Monte Carlo assessment of coded aperture tool for breast imaging: a Mura-mask case study

Monte Carlo assessment of coded aperture tool for breast imaging: a Mura-mask case study 1 2 corresp first-author Corresponding author, okadri@cern.ch Corresponding author, okadri@cern.ch okadri@cern.ch 1 Department of Radiological Sciences. College of Applied Medical Sciences. King Saud University. PO Box 10219. Riyadh 11433, Saudi Arabia Department of Radiological Sciences. College of Applied Medical Sciences. King Saud University. PO Box 10219. Riyadh 11433, Saudi Arabia National Center for Nuclear Sciences and Technologies, 2020 Tunis, Tunisia National Center for Nuclear Sciences and Technologies, 2020 Tunis, Tunisia The main purpose of this work was to perform a rigorous computational study on scintimammography with a Mura-mask based on Monte Carlo simulation of voxelized breast phantoms. Three main objectives were addressed: (i) verification of Geant4 version 10.4, (ii) optimization of the imaging setup, and (iii) small tumor detection and localization. We successfully verified the Geant4-based imaging of a commonly used phantom in the field. We used a Mura-mask with a 41× 41 array pattern with adjustable thickness, material, and hole shape (box and cylinder); a low energy high resolution collimator with different hole shapes (cylinder and hexagon); and a voxelized breast phantom with different sizes (small, medium, and large) and glandularity percentages (low, medium, and high). We also compared the detector crystal outputs of CdZnTe and NaI(Tl). The simulation was followed by a deconvolution procedure, and the data (images) were statistically emphasized. Statistical metrics indicate that the Mura-mask (W material with 1.5 mm thickness and box holes) combined with a CdZnTe detector leads to the optimum point spread function. Finally, a preliminary study on small sized tumor detection and localization was conducted with different tumor-to-background ratios (from 2 to 12). Tumors with diameters of 5 and 8 mm could be detected, while those of 2 mm were undetectable. Nevertheless, this study enhances our understanding of the early detection of tumors in the field of scintimammography. Geant4 Voxelized Breast Phantom Scintimammography Mura-mask 1 Introduction 1 Global cancer statistics published in 2018 showed that the number of new cancer cases and cancer deaths worldwide are 18.1 and 9.6 million, respectively. Closely followed by lung cancer, breast cancer is the most commonly diagnosed cancer (11.6% of new cases) and the primary cause of cancer death (6.6%) in females [ 1 1 ]. However, over the past three decades, there has been a decline in breast cancer mortality thanks to early detection with improved screening, advances in treatment, and increased awareness. Within that context, scintimammography (SM) serves as a complementary procedure to mammography. The widely used radiopharmaceuticals for this technique are based on the 99m Tc tracer [ 2 2 ]. Moreover, the limitations in terms of image resolution due to current detection system capabilities (crystal, collimator, etc.) must be overcome to detect small sized tumors. Consequently, the detection of small sized tumors during breast imaging remains an important topic to be investigated. Among the existing techniques, Monte Carlo simulation is considered as the most suitable tool to mimic the particles moving through matter in a realistic scheme. To study the emission and transmission of photons through human tissue/organ, the simulation technique has been proved as a powerful complement. It helps to investigate the problem through simple and complex geometry models. Many modern codes, including MCNP [ 3 3 ], EGSnrc [ 4 4 ], PENELOPE [ 5 5 ], FLUKA [ 6 6 ]), and Geant4 [ 7 7 ] and its derivative GATE [ 8 8 ] are commonly applied for those purposes. Consequently, the realistic modeling of computational human organs/tissues with voxels was considered as a new era of research in the field of SM. Such models were successfully incorporated into MC simulation-based programs for more investigation and optimization [ 9 9 - 11 11 9-11 ]. Nowadays, researchers focus on the coded aperture imaging technique, where a mask array consisting of a pattern of transparent and opaque elements is placed in front of a position-sensitive detection plane [ 12 12 ]. A radiation source located somewhere within the field of view of the imager casts a shadow of the mask plane onto the detection plane. One of the most important considerations in coded aperture imaging is the mask design [ 13 13 ]. The main advantage of coded aperture imaging is the increased signal-to-noise-ratio (SNR) compared to that of the pinhole technique. Development of coded aperture techniques can balance the tradeoff between SNR and resolution [ 14 14 - 16 16 14-16 ]. Alnafea et al. [ 17 17 ] focused on the use of modified uniformly redundant array (Mura) [ 18 18 ] coded aperture methods in SM and found that a tumor-to-background (TBR) of 20:1 is required to visualize a 10 mm wide lesion. In nuclear medical imaging, as the reconstructed images from coded projections contain artifacts and suffer from poor spatial resolution in the longitudinal direction (defined from the detector towards the source), Martineau et al. [ 19 19 ] and Ikenna Odinaka et al. [ 20 20 ] worked on reducing artifacts, improving spatial resolution, and increasing the computation speed of the decoded images. To the best of our knowledge, this is the first rigorous study on Mura-masks for SM based on Monte Carlo simulation of voxelized breast phantoms. To address the problems outlined above, we propose a computational framework to realistically model a specific scintimammography imaging setup. It consists of the full modeling of a voxelized breast phantom with adjustable global shape (small, medium, and large) and glandularity percentage (25%, 50%, and 75%); a detection head (CdZnTe or NaI(Tl) crystal); a low energy high resolution (Lehr) collimator; and a Mura-mask tool. Our three main goals can be summarized as follows: (i) verification of Geant4, (ii) optimization of the setup, and (iii) small tumor detection and localization. Thus, we first conducted a rapid checkout of the Geant4-based imaging of a commonly used phantom in nuclear medicine and the attenuation behavior of a 99m Tc photon beam through W and Pb material sheets. Then, we discussed the optimization process by controlling some statistical metrics of the point spread function (PSF) for each situation. Finally, we investigated the tumor detectability under the optimum imaging conditions. This paper will be of great interest to doctors, technicians, students, and radiation physics researchers and can be considered as a continuation of radiotherapy research outside of imaging. 2 Materials and Methods 1 2.1 Monte Carlo simulation procedure 2 In the following subsections we will describe the "Picker Nuclear Thyroid Phantom" used for verification purposes of the adopted simulation and decoding methodologies. Then, a brief description of the 3D mathematical models of the breast will be provided. Moreover, the coded aperture (Mura-mask) and Lehr collimator used will be described. Next, we will group all components of the imaging modality. Finally, a description of the Geant4-based program used in this work will be provided. 