## 3 Results and Discussion
In our previous study, considering that the layered fibrous structures can result in deviations of MMPD linear birefringence orientation parameters, we proposed a modified MMPD parameter \(\theta_{e}\) to more accurately represent the fast axis orientation of the complicated linear birefringent structures in tissue samples [26]. Meanwhile, it was also found that while applying the MMT parameters \(\phi_{2434}\), \(\phi_{4243}\) to the fibrous tissue samples, they exist with positive or negative deviations from the ideal values. Hence, according to the experimental results, we proposed a modified MMT parameter, \(\phi_{qr}\) shown in Equation (16), for layered linear birefringent structures. To verify its effectiveness, the correlation and statistical analysis are conducted with the variance of parameters groups (\(\theta_{e}\), \(\phi_{2434}\)), (\(\theta_{e}\), \(\phi_{4243}\)) and (\(\theta_{e}\), \(\phi_{qr}\)), whose results are shown in Table 6 and Figure 5. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Type**} & \multirow{3}{*}{**Tissues**} & \multicolumn{6}{c}{**Linear Retardance**} \\ \cline{3-8}  & & \multicolumn{3}{c}{\(R^{2}\)} & & \multicolumn{3}{c}{\(p\)} \\ \cline{3-8}  & & \(\delta\)**–\(t_{2434}\)** & \(\delta\)**–\(t_{2425}\)** & \(\delta\)**–\(t_{qr}\)** & \(\delta\)**–\(t_{2434}\)** & \(\delta\)**–\(t_{2434}\)** & \(\delta\)**–\(t_{qr}\)** \\ \hline \multirow{4}{*}{Backward} & breast & 0.65 & 0.76 & 0.73 & \(<\)0.05 & \(<\)0.05 & \(<\)0.05 \\  & rat-skin & 0.46 & 0.65 & 0.68 & \(<\)0.01 & \(<\)0.01 & \(<\)0.01 \\  & porcine-intestine & 0.73 & 0.74 & 0.74 & \(<\)0.01 & \(<\)0.01 & \(<\)0.01 \\  & porcine-stomach & 0.33 & 0.16 & 0.22 & \(<\)0.01 & \(<\)0.01 & \(<\)0.01 \\  & porcine-liver & 0.65 & 0.89 & 0.84 & \(<\)0.01 & \(<\)0.01 & \(<\)0.01 \\  & Total & 0.63 & 0.65 & 0.66 & \(<\)0.01 & \(<\)0.01 & \(<\)0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Correlation and statistical analysis comparison results between backscattering measured MMT and MMPD linear retardance parameters for each kind of bulk tissue samples. Figure 4: Comparison of MMT and MMPD linear retardance parameters of bulk tissue samples. (**a**) Linear retardance MMPD parameter \(\delta\) plotted against its counterpart MMT parameter \(t_{2434}\) for correlation analysis with all five kinds of bulk tissue samples. (**b**) Statistical analysis bar chart of linear retardance related MMPD parameter \(\delta\) and MMT parameter \(t_{2434}\) for each kind of bulk tissue samples. (**c**) Linear retardance MMPD parameter \(\delta\) plotted against its counterpart MMT parameter \(t_{4243}\) for correlation analysis with all five kinds of bulk tissue samples. (**d**) Statistical analysis bar chart of linear retardance MMPD parameter \(\delta\) and MMT parameter \(t_{4243}\) for each kind of bulk tissue samples. (**e**) Linear retardance MMPD parameter \(\delta\) plotted against its counterpart MMT parameter \(t_{qr}\) for correlation analysis with all five kinds of bulk tissue samples. (**f**) Statistical analysis bar chart of linear retardance MMPD parameter \(\delta\) and MMT parameter \(t_{qr}\) for each kind of bulk tissue sample.