# A Parametric Identification Method of Human Gait Differences and its Application in Rehabilitation
## 3 Results
### Patient Group  
Based on the same commonality points and mathematical models with the normal group, the shape parameters of the patient group were calculated and are displayed in Table 4. It can be seen that the parameters of most subjects were beyond the normal ranges to varying degrees. Figure 7 also shows every gait periodic curve of the patients, which can further explain and verify the characterization of shape parameters. Here, we defined that patients A and B were the ones in the second month of rehabilitation, patients C and D were in the third month, and patients E and F were in the sixth month for convenience. For the hip joint, the latter two parameters of patients A and B were smaller than the normal range, representing that the waves in the two places were lower than the curve distribution area of the normal group, which was consistent with the results of the red and orange lines in Figure 7a. In the third month of convalescence, only the second parameter of patient C was smaller while the last two parameters of patient D were smaller, indicating that the second wave of patient C and the last two waves of patient D were less than the normal distribution range. Moreover, the parameters' values showed that the amplitudes of patients C and D were larger and tended to be normal compared to that of patients A and B, which is indicated by the gray and purple lines. In the sixth month of recovery, the parameters of patients E and F were within the normal range, except for the last parameter of patient E, as shown in the pink and blue lines. For the knee joint, the third parameters of patients A, B, and C, and the second parameters of D, E, and F were all lower than the normal range. It can also be seen from Figure 7b that the third amplitudes of patients A, B, and C presented a state far away from normal gradually, and the second  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**Shape Parameters of the Patient Group**} \\ \hline  & \multicolumn{3}{c}{Hip} & \multicolumn{3}{c}{Knee} & \multicolumn{3}{c}{Ankle} \\ \hline  & \(\lambda_{0}\) & \(\lambda_{1}\) & \(\lambda_{2}\) & \(\lambda_{0}\) & \(\lambda_{1}\) & \(\lambda_{2}\) & \(\lambda_{0}\) & \(\lambda_{1}\) & \(\lambda_{2}\) & \(\lambda_{3}\) & \(\lambda_{4}\) & \(\lambda_{5}\) \\ \hline A & \(-2.26\) & \(0.02\,\)* & \(-2.77\,\)* & \(-2.80\) & \(1.08\) & \(-2.96\,\)* & \(-6.00\,\)* & \(-13.20\) & \(1.12\) & \(-17.00\) & \(-  
amplitudes of patients D, E, and F were just slightly less than normal. These phenomena revealed that most of the patients with a short recovery period were mainly abnormal in the third parameter. For the ankle joint, the first, fifth, and sixth parameters of patient A, the first, second, and fifth parameters of patient B, and the fifth parameter of patient C were all smaller. It should be noted that the first and fifth parameters of patients A and B were not only smaller than the normal range but also reached the critical values from Equation (9), indicating that they could not be effectively fitted. For patient D, the first and fourth parameters were larger and the second parameter was smaller. The first parameter of patient E was larger while the sixth parameter of patient F was smaller. Figure 7c also expresses that patients A and B were significantly lower than the normal range at the first and fifth amplitudes corresponding to the abnormal parameters, as seen by the red and orange lines. Patient C (grey line) was slightly lower than the normal value at the fifth amplitude, and the curve of patient D (purple line) tended to the normal ranges. By contrast, the curves of patients E and F (pink and blue lines) in the sixth month of recovery basically belonged to the normal range. Consequently, the properties of shape parameters were consistent with the data graphics, so the shape parameters can effectively reflect the normal and abnormal gait. Furthermore, the results of the shape parameters' ranges from the normal group and patient group were very similar with the previous assumptions.