## 2 Materials and Method
### Simulation
#### 2.1.7 Breast Model  
A set of six breast phantoms of different thicknesses was used in the simulations. These virtual phantoms enabled a simplified simulation of the anatomical structure of the breast (Figure 4). The phantoms had the shape of a half cylinder with a radius of r = 8 cm. Their structure was similar to that of the model used in computer simulations for dosimetry [24; 25; 26; 27; 28; 29]. The location of the modeled tumor (cylinder 1 cm in diameter and 1 cm high) depended on the thickness of the phantom. The tumor's \(x\) and \(y\) coordinates were determined so that the tumor would be projected onto the highlighted area of the image detector. The coordinates of the center of the simulated tumor are as follows:  
\[x=\frac{x_{det}}{SID}\big{(}STD-0.5h_{p}\big{)} \tag{4}\]  
and  
\[y=\frac{y_{det}}{SID}\big{(}STD-0.5h_{p}\big{)}, \tag{5}\]  
where \(h_{p}\) is a breast phantom thickness.  
The outer part, with a thickness of 5 mm, was made of adipose tissue, and the inner part consisted of a mixture of glandular and adipose tissue in the proportions determined by the level of glandularity (Table 2). The composition of the simulated tissues and the density of adipose tissue (\(\rho_{a}\)) and glandular tissue (\(\rho_{g}\)) were determined based on the work of [PERSON] et al. [30]. It was assumed that the neoplastic tissue has the same composition as the glandular tissue, but it is characterized by a higher density (\(\rho_{t}\)) [31; 32]. Detailed data on the elemental composition and tissue density are presented in Table 3.  
Figure 4: The virtual breast phantom model with a thickness h\({}_{p}\) of 53 mm. Visible external (orange) and internal (blue) parts, as well as an element imitating a cancerous tumor (yellow), are shown.  
The density of the tissue mixture in the inner part of the breast phantom was determined using the following equations (according to [PERSON] [25]):  
\[\rho_{m}=\rho_{a}v_{a}+\rho_{g}v_{g} \tag{6}\]  
and  
\[v_{g}=(\frac{1-g\rho_{g}}{g\rho_{a}}+1)^{-1}, \tag{7}\]  
where \(g\) is glandular (mass fraction), \(v_{g}\) is the glandular tissue volume, and \(v_{a}\) is the adipose tissue volume.  
The inner part of the phantom was defined as a logical detector to register the dose absorbed in the breast. Using the simulation program, the energy deposited in this area was recorded, and the dose value was then determined. The use of logical detectors was discussed in [34]. The dose recorded in this way was considered equivalent to the average glandular dose. The simulations, in a simplified manner, factored in the effect of radiation scattering through tissues not directly subject to imaging, such as a chest and a compression plate. The chest was defined as a 15 cm \(\times\) 25 cm \(\times\) 5 cm cuboid filled with water (\(\rho\) = 1.0 g/cm\({}^{3}\)), adjacent to the edge of the table and the breast phantom. The pressure plate closely adhered to the breast surface, which determined its position in the simulations. The dimensions of the plate were similar to those of the image detector (24 cm \(\times\) 30 cm). The plate thickness of 2.6 mm corresponded to the thickness of real plates found in digital mammography. It was assumed that the element was made of polycarbonate with a density of \(\rho\) = 1.2 g/cm\({}^{3}\).