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Optimal photon energy comparison between digital breast tomosynthesis and mammography: A case study
Physica Medica 30 (2014) 482e488
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Original paper
Optimal photon energy comparison between digital breast tomosynthesis and mammography: A case study S. Di Maria a, *, M. Baptista a, M. Felix a, N. Oliveira b, N. Matela b, L. Janeiro c, P. Vaz a, L. Orvalho d, A. Silva d a
Centro de Ciência e Tecnologias Nucleares, Instituto Superior Técnico, Universidade de Lisboa, Estrada Nacional 10, Km 139,7, 2695-066 Bobadela, Portugal Universidade de Lisboa, Faculdade de Ciências, Instituto de Biofísica e Engenharia Biomédica, Campo Grande, 1749-016 Lisboa, Portugal Escola Superior de Saúde da Cruz Vermelha Portuguesa, Avenida de Ceuta, 1, Edifício Urbiceuta, 1300-125 Lisboa, Portugal d Serviço de Imagiologia, Hospital da Luz, Avenida Lusíada, 100, 1500-650 Lisboa, Portugal b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 November 2013 Received in revised form 9 February 2014 Accepted 13 February 2014 Available online 5 March 2014
A comparison, in terms of the optimal energy that maximizes the image quality between digital breast tomosynthesis (DBT) and digital mammography (DM) was performed in a MAMMOMAT Inspiration system (Siemens) based on amorphous selenium flat panel detector. In this paper we measured the image quality by the signal difference-to-noise ratio (SDNR), and the patient risk by the mean glandular dose (MGD). Using these quantities we compared the optimal voltage that maximizes the image quality both in breast tomosynthesis and standard mammography acquisition mode. The comparison for the two acquisition modes was performed for a W/Rh anode filter combinations by using a 4.5 cm tissue equivalent mammography phantom. Moreover, in order to check if the used equipment was quantum noise limited, the relation of the relative noise with respect to the detector dose was evaluated. Results showed that in the tomosynthesis acquisition mode the optimal voltage is 28 kV, whereas in standard mammography the optimal voltage is 30 kV. The automatic exposure control (AEC) of the system selects 28 kV as optimal voltage both for DBT and DM. Monte Carlo simulations showed a qualitative agreement with the AEC selection system, since an optimal monochromatic energy of 20 keV was found both for DBT and DM. Moreover, the check about the noise showed that the system is not completely quantum noise limited, and this issue could explain the experimental slight difference in terms of optimal voltage between DBT and DM. According to these results, the use of higher voltage settings is not justified for the improvement of the image quality during a DBT examination. Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: Digital mammography Digital breast tomosynthesis Image quality Mean glandular dose Monte Carlo simulations
Introduction Mammography is nowadays the most effective and accurate method for early detection of small malignant lesions in the female breast for the screening of the population. Nevertheless it was also reported that, both in screen-film mammography (SFM) and digital mammography (DM), about 15e30% of detectable cancers in screening programs are not detected [1]. A major role in the nondetectability could be addressed to the dense breast structure superimposed onto two-dimensional plane. A relatively new technique, called digital breast tomosynthesis (DBT), is being investigated as alternative to the traditional 2D mammography or as complementary technique [2] in order to overcome the above described problems. * Corresponding author. E-mail address: [email protected] (S. Di Maria).
Even if DBT is currently appearing in preliminary clinical studies, a lot of optimization work must be carried out in terms of the choice of the most suitable parameters, which maximize image quality within the limits imposed by breast dosimetry, as the angular range, number of projections, X-ray energy and reconstruction algorithm. Namely, before a new screening tool technology could be proposed, it will be important to pinpoint characteristics that could improve or complement the current available technique. Concerning the X-ray energy optimization, it is known that in breast radiography the best image quality at constant dose is obtained using photons of energies around 20 keV, since photons with lower energy are highly absorbed by the patient, while those at higher energies yield a low contrast. Moreover the As Low As Reasonably Achievable (ALARA) principle on dose delivered to the patient requires the use of the automated exposure control (AEC) system that is capable to ensure the optimal exposure of the image receptor compensating for breast thickness and composition.
http://dx.doi.org/10.1016/j.ejmp.2014.02.001 1120-1797/Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
S. Di Maria et al. / Physica Medica 30 (2014) 482e488
Consequently different studies in SFM and DM were conducted in order to understand the characteristics required of a spectrum suitable for a given detection task, as lesion type (tumor mass or calcification), breast thickness and breast composition [3]. If an appropriate anode/filter combination and energy is used for each detection task, the mean glandular dose (MGD) to the breast could be reduced up to 50% if a W/Rh anode/filter combination is used instead of Mo/Mo [3]. In particular, in optimization studies which aim is to evaluate the optimal voltage that maximizes the image quality, the optimal monochromatic photon energy knowledge is essential. In fact, once this information is known, it is more straightforward to associate an optimal voltage and filter/anode combination for a real polychromatic spectrum used in routine mammography clinical examinations. For example in DM, Bernhardt et al. [3] clearly demonstrated that there is a unique quantum energy which delivers the highest signal difference-to-noise ratio (SDNR) and that the best approximation to the ideal monochromatic spectrum can be achieved using a tungsten/rhodium (W/Rh) anode/filter combination. Regarding the DBT, several studies highlight that the choice of the W/Rh anode/filter combination could be beneficial for image quality. Nevertheless it is still not clear which could be an optimal tube voltage in DBT. Some authors state that higher voltages than the ones used in standard mammography could be beneficial, whereas others indicate an improvement when lower mammographic energies are used [2]. The aim of this work was to evaluate the best photon energy that maximizes the SDNR in DBT and in particular to study how the optimal energy varies between DM and DBT for a given detection task. To reach this objective the optimal voltage was calculated by acquiring different images (by selecting a W/Rh anode/filter combination) with a DBT system at different kVp and taking into account a 45 mm thick breast phantom. The optimal voltage was calculated for both breast tomosynthesis and standard mammography techniques. The qualitative trend of the optimal voltages obtained by experimental calculations was then compared with Monte Carlo (MC) simulations. Finally, in order to assess how the optimal energy that maximizes the image quality could be affected by different sources of noise (quantum, electronic and structured), a quantum noise check of the DBT/DM system was performed. Materials and methods Image acquisitions and dose measurements For the image acquisitions, a MAMMOMAT Inspiration system (Siemens) was used both for standard mammography and breast tomosynthesis. This medical equipment provides an integrated 24 cm 30 cm amorphous selenium (a-Se) detector. In standard mammography modality it allows the use of different anode/filter combinations, such as W/Rh and Mo/Mo and different acquisition modes, such as in manual and in AEC mode. Regarding the tomosynthesis acquisition mode, only the W/Rh anode/filter combination is preprogrammed. For this reason the comparison in terms of the optimal energy that maximizes the image quality between DM and DBT was performed only for the W/Rh anode/filter combination. Moreover several published studies [2,3] showed that the W/ Rh anode/filter combination could be beneficial for both imaging modalities (Fig. 1). The angular range spans over a nominal interval of 50 with a total of 25 projections with a frame rate of up 2 images per second. The selected X-ray source of the system, both for DM and DBT consists of a tungsten target and a 50-mm-thick rhodium (with an additional filtration of 1 mm of Beryllium). This study was performed with a breast-shaped phantom of 45 mm thickness and a
483
Figure 1. MAMMOMAT inspiration system (Siemens) used for measurements, both in DBT and DM mode.
