are tube potential, anode/filter combination and contrast calculated for a 0.2 mm thick Al sheet along with the tube load (mas), PV, SDNR, and detectability index. mas PV Contrast SDNR Detectability index Thickness (mm) Anode/filter Tube voltage (kv) H S H S H (%) S (%) H S H S 20 W/Rh W/Rh W/Rh W/Rh W/Rh W/Rh The c-d curves acquired for the modified AEC scheme for both homogeneous and structured backgrounds are plotted in Figs. 7(a) and 7(b). It can be seen that the modified scheme results in a constant threshold gold thickness for the 0.1 mm disc, with a mean value of 1.05 µm (maximum deviation = 5%). In particular, threshold gold thickness for all PMMA thicknesses is on or below the achievable value of the European guidelines. These data also show that a scheme that keeps SDNR constant versus equivalent PMMA thickness also holds threshold gold thickness constant. For the 0.1 mm diameter and considering thicknesses only above 40 mm, threshold gold thickness is constant to within 10% (ranging between 1.00 and 1.10 µm). This value can be compared to the increase of 62% in threshold gold thickness as a function of thickness for the default AEC mode. For the structured background for the modified AEC, threshold gold thickness for the 0.1 mm disc is the same to within 3%, varying from 1.36 to 1.40 µm. It can also be seen that the structured background increases threshold gold thickness compared to the homogeneous case, with a larger influence on diameters above 0.25 mm [as for Fig. 6(b)]. Figure 8 shows MGD for the default OPDOSE mode with homogeneous and structured backgrounds and for the modified scheme (constant detectability from 40 mm onward). The doses calculated for the default OPDOSE mode are very similar for the structured and the homogeneous background, indicating close correspondence between the 10 mm BR3D sheet and 10 mm PMMA. MGD for the modified mode is equal to those for the default OPDOSE mode at 20 and 30 mm PMMA and higher by 15%, 27%, 43%, and 73% for 40, 50, 60, and 70 mm PMMA thicknesses, respectively. Despite this increase in dose, MGD remains within the achievable limit given by the European guidelines DISCUSSION Figures 4 and 6 show SDNR, detectability index, and c-d analysis obtained as a function of phantom thickness using the default AEC mode, as currently set up on Siemens MAMMO- MAT Inspiration. There is a strong correspondence between the three indices which all show a reduction in detectability as PMMA thickness increases. This is illustrated in Fig. 9, which plots the change in these parameters normalized to their values at 40 mm PMMA. This result is of note as it explicitly supports the use of SDNR to predict the threshold gold thickness at other PMMA thicknesses in the European guidelines and therefore also the hypothesis used to generate the data for Table I. When switching to a background containing structured noise, all three indices show an absolute reduction in FIG. 7. c-d curves measured in homogeneous background for phantoms thickness of mm for the modified AEC mode. Tube potential, A/F combination, and mas for these curves are given in Table III.

11 3844 Salvagnini et al.: Tailoring automatic exposure control toward constant detectability 3844 FIG. 8. MGD values showed for the default AEC mode for both homogeneous and structured backgrounds and for the modified AEC mode. detectability at any given thickness compared to the homogeneous case. The use of a structured background results in a different trend of detectability versus thickness. In homogeneous PMMA, SDNR drops by 39% and detectability index 37% in going from 20 to 70 mm; introduction of the structured BR3D plate changed these figures to 22% (SDNR) and 6% (d ), respectively (Fig. 4). The change in contrast versus PMMA thickness is similar with and without structure (Table II); hence, the increased standard deviation or NNPS from the structure is playing a large role in determining the absolute values, as might be expected. It is likely that the degree of reduction will depend on properties of the FIG. 9. SDNR, detectability index, and threshold gold thickness for 0.1 mm diameter disc normalized at 40 mm for the Siemens MAMMOMAT Inspiration default OPDOSE mode. Error bars show average uncertainty on threshold gold thickness value. structured background this study has used BR3D structure. The average reduction in SDNR (in going from homogeneous to structured background) is 20% (range of 12% 31%), while for the detectability index for a 0.1 mm diameter, the average is 44% (range of 33% 55%), indicating that the structured background has a larger influence on the detectability index. This can be compared with an increase in threshold gold thickness of approximately just 10% for the 0.1 mm disc, which is less than that predicted either by SDNR or the detectability index. The difference found in the absolute reduction of detectability for T t compare to d and SDNR results can be due to the performance of the human reading in structured background. Figure 10(a) examines this more closely, where the measured c-d curves for 50 mm PMMA are plotted for the homogeneous and structured backgrounds. This figure shows that the impact of the structured noise is greater for larger diameter discs, where the increase in threshold gold thickness for 1 mm diameter discs is approximately 50%. This is consistent with the data of Kotre 33 and Huda et al. 34 where structured noise was shown to have a larger influence on object detectability for objects of diameter >1 mm. Presented in Fig. 10(b) is the trend predicted for threshold gold thickness, calculated using the NPWE model. The curve for the homogeneous case was scaled to match the value of 1.10 µm gold thickness for the 0.1 mm diameter; the same scaling was then used for the structured background calculation. This figure shows that a reasonable agreement with the observer result is seen for the larger diameters (e.g., a 50% increase at 1.0 mm diameter), but that the NPWE model overestimates the influence of the structured background on object detectability at smaller details (e.g., predicts a 35% increase predicted for 0.1 mm diameter). This also suggests that the human observers are more efficient in a (nominal) structured background than a nonprewhitening approach, i.e., they can account (decorrelate or prewhiten) for the correlation present in the structured background to some extent when preforming the detection task for small details. Table III shows that the mas and hence the patient dose could be reduced for PMMA thicknesses below 40 mm for the modified AEC; however, doses are below the achievable level and low in absolute terms compared to larger thicknesses. Any reduction in mas would lead to a reduction in detectability and hence, no adjustment was made to the default AEC settings for PMMA thickness 40 mm. As expected, doses increase for the modified AEC relative to the default AEC for PMMA thicknesses above 40 mm but remain below the achievable limit set in the European guidelines (Fig. 8). These modified AEC settings (Table III), i.e., constant detectability for breast thicknesses above 49 mm, were then programmed for two Siemens MAMMOMAT Inspiration systems, in preparation for data acquisition for a clinical study on detectability in clinical backgrounds. A consequence of the modified AEC is that the PV no longer remains constant as PMMA (or object) thickness increases; for the modified system, the PV is constant up to 40 mm PMMA, at 345, and then PV increases systematically to 380, 400, and 500 at 50, 60, and 70 mm PMMA, respectively. Hence, the SNR (i.e., linearized PV divided by linearized standard deviation) for the default AEC