Effective detective quantum efficiency (edqe) and effective noise equivalent quanta (eneq) for system optimization purposes in digital mammography

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1 Effective detective quantum efficiency (edqe) and effective noise equivalent quanta (eneq) for system optimization purposes in digital mammography Elena Salvagnini a,b, Hilde Bosmans a, Lara Struelens b, Nicholas W. Marshall a a UZ Gasthuisberg, Department of Radiology, Herestraat 9, B-3 Leuven, Belgium; b SCK CEN, Boeretang, Mol, Belgium ABSTRACT Effective detective quantum efficiency (edqe) and effective noise equivalent quanta (eneq) were recently introduced to broaden the notion of DQE and NEQ by including system parameters such as focus blurring and system scatter rejection methods. This work investigates edqe and eneq normalized for mean glandular dose (eneq MGD ) as a means to characterize and select optimal exposure parameters for a digital mammographic system. The edqe was measured for three anode/filter combinations, with and without anti-scatter grid and for four thicknesses of poly(methylmethacrylate) (PMMA). The modulation transfer function used to calculate edqe and eneq was measured from an edge positioned at,,6,7 mm above the table top without scattering material in the beam. The grid-in edqe results for all A/F settings were generally larger than those for grid-out. Contrarily, the eneq MGD results were higher for grid-out than gridin, with a maximum difference of 61% among all A/F combinations and PMMA thicknesses. The W/Rh combination gave the highest eneq MGD for all PMMA thicknesses compared to the other A/F combinations (for grid-in and grid-out), supporting the results of alternative methods (e.g. the signal difference to noise ratio method). The eneq MGD was then multiplied with the contrast obtained from a.mm Al square, resulting in a normalized quantity that was higher for the W/Rh combination than for the other A/F combinations. In particular, the results for the W/Rh combination were greater for the grid-in case. Furthermore, these results showed close agreement with a non-prewhitened match filter with eye response model observer (d ) normalized for MGD. Keywords: FFDM, effective Detective Quantum Efficiency (edqe), effective Noise Equivalent Quanta (eneq), detectability index (d ), Modulation Transfer Function (MTF), SdNR, image quality. 1. DESCRIPTION OF PURPOSE The quantities effective detective quantum efficiency (edqe) and effective noise equivalent quanta (eneq) can be seen as a development of the work of Wagner et al [1], by Samei et al [] and Ertan et al [3] with application to digital radiographic systems. The edqe is an attempt to broaden the notion of the detector centric metric of detective quantum efficiency (DQE) to include system parameters such as focus blurring and system scatter rejection methods. This study applies the edqe and eneq methodology to a digital mammographic system. The formulation of edqe attempts to compare a system against an ideal imaging system with perfect x-ray detection and scatter rejection, however a patient dose marker is not included. For this reason, eneq normalized for the mean glandular dose (MGD) was included in this study (eneq MGD ), as system configurations that produce high edqe may not be the best clinical choice. It is possible that the patient dose associated with parameters that give a high value edqe could be higher than the patient dose of configuration that is suboptimal in terms of edqe. The eneq MGD describes the impact of the patient dose on the chosen configuration but this term does not give any indication on object detectability. As an example, lower patient dose configurations (eg grid-in), can lead to higher eneq MGD without leading to higher object detectability in images. For this reason, we decided to extend eneq MGD with an object contrast (C%) that is characteristic for the studied configurations, and named this quantity eneq DC.. Medical Imaging 1: Physics of Medical Imaging, edited by Norbert J. Pelc, Robert M. Nishikawa, Bruce R. Whiting, Proc. of SPIE Vol. 8313, 8313H 1 SPIE CCC code: 165-7/1/$18 doi: / Proc. of SPIE Vol H-1