composition equivalent to 50% glandular and 50% adipose tissue (CIRS phantom [4]). Images of the phantom were acquired in manual mode, using a peak tube voltage ranging from 24 kVp to 34 kVp at intervals of 2 kV. The 2D projections were then reconstructed by the dedicated software of the system with a filtered back projection (FBP) method. The image quality analysis was performed in the phantom flat contrast detail (100% glandular tissue composition) which simulates a typical tumor density. Both in DM and DBT, the dimensions of the ROI were set to 6 6 mm2. Concerning the DBT reconstructed images, the SDNR was calculated as average of three central slices relatively to the tumor mass. Before SDNR calculations, a check about the linearity between pixel value and detector dose was performed in the dose ranges used in these measurements. For each setting, entrance surface dose (ESD) was measured and the corresponding MGD was calculated according to the Dance formalisms [5], both for DM and DBT. Dose measurements were performed using LiF:Mg,Ti thermo luminescent dosimeters (TLD100, THERMO SCIENTIFIC [6]). The TLD chips were inserted in a thin Mylar holder (17 mg/cm2) and for each measurement 4 TLD’s were used. The dosimeters were re-set the day before the irradiations and read according to the usual procedures the day after the irradiations took place. Since the TLD’s were placed on the top of the breast phantom, the measured entrance dose includes also the backscatter fraction. Additionally, since the half value layer was not measured, an average value for the backscatter factor (BF) of 1.09 was chosen. Nevertheless the BF for mammographic X-ray spectra can vary between 1.07 and 1.13 [5], so an uncertainty of about 2e5% on the ESD could be taken into account. Furthermore, typical uncertainties for these TLDs measurements are of about 10%. This value considers the contribution of the efficiency correction factor, the reader calibration factor and the stability of the quality control correction factor. Determination of FOM Image quality optimization involves a compromise between radiation dose and image quality. This last parameter should be
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Figure 2. Left: representation of the dimensions of the modeled compressed breast: 4.5 cm breast thick and chest wall-nipple distance of 12.5 cm. Right: geometry of the breast and tumor mass, in the transverse plane, developed for de MCNPX simulations.
defined in relation to the MGD, since the improvement of image quality can be accomplished by applying a higher dose level as long as the image noise is dominated by quantum noise [3]. In this condition, a higher number of quanta (namely more radiation exposure) make more absolute but less relative noise in the image. There are other sources of noise (see “Quantum limited noise check” subsection), but quantum noise defines an “ideal” noise level below which cannot be further reduced. In DM the use of the Figure of Merits (FOMs) is a parameter generally used to compare techniques and exposure factors when task-optimization studies are performed [3]. From literature, the FOMs seem to be an evolving image quality parameter which could have different definitions. In this work, concerning the SDNR used on the acquired images, in order to remove correlated noise associated with phantom defects, detector non-uniformity and heel effect, the definition described by Williams et al. [7] was used. Once the SDNR and MGD were calculated, the following FOM was used to compare the image quality at each kVp, both in DBT and DM mode:
FOM ¼
SDNR2 MGD
(1)
Since the goal of this work is to compare the relative trade-off between image quality and MGD for a given acquisition system, the FOMs here shown, are expressed in arbitrary units (a.u.). In particular the influence of the spatial resolution [8], blurring and the effect of any visual system were neglected [3]. MCNPX simulations MC simulations were used to check the qualitative trend of the optimal energy between 2D standard mammography and 3D breast tomosynthesis. For this reason a Monte Carlo N-Particle eXtended (MCNPX) code, version 2.7.0 [9], for photon transport simulation was used (Fig. 2). Considering the relatively low energy range of diagnostic X-ray and that the tally volume considered in the present work is large with respect to the electron range, it can be assumed that the condition of charged particle equilibrium (CPE) is satisfied in the breast tissue. Therefore, it is valid to assume that the absorbed dose is equal to the collision kerma and the energy locally transferred to the electrons is also locally absorbed. Consequently, to perform the MC calculations, only the photon physics mode (kerma approximation) was selected [9]. A spherical object, with diameter of 5 mm, composed of 100% glandular tissue, was placed at the center of the compressed breast, to simulate a tumor. In addition, the simulation included an X-ray point source, as an approximation of the focal spot of the X-ray tube. The point isotropic photon source was collimated into a cone, to ensure the photon emission in the direction of the detector and a source to image distance (SID) of 65 cm, for the 0 tomosynthesis projection, was set.
