# Duty Factor Reflects Lower Limb Kinematics of Running
## 4 Discussion  
In this study, in accordance with our hypothesis, DFhigh was relying on more lower limb flexion during \(t_{\rm c}\) than DFlow despite a similar knee flexion at FS. In addition, DFhigh was striking the ground using the rearfoot while the midfoot was used in DFlow. These two DF groups allow one to distinguish between two lower limb kinematic mechanisms in running. The DF values in our sample of runners (Table 1) were similar to those previously reported in the literature at similar running speeds and agree with the fact that DF values of running locomotion should be under 50.0% [17; 54; 60]. DFlow exhibited significantly shorter \(t_{b}\) and \(t_{p}\) but longer \(t_{e}\) and \(t_{d}\) associated with larger \(\Delta z_{\rm COM,\epsilon}\) and \(\Delta z_{\rm COM,\delta}\) than DFhigh (Table 2). In addition, with increasing running speed, DFhigh was more prone to decrease \(t_{b}\) and \(t_{p}\) and to increase \(t_{e}\) and \(t_{d}\) than DFlow (Table 2). Increasing the running speed leads to the decrease of \(t_{c}\) and increase of \(t_{f}\). Therefore, as DFhigh runners start from larger \(t_{c}\) and smaller \(t_{f}\) at 8 km/h than DFlow and as \(t_{c}\) and \(t_{f}\) cannot indefinitely decrease and increase, respectively, the observed results naturally follow. These findings are in agreement with the observations of [PERSON] et al. (2019). The running wheel was more vertical for DFlow than DFhigh while the antero-posterior range of motion was similar between groups (Figure 4). However, DFlow was shown to use a more anterior running wheel than DFhigh while DFhigh  
Figure 4: Running wheel for the high (DFhigh) and low (DFlow) duty factor running groups while running at 14 km/h. The running wheel is defined as the vertical versus antero-posterior position of the center of mass of the foot segment, expressed as a percentage of participant’s leg length. Position (0, 0) defines the point where the center of mass of the foot segment strikes the ground. FS: foot strike and TO: toe-off. a more posterior one than DFlow (Figure 4). These different running wheels are reflecting the different temporal characteristics and COM displacements between the DF groups. As DFlow depicted larger \(t_{d}\) and \(\Delta z_{\text{COM},d}\) than DFhigh, their vertical speed and thus vertical kinetic energy was higher at impact. In addition, the smaller \(t_{b}\) and \(t_{p}\) and therefore \(t_{c}\) observed in DFlow are indications that these runners have a presumably higher stiffness of the lower limb than DFhigh [61]. These observations led to the idea that DFlow relies on the reuse of elastic energy (optimization of the spring-mass model) while DFhigh limits vertical displacement of the COM and promote forward propulsion (pulley system) to minimize running economy [17]. Similar conclusions were drawn when classifying runners based on a subjective evaluation of the spontaneous overall running pattern [19]. Besides a different strategy to minimize running economy between these two DF groups, these differences in running biomechanics also suggest different lower limb kinematic mechanisms. Following the classification of FS pattern proposed by [PERSON] and [PERSON] (2012), DFhigh exhibited a rearfoot strike pattern [62] at FS while DFlow was midfoot strikers (Table 7). The fact that DFlow did not show a clear forefoot strike pattern is probably related to the fact almost 90% of the population is striking the ground with the rearfoot [63] and that the inclusion criteria of this study were not specifically based on the strike pattern. Nevertheless, taken as a group, DFlow runners were certainly using more their midfoot and forefoot than DFhigh (Table 7). Accordingly, a significantly more pronounced forefoot angle was observed at IA and MS for DFlow than DFhigh, suggesting that DFhigh is relying more on the rearfoot during \(t_{a}\) and \(t_{b}\) than DFlow. This is also partly explaining why the foot segment angle is not exactly zero at MS.