## 4 Discussion
### Modelling Constrains  
In this section, the model constrains are reviewed in order to delimit the scope of the presented study:  
(I) The results obtained in this study were obtained from the numerical modelling of healthy and tumoral breast tissues, considering conditions that were as near to real ones as possible. Nevertheless, it should be kept in mind that the real situation is complex and involves a great number of factors that are difficult to simulate; assumptions to simplify it, making it more manageable for numerical study, have to be taken into account. Some limitations due to these factors are as follows:  
1. The assumed model geometry is based on a 3D semi-ellipse shape that is commonly used in this kind of research. The actual anatomy of the breast deviates from this ideal model, which could constrain the internal and superficial thermal distributions presented here. In a real case, the subject position could be adapted in such a way as to obtain a symmetrical configuration, e.g., in a prone position with free breasts. 2. Considering the internal anatomy of the mammary gland as a cluster of lobes connected by ducts to the nipple produced a certain symmetry in terms of geometry that could idealize the results. 3. Different breast components were interfaced without considering the connective tissue between them; as a consequence, the effect of this was not considered in assessing temperature behavior at tissues boundaries. 4. All tumors were considered at the same depth and spherical geometries to evaluate thermal profiles under the same boundary conditions. 5. Environment conditions were considered stable, which means that no changes in external temperature were considered. 6. No temperature changes during the menstrual cycle were considered. 7. Natural body movements (e.g., breathing), and how they could affect the acquisition of an internal and external thermograms, were not considered. 8. No extensive clinical data were considered. Despite these factors, the proposed model is within the considerations made in models presented in similar works. In fact, the breast geometry used is closer to that of real breast anatomy than that achieved in the multilayer approach. In future study, some of the described aspects could be addressed; a parametric study considering variable tumor size and location could be performed, including the effect of connective tissues on thermal distributions. (II) The conditions considered in this work belong to a standard model of breasts. Specific characteristics related to age, ethnic group, individual condition, or another particular feature were not represented in these numeric simulations. For this reason, the results should not be generalized universally. In future work, the conditions for a determined group could be analyzed to reflect their influence on the obtained temperature and gradient results. (III) At this stage, the proposed model was used to study the behavior of the breast thermal profile given a set of conditions that influence it using numerical solutions based on a bioheat mathematical model. In reality, there are several factors that could affect its sensitivity and specificity, which are strongly dependent on those related to the sensitivity and specificity of the imaging technologies used to acquire thermal maps. In that sense, in the near future, an extended analysis considering false-positive or false-negative thermo-grams could be performed to assess how our proposal based on the gradient examination of thermal distribution could overcome current constraints. In that moment, there should be the conditions to quantify the misclassification of the model and to consider ethical implications in a more realistic way. At this moment, it is possible to state that our model analyses changes in the thermal emissions of involved tissues, and that from a purely theoretical perspective, this approach generates information related to the tumor heat generation rate. (IV) One parameter that could bias the presented results is the position of the tumor.