The image detector was simulated with a semi-deterministic radiography tally which generates the transmitted image projection. Then, the simulated 2D projections were converted in ASCII files through the Gridconv program supplied by the MCNPX distribution. Since the a-Se detector is an energy integrating detector, the quantity taken into account in the radiography tally was the energy fluence. The flat panel detector (24 cm 30 cm) of the DBT system was implemented as a matrix with 704 896 pixels. These simulated pixel dimensions are not the same as the real pixel dimensions of the DBT/DM system used for phantom measurements (85 mm pixel size). However, since the simulation of detectors with such as pixel dimensions is very time consuming, and since the lesion dimension here simulated was of 5 mm, the choice of the simulated pixel dimension was chosen according to a compromise between these two factors. Every pixel in the detector array receives a ray trace contribution from each source or scatter event, to eliminate the statistical fluctuations along the detector grid. For the detector model it was assumed 100% absorption efficiency (ideal detector). This assumption is quite good, since the absorption efficiency of direct converting a-Se detector is more than 98% for a 20 keV monochromatic X-ray. For all the simulation runs, only primary radiation was taken into account, which corresponds to consider that an antiscatter grid was implemented. The whole arrangement was placed in air environment. Neglecting the scatter radiation is an ideal assumption. Nevertheless it has been shown that including the scatter radiation in this type of studies, the optimal energy that maximizes the image quality parameter is not affected by the presence of the scatter radiation, namely only the absolute value of the FOM is affected [10] In this study, the DBT projection images set simulated consisted of 25 projections, over an angular range from 24 to þ24 , in 2 steps. The detector remained stationary, while the X-ray point source moved in the range of the angular arc referred. Thereby, the simulation was repeated for each projection angle with monochromatic X-rays of energies in the range between 18 and 28 keV, in 2 keV steps. The 25 simulated projections were then reconstructed through a Simultaneous Iterative Reconstruction Technique (SART), a non-statistical algorithm which is the variation of Algebraic Reconstruction Technique (ART). The FOM in the reconstructed images obtained through MC simulations was calculated as the Eq. (1) above described, but in this case the SDNR was calculated according to the following expression:
SDNR ¼
SB SO
sB
(2)
where SO and SB are the mean signal of the object of interest and the background, respectively, while sB is the standard deviation of the noise over an area which has the same size as the object of interest.
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Figure 3. Measured image quality parameter for a 100% glandular detail embedded in a 4.5 cm breast thick both for DBT and DM. In DBT the optimal voltage is 28 kV, whereas in DM a value of 30 kV was found (12% standard deviation on the FOM).
Since a quantum noise limited system was assumed, only Poisson noise was taken into account as standard deviation of the background and namely the following expression was used for DM [5]:
sBDM ¼
pffiffiffiffiffiffiffiffiffiffiffi E2 $N
(3)
where N represents the number of photons impinging on the detector and E refers to the mean energy of the incident photon. For the DBT case, the background standard deviation was calculated before the image reconstruction process in the 2D projections, and in particular the following line of reasoning was considered: after the logarithmic processing, the signal P is proportional to the attenuation coefficient according to:
Z P ¼
mðxÞdx ¼ ln
N0 N
(4)
where N and N0 are the attenuated and non-attenuated photon beam, respectively, and m(x) is the attenuation coefficient at position x along the ray path. Applying the error propagation law to the logarithmic expression, and neglecting the scatter radiation and the uncertainty on the source photon beam N0, the background standard deviation for DBT considered in this work was:
sBDBT
pffiffiffiffiffi Ni ¼ N i i ¼ 24 þ24 X
(5)
where Ni is the number of the incident photons for each projection i. Quantum limited noise check The optimal performance of a digital mammography system depends on the different noise sources that could degrade the overall image quality. Image noise can be divided into three main sources, such as the total pixel variance SD2 can be written as [11]:
SD2 ¼ SD2e þ SD2q þ SD2s
(6)
where SD2e is the electronic noise arising from electronic read-out of the pixels and is independent of dose, SD2q is the quantum noise
(SDq has a square root relationship with detector dose) and SD2s is the structured noise arising from the spatial fixed variation of the image gain (SDs is proportional to the detector dose). To study if the system used for measurements was quantum limited and to check if other sources of noise could affect the optimal energy estimation in DBT and DM, the noise analysis using the pixel variance method described in Bouwman et al. [11] was taken into account. If relative noise is used, and the system is quantum noise limited, the noise of the system could be parameterized according to the following formula [11]:
SD ¼ Kn $Dn pv
(7)
where pv is the image pixel value, SD is the standard deviation, n is 0.5 if the image noise is purely quantum noise and kn is the noise coefficient. In order to perform this type of analysis, a sequence of 10 flat-field images at different entrance dose values (in the entrance dose range of about 80e4000 mGy) was acquired. Results and discussions Phantom measurements The optimal voltage that maximizes the FOM, both in DM and in DBT is shown in the Fig. 3. As can be seen, the optimal voltage for DBT techniques is 28 kV, whereas for DM the optimal voltage is 30 kV. The uncertainty on the FOM was calculated as error propagation of different contributions: the uncertainty on the pixel values was assumed less than 4%, while for the TLDs measurements an uncertainty of 10% was taken into account. For this reason a total standard deviation of 12% was considered for the FOM. As shown in Fig. 3, the FOM curve for mammography is quite flat (there is a difference of about 20% between the lowest and the highest FOM value), indicating a tolerance against non-optimal voltage setting [3]. Moreover, as shown in the Fig. 3, selecting an optimal voltage of 30 kV instead of 28 kV as suggested by the AEC, there is an increase of the FOM of about 14%. The presence of a maximum in the FOM curve for DBT seems more marked since there is a difference of about 40% between the
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Figure 4. FOM results obtained by MC simulations for 4.5 cm breast thick and a tumor mass detail (100% glandular composition) both for DBT and DM.
lowest and the highest FOM value. The results indicate that the reconstruction algorithm (in this case FBP method), as well as the presence of other sources of noise, could have some influence on the optimal voltage that maximizes the FOM with respect to the DM acquisition mode. Moreover the optimal voltage for a 50% glandular breast with a thickness of 4.5 cm found in these set of phantom measurements is in agreement with the AEC of the DBT acquisition mode. Concerning the DM manual acquisition mode, the best voltage found in this work differs with the AEC voltage value (also in DM the AEC chooses an optimal voltage of 28 kV). It is interesting to see how our results, are qualitatively in agreement also with the results showed by S.J. Feng et al. [2] (it is worth to say that in their work an Hologic system was used). In the S.J. Feng et al. study, the Hologic AEC settings chooses an optimal voltage of 29 and 28 kV for DBT and DM respectively for a 4 cm thick breast phantom and 50% glandular composition, as the one used in this study. Even if in these two works the same anode/filter combination and phantom are used, some slight differences could be in part explained by the different equipment used. Monte Carlo simulations The 2D simulated projections for each monochromatic energy (25 projections for each energy) were then reconstructed through the SART reconstruction method and the SDNR was calculated. The
simulated optimal energies that maximize the FOM, both in DM and DBT are shown in the Fig. 4. It can be seen that, in qualitative agreement with the results of the measured optimal voltages above discussed, there is an optimal monochromatic energy that maximizes the FOM, and in this case the maximum is the same for DM and DBT (20 keV). This trend is in agreement with the optimal voltage of the AEC of the system, since a 28 kV voltage is selected both for DBT and DM. Also, through the Siemens X-ray spectrum generator tool [12] it is possible to calculate the mean energy of the polychromatic spectrum. In this way, considering the mean energy of the 28 kV and 30 kV W/Rh polychromatic spectra (respectively 19.06 keV and 19.36 keV), the agreement of the simulation results with measurements ones in terms of the optimal energy that maximizes the FOM, is quite evident. The MC simulations were performed with a simplified detection system where only the quantum noise was considered. Nevertheless, these MC results show that this assumption is qualitative compatible with the AEC system results. Namely, looking at the AEC of the medical equipment, when changing from DM to DBT mode, the reconstruction algorithm, as well as other sources of noise, seems not to influence the optimal energy that maximizes the image quality parameter. We remark that in the measurements an FBP reconstruction method was used, whereas a SART method was used to reconstruct the 2D simulated projections in the MC study. Moreover even when iterative reconstruction methods are used, as for example in the IMS Giotto TOMO system, the same beam quality, as the one found in this study, is used for the same detection task considered in the present work [13]. Quantum limited noise check
Figure 5. Relative noise against detector dose. The result of the fit indicates that the system is not completely quantum nose limited (n ¼ 0.46431).
