## 3 Results
### Results from Superficial Temperatures for Breast with Tumors and Healthy Tissue  
In this section, a quantitative analysis of thermal data from the breast surface is presented. As a reference, in Figure 8, thermal distribution maps for the cases of healthy breast (Figure 8a), breast with a tumor of 5 mm in diameter (Figure 8b), 6 mm (Figure 8c), and 8 mm (Figure 8d) are shown. It is appreciated that, for the breast with the smallest tumor (5 mm), the temperature variations on the surface section above the tumor's location showed values of less than 0.1 \({}^{\circ}\)C. All tumor centers were approximately located at the coordinates x = 7.0 mm; y = 52, 51.5, and 50.5 mm (for tumors of 5, 6, and 8 mm in diameter, respectively); and z = 7.5 mm. All of them were located at 15 mm of depth from the surface, measured along the \(y\) axis. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l} \hline \multicolumn{1}{c}{} & \multicolumn{3}{c}{**Healthy Tissue**} & \multicolumn{12}{c}{**Tumorial Zone**} & \multicolumn{3}{c}{**Healthy Tissue**} \\ \hline  & & & \multicolumn{12}{c}{**Zone Warmed by Tumor Growth**} \\  & & & & & & & & **(zWTG)** & & & & & & & \\ \multicolumn{12}{c}{**T. D. [mm]**} \\ \multirow{2}{*}{**T. D. [mm]**} & \multirow{2}{*}{\(\mathbf{P_{0}}\)**} & \multirow{2}{*}{\(\mathbf{P_{1}}\)**} & \multirow{2}{*}{\(\mathbf{P_{2}}\)**} & \multirow{2}{*}{\(\mathbf{P_{3}}\)**} & \multirow{2}{*}{\(\mathbf{P_{4}}\)**} & \multirow{2}{*}{\(\mathbf{P_{5}}\)**} & \multirow{2}{*}{**Black**} & \multirow{2}{*}{\(\mathbf{P_{6}}\)**} & \multirow{2}{*}{\(\mathbf{P_{7}}\)**} & \multirow{2}{*}{\(\mathbf{Blue}\)} & \multirow{2}{*}{\(\mathbf{P_{8}}\)} & \multirow{2}{*}{\(\mathbf{P_{f}}\)} \\  & & & & & & & & & & & & & & & & \\ \hline \multirow{2}{*}{5} & T & 27.79 & 28.13 & 32.79 & 32.9 & 33.13 & 33.20 & 33.62 & 34.67 & 35.08 & 34.53 & 33.22 & 28.18 & 27.84 \\  & \(\
abla\)T & 0.167 & 0.328 & 0.016 & 0.030 & 0.025 & 0.034 & 0.199 & 0.831 & \(\approx\) 0 & \(-0.890\) & \(-0.301\) & \(-0.333\) & \(-0.170\) \\ \hline \multirow{2}{*}{H. E. C.} & T & 27.79 & 28.13 & 32.67 & 32.75 & 32.88 & 32.9 & \(-\) & 32.8 & 32.73 & 32.65 & \(-\) & 28.15 & 27.8 \\  & \(\
abla\)T & 0.167 & 0.328 & 0.016 & 0.016 & \(\approx\)0 & \(-0.028\) & \(-\) & \(-0.030\) & \(-0.011\) & \(-0.103\) & \(-\) & \(-0.330\) & \(-0.167\) \\ \hline \multirow{2}{*}{6} & T & 27.81 & 28.15 & 32.89 & 33.02 & 33.27 & 33.36 & 33.55 & 34.79 & 35.21 & 34.63 & 33.00 & 28.20 & 27.85 \\  & \(\
abla\)T & 0.169 & 0.332 & 0.028 & 0.029 & 0.014 & 0.044 & 0.118 & 0.490 & \(\approx\) 0 & \(0.7755\) & \(-0.239\) & \(-0.337\) & \(-0.172\) \\ \hline \multirow{2}{*}{H. E. C.} & T & 27.80 & 28.14 & 32.75 & 32.84 & 32.97 & 32.99 & \(-\) & 32.92 & 32.83 & 32.71 & \(-\) & 28.16 & 27.82 \\  & \(\
abla\)T & 0.169 & 0.331 & 0.016 & 0.011 & \(-\) & \(-0.023\) & \(\approx\)0 & \(-\) & \(-0.021\) & \(-0.039\) & \(-0.092\) & \(-\) & \(-0.333\) & \(-0.170\) \\ \hline \multirow{2}{*}{8} & T & 27.84 & 28.18 & 33.16 & 33.33 & 33.67 & 33.86 & 34.04 & 35.56 & 36.15 & 35.38 & 33.4 & 28.25 & 27.90 \\  & \(\
abla\)T & 0.173 & 0.340 & 0.044 & 0.034 & 0.023 & 0.070 & 0.180 & 0.749 & \(\approx\) 0 & \(-0.898\) & \(-0.288\) & \(-0.347\) & \(-0.177\) \\ \hline \multirow{2}{*}{H. E. C.} & T & 27.82 & 28.16 & 32.92 & 33.01 & 33.15 & 33.17 & \(-\) & 33.14 & 33.03 & 32.84 & \(-\) & 28.18 & 27.84 \\  & \(\
abla\)T & 0.172 & 0.338 & 0.025 & \(\approx\)0 & \(-0.015\) & 0.011 & \(-\) & \(-0.019\) & \(-0.046\) & \(-0.082\) & \(-\) & \(-0.340\) & \(-0.172\) \\ \hline \end{tabular}
\end{table} 
Table 5: Temperature and gradient values for marked points in the horizontal path. Cases of breasts with tumors of 5 mm, 6 mm and 8 mm in diameter and a healthy case are included. In all cases, the highest temperature (37 \({}^{\circ}\)C) was found in the base of the breast (stuck to the chest). In the healthy case, it decreased uniformly as breast surface (\"skin\") approached the nipple, where a slight increment was detected.