## 3 Results and Discussion
### Chicken Breast Muscle Tissue
It is noted that the relationship between \(\mu_{s}^{{}^{\prime}}\) and temperature established above allows us to obtain the temperature distribution of a tissue sample from the \(\mu_{s}^{{}^{\prime}}\) image of the sample. To achieve this goal, the \(\mu_{s}^{{}^{\prime}}\) values within the image domain were classified into a few different ranges and then mapped into temperatures using the methods shown in Table 3. As we only established the relationship between \(\mu_{s}^{{}^{\prime}}\) and temperature between 45 and 59 \({}^{\circ}\)C in this study, the tissue temperature was set to be the ambient temperature (i.e., 21 \({}^{\circ}\)C) if the \(\mu_{s}^{{}^{\prime}}\) value was lower than that at 45 \({}^{\circ}\)C. The temperature maps of porcine and chicken breast muscle samples at 10 min after HIFU treatment were obtained based on the polynomial model and exponential model, and the resulting temperature maps are shown in Figure 6.  
In addition to the temperature estimation, the real-time optical property changes in tissue imaged by DOT themselves could be directly utilized as indicators of HIFU treatment progression to optimize the treatment. Furthermore, the quantitative correlation between \(\mu_{s}^{{}^{\prime}}\) and temperature indicates that this approach has the potential to predict tissue temperature at the HIFU focal point during HIFU therapy. While these results are promising, we still noticed that the precision of the temperature prediction by utilizing this method is not good as that of traditional thermometry, such as a thermocouple. By increasing the temporal resolution of the DOT imaging system, the recovered volumetric \(\mu_{s}^{{}^{\prime}}\) distribution will be more stable and prone to less errors by applying more averaging. Therefore, the precision of temperature prediction will increase when the temporal resolution is increased. Additionally, we noticed that a limitation of this approach is that the relationship between temperature and \(\mu_{s}^{{}^{\prime}}\) is nonlinear, which adds the complexity of this approach. The primary reason is that the changes in optical properties are directly related to thermal dose. Therefore, it may cause delays in optical property changes with temperature. However, if all parameters associated with HIFU stay the same, the whole treatment process should be repeatable, which has been demonstrated by the extensive experiments presented in this work. Thus, this nonlinear relationship between temperature and optical property (\(\mu_{s}^{{}^{\prime}}\)) still could be used to predict the temperature changes during HIFU treatment. Considering \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **S1** & **S2** & **S3** & **S4** & **S5** & **Average** \\ \hline \multirow{2}{*}{**Polynomial**} & 1 st & 1.45 & 1.38 & 2.37 & 2.12 & 1.00 & **1.67** \\  & 2 nd & 0.47 & 0.36 & 0.28 & 0.31 & 0.52 & **0.39** \\ \hline \multirow{2}{*}{**Exponential**} & & 1.00 & 0.97 & 1.07 & 0.90 & 0.79 & **0.94** \\ \hline \end{tabular}
\end{table} 
Table 2: Root mean square error (RMSE) of five chicken breast samples (units: \({}^{\circ}\)C). \begin{table}
\begin{tabular}{c c c c c c} \hline  & & **Polynomial (P)** & & **Exponential (E)** \\ \hline \multirow{2}{*}{Pocrine} & \(\mu_{s}^{{}^{\prime}}\) (mm\({}^{-1}\)) & \textless{}0.33 & [0.33, 0.49) & [0.49, 1.5] & \textless{}0.49 & [0.49, 1.5] \\  & T (\({}^{\circ}\)C) & 21 & P\_1 st & P\_2 nd & 21 & E \\ \hline \multirow{2}{*}{Chicken} & \(\mu_{s}^{{}^{\prime}}\) (mm\({}^{-1}\)) & \textless{}0.16 & [0.16, 0.22) & [0.22, 0.7) & \textless{}0.16 & [0.16, 0.7] \\  & T (\({}^{\circ}\)C) & 21 & P\_1 st & P\_2 nd & 21 & E \\ \hline \end{tabular}
\end{table} 
Table 3: Mapping between \(\mu_{s}^{{}^{\prime}}\) and temperature (T) (P_1 st: fittings using polynomial model in the 1 st stage; P_2 nd: fittings using polynomial model in the 2 nd stage).