In order to check if the system used for measurements was quantum noise limited (as supposed by MC simulations), the relative noise for each flat-field image was plotted against the detector dose and a power fit (defined in the Eq. (7)) was performed (Fig. 5). The results indicate that the system is not purely quantum noise limited, since the n-value is 0.464 0.07. According the work of Bouwman et al. [11], if the n value differs from 0.5, the contribution of other noise sources could affect the quality of the image. In particular, if the n-value is lower than 0.5, this could mean that a high structured noise may be present in the system. In DBT, due to the 3D acquisition mode, the structural noise can be reduced. Nevertheless, according to a study based on a Noise Power Spectrum (NPS) analysis [14] which aimed to characterize the noise
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Figure 6. Experimental FOMs calculated in the 0 and 24 degree projection, respectively. The evaluation of the optimal voltage in these cases seems to be affected by other sources of noise.
texture, the structured noise in DBT is quite close to the DM one. According to this work’s phantom results, and taking also into account the uncertainties involved, it seems that in DBT, a higher structured noise is better compensated with a lower voltage setting (28 kV), whereas in DM a higher voltage setting (30 kV) appears to be more beneficial in maximizing the FOM. We want to stress here that this study is centered on the evaluation of the optimal energy that maximizes the image quality parameter and namely we are neglecting the quantitative variation of the FOM between the two different acquisition modes (DBT and DM). MC simulations showed that in a completely quantum noise limited system, the optimal energy does not change between DBT and mammography. Moreover, the presence of other sources of noise in the system could influence the optimal energy evaluation. The non-quantum limited characteristic of the system is quite visible when the single 2D
projections used in DBT for the reconstruction, are analyzed. In fact, calculating the optimal energy that maximizes the FOM in the 2D projections before the reconstruction step, it is possible to see how the FOM is no more sensitive to the optimal voltage in that kV interval. In Fig. 6, the 0 and 24 projections are showed as sample, and it is observed that the standard deviation on the FOM reaches an average value of about 15% because of the increasing pixel standard deviation which reaches a mean value of about 7%. In these cases, when the entrance dose levels range between 50 and 100 mGy, other sources of noises, as the electronic noise could affect the image quality. Instead, if analyzing the 2D projections obtained through MC simulations (see Fig. 7), where only quantum noise was taken into account, the FOM is still sensitive to the optimal energy. This occurs even if the maximum is different in the two projection angle considered (a maximum of 20 keV for the 0 projection was
Figure 7. MC FOMs calculated in the 0 and 24 degree projection respectively. In this case, the optimal energy at 0 projection was 20 keV, whereas for the 24 projection an optimal energy of 18 keV was evaluated.
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observed, whereas a maximum of 18 keV was found for the 24 projection). The effect of the anisotropy introduced by the DBT acquisition mode could introduce misregistration and additional noise in DBT reconstructions. Nevertheless, in terms of the optimal energy evaluation, our MC results showed that the final reconstructed image in DBT is not affected by this optimal energy shift in the different projections with respect to the DM case, just as happens with the AEC of the DBT/DM system. The situation becomes worse when real data are analyzed. As previously shown, the effect of other sources of noise (see Fig. 6) seems to affect in a major extent the optimal voltage evaluation in the single 2D projection. The slightly difference in the optimal voltage evaluation between DM and DBT could be explained by these additional noise propagation in the reconstruction process. Conclusions In this work we performed a comparison study about the optimal energy that maximizes the image quality parameter both in DBT and DM. The correct choice of the optimal energy for lesions detection is an important issue since allows to avoid useless delivered dose to the patients (by using energies lower than the optimal ones), or to avoid blurring in the final image (by using energies higher than the optimal ones). The measurements performed, showed that the optimal voltage with a W/Rh anode/filter combination for a 4.5 cm thick breast phantom of 50% glandular composition in DBT acquisition mode is 28 kV, whereas in DM the optimal voltage is 30 kV. On the other hand, the MC results suggest that the optimization AEC system works under the same hypothesis (quantum noise limited and no effect of the reconstruction method) undertaken in the MC simulations performed in this study. Namely, there is no variation in the optimal energy choice when considering the DBT or the DM for a 4.5 cm thick breast. This study presents several limitations. Firstly the 2D MC projections were reconstructed through a SART method, while the measured 2D projections were reconstructed through the FBP. This issue makes the results here presented only indicatives concerning the relation between the optimal energy that maximizes the image quality parameter and the reconstruction method. A second limitation of this MC work is the non-inclusion of the combined effect of the reconstruction algorithm together with other sources of noise on the optimal energy evaluation that maximizes the FOM. The inclusion of these effects in the MC model is quite complex and is beyond the aim of this work. Nevertheless, as shown in the phantom measurements, the possible combined effect above mentioned on the optimal energy evaluation for each detection task, could take to consider an optimal voltage for DBT
slightly lower than in DM. Consequently, accordingly to these results, the use of higher voltage values in DBT could be not justified for the image quality improving during a breast examination. Finally, in the optimization work here described, only one breast thickness was taken into account. In order to fully optimize a DBT/ DM acquisition system it will be important to perform further studies with other breast thicknesses and different lesion types. Despite these limitations, this work gives insights toward a deeper understanding about the optimal energy evaluation in DBT.
Acknowledgements The authors would like to thank the team of the Individual Monitoring Laboratory of the CTN/IST for TLDs reading and calibration, and A. Taibi for valuable discussions.
