## 4 Results and Discussion
The classification results of Figure 9b obtained by the SOM method in Table 2 demonstrate that 33 cases are successfully classified. One case of the normal liver is falsely classified as abnormal. The follow-up study demonstrates that this false \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of MR Tagging Images** & **Normal Liver** & **Abnormal Liver** & **Difference between Two Groups** \\ \hline
16 (mm), sagittal & 68.7 & 62.8 & 5.9 \\
20 (mm), sagittal & 58.2 & 55.4 & 2.8 \\
16 (mm), coronal & 54.2 & 69.2 & 5.0 \\
20 (mm), coronal & 47.3 & 60.7 & 3.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average values of the difference in the power spectrum (DPS) 1. Figure 7: Comparing the DPS values between normal (��❝�) and abnormal cases (a) in four different types of grids with different scan directions and tag intervals by \(t\) test, the significance level has the maximum \(p\) value in 16 mm sagittal grid with \(p\) = 0.05, which is identical to the results from the BE method. classification may be caused by the subtle breathing action of the healthy patient, which makes the deformation of the liver insufficient. Figure 8: Results of calculated bending energy (**a**) and the differences in power spectra (**b**) for normal (**c**) and abnormal cases (**d**). Figure 9: Classification of normal cases (**e**) from abnormal cases (**a**) with two features: bending energy vs. difference in power spectrum by (**a**) automatic placement of landmarks vs. DPS from original image and (**b**) manually placing landmarks vs. DPS from the segmented liver image. In contrast to the 10+ min required to manually place corresponding landmarks on MR-tagging image pairs, segmentation of the liver region shown in Figure 5 only takes 1-2 min, since the demand for accuracy is not very high, which implies that FFT is faster than time domain processing, as there is no difference in the calculation of BE and DPS values. There are some limitations to our study, and these should be improved upon in future work. First, for the bending energy method, the results change based on the number of LMs used for calculation. Therefore, it is necessary to calculate the bending energy with the same number of the LMs in all cases. Second, this study is based on 2D processing, but liver deformation occurs in three dimensions. Using 3D BE/DPS values may greatly improve the precision of the assessment. Third, this study was conducted as preliminary technical development research, and considerable time and effort were expended to manually define the coordinates and record the values. We have now started to develop an automated algorithm to calculate BE values with cine-tagging MR images, as well as the automatic segmentation of the liver region for calculating the DPS value. Although the results are not yet satisfying, this MR elastography might be more practically incorporated into an MR imaging protocol if the output of the BE/DPS values are fully automated by implementing more intelligent algorithms. Finally, for the abnormal cases, there is no statistical difference between the BE/DPS values with F1/F2 and F3/F4, which is regarded as an important boundary for staging the fibrosis into curable or carcinoma control groups in clinical management. This may be due to either methodological errors in guiding the patients to breath without standard criteria or a low number of experimental datasets. We believe that, with more cases and with a more accurate and efficient liver extraction method, the deformation of tags would have a higher correlation coefficient with the abnormal group. It is possible not only to discriminate fibrotic and cirrhotic livers but also to differentiate individual fibrosis stages by using BE/DPS values or combining them with other effective features [28].