2.1.1 Picker Nuclear Thyroid Phantom 3 Embedded into a sheet of Perspex material with dimensions 100 mm× 100 mm× 18.4 mm, the Picker phantom contains four nodules (three called "cold" and one called "hot") forming two lobes, as shown in Figure 1 Figure 1 . It is filled with a solution of water and a 99m Tc radioisotope such that the right-to-left uptake ratio is 2:1. The three cold nodules present no radioactivity, whereas the hot one has the same activity as the other lobe background, meaning it has double the lobe activity of a cold one. In the same figure, cold and hot nodules are colored with black and white, respectively. Moreover, the right and left lobes are colored with black and gray for clarity purposes [ 21 21 , 22 22 ]. To incorporate such irregular shape into the Monte Carlo simulation, we converted the phantom into voxels of dimension 0.25× 0.25× 18.4 mm. 2.1.2 Breast phantom 3 Based on the 3D mathematical models of the prone breast provided by Bliznakova et al. [ 23 23 ], we were able to generate nine of them. Each model, including skin, duct system, adipose, and glandular tissues, was adjustable in terms of size (small (S), medium (M), or large (L)) and glandularity percentage (low (L), medium (M), or high (H)). As shown in Figure 1(b) Figure 1(b) , the global dimensions for S, M, and L are 40 mm× 80 mm× 80 mm, 55 mm× 110 mm× 130 mm and 80×140× 180 mm, respectively, and the glandularities for L, M, and H are 25%, 50% and 75%, respectively. Hereafter, we use the above abbreviations to refer to each model; for example, the small breast model with low glandularity is referred to as SL. Each model was voxelized with a 1 mm× 1 mm× 1 mm voxel size. The densities and elemental compositions of the materials used are listed in Table 1 Table 1 . 1 1 Material 1 1 Density(g/cm 3 ) 1 1 H 1 1 C 1 1 N 1 1 O 1 1 Remains 1 1 Adipose 1 1 0.93 1 1 11.2 1 1 61.9 1 1 1.7 1 1 25.1 1 1 0.1 1 1 Glandular/Duct 1 1 1.04 1 1 10 1 1 18.4 1 1 3.2 1 1 67.9 1 1 0.5 1 1 Skin 1 1 1.09 1 1 10 1 1 20.4 1 1 4.2 1 1 64.5 1 1 0.9 2.1.3 Mura-mask 3 In this work, we used a Mura-mask with a 41× 41 array pattern. It has a fixed hole distribution and adjustable thickness (from 0.25 to 2.5 mm), holder material (W or Pb), and hole shape (box or cylinder). Each box shaped hole has a facet size of 2 mm × 2 mm and each cylinder shaped one has a diameter of 2 mm. Similarly to the desired mask, as described in the literature, it contains 50% open/close area, i.e., the same surface area of gamma-ray-opaque and gamma-ray-transparent zones ( Fig. 2(b) Fig. 2(b) ). The overall shape has dimensions of 82 mm× 82 mm, embedded into a 600 mm × 600 mm opaque holder with adjustable thickness. A more detailed description was given by Alnafea et al. [ 17 17 ]. 2.1.4 Lehr collimator 3 During this study, the Lehr collimator was simulated for comparison purposes. It consisted of a regular distribution of hexagonal holes along a lead sheet with dimensions 328 mm × 328 mm × 35 mm. Each hexagonal hole had an inner diameter of 1.5 mm and a septa thickness of 0.2 mm, forming a collimator structure with a matrix array of 222× 192 holes. Cylindrical hole radii were adjusted to have the same area as the hexagonal ones. More detailed descriptions were provided by Alfuraih et al. [ 9 9 ] and Vieira et al.[ 25 25 ]. 