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Original paper
Optimal photon energy comparison between digital breast tomosynthesis and mammography: A case study S. Di Maria a, *, M. Baptista a, M. Felix a, N. Oliveira b, N. Matela b, L. Janeiro c, P. Vaz a, L. Orvalho d, A. Silva d a
Centro de Ciência e Tecnologias Nucleares, Instituto Superior Técnico, Universidade de Lisboa, Estrada Nacional 10, Km 139,7, 2695-066 Bobadela, Portugal Universidade de Lisboa, Faculdade de Ciências, Instituto de Biofísica e Engenharia Biomédica, Campo Grande, 1749-016 Lisboa, Portugal Escola Superior de Saúde da Cruz Vermelha Portuguesa, Avenida de Ceuta, 1, Edifício Urbiceuta, 1300-125 Lisboa, Portugal d Serviço de Imagiologia, Hospital da Luz, Avenida Lusíada, 100, 1500-650 Lisboa, Portugal b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 November 2013 Received in revised form 9 February 2014 Accepted 13 February 2014 Available online 5 March 2014
A comparison, in terms of the optimal energy that maximizes the image quality between digital breast tomosynthesis (DBT) and digital mammography (DM) was performed in a MAMMOMAT Inspiration system (Siemens) based on amorphous selenium flat panel detector. In this paper we measured the image quality by the signal difference-to-noise ratio (SDNR), and the patient risk by the mean glandular dose (MGD). Using these quantities we compared the optimal voltage that maximizes the image quality both in breast tomosynthesis and standard mammography acquisition mode. The comparison for the two acquisition modes was performed for a W/Rh anode filter combinations by using a 4.5 cm tissue equivalent mammography phantom. Moreover, in order to check if the used equipment was quantum noise limited, the relation of the relative noise with respect to the detector dose was evaluated. Results showed that in the tomosynthesis acquisition mode the optimal voltage is 28 kV, whereas in standard mammography the optimal voltage is 30 kV. The automatic exposure control (AEC) of the system selects 28 kV as optimal voltage both for DBT and DM. Monte Carlo simulations showed a qualitative agreement with the AEC selection system, since an optimal monochromatic energy of 20 keV was found both for DBT and DM. Moreover, the check about the noise showed that the system is not completely quantum noise limited, and this issue could explain the experimental slight difference in terms of optimal voltage between DBT and DM. According to these results, the use of higher voltage settings is not justified for the improvement of the image quality during a DBT examination. Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: Digital mammography Digital breast tomosynthesis Image quality Mean glandular dose Monte Carlo simulations
Introduction Mammography is nowadays the most effective and accurate method for early detection of small malignant lesions in the female breast for the screening of the population. Nevertheless it was also reported that, both in screen-film mammography (SFM) and digital mammography (DM), about 15e30% of detectable cancers in screening programs are not detected [1]. A major role in the nondetectability could be addressed to the dense breast structure superimposed onto two-dimensional plane. A relatively new technique, called digital breast tomosynthesis (DBT), is being investigated as alternative to the traditional 2D mammography or as complementary technique [2] in order to overcome the above described problems. * Corresponding author. E-mail address: [email protected] (S. Di Maria).
Even if DBT is currently appearing in preliminary clinical studies, a lot of optimization work must be carried out in terms of the choice of the most suitable parameters, which maximize image quality within the limits imposed by breast dosimetry, as the angular range, number of projections, X-ray energy and reconstruction algorithm. Namely, before a new screening tool technology could be proposed, it will be important to pinpoint characteristics that could improve or complement the current available technique. Concerning the X-ray energy optimization, it is known that in breast radiography the best image quality at constant dose is obtained using photons of energies around 20 keV, since photons with lower energy are highly absorbed by the patient, while those at higher energies yield a low contrast. Moreover the As Low As Reasonably Achievable (ALARA) principle on dose delivered to the patient requires the use of the automated exposure control (AEC) system that is capable to ensure the optimal exposure of the image receptor compensating for breast thickness and composition.
http://dx.doi.org/10.1016/j.ejmp.2014.02.001 1120-1797/Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
S. Di Maria et al. / Physica Medica 30 (2014) 482e488
Consequently different studies in SFM and DM were conducted in order to understand the characteristics required of a spectrum suitable for a given detection task, as lesion type (tumor mass or calcification), breast thickness and breast composition [3]. If an appropriate anode/filter combination and energy is used for each detection task, the mean glandular dose (MGD) to the breast could be reduced up to 50% if a W/Rh anode/filter combination is used instead of Mo/Mo [3]. In particular, in optimization studies which aim is to evaluate the optimal voltage that maximizes the image quality, the optimal monochromatic photon energy knowledge is essential. In fact, once this information is known, it is more straightforward to associate an optimal voltage and filter/anode combination for a real polychromatic spectrum used in routine mammography clinical examinations. For example in DM, Bernhardt et al. [3] clearly demonstrated that there is a unique quantum energy which delivers the highest signal difference-to-noise ratio (SDNR) and that the best approximation to the ideal monochromatic spectrum can be achieved using a tungsten/rhodium (W/Rh) anode/filter combination. Regarding the DBT, several studies highlight that the choice of the W/Rh anode/filter combination could be beneficial for image quality. Nevertheless it is still not clear which could be an optimal tube voltage in DBT. Some authors state that higher voltages than the ones used in standard mammography could be beneficial, whereas others indicate an improvement when lower mammographic energies are used [2]. The aim of this work was to evaluate the best photon energy that maximizes the SDNR in DBT and in particular to study how the optimal energy varies between DM and DBT for a given detection task. To reach this objective the optimal voltage was calculated by acquiring different images (by selecting a W/Rh anode/filter combination) with a DBT system at different kVp and taking into account a 45 mm thick breast phantom. The optimal voltage was calculated for both breast tomosynthesis and standard mammography techniques. The qualitative trend of the optimal voltages obtained by experimental calculations was then compared with Monte Carlo (MC) simulations. Finally, in order to assess how the optimal energy that maximizes the image quality could be affected by different sources of noise (quantum, electronic and structured), a quantum noise check of the DBT/DM system was performed. Materials and methods Image acquisitions and dose measurements For the image acquisitions, a MAMMOMAT Inspiration system (Siemens) was used both for standard mammography and breast tomosynthesis. This medical equipment provides an integrated 24 cm 30 cm amorphous selenium (a-Se) detector. In standard mammography modality it allows the use of different anode/filter combinations, such as W/Rh and Mo/Mo and different acquisition modes, such as in manual and in AEC mode. Regarding the tomosynthesis acquisition mode, only the W/Rh anode/filter combination is preprogrammed. For this reason the comparison in terms of the optimal energy that maximizes the image quality between DM and DBT was performed only for the W/Rh anode/filter combination. Moreover several published studies [2,3] showed that the W/ Rh anode/filter combination could be beneficial for both imaging modalities (Fig. 1). The angular range spans over a nominal interval of 50 with a total of 25 projections with a frame rate of up 2 images per second. The selected X-ray source of the system, both for DM and DBT consists of a tungsten target and a 50-mm-thick rhodium (with an additional filtration of 1 mm of Beryllium). This study was performed with a breast-shaped phantom of 45 mm thickness and a
483
Figure 1. MAMMOMAT inspiration system (Siemens) used for measurements, both in DBT and DM mode.
