## 8 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Patient No.**} & **Computed Tumor Size** [**mm**] & **Doctor’s Size [**mm**] & **Computed Depth [mm]** & **Percentage Error (Tumor Size)** [**\%**] \\ \hline
1 & 23 & up to 25 & 23.78 & 8 \\ \hline
2 & 42 & 45 & 31.99 & 6.7 \\ \hline
3 & 21.5 & 23 & 28.18 & 6.5 \\ \hline
4 & 17.5 & 16 & 23 & 9.3 \\ \hline
5 & 16.1 & 15 & 25.1 & 7.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Estimated tumor depth and diameter compared with the doctor’s conclusion. breast, while thermal models are uniform in blood perfusion. The computed temperature at the hotspot is 34.6 \({}^{\circ}\)C, which is validated by the thermographic hotspot temperature with almost the same temperature, resulting in a percentage error of only 0.23%. In general, the measured (Figure 11a) and computed (Figure 11b) temperature distributions for the second patient's breast match, while the temperature at hotspot was calculated as 34.8 \({}^{\circ}\)C. However, the predicted temperature distribution is also quite uniform compared with the thermogram, which may be due to the non-uniform blood perfusion and vessel distribution in the real breast in comparison with the uniform perfusion in the model, as previously discussed. The numerical model was validated since the location and temperature of the hotspot agree well with the corresponding measurements; the percentage error was at 0.43%. Figure 12 shows a comparison between the measured breast temperature distribution (Figure 12a) and estimated multilayer model prediction (Figure 12b) for the third patient. The doctor concluded that the tumor is located in the upper left quadrant, which can also be seen as a hotspot in the multilayer model prediction. As in the two previous cases, the  
Figure 11: Comparison of measured (**a**) and computed (**b**) temperature distributions (patient No. 2) with a percentage error of 0.43% in hotspot temperature prediction. Figure 10: Comparison of measured (**a**) and computed (**b**) temperature distributions (patient No. 1) with a percentage error of 0.23% in hotspot temperature prediction. highly irregular small temperature distribution in the real breast cannot be captured by the model due to the uniform blood perfusion assumption used. In Figure 13, a comparison of the thermal image (Figure 13a) and computed (Figure 13b) temperature contours for patient four is presented. In the thermogram, the temperature at the hotspot is 34.42 \({}^{\circ}\)C, while the computed temperature at that point is 34.5 \({}^{\circ}\)C, which is very close to the former with a percentage error of 0.23%. In addition, the locations of the hotspots in both the thermogram and the predicted contours agree well. Figure 12: Comparison of measured (**a**) and computed (**b**) temperature distributions (patient No. 3) with a percentage error of 0.12% in hotspot temperature prediction. Figure 13: Comparison of measured (**a**) and computed (**b**) temperature distributions (patient No. 4) with a percentage error of 0.23% in hotspot temperature prediction. Figure 16: A 3D model with computed parameters (Patient No. 2). Figure 17: A 3D model with computed parameters (Patient No. 3). Figure 18: A 3D model with computed parameters (Patient No. 4). The proposed tool for tumor detection shows its usefulness based on the real patient data. The presented results are based on two kinds of breast models: homogeneous and multi-layer models. The homogeneous model was used as a starting point in the calculation of parameters such as conductivity, density, specific heat, and blood perfusion rate. The calculated parameters enabled the estimation of the tumor size and its location. Subsequently, the content percentage in the multi-layer model was determined. The final results were then validated by the doctor through medical examination and thermograms.