2.1.5 Imaging Modality 3 The detection system, including the Mura-mask/Lehr collimator, crystal detector, and backscatter compartment, formed the main part of the simulation procedure in this work, as shown in Fig. 2(a) Fig. 2(a) . The adjustable material of the crystal detector, NaI(Tl) or CdZnTe, has a surface of 328× 328 mm and a thickness of 9.5 and 5 mm, respectively, as provided elsewhere [ 17 17 ]. The detector was pixelated in with a 1 mm× 1 mm pixel size. NaI(Tl) material has a density of 3.7 g/cm 3 and three elemental compounds of Na (15.2%), I (83.8%), and Tl (1%) according to Garcia et al. [ 26 26 ]. Cadmium zinc telluride was modeled as three elemental compounds of Cd (36.81%), Zn (21.41%), and Te (41.78%) with a density of 5.78 g/cm 3 [ 27 27 ]. The backscatter compartment was made of Pyrex material and had dimensions of 328 mm × 328 mm × 68 mm. 2.1.6 Geant4-based program 3 As shown in Fig. 2(a) Fig. 2(a) , the major axis of the breast phantom was set parallel to the XY plane, and the object-to-mask distance was measured between their centers. The Lehr collimator was set in front of the crystal detector. Three spherical tumors characterized by the same elemental compositions and densities of the breast tissues with diameters of 8, 5, and 2 mm were included at three different depths. The positions were chosen to simulate a deeper scenario, where tumors are located on the X axis ( Z =0), a superficial scenario, where they are located close to the phantom surface, and a third scenario that lies between the two. Note that for all scenarios, Z =0, and the X and Y coordinates change. We placed the tumor with a diameter of 8 mm at the base of the breast phantom, whereas the 2 mm diameter tumor was placed close to the top of the breast phantom (nipple), and the 5 mm diameter tumor was placed between both locations. During all simulations, we activated the Bremsstrahlung, ionization, and multiple scattering models for electrons with an energy threshold of 990 eV, allowing almost full tracking of particle history. For the photon particles, we activated the Compton effect, the Photoelectric effect, and Rayleigh scattering with a cutoff energy of 990 eV. The standard electromagnetic physics options governed by the specific physics builder "G4EmStandardPhysics" were used to fulfill our purposes. Thanks to the multithreading option provided by Geant4 [ 28 28 , 29 29 ], all the simulations had a reasonable run time, despite the complexity of the experimental setup. Moreover, we utilized another tool for the simulation of the large number of voxels (breast phantoms, Mura-mask, and Lehr collimator) called nested parameterization owned by the class "G4VNestedParameterization", which allows the memory allocated by hardware to be minimized during the execution phase of the simulation. For all the cases, we fixed the mask-to-detector distance to be three times the source-to-mask distance in order to have a magnification factor of 3.0 for better image resolution of this near-field and medium phantom size application. Energy deposition of particles in the detector crystal was used to form coded images. We carried out our simulations on laptops (for testing) and two Dell Precision T7610 workstations, each with a 40-core Intel Xeon E5-2680v2 CPU at 2.80 GHz and 256 GB RAM. The operating system used for the management of all workflow was Ubuntu 14.04. The number of generated primary particles exceeded 2× 10 9 , as we focused the generation towards the Mura-mask or the Lehr collimator only. In our case, the number of detected counts (primary particles) through the Mura-mask was half of the generated primaries, as the open area (holes) formed 50% of the field of view. This gave us a statistical uncertainty of no more than 1% for all studied cases, with run time ranging from 20 min to more than 7 h. 2.2 Data Analysis Procedure 2 2.2.1 Image deconvolution 3 Basically, the coded aperture imaging procedure involved the construction of the decoding matrix ( G ij ) corresponding to the mask-array pattern ( A ij ), in order to reconstruct the image M from a projected one, P , in the following way [ 30 30 , 31 31 ]: <math