composition equivalent to 50% glandular and 50% adipose tissue (CIRS phantom [4]). Images of the phantom were acquired in manual mode, using a peak tube voltage ranging from 24 kVp to 34 kVp at intervals of 2 kV. The 2D projections were then reconstructed by the dedicated software of the system with a filtered back projection (FBP) method. The image quality analysis was performed in the phantom flat contrast detail (100% glandular tissue composition) which simulates a typical tumor density. Both in DM and DBT, the dimensions of the ROI were set to 6 6 mm2. Concerning the DBT reconstructed images, the SDNR was calculated as average of three central slices relatively to the tumor mass. Before SDNR calculations, a check about the linearity between pixel value and detector dose was performed in the dose ranges used in these measurements. For each setting, entrance surface dose (ESD) was measured and the corresponding MGD was calculated according to the Dance formalisms [5], both for DM and DBT. Dose measurements were performed using LiF:Mg,Ti thermo luminescent dosimeters (TLD100, THERMO SCIENTIFIC [6]). The TLD chips were inserted in a thin Mylar holder (17 mg/cm2) and for each measurement 4 TLD’s were used. The dosimeters were re-set the day before the irradiations and read according to the usual procedures the day after the irradiations took place. Since the TLD’s were placed on the top of the breast phantom, the measured entrance dose includes also the backscatter fraction. Additionally, since the half value layer was not measured, an average value for the backscatter factor (BF) of 1.09 was chosen. Nevertheless the BF for mammographic X-ray spectra can vary between 1.07 and 1.13 [5], so an uncertainty of about 2e5% on the ESD could be taken into account. Furthermore, typical uncertainties for these TLDs measurements are of about 10%. This value considers the contribution of the efficiency correction factor, the reader calibration factor and the stability of the quality control correction factor. Determination of FOM Image quality optimization involves a compromise between radiation dose and image quality. This last parameter should be
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Figure 2. Left: representation of the dimensions of the modeled compressed breast: 4.5 cm breast thick and chest wall-nipple distance of 12.5 cm. Right: geometry of the breast and tumor mass, in the transverse plane, developed for de MCNPX simulations.
defined in relation to the MGD, since the improvement of image quality can be accomplished by applying a higher dose level as long as the image noise is dominated by quantum noise [3]. In this condition, a higher number of quanta (namely more radiation exposure) make more absolute but less relative noise in the image. There are other sources of noise (see “Quantum limited noise check” subsection), but quantum noise defines an “ideal” noise level below which cannot be further reduced. In DM the use of the Figure of Merits (FOMs) is a parameter generally used to compare techniques and exposure factors when task-optimization studies are performed [3]. From literature, the FOMs seem to be an evolving image quality parameter which could have different definitions. In this work, concerning the SDNR used on the acquired images, in order to remove correlated noise associated with phantom defects, detector non-uniformity and heel effect, the definition described by Williams et al. [7] was used. Once the SDNR and MGD were calculated, the following FOM was used to compare the image quality at each kVp, both in DBT and DM mode:
FOM ¼
SDNR2 MGD
(1)
Since the goal of this work is to compare the relative trade-off between image quality and MGD for a given acquisition system, the FOMs here shown, are expressed in arbitrary units (a.u.). In particular the influence of the spatial resolution [8], blurring and the effect of any visual system were neglected [3]. MCNPX simulations MC simulations were used to check the qualitative trend of the optimal energy between 2D standard mammography and 3D breast tomosynthesis. For this reason a Monte Carlo N-Particle eXtended (MCNPX) code, version 2.7.0 [9], for photon transport simulation was used (Fig. 2). Considering the relatively low energy range of diagnostic X-ray and that the tally volume considered in the present work is large with respect to the electron range, it can be assumed that the condition of charged particle equilibrium (CPE) is satisfied in the breast tissue. Therefore, it is valid to assume that the absorbed dose is equal to the collision kerma and the energy locally transferred to the electrons is also locally absorbed. Consequently, to perform the MC calculations, only the photon physics mode (kerma approximation) was selected [9]. A spherical object, with diameter of 5 mm, composed of 100% glandular tissue, was placed at the center of the compressed breast, to simulate a tumor. In addition, the simulation included an X-ray point source, as an approximation of the focal spot of the X-ray tube. The point isotropic photon source was collimated into a cone, to ensure the photon emission in the direction of the detector and a source to image distance (SID) of 65 cm, for the 0 tomosynthesis projection, was set.
