###### Abstract  
The computational modelling and analysis of internal and external temperature distributions and their gradients, associated with the first stage of mammary tumors, was performed to relate thermal parameters to relevant tumor characteristics. A realistic 3D geometric model of breast anatomy was used to simulate tumor cases that were characterized in real life at their primary clinical stage. The thermophysical parameters of three tumors were extracted to implement the models; a fourth case without a tumor was used as a reference to provide quantitative measurements of temperature increases and gradient changes. The analysis considered superficial and internal temperature distributions and gradients, computed throughout specific paths. Finally, an evaluation was made of the ability of the thermometric technologies available today to detect the changes estimated in simulations. Maximum temperature increments in the range of 2.30 to 3.20 \({}^{\circ}\)C and in the range of 0.15 to 0.30 \({}^{\circ}\)C were found on internal and superficial paths, respectively. Internal gradient peak magnitudes fluctuated within the range of 0.34 to 1.14 \({}^{\circ}\)C/mm. Thermal results indicated a direct correlation between tumor size and temperature rise. Nevertheless, gradient results showed that the heat generation rate, an indicator of tumor malignancy, was directly proportional to internal gradient maximum peaks, which were related to tumor boundaries regardless of tumor size. t +
Footnote †: journal: Medical  
allergies to the contrast agent. Additionally, the radiation dose delivered to the patient is approximately twice the dose delivered by conventional mammography [8]. Ultrasound screening has been used as a complementary technique to mammography and magnetic resonance imaging, even being capable of differentiating between benign and malignant lesions. US is also recommended in cases of high-risk patients that are intolerant to MR imaging, patients with dense breast tissue, and young women with palpable lesions. However, the US image interpretation is strongly dependent on physician skill. Some relevant limitations are its low capacity to detect intraductal lesions [3] and its relative low specificity, producing unnecessary recalls and biopsies [2]. The size of the lesion is also an important factor: focused US provides an 86% rate of detection for masses larger than 15 mm, with this percentage reducing to 50% for masses of 5 mm or smaller. These findings were obtained using MRI as reference [3]. The Doppler US is focused to evaluate the microvascular flow present in breast lesions. It is a complementary technique that can be used to improve lesion classification [2]. It can be susceptible to artifact-produced mistakes [3]. On the other hand, elastography, which provides a measure of lesion stiffness, is an approach used in combination with B-mode US. The combination of shear wave elastography and strain elastography could improve the method's sensitivity and specificity [2]. Its main limitations are its capability to characterize deep lesions [3] and the high experience curve required to perform examinations and to interpret results [2]. MRI is a highly sensitive screening technique, but it presents a limited specificity [8]. Also, molecular breast imaging (MBI) and positron emission tomography (PET) are alternatives to nuclear medicine techniques. They use radiopharmaceutical agents to provide functional information about cells. Although these techniques have high cancer detection rates and high spatial resolutions (\(\approx\)2 mm), they are not recommended for use in periodic screening due to whole-body radiation doses. In this context, niche thermographic techniques can be established, such as non-ionizing approaches. These are capable of detecting internal and superficial thermal changes associated with the very early stages of breast cancer due to the perceptible thermal increments related to metabolic and vascular activity, which are present from the initial stages of tumor formation [9].