display="block" id="M1"><mrow><msub><mi>G</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mrow><mo>{</mo><mrow><mtable columnalign="right"><mtr columnalign="right"><mtd columnalign="right"><mn>1</mn></mtd><mtd columnalign="right"><mrow><mtext>if</mtext></mrow></mtd><mtd columnalign="right"><mrow><mi>i</mi><mo>+</mo><mi>j</mi><mo>=</mo><mn>0,</mn></mrow></mtd></mtr><mtr columnalign="right"><mtd columnalign="right"><mn>1</mn></mtd><mtd columnalign="right"><mrow><mtext>if</mtext></mrow></mtd><mtd columnalign="right"><mrow><msub><mi>A</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mn>1,</mn><mo stretchy="false">(</mo><mi>i</mi><mo>+</mo><mi>j</mi><mo>≠</mo><mn>0</mn><mo stretchy="false">)</mo><mn>,</mn></mrow></mtd></mtr><mtr columnalign="right"><mtd columnalign="right"><mrow><mo>−</mo><mn>1</mn></mrow></mtd><mtd columnalign="right"><mrow><mtext>if</mtext></mrow></mtd><mtd columnalign="right"><mrow><msub><mi>A</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mn>0,</mn><mo stretchy="false">(</mo><mi>i</mi><mo>+</mo><mi>j</mi><mo>≠</mo><mn>0</mn><mo stretchy="false">)</mo><mn>.</mn></mrow></mtd></mtr></mtable></mrow></mrow></mrow></math> 2.2.2 Statistical parameters 3 For a meaningful comparison of two given images with X and Y signals and x i and y i pixel values, we used an ImageJ plugin, published by the Biomedical Imaging Group [ 32 32 ] to calculate the following statistical parameters [ 33 33 ]: <math display="block" id="M2"><mrow><mi>S</mi><mi>N</mi><mi>R</mi><mo>=</mo><mn>10</mn><mi>log</mi><mrow><mo>[</mo><mrow><mfrac><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover></mstyle><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup></mrow><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover></mstyle><msup><mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><msub><mi>y</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></mrow></mfrac></mrow><mo>]</mo></mrow><mn>,</mn></mrow></math> <math display="block" id="M3"><mrow><mi>P</mi><mi>S</mi><mi>N</mi><mi>R</mi><mo>=</mo><mn>10</mn><mi>log</mi><mrow><mo>[</mo><mrow><mfrac><mrow><mi>max</mi><msup><mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></mrow><mrow><mfrac><mn>1</mn><mi>N</mi></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover></mstyle><msup><mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><msub><mi>y</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></mrow></mfrac></mrow><mo>]</mo></mrow><mn>,</mn></mrow></math> <math display="block" id="M4"><mrow><mi>M</mi><mi>A</mi><mi>E</mi><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover></mstyle><mo>|</mo><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><msub><mi>y</mi><mi>i</mi></msub><mo>|</mo><mn>,</mn></mrow></math> <math display="block" id="M5"><mrow><mi>R</mi><mi>M</mi><mi>S</mi><mi>E</mi><mo>=</mo><msqrt><mrow><mfrac><mn>1</mn><mi>N</mi></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover></mstyle><msup><mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><msub><mi>y</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></mrow></msqrt><mn>,</mn></mrow></math> where SNR, PSNR, MAE, and RMSE represent signal-to-noise ratio, peak of SNR, mean absolute error, and root mean square error. N refers to the total number of pixels per image; here, it is equal to 328× 328. We also introduced a parameter called quality factor (QF) to select the configuration providing the best PSF. For a reconstructed image M, as the PSF is proportional to contrast ( C ), SNR , maximum pixel value (Max), and the inverse of the full width at half maximum (FWHM), we calculated the parameter as follows: <math display="block" id="M6"><mrow><mi>Q</mi><mi>F</mi><mo>=</mo><mfrac><mrow><mi>C</mi><mo>×</mo><mi>S</mi><mi>N</mi><mi>R</mi><mo>×</mo><mi>M</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>F</mi><mi>W</mi><mi>H</mi><mi>M</mi></mrow></mfrac></mrow></math> For a given region of interest, the contrast was calculated according to the same area (of the same image) considered as background. 