## 4 Discussion  
In this study, we used in vivo motion analysis and multibody musculoskeletal models to test the hypothesis that a higher improvement in clinical and functional outcome shown in DDH patients who received hip abductor strengthening after hip replacement [10], would result in different musculoskeletal loads (i.e., joint contact forces and muscle forces) during walking compared to patients who performed standard rehabilitation only. Gait analysis revealed mild abnormalities in the time-distance parameters and in the pelvic and hip kinematics, with few significant differences between the two groups (Tables 2 and 3). Although only few articles are available for gait analysis in DDH patients operated on hip prosthesis [11; 19; 29], our results are in general agreement with findings of slower gait, shorter stride, reduced range of motion in the sagittal and coronal planes [11], and lower pelvic rotation in the coronal plane [29] with respect to healthy subjects. In  
Figure 3: Linear correlations between gait speed and hip contact force peaks in all walking trials, for the Study Group (**A**) and Control Group (**B**). Correlation coefficients (R) are reported and indicated with an asterisk (*) when statistically significant (\(p<0.05\)). Figure 2: Boxplot distributions of the peaks of hip contact forces during gait compared between the Study and Control Groups, in the operated leg (**A**) and contralateral leg (**B**). \(P\)-values are reported for the significant differences between groups (Mann–Whitney U-test). addition, functional outcome data in terms of 10 Meter Walk Test, Harris Hip Score and WOMAC demonstrated a better outcome in the Study Group with results very similar to those of the entire sample of patients reported in [10] (Table S1). Overall, the protocol for abductor muscle strengthening has a mild effect on joint contact forces and muscle forces during walking in the operated limb. We would have expected a more marked effect of strengthening on loads from the hypothesis tested, given the significant difference in abduction strength between groups [10], and the major influence of hip abductor strength on joint contact forces shown in a previous simulation study [30]. In the present study, the patients in the Study Group generally experienced a greater hip force in the operated limb compared to the Control Group (Figures 1 and 2), although with significant differences in a small portion of the gait cycle. This mild difference in hip contact force is, however, likely related to gait speed, which was greater in the Study Group (Table 3, Figure 3). The influence of gait speed on hip contact force during the gait cycle can also explain the force pattern where a typical two-peak pattern is present, more similar to that in both healthy population and THR patients, with a lower force magnitude in both peaks compared to the healthy [28; 31]. As we found speed as an influent parameter in our results (Figure 3), we performed a post-hoc analysis where we tried to remove the two slower walking patients from the six patients of the Control Group, with all possible cautions in interpreting the results, given the small number of subjects. This led to a more physiological pattern of hip contact force (i.e., more marked double-bump), but the statistical significance of the differences between groups was only changed slightly. Therefore, we decided to keep all patients in the Control Group, considering also that the two slower patients were globally not more nor less involved than the others. The lack of differences in muscle forces of the hip abductors and flexors between limbs is difficult to interpret, also considering that there is no consensus in the literature about the effect of impaired muscle status on joint contact forces. Unfortunately, no similar studies are available on hip contact and muscle forces after THR in DDH patients, indeed this is the first study that analyzed the musculoskeletal loads during gait in DDH patients after THR.