2 The purpose of this work was (1) to perform a full characterization of the digital mammography system efficiency using edqe as opposed to an DQE approach that focuses on the detector, () to investigate the influence of the mean glandular dose using eneq MGD, and (3) to relate eneq DC with a well known and accepted detectability index, the nonprewhitened match filter [] with eye response [5] (NPWE) model observer (d ). The combined use of these indexes can indicate the optimal choice of beam quality and system configuration for use in clinical examinations.. METHODS The study was performed using a Siemens MAMMOMAT Inspiration (Siemens AG Healthcare, Erlangen, Germany) equipped with a-se detector with 85 µm pitch and a selenium layer thickness of µm. This system utilizes three different A/F combinations (Mo/Mo, W/Rh and Mo/Rh), has a nominal focal spot dimension of.3 mm and an SID of 65 mm. The system can be operated with and without the anti-scatter grid. The grid is a linear type, with a ratio of 5:1, lead septa and strip density of 31 lines/cm. Detector response was measured for the four PMMA thicknesses using typical tube potential values and all available A/F combinations. Air kerma at the detector was measured with a calibrated Barracuda MPD dose detector and the pixel values (PV) taken from For Processing ( Flatfield ) images. The anti-scatter grid was removed for the detector response measurements. PV was plotted against air kerma at the detector (DAK) to give four detector response curves; these were used to linearize the PV data before any calculation was performed. The edqe [] was calculated for all A/F combinations for four PMMA thicknesses:,, 6 and 7mm. The equation used was: edqe( u' ) = MTF ( u' ) (1 SF ) NNPS( u' ) TF E q (1) Where u = spatial frequency corrected to the object plane, MTF= modulation transfer function, SF=scatter fraction, NNPS = normalized noise power spectrum, TF=narrow beam transmission factor of PMMA, E= pre-phantom exposure corrected at the detector plane, q= number of photons per µgy per unit area. The scatter fraction SF was estimated using the beam stop method [6] using six Pb disks of diameter ranging from to 3 mm. The primary radiation component was estimated by placing the PMMA at the output of the tube using a narrow beam geometry to produce a low scatter image. Using the same configuration, the Pb disks were positioned in the beam at the detector and the pixel values behind the disk are used to estimate the detector glare component. Finally, acquiring full field images with the PMMA placed at the detector gave the total signal (primary, glare and scatter components). The total signal was calculated as the mean PV in the same region of interest where primary radiation and glare were estimated. Consequently subtracting the pixel values of the scatter free configuration images and the pixel values representing detector glare from the total signal gave scattered radiation component. The narrow beam transmission factor (TF) was measured by placing the Barracuda MPD on the detector cover and collimating the x-ray beam to be slightly larger than the MPD. The PMMA was placed at the output at the X-ray tube. The air kerma was than acquired for all the A/F combinations at typical tube potentials with and without the PMMA in the beam. The ratio of the measured air kerma with and without PMMA gave the narrow beam transmission factor. The NNPS was calculated from homogeneous PMMA images acquired using automatic exposure control. These measurements were made with the grid in and out of the x-ray beam. The algorithm usedto estimate the noise power spectrum is described elsewhere; [7] the final NNPS estimate was taken from a radial average of the ensemble (including the and 9 spatial frequency axes), as the NNPS was found to be isotropic. Two NNPS results were estimated for every image and averaged, each NNPS was estimated using a region size of 51 by 51 divided in record size of 56 by 56 pixels with 5% overlap in both x- and y- directions. In the first part of the study, MTF was measured using a version of the edge method [7-8], under both clinical scatter conditions (edge placed on top of PMMA blocks) and for two different low scatter geometries (edge placed on top of the detector and edge placed at different heights above the detector, without PMMA), to investigate the influence Proc. of SPIE Vol H-

