Physical breast phantoms can be a valuable asset for the development, optimization and evaluation of X-ray modalities for breast imaging. Apart from quality control and testing of already existing devices, the use of physical phantoms can provide essential information for the design and development of new imaging techniques. A key factor reigniting interest in the construction of breast phantoms stems from emerging three-dimensional X-ray imaging modalities, and the need for their evaluation and further optimization. Phantoms can serve as testing objects for adjusting acquisition geometries and parameters, provide feedback on reconstruction algorithm accuracy, and enable image quality evaluation and dosimetric measurements. Additionally, in the final step towards clinical practice, physical phantoms can prove to be a helpful tool for better designing clinical trials, limit human involvement only to necessary and thus reduce the associated costs and extra irradiation [1, 2].

Several physical phantoms for mammography have been reported in the literature [3-7]. In most of them, pοlymethyl methacrylate (PMMA) and epoxy resins are used as suitable materials mimicking the breast tissues. A thorough review of breast phantoms for X-ray imaging, which includes both physical and computerized models (software phantoms), is reported by Glick et al. [8]. Most of the developed physical breast phantoms address 2D imaging, such as the Rachel anthropomorphic phantom (Gammex 169, Gammex Inc., Middleton, WI) [7] or the TORMAX (Leeds Test Objects) [6] containing low and high contrast features surrounded by homogeneous background, while very few could be used for 3D imaging modalities. Breast Tomosynthesis (BT) is one such modality allowing pseudo-three-dimensional imaging of the breast, with a widely accepted diagnostic value [9, 10]. The influence of overlapping tissues, naturally existing in 2D mammography and possibly limiting the visibility of an abnormality, is effectively reduced in BT. Several software phantoms with a heterogeneous background suitable for BT have been investigated [11-16] and used for assessment and optimization studies [17-19]. Among the physical phantoms that have been developed, a phantom modeling of the non-uniform breast structure is the BR3D (CIRS Inc., Norfolk, VA, USA) [20]. This phantom consists of semicircular slabs with an equal thickness of 1cm and is made of two tissue-equivalent materials swirled together, corresponding to a 50/50 mixture of glandular and adipose tissue. In general, most of the commercially available physical phantoms do not reflect the heterogeneous appearance of breast tissue, nor do have they features embedded in different depths, which make their suitability as testing objects for BT highly questionable.

However, BT similarly to 2D mammography, is an imaging modality based on the attenuation of X-ray beams. Thus, in the range of energies suitable for screening, the difference in the attenuation coefficients between healthy and cancerous breasts is relatively small, resulting in poor tumor contrast. Phase contrast (PhC) imaging is an emerging technique that can enhance contrast at the boundaries of the structures due to phase shift arising from the difference in the refractive properties between the two materials [21-23]. This imaging technique is based not only on X-ray attenuation but also on the X-ray phase change arising from diffraction and refraction effects during X-ray scattering. Phase contrast takes place at the boundaries between materials whose refractive indices differ from each other. Tissues composed of low Z-elements, such as breast masses, produce low absorption contrast but considerable phase contrast [24, 25]. As a result, better visualization of possible abnormalities is achieved and especially in their edges, providing easier identification of lesions, characterization and finally a diagnosis. The use of PhC mode for the acquisition of BT images could combine the advantages of both techniques, producing edge-enhanced images with limited tissue overlapping. Towards this direction, a few preliminary studies using in-line (free space propagation) mode PhC tomosynthesis for imaging the breast have been conducted with simple homogeneous phantoms [26, 27], while a feasibility study including phantoms with heterogeneous texture as well was carried out by Bliznakova et al., at a Synchrotron radiation facility [28]. In a recent study, conducted also at a Synchrotron facility, we have reported on the feature edge enhancement that was observed in PhC tomosynthesis images acquired using a highly heterogeneous physical phantom composed of an egg white part and lard [29]. However, PhC imaging with the use of synchrotron radiation is far from being applicable in every day clinical practice. Instead, PhC imaging employing high-resolution detectors combined with polychromatic microfocus X-ray tubes could solve some of the practical limitations, like geometry and production of monochromatic beam [30, 31]. Photon counting detectors like Medipix have the appropriate resolution for PhC breast imaging, and therefore, motivate further studies for future clinical use [32]. Several investigations on low contrast objects were performed, showing their suitability for X-ray radiography of soft tissues and low contrast objects [33].