3 Results and Discussion 1 3.1 Geant4 Evaluation 2 The modeling of the 99m Tc photon beam with a Gaussian with a mean energy of E 0 =140.5 keV and standard deviation of <math id="M7"><mrow><mi>σ</mi><mo>=</mo><mn>1</mn><mo>/</mo><msqrt><mrow><msub><mi>E</mi><mn>0</mn></msub></mrow></msqrt></mrow></math> allowed us to simulate the attenuation ability of commonly used materials (W and Pb) for coded aperture masks. As shown in Fig. 3 Fig. 3 , a W thickness of 1.5 mm can attenuate the photon beam to approximately 99%, which validates studies that assume the photon beam to be monoenergy with E 0 =140 keV. To evaluate the Geant4-based simulation of the imaging procedure using the Mura-mask (41 × 41 array pattern), Figure 4 Figure 4 shows the decoded image of the simulated shadow of the Picker thyroid phantom. This figure clearly shows the four nodules (three cold and one hot). These findings confirm the right-to-left lobe uptake of 2:1, allowing us to conclude that we can safely continue to simulate such targets using the Mura-mask tool. However, the high background, which is normally used in far-field applications, such as astronomy, constitutes a limitation of our research; thus, there is a need to thoroughly investigate that topic. Such background may be caused by two factors: secondary particles scattered by the Mura-mask and improper deconvolution method. As a preliminary attempt, we aimed to conduct simulations without taking into account the energy deposited by secondaries by applying an energy window of 10%, and the results are shown in Fig. 4 Fig. 4 . However, for the main objectives of this study, we can be satisfied with our findings. 3.2 PSF Optimization 2 Figure 5 Figure 5 presents a set of three illustrative examples of simulated and decoded images corresponding to the PSF for mask thicknesses of 1.0, 1.5, and 2.0 mm. The CZT crystal detector and Mura-mask with box shaped holes located 10 cm from the source were used. Figure 6 Figure 6 shows the previously defined statistical parameter QF eqQF calculated for 36 studied cases. These values resulted from the simulation and decoding of the PSF with adjustment of the detector crystal (CZT/NaI), Mura-mask hole shape (box/cylinder), mask thickness (0.25/0.5/1/1.5/2/2.5 mm), and source-to-mask distance (10/12/ 14cm). Our findings confirm the choice of 1.5 mm as the optimum mask thickness for the W material (highest QF value). Also, as concluded by many works [ 17 17 ], we confirmed that the CZT crystal detector has better performance than NaI(Tl) for this kind of imaging modality. Moreover, the box shaped mask holes presented better QF than the cylinder ones. This can be explained by more loss of useful data of the shadow when using circle (cylinder) in place of square (box) shaped holes. We conclude that the optimum PSF values can be acquired by the CZT detector crystal and 1.5 mm Mura-mask with box shaped holes. Also, 12 cm was found to be the best source-to-mask distance. Additionally, a comparison of the Mura-mask to the Lehr collimator with cylindrical/hexagonal hole shapes for the above optimum parameters is shown in Fig. 7 Fig. 7 . For that purpose, we simulated the nine realistic breast phantoms (SL/SM/SH/ML/MM/MH/LL/LM/LH) with a uniform radioactivity distribution (no tumors included). The plotted statistical parameters, according to eqSNR,eqPSNR,eqMAE,eqRMSE, reveal first that when comparing Mura-mask