## 8 Results and Discussion  
In this study, five patients' data were used to perform the patient-specific reverse thermal modeling and tumor diagnosis in order to demonstrate the capabilities of the technique developed and to validate the models built. Table 3 demonstrates the age and demographic details of each patient. A mesh convergence study should be conducted before the analysis is performed so that the simulation results will not be improperly influenced by the mesh generated; simultaneously, computational efficiency and numerical accuracy can be achieved. In order to find the optimal number of elements for running a simulation, the temperature probes were performed at the nipples to check the predicted temperature values for convergence. By increasing the number of elements, differences between readings at the probes were compared, until an average difference of 1% was reached. Table 4 shows the mesh convergence process for patient number one. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Elements** & **Temperature** & **Difference (\%)** \\ \hline
280,414 & 34.01 & \\ \hline
320,584 & 35.3 & 3.79 \\ \hline
401,383 & 34.55 & 2.12 \\ \hline
442,842 & 34.2 & 1.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mesh convergence study for patient number one. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Patient** & **Age** & **Sex** & **Number of** & **Number of** & **Age of First** & **Highty of** & **Age of First** & **History of** & **Age of** & **Age at** \\
**Number** & & & **Pregnancy** & **Births** & **Births** & **Breast** & **MentRNA-** & **MentRNA-** & **MentRNA-** \\ \hline
1 & 59 & Female & 5 & 2 & 25 & 1 & 14 & 53 \\
2 & 45 & Female & 9 & 7 & 19 & 0 & 12 & Not started \\
3 & 59 & Female & 5 & 2 & 25 & 1 & 14 & 53 \\
4 & 58 & Female & 4 & 3 & 22 & 0 & 12 & 49 \\
5 & 52 & Female & 3 & 2 & 23 & 0 & 12 & 51 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Age and demographic details of each patient. Figure 9: Block diagram of the proposed research. Table 5 presents the results of the mesh convergence study, which shows the optimal number of elements for patients' breast models with which mesh convergence was achieved. Table 6 includes the extracted tissue parameters of three patients' breasts using reverse thermal modeling; these were based on a homogeneous model using the healthy breast's data as inputs. The parameters were subsequently used as initial guesses for a multilayer model simulation to estimate the specific tissue parameters of each layer in the diseased breast. Using the homogeneous breast model's parameters as initial guesses, specific parameters of gland and fat, including conductivity, density, specific heat, and blood perfusion rate, were estimated (Tables 7-11). Based on the estimated fat layer dimension, the content of gland and fat were calculated in percentage. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Patient**} & \multirow{2}{*}{\begin{tabular}{c} **Conductivity** \\ **[W/m °C]** \\ \end{tabular} } & \multirow{2}{*}{**Density** [kg/m3]**} & \multirow{2}{*}{\
\begin{tabular}{c} **Specific Heat** \\ **[J/kg °C]** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Blood Perfusion** \\ **[mL/s/mL]** \\ \end{tabular} } \\ \hline
1 & 1.49 & 901.51 & 2201.51 & 0.00015794 \\ \hline
2 & 1.34 & 951.26 & 2010.48 & 0.00011972 \\ \hline
3 & 1.14 & 997.24 & 1812.25 & 0.00010012 \\ \hline
4 & 1.25 & 998.67 & 1849.25 & 0.00010876 \\ \hline
5 & 1.32 & 1047.82 & 1797.17 & 0.00010172 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Estimated parameters of the homogeneous model.