3 of different MTF curves on edqe. Following initial analysis, the MTF required for edqe was measured using a low scatter geometry, with the edge placed at different heights above the detector. The latter MTF was measured at 8 kv and W/Rh A/F setting with mm Al at the x-ray tube exit port. A steel plate of dimension 1 x 1 mm and thickness 1 mm with machined straight edges was positioned at,, 6 and 7 mm from the detector top without scatter material in the beam (referred to as Free-Air MTF). The edge was angled slightly (1 to 5 ) against the pixel matrix and images were acquired at a DAK of about 5µGy. The eneq was calculated for the same conditions as the edqe and normalized to the mean glandular dose (MGD) using the equation: MTF ( u') (1 SF ) 1 eneq MGD ( u') = () NNPS( u') MGD where MGD = mean glandular dose and u and SF, MTF and NNPS are the same terms used for the calculation of the edqe. The MGD was calculated using the method of Dance et al [9] : MGD = Kgsc (3) where K is the incident air kerma at the upper surface of the breast, measured without backscatter, the factor g is the incident air kerma to mean glandular dose conversion factor for a glandularity of 5%, the factor c corrects for the difference in breast composition from 5% glandularity and the factor s corrects for the x-ray spectrum used. The eneq MGD was than corrected for the object contrast factor (C%). The contrast was estimated using. mm Al square of 1x1 mm, applying equation () PVBkg PVAl C% = () PVBkg Where PV Bkg is the mean pixel value of a region of interest (ROI) of 5x5mm in the PMMA and PV Al is the mean pixel value of a region of interest (ROI) of 5x5mm in the Al. Through the text we will refer to the eneq MGD corrected for object contrast as eneq DC., with DC we want to indicate that the term is weighed for patient Dose and object Contrast. Equation 5 was used to calculate eneq DC. eneqdc ( u' ) = eneqmgd ( u') C% (5) The detectability in this study was calculated using the NPWE observer in equation (6): d' = π C S ( f ) MTF S( f ) MTF ( f ) VTF( f ) ( f ) VTF fdf ( f ) NNPS( f ) fdf (6) where C is the contrast measured using the. mm Al square, f is the spatial frequency, MTF(f) is the detector modulation transfer function, NNPS(f) is the normalized noise power spectrum and VTF(f) is the Visual Transfer Function. The VTF given by Kelly [1] was used for a nominal image magnification of 1.5 and viewing distance of mm 7. The signal was defined for a disc-like object of.1 mm diameter using equation (7): d J ( df ) S( f ) 1 π = (7) f Proc. of SPIE Vol H-3

4 where J 1 is a Bessel function of the first kind and d is the object diameter. Calculation of d requires measurement of the MTF and NNPS. These parameters were calculated as described above. In particular for the MTF calculation a low scatter geometry (detector MTF) was used at 8 kv and W/Rh A/F setting. Finally d was squared and normalized to MGD for comparison with the eneq DC results. 3. RESULTS AND DISCUSSION Before performing a full characterization of the system, an investigation of the influence of the MTF used in the edqe equation was performed. In the works of Samei et al [] and Ertan et al [3] the MTF was calculated from an edge placed on the top of the phantom. This configuration introduces a low frequency drop (LFD) in the MTF curve, even if a small region of interest (ROI) is used to calculate the MTF. Taken together with the SF correction, this can lead to an over-estimation of the scatter effect on the efficiency of the system thus a reduction in the edqe curves. For this reason it was decided to investigate the influence of three different MTF methods on the edqe equation: i) MTF measured with the edge placed at the phantom entrance (with scatter) (Samei et al) for two ROI sizes (7x7mm and xmm) ii) the detector MTF (edge on the detector) iii) the Free-Air