to Lehr collimator (cylinder or hexagonal holes shape), they behave in the same manner. This is clear from our previous findings ( Fig. 7 Fig. 7 ) that the box shape leads to an approximate tenfold order of magnitude (in terms of QF) compared to the cylindrical shape. Additionally, when studying the effect of the breast phantom shape and glandularity percentage, we observed an almost constant SNR and descending and ascending behaviors of PSNR, MAE, and RMSE. We can observe that the glandularity percentage decreased the PSNR, which confirms the theory of particle interaction through matter explained by the fact that glandular and adipose tissue densities are 1.04 and 0.93 g/cm 3 , respectively, according to Hammerstein et al. [ 34 34 ]. 3.3 Tumor Detection and Localization 2 Due to the limitations of the field of view and the z-depth, we are limited in this case to small and medium phantom shapes. In particular, we studied the SL and MM cases as typical examples. Figure 8 Figure 8 shows the computed contrast, calculated as the ratio of tumor-to-background signals, for different tumor sizes (8 mm (a), 5 mm (b), and 2 mm (c)), locations (position 1/2/3), and TBRs (from 2 to 12). We found that tumors with diameters of 8 and 5 mm can be observed for the MM case at any position and for any TBR value, whereas the tumor size of 2 mm is better detected for the SL case. For the SL phantom and for 8 mm, 5 mm, and 2 mm tumor size, the average values and standard deviations of the contrast were 0.65 ± 0.02, 0.75 ± 0.02, and 0.99± 0.03, respectively. For the MM phantom with 8 mm, 5 mm, and 2 mm tumor size, the average values and standard deviations of contrast were 1.75 ± 0.05, 1.07 ± 0.04, and 0.85± 0.03, respectively. The computed statistical parameters are listed in Table 2 Table 2 for the same conditions. For that, we take the decoded image with TBR=25 as a reference, for each possible couple of phantom type and tumors position. The degradation of MAE and RMSE, for a given case, going from TBR=2 to 12, is seen and logically explained by the closeness to the reference image. Also, for the same couple of phantom type and TBR, MAE and RMSE increased from positions 1 to 2 to 3. 1 1 Phantom 1 1 Position 1 1 TBR 1 1 SNR(dB) 1 1 PSNR(dB) 1 1 RMSE 1 1 MAE 1 1 SL 1 1 1 1 1 2 1 1 24.3 1 1 33.4 1 1 2.7E6 1 1 1.9E6 1 1   1 1   1 1 3 1 1 24.6 1 1 33.8 1 1 2.5E6 1 1 1.8E6 1 1   1 1   1 1 4 1 1 24.9 1 1 34.0 1 1 2.5E6 1 1 1.7E6 1 1   1 1   1 1 5 1 1 25.5 1 1 34.7 1 1 2.3E6 1 1 1.6E6 1 1   1 1   1 1 6 1 1 25.9 1 1 35.0 1 1 2.2E6 1 1 1.6E6 1 1   1 1   1 1 8 1 1 26.5 1 1 35.7 1 1 2.0E6 1 1 1.5E6 1 1   1 1   1 1 10 1 1 27.5 1 1 36.6 1 1 1.8E6 1 1 1.3E6 1 1   1 1   1 1 12 1 1 28.4 1 1 37.5 1 1 1.6E6 1 1 1.2E6 1 1   1 1   1 1 Mean 1 1 26.0 1 1 35.1 1 1 2.2E6 1 1 1.6E6 1 1   1 1   1 1 σ 1 1 1.4 1 1 1.4 1 1 3.3E5 1 1 2.1E5 1 1   1 1 2 1 1 2 1 1 22.9 1 1 31.5 1 1 3.2E6 1 1 2.3E6 1 1   1 1   1 1 3 1 1 23.2 1 1 31.9 1 1 3.1E6 1 1 2.2E6 1 1   1 1   1 1 4 1 1 23.7 1 1 32.4 1 1 2.9E6 1 1 2.1E6 1 1   1 1   1 1 5 1 1 24.0 1 1 32.6 1 1 2.8E6 1 1 2.0E6 1 1   1 1   1 1 6 1 1 24.4 1 1 33.1 1 1 2.7E6 1 1 2.0E6 1 1   1 1   1 1 8 1 1 25.2 1 1 33.9 1 1 2.4E6 1 1 1.8E6 1 1   1 1   1 1 10 1 1 26.2 1 1 34.8 1 1 2.2E6 1 1 1.6E6 1 1   1 1   1 1 12 1 1 27.1 1 1 35.8 1 1 2.0E6 1 1 1.5E6 1 1   1 1   1 1 Mean 1 1 24.6 1 1 33.2 1 1 2.7E6 1 1 1.9E6 1 1   1 1   1 1 σ 1 1 1.4 1 1 1.4 1 1 4.0E5 1 1 2.7E5 1 1   1 1 3 1 1 2 1 1 19.2 1 1 27.6 1 1 4.9E6 1 1 3.8E6 1 1   1 1   1 1 3 1 1 19.6 1 1 27.9 1 1 4.7E6 1 1 3.6E6 1 1   1 1   1 1 4 1 1 19.9 1 1 28.3 1 1 4.6E6 1 1 3.5E6 1 1   1 1   1 1 5 1 1 20.4 1 1 28.7 1 1 4.3E6 1 1 3.3E6 1 1   1 1   1 1 6 1 1 20.8 1 1 29.1 1 1 4.1E6 1 1 3.1E6 1 1   1 1   1 1 8 1 1 21.7 1 1 