## 2 Methodology
### Simulation Properties  
The simulation focuses on tumors with a diameter of 5, 6, and 8 mm and all tumors located at a depth of 15 mm from the skin surface, specifically inside of one of the milk ducts. A healthy case (without a tumor) was considered too. It was used as a reference for when a temperature increase associated with a lesion was not present.  
The tissue properties defined in the computational model were thermal capacity (\(C_{p}\)), thermal conductivity (\(K\)), density (\(\rho\)), and heat generation rate (\(Q_{m}\)).  
These properties were defined based on data reported in previous works and that had been validated to be typical values accepted in the breast modelling field. The considered values and the references they were taken from are shown in Table 1. In the case of the heat generation rate of tumors, the fundamental equation proposed by [PERSON] [47] to calculate \(Q_{m}\) from tumor diameters was not applied due to it just being valid for tumors with a diameter \(\geq\) 10 mm. Then, values approximated from real cases by [20] using a dynamic neural network were considered.  
In addition to previously mentioned parameters, among the thermophysical properties considered were those corresponding to blood for each domain; these were obtained from [PERSON] and [PERSON] [19] and [PERSON] [17]. They are shown in Table 2.  
For all domains, the initial temperature value was set to 37 \({}^{\circ}\)C. As boundary conditions, a fixed temperature was assigned for the thoracic wall equal to an arterial temperature of 37 \({}^{\circ}\)C and convective heat flux was added to the upper contour of the dome (counterpart to the epidermis), with a coefficient of heat transfer of 13.5 [W/(m\({}^{2}\)\({}^{\circ}\)C)] and with an environmental temperature of 20 \({}^{\circ}\)C.  
Regarding the mesh, a tetrahedral element of the second order was used; the maximum and minimum element sizes were 3.9 mm and 0.167 mm, respectively, as shown in Figure 1. For the simulated models, the discretization time was 1 min 3 s, 1 min 5 s, 1 min 7 s, and 1 min 10 s and the simulation time was 1 min 49 s, 1 min 49 s, 1 min 51 s, and 2 min 55 s for tumor sizes of 5 mm, 6 mm, and 8 mm, and for healthy tissue, respectively.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Domain**} & \multicolumn{4}{c}{**Property**} \\ \cline{2-5}  & \(C_{p}\) [J/(kg \({}^{\circ}\)C)] & \(K\) [W/(m \({}^{\circ}\)C)] & \(\rho\) [kg/m\({}^{3}\)] & \(Q_{m}\) [W/m\({}^{3}\)] \\ \hline Fat & 2348 [48] & 0.21 [11; 48] & 911 [48] & 400 [19] \\ \hline Gland & 3475 [10] & 0.48 [19] & 1080 [19] & 700 [19] \\ \hline Tumor & 3475 [10] & 0.48 [19] & 1080 [19] & VAR [20] \\ \hline Dermis & 3475 [10] & 0.3140 [10] & 1050 [10] & 368.1 [17] \\ \hline Epidermis & 3475 [10] & 0.2093 [10] & 1050 [10] & 0 [17] \\ \hline \hline \end{tabular} VAR means variable. Value depends on tumor case.  
\end{table}
Table 1: Thermophysical properties of tissues.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Domain**} & \multicolumn{4}{c}{**Property**} \\ \cline{2-5}  & \(T_{a}\) [\({}^{\circ}\)C] & \(C_{p,b}\) [J/(kg \({}^{\circ}\)C)] & \(W_{b}\) [I/s] & \(\rho_{b}\) [kg/m\({}^{3}\)] \\ \hline Fat & 37 & 4200 & 0.0002 & 1060 \\ \hline Gland & 37 & 4200 & 0.0006 & 1060 \\ \hline Tumor & 37 & 4200 & 0.012 & 1060 \\ \hline Dermis & 37 & 4200 & 0.0002 & 1200 \\ \hline Epidermis & 37 & 4200 & 0 & 1200 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Thermophysical properties of blood.