# Implementation of a Breast Phantom with Acoustic Properties for Ultrasonic Thermometry
## 6 Conclusions  
A multilayer breast phantom was developed to mimic the ultrasonic behavior of tissues that compound human breast tissue in a temperature range of 32 \({}^{\circ}\)C to 36 \({}^{\circ}\)C. The objective was to provide a viable phantom to assess thermometric applications oriented toward cancer diagnosis. The phantom was composed of adipose, glandular, and tumoral layers; the glandular and tumoral phantoms consist of a mixture based on agar, distilled water, vegetable oil, sodium chloride, and detergent. Different concentrations of these materials were used depending on the type of tissue. The breast fat was simulated with a liquefied layer of lard. A variant of this phantom without the tumoral layer was reproduced to mimic a healthy breast. In the first stage, individual samples of each layer were created and inspected in the specified temperature range using an ultrasonic pulse-echo method. As a second step, phantoms consisting of two (fat and gland) or three (fat, gland and tumor) superposed layers were constructed and inspected in the same temperature range. To evaluate the SOS changes with temperature variation in each layer, the cross-correlation technique was applied to the acquired ultrasonic signals and delays between interlayer echoes were obtained using the signal at the lower temperature of 32 \({}^{\circ}\)C (taken as the basal temperature of the breast surface) as a reference. Afterwards, linear regression was used to obtain the relation between the SOS and the temperature for each type of phantom. The obtained equations were \(C(T)=(-3.8061)T+1583.2[\mathrm{m/s}]\); \(C(T)=(0.6204)T+1515.0[\mathrm{m/s}]\) and \(C(T)=(1.5743)T+1522.3[\mathrm{m/s}]\) for adipose, glandular, and tumoral phantoms, respectively. In all cases, all average measurements fall into a confidence interval of 95%. The results confirmed that the SOS in the different tissues followed a linear relationship with temperature; this finding is consistent with previously reported data. While the phantom models in this study effectively replicated the acoustic properties of breast tissue, limitations such as the need for greater precision in simulating individual tissue variations were identified. Not all acoustic and thermal parameters were measured to validate the phantom's behavior in response to temperature variation; this is because the main objective of the developed phantom is thermal estimation based on the SOS measurement. However, the composition of the mixture was formed by components that have been previously proven to have similar thermal properties as breast tissue. In a future study, the development of a more realistic phantom that approximates multiple thermal properties of tissue could be addressed, improving the phantom models and their clinical validation. Another important characteristic in this kind of application is the characterization of expansion coefficients; ultrasonic thermometric methods currently consider this issue to be negligible, but it could introduce undesirable deviations in the measurements. Finally, additional measurement repetitions could be performed to enable us to obtain more representative statistics. However, our measurements fall into the classical sample set reported in other works. Conceptualization, R.V.A.M. and I.B. ; Data curation, R.V.A.M. ; Formal analysis, R.V.A.M., I.B. and A.R.-G.; Funding acquisition, I.B. ; Investigation, R.V.A.M., I.B. and A.R. G.; Methodology, R.V.A.M., I.B. and A.R.-G.; Project administration, I.B. and A.R.-G.; Resources, I.B. ; Software, R.V.A.M. ; Supervision, I.B. and A.R.-G.; Validation, I.B. and A.R.-G.; Visualization, R.V.A.M., Writing--original draft, R.V.A.M. ; Writing--review and editing, I.B. and A.R.-G. All authors have read and agreed to the published version of the manuscript.