# Analysis of the Refraction Effect in Ultrasound Breast Tomography
## 1 Introduction  
There is no doubt that widespread and effective women's diagnostics regarding the risk of breast cancer is a major worldwide problem [1, 2]. Imaging of breast lesions is currently the primary method for their detection and initial clinical suspicion of malignancy [3]. Histopathological examination of the material obtained by biopsy is performed to confirm suspicion of a malignancy of breast cancer diagnosed by imaging. The most common diagnostic imaging examinations for early detection of breast cancer are X-ray mammography (MMG) and B-mode conventional ultrasound (USI). In older women, a higher detection rate is observed with MMG, which, in addition to the risks associated with X-ray exposure [4], can be painful due to the need for mechanical compression of the breast [5]. Mammography of dense breasts (mainly in young women) and implant-informed breasts is not reliable due to frequent false negative results [6, 7, 8], whichsignificantly cause delay in cancer diagnosis. Furthermore, mammography results are affected by premenopausal or postmenopausal status and the use of hormone replacement therapy [9]. There is also a potential risk of cumulative effects of ionizing radiation. The risk of cancer increases by approximately 1% per five mammography tests, so physicians do not recommend mammography screening more often than every 2 to 3 years or in women under 40 years of age. Mammographic screening also has limitations, such as overdiagnosis and overtreatment [10]. 2D mammography, despite being the only screening method, is being phased out in many countries (e.g., Switzerland) due to its low effectiveness [11]. Recently, a new mammographic test has been introduced, called 3D mammography (tosmosynthesis). The test shows higher sensitivity compared to traditional mammography (2D). However, the method is very similar because it is based on X-rays and therefore has the same contraindications. Extending mammographic screening to include additional conventional ultrasound imaging, especially in dense breast tissue, significantly increases the chance of early cancer detection [12; 13]. The high sensitivity of USI [14] is, in turn, limited by its low specificity [15]. This causes false positive results, increasing the number of unnecessary biopsies [6]. Furthermore, results of studies presented in the literature suggest that it is difficult to precisely distinguish ultrasound-guided isoechogenic lesions in the surrounding fat. These disadvantages of MMG and USI mean that, despite regular screening, breast cancer is often not diagnosed in its early stages. Magnetic resonance imaging (MRI) has become the preferred method of breast examination for women at high risk of developing cancer. The use of this method in the detection of breast cancer is significant due to its high sensitivity and moderate specificity for tumor masses larger than 5 mm, including ductal carcinoma in situ (DCIS) [16]. With the ability to analyze breast morphology, magnetic resonance imaging provides qualitative and quantitative data on tumor vascularization, allowing differentiation of benign from malignant masses. However, magnetic resonance tomography scanners are very expensive due to the price of the equipment itself, the need to maintain it in special rooms, and the maintenance and hiring of qualified staff. In addition, intravenous administration of contrast agents can be required, which may enter the extravascular space or cause allergic reactions. The administration of contrast agents is limited in patients with kidney or liver disease. These disadvantages, as well as the cost of MRIs, limit the use of this method in the diagnosis of the female breast and make public MRI screening unattainable to date. As we can see, there is currently no ideal diagnostic method that can be recommended to any woman for breast examination. The market for diagnostic breast imaging devices is not sufficiently saturated due to the imperfections of each of the available methods.