# Analysis of the Refraction Effect in Ultrasound Breast Tomography
## 1 Introduction
A novel hybrid method that can overcome most of the disadvantages of MMG, USI, and MRI is ultrasound breast tomography (UBT). Recently, several research centers around the world performed work to build a prototype of the ultrasound computer tomography device for a breast screening imaging tool in women (with the ability to scan, measure, acquire data, and reconstruct and process images in vivo) [17; 18; 19; 20; 21]. The design, operation and imaging methods of each device are specific and varied. One of the few advanced prototypes of in vivo hybrid ultrasound breast tomography scanners was developed in Poland by DRAMINSKI S.A. company [20; 21]. The device uses transmission ultrasound tomography (UTT) and reflection ultrasound tomography (URT) modalities [22] to image female breast tissue, as well as the omnidirectional (full-angle) spatial compound ultrasound imaging modality (FASCI) by assembling multiple ultrasound images acquired at angles selected from 0 to 360\({}^{\circ}\)[23], analogous to the so-called compound imaging (CI) method. The FASCI modality is used as a complement to the UTT and URT modalities. This approach enables the acquisition of comprehensive diagnostic information on the tissues under study. It should be noted that physicians are extremely interested in the additional B-mode echographic breast imaging modality implemented in the ultrasound tomography scanner as a well-known standard for medical diagnosis. The device, which combines several ultrasound technologies, is universal (no age limits) and neutral for health (no ionizingradiation or contrast agents). The use of a UBT scanner in breast screening is expected to create a new world standard in breast disease diagnostics. The quality of quantitative images obtained as a result of the reconstruction process from the measurement of the transmission transit time of ultrasound wave pulses with the use of the hybrid UBT scanner is adversely affected by the phenomenon of beam refraction at the water and submerged breast border (also in inhomogeneities in the breast structure [24]). The influence of this phenomenon can be considered and significantly reduced using waveform tomography, ray-based inversion, ray-tracing, and ray-linking methods [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35]. However, this requires the acquisition of a preconstructed pattern and is limited by extreme computational costs, despite the possibility of using various simplifications and regularizations, as well as by the need to acquire, store, and process a huge amount of measurement data. These methods essentially undermine breast imaging during or immediately after in vivo scanning, significantly increasing the cost of manufacturing the UBT scanner. In the present study, research was conducted to minimize the effect of the phenomenon of refraction on quantitative ultrasound tomography imaging of breast structure in a manner that does not require complex computational techniques or waveform or inversion image reconstruction methods [32; 33; 34; 35]. To this end, the effect of refraction on transmission tomography measurements of the transit time of an ultrasound wave through female breast tissue under immersion conditions in water was analyzed. It was found that refraction introduces the largest measurement errors in the area of the water/breast interface and can be reduced by the appropriate choice of water temperature and changing the breast geometry. In vivo test breast examinations were performed on the owned prototype hybrid ultrasound tomography scanner. The results obtained allowed us to improve the quality of reconstructed breast images using an efficient transformation algorithm that assumes straight-line ultrasound propagation paths between transmitters and receivers [22], without the need for special hardware in the form of expensive and energy-intensive GPU graphics cards [30].