The progress in 3D printing brings the potential for creating low-cost breast phantoms directly from the software 3D models. Ongoing research focuses on improving printing methods and limitations concerning the precision or ability to print different materials simultaneously, but also on finding suitable mimicking materials. In the X-ray breast imaging field, there have been a few studies investigating the suitability of 3D printing materials as tissue substitutes, in terms of their attenuation coefficients in the mammographic energy range for the development of physical breast phantoms [34-36]. In a recent study, Ivanov et al. [37], investigated the suitability of seven thermoplastic polymers (ABS, Brick, Hybrid, Nylon, PET-G, PLA and PVA) and ten polymer resins (Black, Clear, Flex, Gray, NDBase, NDC+B, NDCast, NDSG, Tough, White). Attenuation coefficients and refractive index decrements of the materials were found to be in the range of 30keV to 60keV, to address the higher energies currently used in PhC [25, 38]. This study [37] showed that ABS combined with resins might be a good representation of adipose and glandular tissue for PhC imaging. Esposito et al. [39], focused on the investigation of the refractive index decrement of the previously mentioned 3D printed materials, with the evaluation based on the phase retrieval algorithm described by Paganin et al. [40]. The models used in 3D printing were created using appropriate designing software or derived from clinical images. Bucking et al. [41], developed printable models for ribs, liver and lung from medical imaging data and described the general workflow followed for creating a 3D printed phantom from CT images or other imaging modalities like MRI. Breast 3D printed models suitable for digital mammography, that are also based on clinical images, have been recently presented by Schopphoven et al. [42]. An open-source code has been introduced by Badal et al. [43], for the creation of such phantoms intended for 2D X-ray imaging, from printable datasets.

The 3D printing techniques can be used either for the preparation of the whole phantom directly, or partly by printing the mold and then filling it with conventional materials to build the final phantom [44]. For CT applications, simple geometric phantoms have been developed with the direct printing method [45-48] using different thermoplastic polymer materials or polymer resins. Moreover, phantoms with the appearance of specific organs are also reported, including the breast [49], spine [50], head [51] or even the whole body [52]. A thorough review of developed phantoms using 3D printing for different body parts and a wide range of imaging modalities (mammography, CT, MRI, PET, Ultrasound, or combinations), is reported by Filippou and Tsoumpas [44]. In a recent review, Tino et al. [53], focused on 3D printed phantoms for X-ray imaging and dosimetry, stressing the growing interest in 3D printing techniques, given their increasing availability and flexibility to efficiently provide customized phantoms or other radiotherapy tools. Specifically for the breast, there are very few phantoms reported with more than one mimicking materials to represent breast tissues involving 3D printing methods. Carton et al. [54], followed the approach of combining 3D printed components and resins that were then manually filled in. Kiarashi et al. [49], developed a 3D printed breast phantom with two variations, the 'Singlet' and 'Doublet'. The latter was a phantom created using two different 3D printed materials to represent fibroglandular and adipose tissues, respectively, while the former involved only one for the fabrication of the mold and conventional materials that were then manually filled in.

Although several physical phantoms have been developed using 3D printing, very little has been done on breast imaging phantoms suitable for X-ray modalities, including both 2D mammography and advanced 3D methods like tomosynthesis with PhC. Thorough studies leading to a specialized physical phantom would enable optimization of this new imaging modality and evaluation of its potential advantages. Our group at the University of Patras has developed software tools and algorithms [11, 55-60] facilitating advanced X-ray breast imaging studies, including tomosynthesis and PhC and has performed simulations [18, 61, 62] and evaluation studies using a Synchrotron facility [29, 63-66]. In the current work, we present physical breast phantoms that can be used for further development and evaluation of such X-ray imaging modalities. Our main objective was to develop phantoms suitable for PhC imaging employing 3D printing techniques. The approach followed was to use a range of suitable 3D printable materials for the preparation of the mold, which is then filled with conventional materials, to represent fibroglandular and adipose breast tissues. Additionally, details describing breast abnormalities 'were embedded in different depths to allow also for tomosynthetic studies. Within our long term goal, we aim to use the developed 3D printed physical breast phantoms to perform extensive PhC tomosynthesis studies, employing high resolution photon counting detectors combined with a polychromatic microfocus X-ray tube setup.

The following graphs show the difference in the linear attenuations (Δμ_m1,paraƒƒin) and refractive index decrements (Δδ_m1,paraƒƒin) at photon energies 30 keV, 45 keV and 60 keV, for all the investigated materials with respect to the paraffin, as calculated from Eq. (1) and Eq. (2) (Section 2.1). The values (Δμ_gland,adipose) and (Δδ_gland,adipose) were also calculated for these energies and are presented in the graphs with the dotted lines.

