## 3 Results and Discussion
### Chicken Breast Muscle Tissue  
Similarly to Section 3.1, Figure 4a shows the photograph of a chicken breast muscle tissue treated by HIFU for 10 min. The damage spot caused by HIFU (indicated by arrow) had a diameter of 5 mm. The reconstructed \(\mu_{s}^{{}^{\prime}}\) images in the XY and YZ plane are shown in Figure 4b. It is shown that \(\mu_{s}^{{}^{\prime}}\) increased almost 2.5-fold by the time the temperature reached 54.8 \({}^{\circ}\)C. The measured temperature and reconstrued \(\mu_{s}^{{}^{\prime}}\) values around the HIFU focus point are shown in Figure 4c,d, respectively. Figure 5 shows the details of the two-degree polynomial and the two-term exponential models. Figure 5a,c shows the fitting curves (solid lines) with the polynomial and exponential models, respectively, along with the average temperature-\(\mu_{s}^{{}^{\prime}}\) data (blue circles) taken from five porcine muscle tissues treated by HIFU for 10 min per sample. We also utilized the data similarly when the temperature was higher than 45 \({}^{\circ}\)C. In the polynomial model, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **S1** & **S2** & **S3** & **S4** & **S5** & **Average** \\ \hline \multirow{2}{*}{**Polynomial**} & 1 st & 2.08 & 1.39 & 2.78 & 1.87 & 1.24 & **1.87** \\  & 2 nd & 0.46 & 0.43 & 0.38 & 0.56 & 0.39 & **0.44** \\ \hline \multirow{2}{*}{**Exponential**} & & 1.29 & 0.91 & 1.83 & 0.89 & 0.80 & **1.14** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Root mean square error (RMSE) of five porcine muscle tissues (units: \({}^{\circ}\)C). Figure 3: Fitting (**a**) polynomial model and (**c**) exponential model to measured DOT data of porcine muscle tissues. Comparison between the temperatures calculated/predicted by (**b**) polynomial and (**d**) exponential methods (solid line), and those measured by a thermometer (scattered points) as a function of \(\mu_{s}^{{}^{\prime}}\). the whole process was divided into two steps (1 st step: 45 to 54 \({}^{\circ}\)C, 2 nd step: 54 to 59 \({}^{\circ}\)C). Then, we compared the calculated temperature (by (b) polynomial and (d) exponential method, solid line) with the measured data (scattered points) of another five samples. Finally, the RMSEs based on chicken breast tissues were calculated, and the results are displayed in Table 2. It was 1.67 \({}^{\circ}\)C in the 1 st step and 0.39 \({}^{\circ}\)C in the 2 nd step for the polynomial model. For the exponential model, the RMSE was 0.94 \({}^{\circ}\)C.  
Figure 4: (**a**) Photograph of a chicken breast sample treated by HIFU along the \(z\)-axis (**b**) Recovered \(\mu_{s}^{\prime}\) distribution in XY and YZ planes (t = 54.8 \({}^{\circ}\)C). (**c**) Temperature versus time and (**d**) recovered \(\mu_{s}^{\prime}\) versus time of five chicken breast samples treated by HIFU in 10 min per sample. Figure 5: Fitting (**a**) polynomial model and (**c**) exponential model to measured DOT data of chicken breast muscle tissues. Comparison between the temperatures calculated/predicted by (**b**) polynomial and (**d**) exponential methods (solid line) and those measured by a thermometer (scattered points) as a function of \(\mu_{s}^{\prime}\). We noticed the difference in the fitting results between the chicken breast and porcine samples. The reason for this difference is likely due to the nonlinear relationship between temperature and optical properties. It may also be related to the differences in acoustic properties (especially acoustic absorption coefficient) of the two different tissues. In addition, we studied the changes in \(\mu_{s}^{{}^{\prime}}\) when HIFU was off and temperature decreased. The results showed only a slight decrease in \(\mu_{s}^{{}^{\prime}}\) with the drop in temperature. The reason is that the optical property changes due to the tissue damage under HIFU treatment are irreversible. While the heating source was revoked and temperature dropped, the optical properties of tissue could not fully recover anymore.