The image detector was simulated with a semi-deterministic radiography tally which generates the transmitted image projection. Then, the simulated 2D projections were converted in ASCII files through the Gridconv program supplied by the MCNPX distribution. Since the a-Se detector is an energy integrating detector, the quantity taken into account in the radiography tally was the energy fluence. The flat panel detector (24 cm 30 cm) of the DBT system was implemented as a matrix with 704 896 pixels. These simulated pixel dimensions are not the same as the real pixel dimensions of the DBT/DM system used for phantom measurements (85 mm pixel size). However, since the simulation of detectors with such as pixel dimensions is very time consuming, and since the lesion dimension here simulated was of 5 mm, the choice of the simulated pixel dimension was chosen according to a compromise between these two factors. Every pixel in the detector array receives a ray trace contribution from each source or scatter event, to eliminate the statistical fluctuations along the detector grid. For the detector model it was assumed 100% absorption efficiency (ideal detector). This assumption is quite good, since the absorption efficiency of direct converting a-Se detector is more than 98% for a 20 keV monochromatic X-ray. For all the simulation runs, only primary radiation was taken into account, which corresponds to consider that an antiscatter grid was implemented. The whole arrangement was placed in air environment. Neglecting the scatter radiation is an ideal assumption. Nevertheless it has been shown that including the scatter radiation in this type of studies, the optimal energy that maximizes the image quality parameter is not affected by the presence of the scatter radiation, namely only the absolute value of the FOM is affected [10] In this study, the DBT projection images set simulated consisted of 25 projections, over an angular range from 24 to þ24 , in 2 steps. The detector remained stationary, while the X-ray point source moved in the range of the angular arc referred. Thereby, the simulation was repeated for each projection angle with monochromatic X-rays of energies in the range between 18 and 28 keV, in 2 keV steps. The 25 simulated projections were then reconstructed through a Simultaneous Iterative Reconstruction Technique (SART), a non-statistical algorithm which is the variation of Algebraic Reconstruction Technique (ART). The FOM in the reconstructed images obtained through MC simulations was calculated as the Eq. (1) above described, but in this case the SDNR was calculated according to the following expression:
SDNR ¼
SB SO
sB
(2)
where SO and SB are the mean signal of the object of interest and the background, respectively, while sB is the standard deviation of the noise over an area which has the same size as the object of interest.
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Figure 3. Measured image quality parameter for a 100% glandular detail embedded in a 4.5 cm breast thick both for DBT and DM. In DBT the optimal voltage is 28 kV, whereas in DM a value of 30 kV was found (12% standard deviation on the FOM).
Since a quantum noise limited system was assumed, only Poisson noise was taken into account as standard deviation of the background and namely the following expression was used for DM [5]:
sBDM ¼
pffiffiffiffiffiffiffiffiffiffiffi E2 $N
(3)
where N represents the number of photons impinging on the detector and E refers to the mean energy of the incident photon. For the DBT case, the background standard deviation was calculated before the image reconstruction process in the 2D projections, and in particular the following line of reasoning was considered: after the logarithmic processing, the signal P is proportional to the attenuation coefficient according to:
Z P ¼
mðxÞdx ¼ ln
N0 N
(4)
where N and N0 are the attenuated and non-attenuated photon beam, respectively, and m(x) is the attenuation coefficient at position x along the ray path. Applying the error propagation law to the logarithmic expression, and neglecting the scatter radiation and the uncertainty on the source photon beam N0, the background standard deviation for DBT considered in this work was:
sBDBT
pffiffiffiffiffi Ni ¼ N i i ¼ 24 þ24 X
(5)
where Ni is the number of the incident photons for each projection i. Quantum limited noise check The optimal performance of a digital mammography system depends on the different noise sources that could degrade the overall image quality. Image noise can be divided into three main sources, such as the total pixel variance SD2 can be written as [11]:
SD2 ¼ SD2e þ SD2q þ SD2s
(6)
where SD2e is the electronic noise arising from electronic read-out of the pixels and is independent of dose, SD2q is the quantum noise
(SDq has a square root relationship with detector dose) and SD2s is the structured noise arising from the spatial fixed variation of the image gain (SDs is proportional to the detector dose). To study if the system used for measurements was quantum limited and to check if other sources of noise could affect the optimal energy estimation in DBT and DM, the noise analysis using the pixel variance method described in Bouwman et al. [11] was taken into account. If relative noise is used, and the system is quantum noise limited, the noise of the system could be parameterized according to the following formula [11]:
SD ¼ Kn $Dn pv
(7)
where pv is the image pixel value, SD is the standard deviation, n is 0.5 if the image noise is purely quantum noise and kn is the noise coefficient. In order to perform this type of analysis, a sequence of 10 flat-field images at different entrance dose values (in the entrance dose range of about 80e4000 mGy) was acquired. Results and discussions Phantom measurements The optimal voltage that maximizes the FOM, both in DM and in DBT is shown in the Fig. 3. As can be seen, the optimal voltage for DBT techniques is 28 kV, whereas for DM the optimal voltage is 30 kV. The uncertainty on the FOM was calculated as error propagation of different contributions: the uncertainty on the pixel values was assumed less than 4%, while for the TLDs measurements an uncertainty of 10% was taken into account. For this reason a total standard deviation of 12% was considered for the FOM. As shown in Fig. 3, the FOM curve for mammography is quite flat (there is a difference of about 20% between the lowest and the highest FOM value), indicating a tolerance against non-optimal voltage setting [3]. Moreover, as shown in the Fig. 3, selecting an optimal voltage of 30 kV instead of 28 kV as suggested by the AEC, there is an increase of the FOM of about 14%. The presence of a maximum in the FOM curve for DBT seems more marked since there is a difference of about 40% between the
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Figure 4. FOM results obtained by MC simulations for 4.5 cm breast thick and a tumor mass detail (100% glandular composition) both for DBT and DM.
lowest and the highest FOM value. The results indicate that the reconstruction algorithm (in this case FBP method), as well as the presence of other sources of noise, could have some influence on the optimal voltage that maximizes the FOM with respect to the DM acquisition mode. Moreover the optimal voltage for a 50% glandular breast with a thickness of 4.5 cm found in these set of phantom measurements is in agreement with the AEC of the DBT acquisition mode. Concerning the DM manual acquisition mode, the best voltage found in this work differs with the AEC voltage value (also in DM the AEC chooses an optimal voltage of 28 kV). It is interesting to see how our results, are qualitatively in agreement also with the results showed by S.J. Feng et al. [2] (it is worth to say that in their work an Hologic system was used). In the S.J. Feng et al. study, the Hologic AEC settings chooses an optimal voltage of 29 and 28 kV for DBT and DM respectively for a 4 cm thick breast phantom and 50% glandular composition, as the one used in this study. Even if in these two works the same anode/filter combination and phantom are used, some slight differences could be in part explained by the different equipment used. Monte Carlo simulations The 2D simulated projections for each monochromatic energy (25 projections for each energy) were then reconstructed through the SART reconstruction method and the SDNR was calculated. The
simulated optimal energies that maximize the FOM, both in DM and DBT are shown in the Fig. 4. It can be seen that, in qualitative agreement with the results of the measured optimal voltages above discussed, there is an optimal monochromatic energy that maximizes the FOM, and in this case the maximum is the same for DM and DBT (20 keV). This trend is in agreement with the optimal voltage of the AEC of the system, since a 28 kV voltage is selected both for DBT and DM. Also, through the Siemens X-ray spectrum generator tool [12] it is possible to calculate the mean energy of the polychromatic spectrum. In this way, considering the mean energy of the 28 kV and 30 kV W/Rh polychromatic spectra (respectively 19.06 keV and 19.36 keV), the agreement of the simulation results with measurements ones in terms of the optimal energy that maximizes the FOM, is quite evident. The MC simulations were performed with a simplified detection system where only the quantum noise was considered. Nevertheless, these MC results show that this assumption is qualitative compatible with the AEC system results. Namely, looking at the AEC of the medical equipment, when changing from DM to DBT mode, the reconstruction algorithm, as well as other sources of noise, seems not to influence the optimal energy that maximizes the image quality parameter. We remark that in the measurements an FBP reconstruction method was used, whereas a SART method was used to reconstruct the 2D simulated projections in the MC study. Moreover even when iterative reconstruction methods are used, as for example in the IMS Giotto TOMO system, the same beam quality, as the one found in this study, is used for the same detection task considered in the present work [13]. Quantum limited noise check
Figure 5. Relative noise against detector dose. The result of the fit indicates that the system is not completely quantum nose limited (n ¼ 0.46431).
