# Implementation of a Breast Phantom with Acoustic Properties for Ultrasonic Thermometry
## 5 Discussion
Although anatomical structure was not implemented, as in [PERSON]'s model [62], its design allows the identification of different tissue types, such as fat and predominantly water-based tissues like the gland and tumor. As mentioned earlier, these tissues exhibit different acoustic behaviors when subjected to temperature changes. In contrast, although [PERSON]'s anatomical model [62] presents a more realistic structure, it is not suitable for inspections at different temperatures due to the melting point of gelatin, which ranges between 27 and 30 \({}^{\circ}\)C according to [PERSON] [63]. This author also points out that the use of agar provides stability at temperatures below 90 \({}^{\circ}\)C and is thermoreversible, making it an ideal material for such applications. According to [PERSON] [17], the speckle tracking technique for temperature estimation establishes a linear relationship between ultrasound time of flight and temperature for increases of less than 10 \({}^{\circ}\)C, which has been validated in biological soft tissues. However, for higher temperature increases, though still below the necrosis threshold, it has been reported that this relationship becomes nonlinear. In this context, the technique remains viable for the temperature estimations proposed here for diagnostic purposes, as its application is confined to the 32 \({}^{\circ}\)C to 36 \({}^{\circ}\)C range, where the behavior remains linear. This interval ensures stable acoustic properties and enables the detection of small thermal changes, as shown graphically in Figure 9 for the tumor phantom case. Furthermore, [PERSON] [78] on computational modeling of breast tissue revealed temperature gradients in both healthy breast tissue and tumors with diameters of 5, 6, and 8 mm, emphasizing that 5 mm tumors exhibit temperature gradients within the range of 33 \({}^{\circ}\)C to 35 \({}^{\circ}\)C, which adds greater relevance to the analysis conducted in this study. The mathematical model proposed to calculate the SOS in fat (Equation (8)), derived from the combination of experiments for the individual case, healthy case, and tumoral case, within the limited range of 32 \({}^{\circ}\)C to 36 \({}^{\circ}\)C, showed a variation of \(-\)3.8061 m/s per \({}^{\circ}\)C. This behavior remained consistent across all experiments and demonstrated strong agreement with the results reported by [PERSON] et al. [55], who indicated values of 1422 m/s \(\pm\) 9 m/s for fatty breast tissue and 1470 m/s for a subcutaneous fat phantom. In the present study, the values obtained fall between these, with 1461.40 m/s at 32 \({}^{\circ}\)C and 1446.18 m/s at 36 \({}^{\circ}\)C for the fat phantom. Figure 10a illustrates the relationship between temperature and SOS, showing a change of \(-\)0.2616 \({}^{\circ}\)C per m/s, as specified in Equation (9). This serves as a predictive model for estimating temperature based on the SOS in fat phantoms. However, it is challenging to compare these results with other studies due to the specific range and the complexity of analyzing layered tissue structures. In contrast, the behavior of the SOS as a function of temperature (Equation (10)) and the temperature estimated from the SOS in the gland phantom (Equation (11)) exhibits a positive slope, as illustrated in Figure 10b. These results are derived from the combination of experiments conducted in each case. Specifically, variations of 0.6204 m/s per \({}^{\circ}\)C are observed, with boundary values of 1534.85 m/s at 32 \({}^{\circ}\)C and 1537.33 m/s at 36 \({}^{\circ}\)C. When comparing these data with those reported by [PERSON] et al. [55] for breast gland phantoms, an error of 1.31% is recorded concerning the lower limit obtained in this study; this error is 1.47% regarding the upper limit. Based on these results, it is confirmed that the change in SOS due to temperature in fat is opposite in direction to the behavior of the SOS in aqueous tissue, as mentioned by other authors [17; 27].