Fig. (5). Difference % in μ (on the left) and δ (on the right) for the selected 3D printing materials with respect to paraffin at 30 keV, 45keV and 60keV. Dotted lines present the values Δμgland,adipose and Δδgland,adipose, for the same energies.

In Fig. (6), some tomographic slices of the phantoms created following the procedure described in Section 2.2, are shown indicatively. In the first column, Figs. (6a and 6c) correspond to the 3D models presented in Figs. (1b and 1c), respectively. In the second column, Fig. (6b and 6d) show two different slices depicting the complex background created from the combination of one of these models (Fig. 1b) with the complex-patterned layer (Fig. 1d).

Fig. (6). Tomographic slices of created phantoms without the complex layer (first column) and with the complex layer embedded (second column).

In Fig. (7), ROIs focusing on the inserted features of interest are depicted. Specifically Fig. (7a) shows the radiographic appearance of CaCO³ specs mimicking a cluster of high-contrast microcalcifications, while Fig. (7b) shows a nylon sphere of 3,2mm representing a low-contrast mass.

In Fig. (8), ROIs of planar images from the phantoms are presented. These images were acquired from phantoms with different combinations of paraffin/resin materials (row a) clear, b) tough and c) flex), at two ODDs 5cm (column i) and 35cm (column ii). In the first column, images based on the attenuation contrast are illustrated, whereas in the second column phase contrast effects contribute to the images. Also in the ROIs of Figs. (8b and 8c), the nylon spheres representing breast masses that were embedded into the base material (paraffin) of the phantoms, are depicted.

Fig. (7). Features of interest mimicking breast abnormalities a) CaCO3 specs representing a cluster of microcalcifications b) nylon sphere (3.2mm) representing a mass.

Fig. (8). ROIs of planar images acquired at ODD 5cm (column i) and ODD 35cm (column ii) from the phantoms with resins, a) Clear, b) Tough and c) Flex.

Similarly, in Fig. (9) ROIs of the images acquired from phantoms with different combinations of paraffin/thermoplastic materials (row a) PET-G, (row b) Nylon, (row c) ABS and (row d) Hybrid at two ODDs, 5cm (column i) and 35cm (column ii) are presented. The two ROIS Figs. (9b and 9c) focus on the low-contrast masses, while Fig. (9a) shows the nylon fiber.

Fig. (9). ROIs of planar images acquired at ODD 5cm (column i) and ODD 35cm (column ii) from the phantoms with thermoplastic materials, a) PET-G, b) Nylon, c) ABS and d) Hybrid.

The presented physical breast phantoms were created by employing 3D printing techniques and are suitable for conventional and X-ray PhC imaging. For the development of phantoms, a single 3D printed material was used for the creation of the mold, followed by a filling process with paraffin-wax and embedded features of interest. A similar approach was followed by Kiarashi et al. [49], for the construction of the 'Singlet' phantom, which was fabricated using a glandular-equivalent 3D printed material and then carefully filled with adipose-equivalent materials (oil, beeswax and a permanent resin) for investigation. In our case, paraffin wax was used as the chosen adipose-equivalent material for all phantoms, while eight 3D printed materials, including both thermoplastics and resins, were investigated to simulate the glandular tissue. Spherical low-contrast lesions (referred as masses) and clusters of high-contrast microcalcifications were considered as the main features of interest, similarly to most commercially available mammography phantoms used for image quality assessment.

The substitute materials used for the creation of the phantoms were selected to mimic both the attenuation and refractive properties of the breast. Thus, the developed phantoms can be used in X-ray PhC applications allowing testing of this modality. More precisely, the phantom could be used for the optimization of reconstruction algorithms, acquisition geometries and parameters potentially leading to superior detectability and visibility of breast lesions. The different combinations with the complex pattern slice that are possible (Figs. 6b and 6d) could result in a tissue-equivalent breast phantom with a heterogeneous background with dynamic thickness and glandularity that could be adapted to the needs, suitable for both 2D and BT studies.