30.1 1 1 3.7E6 1 1 2.8E6 1 1   1 1   1 1 10 1 1 22.7 1 1 31.0 1 1 3.3E6 1 1 2.5E6 1 1   1 1   1 1 12 1 1 23.7 1 1 32.0 1 1 3.0E6 1 1 2.3E6 1 1   1 1   1 1 Mean 1 1 21.0 1 1 29.3 1 1 4.1E6 1 1 3.1E6 1 1   1 1   1 1 σ 1 1 1.5 1 1 1.5 1 1 6.56E5 1 1 4.9E5 1 1 MM 1 1 1 1 1 2 1 1 28.4 1 1 36.8 1 1 1.2E6 1 1 8.9E5 1 1   1 1   1 1 3 1 1 28.7 1 1 37.1 1 1 1.2E6 1 1 8.5E5 1 1   1 1   1 1 4 1 1 28.9 1 1 37.3 1 1 1.1E6 1 1 8.5E5 1 1   1 1   1 1 5 1 1 29.1 1 1 37.5 1 1 1.1E6 1 1 8.4E5 1 1   1 1   1 1 6 1 1 29.1 1 1 37.5 1 1 1.1E6 1 1 8.3E5 1 1   1 1   1 1 8 1 1 29.6 1 1 38.0 1 1 1.1E6 1 1 8.0E5 1 1   1 1   1 1 10 1 1 30.0 1 1 38.5 1 1 1.0E6 1 1 7.6E5 1 1   1 1   1 1 12 1 1 30.1 1 1 38.5 1 1 9.9E5 1 1 7.6E5 1 1   1 1   1 1 Mean 1 1 29.2 1 1 37.7 1 1 1.1E6 1 1 8.2E5 1 1   1 1   1 1 σ 1 1 0.6 1 1 0.6 1 1 7.2E4 1 1 4.2E4 1 1   1 1 2 1 1 2 1 1 27.6 1 1 35.6 1 1 1.3E6 1 1 1.0E6 1 1   1 1   1 1 3 1 1 27.9 1 1 35.9 1 1 1.3E6 1 1 1.0E6 1 1   1 1   1 1 4 1 1 28.0 1 1 36.1 1 1 1.3E6 1 1 1.0E6 1 1   1 1   1 1 5 1 1 28.2 1 1 36.3 1 1 1.2E6 1 1 9.8E5 1 1   1 1   1 1 6 1 1 28.4 1 1 36.4 1 1 1.2E6 1 1 9.6E5 1 1   1 1   1 1 8 1 1 28.9 1 1 37.0 1 1 1.1E6 1 1 9.0E5 1 1   1 1   1 1 10 1 1 29.3 1 1 37.3 1 1 1.1E6 1 1 8.6E5 1 1   1 1   1 1 12 1 1 29.9 1 1 38.0 1 1 1.0E6 1 1 8.0E5 1 1   1 1   1 1 Mean 1 1 28.5 1 1 36.6 1 1 1.2E6 1 1 9.5E5 1 1   1 1   1 1 σ 1 1 0.7 1 1 0.7 1 1 9.9E4 1 1 7.8E4 1 1   1 1 3 1 1 2 1 1 26.3 1 1 34.4 1 1 1.5E6 1 1 1.2E6 1 1   1 1   1 1 3 1 1 26.6 1 1 34.7 1 1 1.5E6 1 1 1.2E6 1 1   1 1   1 1 4 1 1 26.8 1 1 34.9 1 1 1.4E6 1 1 1.2E6 1 1   1 1   1 1 5 1 1 27.3 1 1 35.4 1 1 1.4E6 1 1 1.1E6 1 1   1 1   1 1 6 1 1 27.5 1 1 35.5 1 1 1.3E6 1 1 1.1E6 1 1   1 1   1 1 8 1 1 27.8 1 1 35.9 1 1 1.3E6 1 1 1.0E6 1 1   1 1   1 1 10 1 1 28.3 1 1 36.4 1 1 1.2E6 1 1 9.8E5 1 1   1 1   1 1 12 1 1 28.9 1 1 37.0 1 1 1.1E6 1 1 9.1E5 1 1   1 1   1 1 Mean 1 1 27.4 1 1 35.5 1 1 1.3E6 1 1 1.1E6 1 1   1 1   1 1 σ 1 1 0.8 1 1 0.8 1 1 1.3E5 1 1 1.0E5 Also, from position 1 to 3, the same remark is valid for both cases of SL and MM (referring to average and standard deviation values provided in the same table). Such behave can be explained by the tumor depth within the phantom, as position 1 corresponds to the deeper one, and position 3 corresponds to the one closer to the breast phantom skin. 4 Conclusion 1 Nowadays, the need for a Monte Carlo simulation technique for breast imaging is obvious in terms of prediction and depth assessment of existing scenarios. Due to the still pending topic of small sized tumor detection, the current study can be considered as an extension of previous works, dealing with the of a Mura-mask for breast imaging to overcome such difficulty in a realistic setting. A Geant4-based simulation of 3D voxelized realistic breast phantoms (small, medium, and large) including tumors with different sizes (8, 5, and 2 mm diameter) and locations (near skin layer, at the central axis, and between them) was conducted. For verification purposes, we successfully checked the imaging of a commonly used phantom for nuclear medicine (Picker Nuclear Thyroid Phantom). 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DOI: 10.1148/130.2.485 http://doi.org/10.1148/130.2.485 Absorbed radiation dose in mammography 10.1007/s41365-019-0682-3 This work was supported by The National Plan for Science, Technology and Innovation (MAARIFAH), King Abdulaziz City for Science and Technology, Kingdom of Saudi Arabia, Award Number (12-MED2516-02). 2019-04-19 2019-06-21 2019-06-26 2019-10-22 2019-11-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2019 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-019-0682-3 http://dx.doi.org/10.1007/s41365-019-0682-3 . 2019 Nuclear Science and Techniques 11 30