## 2 Materials and Methods
### Generation of Training Data  
Creating an extensive empirical dataset for EIT is hindered by the invasive nature of biopsy collection and ethical complexities. Obtaining real-case data is challenging due to privacy constraints and patient consent requirements. Simulations serve as a non-invasive and cost-effective alternative, allowing for the generation of diverse training data and the exploration of imaging parameters, crucial for refining EIT systems in breast cancer detection. For the training data we have used the general approach explained by [PERSON] et al., where they were able to produce EIT images from real-world measurements, but trained the ANN using only simulated data [17]. We used finite element method (FEM) simulation for the open source Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS) library [18]. EIDORS is a community-driven software package written in Matlab for FEM simulation in an EIT setting. The structure of the anatomical female breast is illustrated in Figure 1. In Figure 2 the used FEM model can be seen. The dimensions of the model are \(50\,\mathrm{mm}\times 154\,\mathrm{mm}\times 92\,\mathrm{mm}\). The electrodes have a radius of \(2.9\,\mathrm{mm}\). Fifteen electrodes are placed on each side of the model, thus, a total of 30 electrodes are involved in the model. The mesh size of the model was set to \(2\,\mathrm{mm}\), as this allows for a trade-off between the spatial resolution of the model and computation time. To avoid overfitting, 7500 different models were created. Each realization of the model was constructed according to the following rules. Figure 1: Structure of the female breast. To simulate the contact between electrode and breast, the contact impedance  
\[Z_{contact}=25\,\mathrm{k}\Omega(1+\lambda_{contact}\cdot n),\]  
where \(Z_{contact}\) is the contact impedance, \(\lambda_{contact}\) is a weighting factor which, weights the contribution of the random sampling and \(n\) is sampled from a normal distribution \(\mathcal{N}(0,1)\). \(\lambda_{contact}\) was set to 1. This allows for modeling the variety in contact impedance. We incorporated four different tissues into the model. On 5 sides of the model, a 2 mm thick layer of skin was introduced. The glandular tissue was positioned within the domain, forming a truncated cone. The wider end of the cone was placed on the side without skin tissue and tapered towards the opposite end. This provided boundaries for the placement of the gland lobes. Within the cone, the lobes were placed randomly. Due to the inability to measure individual lobes, they were approximated as larger lobes [19]. These larger lobes had radii in all three spatial axes \(r\) sampled from a normal distribution \(\mathcal{N}(3,0.513)\) with 1.46 mm \(\leq r\leq\) 4.64 mm, as reported in [19]. The orientation of these larger lobes was determined randomly by sampling all three Euler angles from 0 to \(2\pi\). A total of 20 larger lobes were positioned within the domain. From these larger lobes, a chain of ellipsoids or spheres with a radius of 1.5 mm extended towards the center of the truncated cone, as shown in Figure 3.  
Just like big lobes in the glandular structure, the tumors are not perfect spheres and are distorted in all three spatial directions. The radii followed a normal distribution with the mean depending on the dataset created and a fixed standard deviation of 1 mm. We analyzed different mean values of radii from 6 mm up to 13 mm. The tumor was placed randomly, however, it was guaranteed that they always had contact with the glandular structure. An example of a tumor placement can be found in Figure 3, where the tumor is marked in yellow. Space that is not filled with any other tissue is assigned to fatty tissue. The values for the conductivities of skin, fat, tumor, and glandular tissue are sampled as follows. In the literature, the values of all these tissue types are not fixed and have variations.