## 5 Conclusions  
A computational realistic model of breasts was simulated, based on a 3D geometry that was near to that of real cases. We considered skin and tumoral, glandular, and fatty tissues. Three tumoral cases and one healthy case were considered; all of them were reproduced based on parameters obtained from real cases reported in the literature. All tumors were considered spherical and were located at a depth of 15 mm. All cases used a diameter of less than 10 mm to simulate the early stages of development, where the traditional scanning techniques do not detect them yet. Thermal phenomena were simulated based on the Pennes Bioheating equation and temperature distributions with their respective gradients were obtained along three paths: internal-vertical, internal-horizontal, and superficial. A thorough analysis of temperature and gradient over these paths allowed us to make the following observations: (a) temperature values along paths in/over the tumor zone were proportional to tumor size, meaning the bigger the tumor size, the greater the temperature increment in/over the tumor zone. (b) Maximum values of internal gradients in the tumoral zone were proportional to the tumor heat generation rate (Qm). This has been correlated with tumor malignancy in previous works [37; 38], showing that the internal gradients could be an indicator of the grade of the malignancy of the tumor, independently of its size. This finding is restricted to the limitations of numerical studies, which, as was explained before, are subject to constrains due to simplification of theorizing. (c) The maximum values of the superficial gradient over the tumoral zone were proportional to tumor size. (d) The zone warmed by the tumor is related to tumor size, i.e., the larger the tumor, the larger the heated area; in fact, we propose a method based on gradient information to quantitatively measure the warmed zone. In all cases the size of this zone was approximately twice the size of the tumor. (e) In the case that just thermal information on the breast surface was available, the location of a tumor could be established more accurately based on maximum differences between gradients than based on maximum differences in temperature (taking as a reference the healthy breast). Finally, (f) maximum temperature differences (regard healthy case) for the internal paths were in the order of a few degrees Celsius, while for the superficial path they were in the order of tenths of a degree Celsius. The purpose of this study was to establish a basis for extending the possibilities of breast cancer detection using thermometric methods and encouraging information extraction from internal and surface thermal maps. In the Introduction section, there is included a resume about the advantages and disadvantages of existing technologies for timely or early breast cancer detection. Regard thermometry, internal or superficial, the main advantages are as followed: non-ionizing radiation is used; it can be applied periodically, as required, without health risk; it is a screening method applicable to any ethnic group or age group; and it can be used in any stage of the reproductive cycle of women's lives. For this reason, this work is oriented to analyzing the possibility of relevant data derivation from breast thermograms and thus providing patients with a more comfortable, secure, and accurate early detection method. The model was implemented as a \"near to real\" case of several breast tumors to establish associations between thermal behavior and tumor parameters that could provide useful information in medical practice. All assumed parameters were carefully set to meet the conditions of the phenomena and to reduce differences with the real-life scenario. The results obtained in this analysis are expected to be close to the ones obtained in a clinical case. Nevertheless, a numerical study is a simplified form for modelling the complex reality and there are implicit deviations due to this fact.