## 4 Case Study
### Results  
Step I: Construction of MS  
After collecting the information (Table 3), we calculated the MD using the formulas given in Section 2.2.1. To compute MD1, we utilised the healthy group data and the 11 features of selection. The 15 healthy subjects were used as the benchmark (healthy) group. The average and standard deviation of every characteristic from the HG were computed (Table 4) and the information from Table 5 was normalised using Equation (1). This normalised information was used to build the correlation matrix and its inverse (see Table 6). Next, the Mahalanobis distances were computed using Equation (4), as presented in Table 7. Likewise, using the inverse correlation matrix (Table 6) generated from the HG data, we computed the Mahalanobis distance for the 10 sets of PG data. The MDs of the HG were approximately equal to one, as shown in Figure 3. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Variables** & **Operational Definition** \\ \hline Step Length (cm) & X1 & Anterior-posterior distance from the heel of one footprint to the heel of the opposite footprint. \\ \hline Stride Length (cm) & X2 & Anterior-posterior distance between the heels of two consecutive footprints of the same foot (left to left, right to right); two steps (e.g., a right step followed by a left step) comprise one stride or one gait cycle. \\ \hline Step Width (cm) & X3 & Lateral distance from the heel centre of one footprint to the line of progression formed by two consecutive footprints of the opposite foot. \\ \hline Stance Time (s) & X4 & The stance phase is the weight bearing portion of each gait cycle beginning at heel contact and ending at toe off of the same foot; stance time is the time elapsed between the initial contact last contact of a single footfall. \\ \hline Swing Time (s) & X5 & The swing begins with toe off and ends with initial contact of the same foot; swing time is the time elapsed between the last contact of the current footfall to the initial contact of the next footfall of the same foot. \\ \hline Single Support Time (s) & X6 & Single support occurs when only one foot is in contact with the ground; single support time is the time elapsed between the last contact of the opposite footfall to the initial contact of the next footfall of the same foot. \\ \hline Double Support Time (s) & X7 & Double support occurs when both feet are in contact with the ground simultaneously; double support time is the sum of the time elapsed during two periods of double support in the gait cycle. \\ \hline Stance Time (\%GC) & X8 & Stance time normalised to stride time. \\ \hline Double Support Time (\%GC) & X9 & Double support time normalised to stride time. \\ \hline Gait Speed (m/s) & X10 & Calculated by dividing the distance walked by the ambulation time. \\ \hline Stride Speed (m/s) & X11 & Calculated by dividing stride length by the stride time. \\ \hline \hline \end{tabular} Note = \(\%\)GC = \(\%\) gait cycle.  
\end{table} 
Table 2: Operational definitions of gait parameters and variables. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**HG**} & \multicolumn{2}{c}{**PG**} \\ \cline{3-6}  & & **Mean** & **SD** & **Mean** & **SD** \\ \hline Step Length & (m) & 0.584 & 0.043 & 0.562 & 0.030 \\ Stride Length & (m) & 1.161 & 0.077 & 1.079 & 0.197 \\ Step Width & (m) & 0.156 & 0.049 & 0.153 & 0.060 \\ Stance Time & (s) & 0.864 & 0.157 & 0.961 & 0.172 \\ Swing Time & (s) & 0.566 & 0.116 & 0.604 & 0.076 \\ Single Support Time & (s) & 1.100 & 0.176 & 1.023 & 0.284 \\ Double Support Time & (s) & 0.312 & 0.087 & 0.390 & 0.094 \\ Stance Time & (\%GC) & 60.502 & 3.409 & 61.186 & 3.381 \\ Double Support Time & (\%GC) & 21.918 & 2.946 & 28.584 & 8.888 \\ Gait Speed & (m/s) & 0.507 & 0.088 & 0.425 & 0.085 \\ Stride Speed & (m/s) & 42.974 & 6.198 & 39.09 & 5.762 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean and standard deviation (SD) of healthy group (HG) and ACLR group (PG) for all variables.