MTF. The results are presented in figure 1 for and 7 mm of PMMA ( and 6 mm presented the same trends). The values of SF, TF, q and E used to obtain these results are presented in table 1. Figure 1 shows that the detector MTF gives the highest edqe, as might be expected, and the MTF estimated with the edge on top of the PMMA with a x mm ROI gives the lowest edqe. This is due to the absence of the focus blurring effects in the detector MTF and to the strong influence of scatter (large LFD) of the MTF calculated from the x mm ROI. The results obtained for Free-Air MTF and 7x7 mm MTF for mm of PMMA are quite similar (maximum difference 1%). Both methods include the focal blurring effects while scattered radiation at mm PMMA does not influence substantially the LFD of the MTF calculated with a 7x7 mm ROI. The influence of the LFD, even using the 7x7 mm ROI, became progressively larger (MTF became lower) as PMMA increased, compared to the Free-Air MTF - again due to the influence of scattered radiation (maximum difference 1%)...3 detector MTF PMMA mm Free-Air MTF PMMA mm 7x7 mm MTF PMMA mm x mm MTF PMMA mm..3 detector MTF PMMA 7mm Free-Air MTF PMMA 7mm 7x7 mm MTF PMMA 7mm x mm MTF PMMA 7mm edqe. edqe Fig. 1 shows edqe calculated using four different MTF methods: detector MTF, Free-Air MTF estimated without scattering material in the beam, and the MTF estimated with the edge placed on top of the PMMA with two different ROIs of 7x7 mm and x mm. The results are presented for mm of PMMA on the left and for 7 mm PMMA on the right. These results highlight the influence of scattered radiation on the MTF; when MTF estimated under clinical condition (edge on top of PMMA) is implemented in the equation 1, which also include a correction for SF, this leads to an overestimation of the scatter effects and consequentially a drop in edqe. The Free-Air MTF was considered a better choice for the edqe calculation as focal spot blurring effects are included without an additional contribution due to Proc. of SPIE Vol H-

5 scattered radiation. A full evaluation of edqe and eneq MGD was then performed using the Free-Air MTF. The values used for the analysis are presented in table 1. Table 1. PMMA thickness, tube potential, scatter fraction (SF) estimated with and without the grid are indicated, these values are common for all the A/F combinations. Number of photons per µgy unit area (q), transmission factor (TF) and prephantom exposure corrected at the detector plane (E) for the AEC mode with and without the grid for each A/F combination are also indicated. PMMA (mm) Tube kv A/F Mo/Mo Mo/Rh W/Rh SF grid IN SF grid OUT q TF grid IN grid OUT q TF grid IN grid OUT q TF grid IN grid OUT Figure shows the results of edqe for all the A/F combinations, with and without antiscatter grid in place for and 7 mm of PMMA. The curves for and 6 mm of PMMA showed trends similar to that of 7mm PMMA. Figure shows that the values of edqe for the digital mammographic system (between 1 and 3%) are higher than those for digital radiographic systems (typically in the range of to 1%) (Samei et al, Ertan et al). This is probably due to the higher system resolution (MTF) and the lower SF. Ertan et al reports a SF of about. and.6 with and without grid respectively, while this work shows a maximum SF of.157 and.59 with and without grid respectively. For mm of PMMA, the edqe results are slightly higher in absence of grid (9% maximum difference), however the grid in and grid out results are quite similar, reflecting the lower values of scattered radiation at mm. The use of W/Rh gives slightly higher edqe values than the other A/F settings. From to 7 mm of PMMA, the edqe values with grid in are higher than grid out (maximum difference of 35%) for all A/F combinations due to increased quantities of scattered radiation., Mo/Mo_IN mm, Mo/Mo_IN 7mm Mo/Rh_IN mm Mo/Rh_IN 7mm W/Rh_IN mm W/Rh_IN 7mm,3 Mo/Mo_OUT mm Mo/Rh_OUT mm,3 Mo/Mo_OUT 7mm Mo/Rh_OUT 7mm W/Rh_OUT mm W/Rh_OUT 7mm edqe, edqe,,1,1,, Fig. shows the edqe results for all the A/F combination of the digital mammographic system, with and without the presence of the antiscatter grid for mm of PMMA (left) and 7 mm of PMMA (right). Proc. of SPIE Vol H-5