In order to check if the system used for measurements was quantum noise limited (as supposed by MC simulations), the relative noise for each flat-field image was plotted against the detector dose and a power fit (defined in the Eq. (7)) was performed (Fig. 5). The results indicate that the system is not purely quantum noise limited, since the n-value is 0.464 0.07. According the work of Bouwman et al. [11], if the n value differs from 0.5, the contribution of other noise sources could affect the quality of the image. In particular, if the n-value is lower than 0.5, this could mean that a high structured noise may be present in the system. In DBT, due to the 3D acquisition mode, the structural noise can be reduced. Nevertheless, according to a study based on a Noise Power Spectrum (NPS) analysis [14] which aimed to characterize the noise
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Figure 6. Experimental FOMs calculated in the 0 and 24 degree projection, respectively. The evaluation of the optimal voltage in these cases seems to be affected by other sources of noise.
texture, the structured noise in DBT is quite close to the DM one. According to this work’s phantom results, and taking also into account the uncertainties involved, it seems that in DBT, a higher structured noise is better compensated with a lower voltage setting (28 kV), whereas in DM a higher voltage setting (30 kV) appears to be more beneficial in maximizing the FOM. We want to stress here that this study is centered on the evaluation of the optimal energy that maximizes the image quality parameter and namely we are neglecting the quantitative variation of the FOM between the two different acquisition modes (DBT and DM). MC simulations showed that in a completely quantum noise limited system, the optimal energy does not change between DBT and mammography. Moreover, the presence of other sources of noise in the system could influence the optimal energy evaluation. The non-quantum limited characteristic of the system is quite visible when the single 2D
projections used in DBT for the reconstruction, are analyzed. In fact, calculating the optimal energy that maximizes the FOM in the 2D projections before the reconstruction step, it is possible to see how the FOM is no more sensitive to the optimal voltage in that kV interval. In Fig. 6, the 0 and 24 projections are showed as sample, and it is observed that the standard deviation on the FOM reaches an average value of about 15% because of the increasing pixel standard deviation which reaches a mean value of about 7%. In these cases, when the entrance dose levels range between 50 and 100 mGy, other sources of noises, as the electronic noise could affect the image quality. Instead, if analyzing the 2D projections obtained through MC simulations (see Fig. 7), where only quantum noise was taken into account, the FOM is still sensitive to the optimal energy. This occurs even if the maximum is different in the two projection angle considered (a maximum of 20 keV for the 0 projection was
Figure 7. MC FOMs calculated in the 0 and 24 degree projection respectively. In this case, the optimal energy at 0 projection was 20 keV, whereas for the 24 projection an optimal energy of 18 keV was evaluated.
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observed, whereas a maximum of 18 keV was found for the 24 projection). The effect of the anisotropy introduced by the DBT acquisition mode could introduce misregistration and additional noise in DBT reconstructions. Nevertheless, in terms of the optimal energy evaluation, our MC results showed that the final reconstructed image in DBT is not affected by this optimal energy shift in the different projections with respect to the DM case, just as happens with the AEC of the DBT/DM system. The situation becomes worse when real data are analyzed. As previously shown, the effect of other sources of noise (see Fig. 6) seems to affect in a major extent the optimal voltage evaluation in the single 2D projection. The slightly difference in the optimal voltage evaluation between DM and DBT could be explained by these additional noise propagation in the reconstruction process. Conclusions In this work we performed a comparison study about the optimal energy that maximizes the image quality parameter both in DBT and DM. The correct choice of the optimal energy for lesions detection is an important issue since allows to avoid useless delivered dose to the patients (by using energies lower than the optimal ones), or to avoid blurring in the final image (by using energies higher than the optimal ones). The measurements performed, showed that the optimal voltage with a W/Rh anode/filter combination for a 4.5 cm thick breast phantom of 50% glandular composition in DBT acquisition mode is 28 kV, whereas in DM the optimal voltage is 30 kV. On the other hand, the MC results suggest that the optimization AEC system works under the same hypothesis (quantum noise limited and no effect of the reconstruction method) undertaken in the MC simulations performed in this study. Namely, there is no variation in the optimal energy choice when considering the DBT or the DM for a 4.5 cm thick breast. This study presents several limitations. Firstly the 2D MC projections were reconstructed through a SART method, while the measured 2D projections were reconstructed through the FBP. This issue makes the results here presented only indicatives concerning the relation between the optimal energy that maximizes the image quality parameter and the reconstruction method. A second limitation of this MC work is the non-inclusion of the combined effect of the reconstruction algorithm together with other sources of noise on the optimal energy evaluation that maximizes the FOM. The inclusion of these effects in the MC model is quite complex and is beyond the aim of this work. Nevertheless, as shown in the phantom measurements, the possible combined effect above mentioned on the optimal energy evaluation for each detection task, could take to consider an optimal voltage for DBT
slightly lower than in DM. Consequently, accordingly to these results, the use of higher voltage values in DBT could be not justified for the image quality improving during a breast examination. Finally, in the optimization work here described, only one breast thickness was taken into account. In order to fully optimize a DBT/ DM acquisition system it will be important to perform further studies with other breast thicknesses and different lesion types. Despite these limitations, this work gives insights toward a deeper understanding about the optimal energy evaluation in DBT.
Acknowledgements The authors would like to thank the team of the Individual Monitoring Laboratory of the CTN/IST for TLDs reading and calibration, and A. Taibi for valuable discussions.
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