## 4 Finite Element Analysis  
A finite element (FE) analysis of a breast model was performed to investigate its response to a compression load, in order to demonstrate the feasibility of the idea and determine the technical specifications to design the prototype of Palpreast, e.g., the spatial resolution of the pressure sensing textile necessary to identify the presence of a nodule. Mechanical properties of tissues are highly sensitive to the structural changes of various physiological and pathological processes. Thus, the characterization of embedded lesions in terms of mechanical properties (such as stiffness and size) provides a means for distinguishing them from diseased tissues. Although women have different breast thickness, shape, and stiffness, the FE analysis is based on a simplified hemispherical breast model characterized by average mechanical properties and a reduced number of details (e.g., heterogeneous tissues). This choice derives from the device concept, which is based on the evaluation of the differences in stiffness between the right and left breast--healthy heterogeneous tissues present in both breasts should have the same behavior, whereas there may be substantial differences between healthy and diseased tissues of the same person. In order to define the [PERSON]'s modulus of the breast and the nodule, we took into account the study of [PERSON] et al. [12], which was based on the application of a similar technology and on in vivo studies on patients. According to this study, the [PERSON]'s modulus of healthy breast tissue was 7 kPa, calculated as the mean value of clinical data of six patients involved in the study (6.9 \(\pm\) 1.4 kPa). Tumors are in general stiffer than healthy tissue, and it is well known that the Young's modulus increases with the malignancy of a tumor [22; 23]. In this research, we performed a parametric analysis with respect to the [PERSON]'s modulus of the inclusion \(\mathrm{E_{nod}}\), in the range 50 to 125 kPa with a step of 25 kPa, according to the in vivo study performed in [12], where the elastic modulus of inclusions increased from 50 kPa (benign fibrocystic tissue) to 123 kPa (ductal carcinoma). Two-dimensional (2D) plane strain and three-dimensional (3D) brick models were implemented under the following assumptions:  
1. The biological tissue and inclusions were homogeneous, linear elastic, and isotropic;
2. The Poisson's ratio of each material is 0.45, i.e., the breast could be considered as an almost incompressible material;
3. The breast was assumed to be placed on a non-deformable hard surface (identifiable with the rib cage), with a no-displacement constraint as boundary condition;
4. The density of each material was set to 1000 kg/m\({}^{3}\) (close to the density of water);
5. Two different breast sizes were investigated--large breast (LB) and medium breast (MB);
6. The ideal breast tissue has a hemispherical shape, whereas the nodule has a spherical shape, whose dimensions are indicated in Figure 4 and Table 1 for 2D model, and Figure 5 and Table 2 for the 3D model;
7. A pressure of 10 kPa was considered to simulate breast palpation. All the FE simulations were modeled using COMSOL Multiphysics 3.5. In order to simulate the behavior of breast tissue with better accuracy, a FE analysis of an idealized 3D breast model (Figure 5) was performed considering the parameters described in Table 2. The dimensions were the same as the 2D models described in Table 1.