# Analysis of the Refraction Effect in Ultrasound Breast Tomography
## 4 Discussion  
Based on the calculations and measurements performed, it was found that in the ultrasound transmission tomography breast scanning procedure for the incidence angles of ultrasound wave beam rays at the water/breast border greater than about 50\({}^{\circ}\), rays are increasingly refracted, resulting in the formation of a \"ring of distortions\" in the reconstructed breast cross-sectional image with distortions increasing in the direction of the cross-sectional border. The thickness of this ring decreases with the ratio of the breast diameter to the diameter of the measurement area. Of course, glandular tissue is not homogeneous and, in addition to the distortion associated with refractions at the cross-sectional boundary of the breast around, which will always occur, distortions associated with heterogeneity of the inner breast tissue may appear in different areas of the image (see Figure 4). Refractions can be particularly detrimental in the vertical plane due to the narrow beam of the ultrasound wave, for which diverging rays may not find their way from the transmitter to the receiver after refraction, due to negligible energy. This phenomenon is explained illustratively in Figure 18, which shows the spatial path of a refracted ultrasound wave beam ray through water and breast tissue from the selected sending transducer to the receiving one of ring array for the selected horizontal measurement plane, and the orthogonal projections of this path in the horizontal and vertical planes. Figure 17: Reconstructed MPR images of breast cross-sections of Patient 1 studied in vivo at a water temperature of 20 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 30 \({}^{\circ}\)C presented in standard and inverted grayscale, respectively, and before and after automatic removal of water pixels around the breast (H—head, F—feet, L—left, R—right, P—posterior, A—anterior). Refractions in the horizontal plane are larger the more the ray is angularly deviated from the diameter of the ring array, and they become significant from the value of the angle of incidence at the water/breast border of about 50\({}^{\circ}\). Refractions in the vertical plane are greater the closer the measured breast section is to the end of the breast (closer to the nipple), but they also become significant from the value of the angle of incidence at the water/breast border of about 50\({}^{\circ}\). Due to refractions in the vertical plane, the cross-section is always measured slightly higher than the geometric center of the transducer ring in their height. This distance increases as the ring array is lowered. On the basis of these calculations, it can be predicted that for a breast of standard size, ultrasound tomography images of its cross-section (especially ultrasound velocity distribution) in the region of about 2 cm from the nipple will have significant errors. To limit the possibility of obtaining large angles of incidence of ultrasound wave beam rays on the breast tip in the vertical plane, it would be necessary to slightly change the breast geometry during measurements by slight vertical stretching or loading of the nipple. It may be a problem in the case of small and dense breasts. Calculations also showed that significant minimization of refraction can be achieved at the water/skin/fat/breast interface by lowering the water temperature to about 32 \({}^{\circ}\)C. Furthermore, calculations showed that the length of time the breast was held at this temperature was not significant, since the results for the model that included the temperature gradient in the subcutaneous fat layer were not significantly different from the results for the model without the gradient. It should be considered here that the calculations were performed for mean values of the parameters of breast skin, fat, and glandular tissue and a fixed thickness of the skin (2 mm) and the fat layer under the skin (5 mm).