6 eneq MGD (x1 5 ) Mo/Mo_IN mm Mo/Rh_IN mm W/Rh_IN mm Mo/Mo_OUT mm Mo/Rh_OUT mm W/Rh_OUT mm eneq MGD (x1 5 ) Mo/Mo_IN 7mm Mo/Rh_IN 7mm W/Rh_IN 7mm Mo/Mo_OUT 7mm Mo/Rh_OUT 7mm W/Rh_OUT 7mm 1 1 Fig. 3 shows the eneq results normalized for MGD for all A/F combinations of the digital mammographic system, with and without the presence antiscatter grid, for mm of PMMA (left) and 7 mm of PMMA (right). Figure 3 shows the results of eneq MGD for all A/F combinations, with and without the anti-scatter grid in place, for and 7 mm of PMMA (the results for and 6 mm of PMMA showed the same trends). Somewhat surprisingly, eneq MGD is higher for grid out than grid in, with a maximum difference of 61% for all the A/F combinations and PMMA thicknesses. This behaviour is due to the lower mas used for the grid out case leading to lower MGD. The results for MGD are shown in figure where the increasing difference in eneq MGD between grid in and grid out geometries can be seen as a function of PMMA. MGD has, in fact, very similar values for all A/F combinations for mm of PMMA, resulting in similar eneq MGD for grid in and grid out for the same A/F. Conversely, MGD is more than doubled for grid in compared to configurations without grid for 7 mm of PMMA. This explains the higher eneq MGD results in absence of anti-scatter grid. The eneq MGD values include patient dose and hence give an indication of system efficiency weighted or normalized for a patient risk related quantity. The eneq MGD curves show that the W/Rh combination gives the highest result for a given PMMA thickness and grid setting, compared to the other A/F settings. The fact that the W/Rh setting gives the highest edqe and eneq values is consistent with the optimal A/F setting found with standard signal difference to noise methods (SDNR) [11]. The eneq MGD does not include aspects related to object detectability and in order to relate eneq MGD to object detectability, the term was corrected according to equation 5. The values of contrast as a function of PMMA thickness for different A/F combinations with and without the anti-scatter grid in place are shown in figure 5. The results of eneq DC are shown in figure 6, at the left, for mm at the left of PMMA and figure 6, at the right, for 7mm of PMMA. Figure 6 shows that the W/Rh A/F combination gives the highest results but in this case the grid in configuration gives higher results (peak difference of 1%) than grid out. This is due to the higher contrast (figure 5) for the grid in geometry because of reduced scattered radiation; the maximum difference is 1% for mm of PMMA and 3% for 7 mm of PMMA for W/Rh A/F combination. For and 6 mm of PMMA the same trend was seen. Proc. of SPIE Vol H-6

7 8 Mo/Mo IN 5% 7 Mo/Rh IN 6 W/Rh IN Mo/Mo OUT % MGD [mgy] 5 3 Mo/Rh OUT W/Rh OUT Acceptable Reachable contrast [%] 15% 1% Mo/Mo IN Mo/Rh IN W/Rh IN 1 5% Mo/Mo OUT Mo/Rh OUT thickness [mm] Fig. shows the MGD results A/F combinations of the digital mammographic system, with and without the presence antiscatter grid. Acceptable and reachable threshold of the European Guideline for mammographic doses are reported for completeness. % W/Rh OUT 6 8 thickness [mm] Fig. 5 shows the contrast as function of thickness for different A/F combination with and without the anti-scatter grid in place.9 Mo/Mo_IN mm.9 Mo/Mo_IN 7mm eneq DC (x1 5 ).6.3 Mo/Rh_IN mm W/Rh_IN mm Mo/Mo_OUT mm Mo/Rh_OUT mm W/Rh_OUT mm eneq DC (x1 5 ).6.3 Mo/Rh_IN 7mm W/Rh_IN 7mm Mo/Mo_OUT 7mm Mo/Rh_OUT 7mm W/Rh_OUT 7mm.. Fig. 6 shows the eneq results normalized for MGD and corrected for contrast for all A/F combinations of the digital mammographic system, with and without the presence antiscatter grid, for mm of PMMA (left) and 7 mm of PMMA (right). Finally as a means of validation of the new figure of merit proposed we compared the results with the well known detectability index d [1]. In order to perform an appropriate (normalized) comparison, the d index was squared and divided by the MGD. The results of this operation are shown in figure 7(a), where the trend follows that obtained for eneq DC, as illustrated in figure 7(b). In fact d /MGD shows larger differences in the results for mm of PMMA for difference A/F combinations than in the results for 7 mm PMMA thickness. Moreover also this index confirms the superiority of the W/Rh A/F combination for,6,7 mm. For mm PMMA the highest results were for the Mo/Mo A/F combination and grid out, but the difference between Mo/Mo grid out and W/Rh grid in was just 6%. Proc. of SPIE Vol H-7

