## 2 Female Breast Carcinoma
### Modelling  
In recent years, in silico studies have become a basic tool in the analysis of various phenomena occurring in living organisms. Numerical modelling, i.e., computer-based simulation is an extremely powerful tool for solving various critical engineering and medical problems. It enables the design of new theoretical solutions without the need to conduct tests on a living organism. The basis of in silico studies for breast cancer is the utilization of adequate numerical models of the female breast in order to best reflect its anatomical structure as well as the electrical and thermal parameters of individual tissues. The first important element for accurate, realistic breast phantoms is the adoption of the appropriate geometry for the computational model. The degree of complexity of breast models available in the subject literature is very wide, ranging from basic two-dimensional (2D), homogeneous (uniform), heterogeneous (multi-tissue or multi-layered) models to very complex, anatomically correct, anthropomorphic, three-dimensional (3D) models, often based on medical imaging including CT or MRI scans. Depending on the percentage composition of the individual tissues used to build the female breast, the following models can be distinguished [6; 47; 48]: predominantly fatty (PF; muscle--10%, gland--20%, fat--70%), scattered fibro-glandular (SFG, muscle--20%, gland--40%, fat--40%), heterogeneously dense (HD; muscle--20%, gland--60%, fat--20%), and extremely dense (ED; muscle--20%, gland--70%, fat--10%). Such models are made up of smaller computational elements (pixels or voxels) to which various parameters of breast tissues are assigned. Bioelectromagnetic models are usually based on different numerical techniques, including the finite element method (FEM) [49], finite volume method (FVM) [50], boundary volume method (BVM) [51], finite-difference time-domain (FDTD) method [52], and others. The utilization of human anatomical models usually leads to many hours of calculations, which often disqualifies them from the optimization process, for which the calculations must be repeated many times to obtain the optimal solution. To save time and computing power, researchers often propose simplified female breast models based on the semi-ellipsoidal, semi-sphere, semi-cylindrical, or semi-anatomical objects [6; 10; 17; 53; 54]. Breast models, which are anatomically correct in terms of their external shape but without a naturalistic internal structure for breast tissues, are also common in the scientific community [55]. To validate virtual female breast models, researchers often create liquid, semi-solid, and solid physical phantoms [56; 57; 58; 59]. A key part of this in silico study was the development of an anatomically based female breast phantom and its tissue parameters that corresponded to experimentally determined equivalents in terms of real laboratory electro-thermal measurements. The authors developed a lifelike anthropomorphic breast model based on MRI scans validated by a 3D-printed plastic breast phantom [60]. The MRI-derived breast model was characterized by a high spatial resolution of 1 mm and contained \(269\times 332\times 202\) cubic cells. Such a model can be characterized as a heterogeneously dense (HD) breast phantom with 51-75% glandular tissue content, which corresponds to the breast structure of a 35-year-old female patient with a tumor. In addition to breast glands (marked in blue in Figure 3) and tumor (pink), the 3D geometric female breast phantom also featured other breast tissues,such as fat (green), breast fat (yellow), skin (red), and muscle (orange). Figure 3 depicts a sectional view (_xy_ slice) of the geometric model passing through the tumor (_z_ = 0) seated at location (0, -12, 12) mm. All the modelled materials are considered as homogeneous, isotropic, and lossy dielectrics.