# Analysis of the Refraction Effect in Ultrasound Breast Tomography
## 3 Results
### In Vivo Breast Measurements  
An in vivo imaging study was performed using the hybrid UBT scanner on the left breast of a woman 35 years of age (Patient 1). The experienced radiologist diagnosed the breast of this patient as type C according to the ACR scale [50], non-uniformly dense, with areas of glandular tissue that can obscure focal lesions. Conventional USI and MMG did not show focal lesions (BI-RADS 1) or microcalcifications in this breast. The axillary fossae were found to be normal within the examined range. Due to its dense and heterogeneous structure, this breast is a difficult case for imaging. Therefore, it should show the refraction phenomenon of the ultrasound beam in UTT imaging.  
Figure 16 shows ultrasound tomography projection velocity values (see Figure 3b) measured for the breast of the Patient 1 in water at 20 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 30 \({}^{\circ}\)C, presented in parallel ray scanning geometry for a selected rotation angle (part of a sinogram) [22], for the first and third coronal cross-section from the breast base, respectively.  
The \(c_{p}\) values of the ultrasound projection velocity were determined as the ratio of the rectilinear path of the wave transition between successive pairs of transmitters and receivers to the measured transition time. Figure 17 shows quantitative ultrasound tomography images of the examined breast (Patient 1) in 3 mutually perpendicular sections (MPR) for water temperatures of 20 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 30 \({}^{\circ}\)C, respectively, reconstructed based on ultrasound wave transit time data collected around the entire breast. In the images visualized in conventional gray scale (values increasing from black to white), the water pixels around the breast were left, and in the images visualized in inverse gray scale were removed automatically using a specially developed algorithm. The water segmentation is performed radially. The algorithm determines, for a given angle, two points at the water-breast and breast-water boundaries. The resulting polygon is blurred and then a mask is generated for the given cross-section. Water statistics of the ultrasound attenuation are used to detect breast boundaries. The algorithm runs automatically and is robust to noise due to the averaging procedures used. The segmentation algorithm does not introduce changes in the structure of the breast image. It is used to automatically detect the boundaries of a breast immersed in water and mask the water pixels.  
Images show quantitative distributions of local ultrasound velocity values in individual sections. The images show characteristic \"distortion rings\" around the borders of breast cross-sections where the ultrasound velocity values are severely underestimated.  
Figure 16: Visualization of ultrasound tomography projection velocity values for the breast of Patient 1 tested in vivo in water at 20 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 30 \({}^{\circ}\)C (measured data), presented in parallel ray geometry for the selected rotation angle: left—for the first coronal section from the breast base; right—for the third coronal section from the breast base.