Concerning the construction of the molds, two 3D printing techniques were employed following the procedures analytically described in sections 2.2.2.1 and 2.2.2.2. The rectilinear pattern was chosen in the FDM technique, to produce better infill density and the thermoplastic materials were dried before printing to avoid moisture absorbance preserving the printing quality. In SLA, the approach followed to make a small hole on the mold, served to avoid pressure-induced forces and improved the printing quality. As shown in Fig. (3), high printing quality was achieved in the molds, with solid and smooth surfaces, especially for the case of the resins printed with SLA. However, in some of the phantoms areas, small air bubbles were observed in the obtained images. These air bubbles are visible in the phantoms shown in Figs. (6b, 6c, 6d) indicatively and were created during the filling process and the manual insertion of features of interest. The formation of such air cavities is undesirable and could be possibly eliminated using a vacuum chamber during the procedure, to avoid air getting trapped inside. Overall, 3D printing brings the potential to create reproducible low-cost phantoms enabling custom designs that can be printed directly from the 3D models. However, there are also limitations mainly related to factors stemming from the current 3D printing technology status, such as an inability to print multiple materials at the same time.

Investigated 3D printed materials were considered in combination with paraffin as the adipose-tissue substitute Fig. (5). All three resins (Clear, Flex and Tough) are suitable and were investigated as glandular substitutes. Among thermoplastic filaments, ABS has a μ value closer to adipose tissues, while the rest could be used as glandular equivalents. Based on the relative differences in both μ and δ, among all combinations with paraffin being used as the adipose substitute, Flex-Paraffin, Nylon-Paraffin and Hybrid-Paraffin were the optimal combinations for the representation of the glandular and adipose tissues, regarding their attenuation and refractive characteristics. The PhC effect was well detected in images obtained with the created phantoms for both resins (Fig. 8) and thermoplastic filaments (Fig. 9).

The comparison between the two columns in Fig. (8) shows that the edges and the contrast of the structures enhanced in the case of higher ODD (column ii), where PhC effects contributed to the image. In Fig. (8b), the sphere can be better visualized for 35cm ODD, where it appears with sharper edges due to the PhC effect, compared to 5cm ODD. The same stands for the spheres in Fig. (8c), where the small one is hardly detected for the case of 5cm ODD. The enhanced contrast of low contrast features such as breast masses remains one of the most important goals of breast imaging and a crucial matter for early detection of breast cancer [76]. Moreover, breast masses are categorized according to their shape and margins [77], so enhanced visualization of their borders is essential. Similarly, in Fig. (9), the low contrast features (spheres and fibers) are better visualized at ODD=35cm for all phantoms due to the PhC effect. The spheres in Figs. (9b and 9c) are characteristic examples, that appear with enhanced resolution of their edges at ODD=35cm. It is worth mentioning that in Fig. (9a) (ii) the nylon fiber is detected due to the PhC effect, whereas for smaller ODDs, it could not be distinguished among the paraffin background.

Visual assessment between the images of the phantoms created using the two different 3D printing techniques FDM and SLA, indicates that the latter proves to be more appropriate for the development of breast phantoms. As observed in Fig. (9) from the images of the phantoms constructed with FDM, the printing patterns are visible, resulting in a rippled and rough surface. This drawback is more evident for Nylon and Hybrid Figs. (9b and 9d). Also, even though the infill density was chosen to be 100%, hollow areas remained in the construction of the molds depicted in the images as black areas. This disadvantage for breast imaging becomes even stronger and unpleasant in the case of PhC, where the edge enhancement takes place (and the printing pattern results in strong artifacts). On the contrary, despite being a more expensive technique, SLA provided rigid and smoother areas with better surface finish (Fig. 8).To sum up , the air cavities and printing artifacts are unwanted in X-ray breast phantoms, especially for PhC imaging, which indicate that SLA and thus the phantoms with molds printed with the three resins (Flex, Clear, Tough) could be considered as more suitable.

The presented study showed that 3D printing techniques can be used for developing complex breast tissue-mimicking phantoms that are suitable for the investigation of multiple X-ray imaging modalities with the same phantom. The investigated techniques produced phantoms that could be used for 2D or 3D imaging techniques, in both attenuation and phase contrast based X-ray mode. Among the different materials and printing techniques investigated, Flex-Paraffin, Nylon-Paraffin and Hybrid-Paraffin were found to be the most suitable choices for mimicking breast tissues, while SLA proved to be more appropriate for the development of breast phantoms giving the resins as substitute materials the lead. Contrary to SLA, FDM produced visible printing patterns resulting in a rippled and rough surface that deteriorated the quality of the acquired X-ray images. The developed physical breast phantoms were imaged using a polychromatic microfocus X-ray tube setup, in order to investigate the presence of PhC effect. Results showed that the PhC effect was present even in ODD of 35cm, rendering the imaging setup suitable for PhC imaging and therefore overcoming one of the main limitations for clinical use of PhC imaging, imposed by synchrotron-based in-line setups.