# Analysis of the Refraction Effect in Ultrasound Breast Tomography
## 2 Materials and Methods
### Method and Measuring System  
To verify the results of the calculation obtained, in vivo patient tests were performed using a prototype of the hybrid UBT scanner developed by the Polish company DRAMINSKI S.A., for the temperature of the water surrounding the breast immersed in the tank, \(T\) = 20 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, 30 \({}^{\circ}\)C, respectively. The water was not heated to body temperature (36.6 \({}^{\circ}\)C) due to the non-standard value, not currently foreseen for use in the scanner. It should be noted that the temperature 20 \({}^{\circ}\)C is a bit too low and patients often indicate discomfort with submerging and holding the breast in the tank for several minutes.  
The view of a prototype of the hybrid UBT scanner developed by DRAMINSKI S.A. is shown in Figure 7.  
The woman lies on the examination bed in a prone position with the breast submerged through the opening into a reservoir of distilled water heated to a fixed temperature. Examination of the selected breast is performed automatically by scanning coronal cross-sections in 1- or 2-mm increments using a vertically moving, multi-element ring array of ultrasonic transducers. The water in the reservoir provides adequate acoustic coupling between the transducers and the breast. The ring array is connected to a mechanical system that positions it at the appropriate depth (on the \(Z\)-axis) and is responsible for its movement on this axis. The array consists of 1024 miniature piezoceramic transducers evenly distributed on the inner side of a ring of diameter \(D_{r}\) = 260 mm surrounding the breast. The elementary transducers have active area dimensions of 0.5 mm \(\times\) 18 mm and operate at approximately 2 MHz central resonant frequency. The  
Figure 6: Temperature dependence of ultrasound velocity in water and fat.  
array is characterized by a wide band of ultrasonic transducers, \(B=1.5\) MHz, due to the well-optimized front matching layer. Each transducer can act as a sending and receiving element. Measurement data acquisition methods are presented in [20,21]. Depending on the length of the breast, approximately 100-200 coronal cross-sections from the base to the nipple are examined. Data acquisition in the transmission modality currently takes 3 s per coronal breast cross-section. In the next version of the prototype, this time will be reduced to about 2 s. Note that the primary limitation here is the transit time of the beam from the sending transducer to the receiving one. Small movements of the patient are not a problem; at most they cause small shifts between individual coronal sections in the 3D image, which can be corrected automatically.  
For the reconstruction of quantitative transmission images of ultrasound velocity distribution (UT\({}_{c}\)) on ultrasound tomography scanner, the transform-based filtered back projection method (FBP) [45], appropriately adapted to introduce projection sets of ultrasound propagation velocity and attenuation values, was used. From individual 2D images (so-called slices), 2D images in orthogonal cross-sections MPR (Multiplanar Reconstruction) [48], and 3D images using the MIP (Maximum Intensity Projection) tomographic technique [49] were also reconstructed.