8 d' /MGD Mo/Mo IN Mo/Rh IN W/Rh IN Mo/Mo OUT 1 Mo/Rh OUT W/Rh OUT 6 8 (a) thickness [mm] (b) Fig. 7 shows (a) d / MGD for all A/F combinations of the digital mammographic system, with and without the presence antiscatter grid as a function of PMMA thickness (b) d /MGD plotted against eneq DC with PMMA thickness as a parameter. d' /MGD Mo/Mo grid IN Mo/Rh grid IN W/Rh grid IN Mo/Mo grid OUT Mo/Rh grid OUT W/Rh grid OUT eneq DC (x1 5 ). CONCLUSIONS A complete characterization of a mammographic system in term of edqe and eneq was performed. The established MTF method for edqe, measured in the presence of scattered radiation, was substituted for a Free-Air MTF measured without scattered radiation but including the focal spot blurring. The edqe method produced results that are largely consistent with standard methods such as signal difference to noise ratio (SdNR) in terms of system characterization [11], but does not include patient dose. For this reason eneq normalized for the MGD was calculated to account for patient risk. After eneq was normalized for MGD, we extended the concept to include object contrast. This quantity, which includes system sharpness and noise characteristics, patient dose and contrast, closely followed results calculated using the established non-prewhitened match filter with eye response (NPWE) model observer (d ). REFERENCES [1] Wagner, R.F., Barnes, G.T., and Askins, B.S., Effect of reduced scatter on radiographic information content and patient exposure: a quantitative demonstration, Med. Phys. 7(1), (198). [] Samei, E., Ranger, N.T., MacKenzie, A., Honey, I.D., Dobbins, J.T., and Ravin, C.E., Effective DQE (edqe) and speed of digital radiographic systems: an experimental methodology., Med. Phys. 36(8), (9). [3] Ertan, F., Mackenzie, A., Urbanczyk, H.J., Ranger, N.T., and Samei, E., Use of effective detective quantum efficiency to optimise radiographic exposures for chest imaging with computed radiography, Proceedings of SPIE 758(1), 7585O-7585O-1 (9). [] Wagner, R.F., and Brown, D.G., Unified SNR analysis of medical imaging systems, Phys. Med. Biol. 3(6), (1985). [5] Monnin, P., Marshall, N.W., Bosmans, H., Bochud, F.O., and Verdun, F.R., Image quality assessment in digital mammography: part II. NPWE as a validated alternative for contrast detail analysis., Phys. Med. Biol. 56(1), 1-38 (11). [6] Carton, A.K., Acciavatti, R., Kuo, J., and Maidment, A.D.A., The effect of scatter and glare on image quality in contrast-enhanced breast imaging using an a-si/csi(tl) full-field flat panel detector, Med. Phys. 36(3), 9 (9). [7] Marshall, N.W., A comparison between objective and subjective image quality measurements for a full field digital mammography system., Phys. Med. Biol. 51(1), 1-63 (6). Proc. of SPIE Vol H-8

9 [8] Samei, E., Flynn, M.J., and Reimann, D.A., A method for measuring the presampled MTF of digital radiographic systems using an edge test device., Med. Phys. 5(1), 1-13 (1998). [9] Dance, D.R., Skinner, C.L., Young, K.C., Beckett, J.R., and Kotre, C.J., Additional factors for the estimation of mean glandular breast dose using the UK mammography dosimetry protocol., Phys. Med. Biol. 5(11), 35-3 (). [1] Kelly, D.H., Motion and vision. II. Stabilized spatio-temporal threshold surface., J. Opt. Soc. Am. 69(1), (1979). [11] Bernhardt, P., Mertelmeier, T., and Hoheisel, M., X-ray spectrum optimization of full-field digital mammography: simulation and phantom study., Med. Phys. 33(11), (6). [1] Eckstein, M.P., Abbey, C.K., and Bochud, F.O., [A practical guide to model observers for visual detection in synthetic and natural noisy images], in Handbook of Medical Imaging 1, SPIE Press, Bellingham, WA, (). Proc. of SPIE Vol H-9