# Implementation of a Breast Phantom with Acoustic Properties for Ultrasonic Thermometry
## 2 Theoretical Framework
### Breast Thermal and Ultrasonic Properties of Interest  
The human mammary tissue is a complex anatomical structure that comprises adipose, glandular, connective, and muscular tissues. It undergoes morphological and physiological changes throughout the female lifecycle, which affect the acoustic properties of the tissue, particularly its ultrasonic response. [PERSON] et al. [54] suggest a correlation between a woman's age and the mean sound velocity and attenuation coefficient in the breast. The SOS and attenuation values in cancerous tissues are higher than those in surrounding normal tissues, such as glandular and fatty tissues. According to [55], the SOS of fatty breast tissue is 1422 \(\pm\) 9 m/s, while the SOS of mammary parenchyma is 1487 \(\pm\) 21 m/s. In relation to malignant and benign breast lesions, they are reported to have SOSs of 1548 \(\pm\) 17 m/s and 1513 \(\pm\) 27 m/s, respectively. In addition, this study documents an SOS of 1515 m/s for a glandular tissue phantom, 1549 m/s for a small tumor phantom, and 1470 m/s for a subcutaneous fat phantom. It is important to note that no ultrasonic SOS values have been found in the literature for each of the tissues that compose the breast at temperature ranges that are characteristic of the early stages of cancer diagnosis (32-36 \({}^{\circ}\)C). Although we have knowledge of the correlation between the ultrasonic velocity and temperature, depending on tissue composition (for fatty tissues, SOS is inversely proportional to temperature increase, while for tissues with higher water content, it is the opposite), there are no concrete estimates for each tissue [17; 27]. The attenuation value ranges from 1.01 to 1.18 (DB/cm/MHz) with a standard deviation of 0.17 to 0.29, depending on the stage. The highest value is observed in premenopausal women [54]. The thermal conductivity value typically ranges between 0.42 and 0.5 (W/m/K) [56]. Phantoms that accurately replicate the physical properties of breast tissue are crucial for testing and evaluating these parameters across various protocols. In ultrasound thermometry for diagnostic purposes, it is necessary to characterize the temperature sensitivity of the phantom ultrasonic parameters to accurately quantify the temperature changes associated with breast lesions. In this context, the SOS is particularly important, while the expansion coefficient is often considered to be negligible. In this work, a phantom to mimic the SOS behavior when temperature increase for fatty, glandular and tumoral layers was developed. Attenuation and thermal conductivity were approximated to those values of real tissue. Review of Ultrasonic Phantoms: Properties of the Materials and Protocols Used for the Construction of Phantoms, Oriented Towards Thermal Applications  
Several researchers have developed breast phantoms for thermal applications; however, many of these phantoms are evaluated at ambient temperature, with a few tested over a limited range of 43-48 \({}^{\circ}\)C [57] in the tumor for HIFU treatment applications. Most of these phantoms are constructed using a single homogeneous medium that approximates certain properties of the tissue; few developments consider a composed phantom. This section reviews some of these studies, discussing the properties of the phantoms and the materials used in their construction. [PERSON] et al. and [PERSON] et al. [58; 59] developed a tissue-mimicking phantom for ultrasound applications based on agar to simulate the SOS in soft tissues, achieving values ranging from 1498 m/s to over 1600 m/s at 22 \({}^{\circ}\)C, with 1540 m/s representing the average speed built into most ultrasound scanners. The study found that the concentration of graphite powder determined the attenuation, while the concentration of n-propanol influenced the SOS. [PERSON] et al. [60] developed an agar-based phantom adaptedfrom the Burlew procedure, incorporating water, agar, graphite powder, methylparaben, and 1-propanol.