## 4 Discussion  
The main result of the present study is that the area and perimeter of PwMS were lower than those of HCs in the knee-angle/ankle-angle diagrams, whereas the differences in the hip-angle/knee angle diagrams did not reach statistical significance; therefore, our hypothesis was partially confirmed. Moreover, EMG activity revealed different leg muscle activation between the two groups during the stance phase. Overall, these findings suggest that the angle-angle diagram, when determined between the knee and the ankle joints, is a sensitive approach to detect gait alterations in ROM and coordination in PwMS with respect to controls while walking on a treadmill at the same speed. We are currently not aware of studies comparing the areas and perimeters of angle-angle diagrams determined at the level of hip, knee and ankle joints in PwMS and controls. Interestingly, [PERSON] et al. [8] reported alterations in intralimb joint coordination and ROM over a period of one year by inspecting the shape and size of hip-knee and knee-angle plots in PwMS and controls; however, the analysis was qualitative without quantifying the areas and perimeters of the loops. In the present study, quantitative analysis was possible through graphical determination of areas and perimeters in the two groups when walking at 1 km/h (PwMS and HCs) and 3 km/h (HCs); however, differences between the two groups at the same speed were computed only at 1 km/h, as the PwMS were not able to walk at speeds higher than 1 km/h. In the latter conditions, PwMS revealed a significantly reduced area (large effect size) and nearly significant perimeters differences compared to the HCs in the knee-angle/ankle-angle diagrams; however, they were able to maintain the goal speed of 1 km/h by increasing gait frequency. PwMS showed high variability within subjects in the area and perimeter in the hip-knee and knee-ankle diagrams between the strongest and weakest legs during a gait cycle (CV = 84/22.75%, Table 3). Additionally, the variability between subjects was high in the weakest (CV = 69.10/37.00%, Table 1) and strongest legs (CV = 72.16/7.77, Table 3). In a representative example of PwMS, the differences in area and perimeter between the weakest and strongest legs highlight a typical pattern (Figure 3A,B); specifically, the reduced conjoint range of motion (hip-knee) of the weakest leg is offset by the strongest leg, and the graph is lengthened along the positive \(X\)-axis values, indicating only forward hip rotation with large knee flexion. This pattern determined a higher perimeter, indicating that the two joints are uncoordinated during a gait cycle. A similar pattern is described by the knee-ankle diagram in which the very limited range of motion of the weakest leg is offset by the contralateral strongest leg (Figure 3B). Together, both diagrams are useful to describe the kinematic characteristics of PwMS when walking. However, as the variability between and within subjects is very high, the individual gait patterns are smoothed when averaging the values of several PwMS (Figure 3C,D). Concerning the HCs, the area and perimeter were more regular between the dominant (right) and nondominant legs (left) (Figure 4A,B); the CVs within subjects were 31% for the area knee angle and 11.24% for the perimeter (Table 3). In contrast, the variability between subjects in HC-1 was similar to that of PwMS in terms of the area and perimeter of both diagrams (hip-knee and knee-angle) (Table 3). Therefore, when the kinematic data of HCs were averaged, the individual characteristics were less appreciable in the graphs (Figure 4C,D). The high variability between HCs can be explained by the walking speed, as 1 km/h is too low and unusual for HCs; in other words, it represents a constraint. This condition reduced the step length and the foot contact near the projection of the centre of mass on the ground; consequently, knee flexion (cushioning effect) was absent, and the limb appeared to be a rigid lever in the hip-knee angle diagram (Figure 4C).