## 3 Results  
### OpenSim Model Verification  
As illustrated in Figure 3, a resemblance was observed between the muscle activation deduced using OpenSim's CMC tool and the EMG data obtained during the present study. The results from the FD analysis demonstrated a significant correlation between ACL strain and force (Figure 4). More specifically, the correlation between ACL force and ACL strain showed strong connection for each CM condition before the running training (R\({}^{2}\) = 0.94, 0.92, and 0.97 for 90\({}^{\circ}\), 135\({}^{\circ}\), and 180\({}^{\circ}\) CM). After completing the running training, the correlation between ACL force and ACL strain showed slightly stronger association as R\({}^{2}\) = 0.97, \(p\) = 0.001 for 90\({}^{\circ}\) CM, R\({}^{2}\) = 0.98, \(p\) = 0.001 for 135\({}^{\circ}\) CM, and R\({}^{2}\) = 0.98, \(p\) = 0.001 for 180\({}^{\circ}\) CM. The One-Dimensional Statistical Nonparametric Mapping (SNPM1d) Comparison Results of Kinematics and Kinetics  
In a case of non-Gaussian distribution of the data we use non-parametric test to compare the time series dataset of (knee angle, moment, and contact force, as well as ACL strain in three horizontal planes during 90\({}^{\circ}\), 135\({}^{\circ}\) and 180\({}^{\circ}\) CM). We observed that ACL strain was lower after IR training during the 90\({}^{\circ}\) CM (Figure 5), and this difference was significant at 0-64%, \(p\) = 0.011 and 92-100%, \(p\) = 0.010 of the stance. Similarly, during the 135\({}^{\circ}\) CM, a lower ACL strain was observed after the IR training, but the difference was only significant at the beginning (0-8%, \(p\) = 0.012) of the stance phase. This was the case with 180 CM as well, however significant difference was not only found at the beginning of CM (0-8%, \(p\) = 0.010) but also at midstance phase as well (50-64%, \(p\) = 0.010). Figure 3: The comparison of the experimentally measured (pink area) and the OpenSim-CMC (blue dashed line) simulated muscle activity for each muscle. The corresponding curves representing the mean values over the stance phase of CM at all three conditions (90\({}^{\circ}\), 135\({}^{\circ}\), 180\({}^{\circ}\)). Abbreviations: BFLH—biceps femoris long head, RECFEM—rectus femoris, GASMED—medial gastrocnemius, TIBANT—tibialis anterior. Figure 4: Below are the correlations between ACL strain and force for the three CM directions, pre- and post-IR. (**A–C**) indicate the correlation between ACL strain and force in the knee joint while performing CM of 90\({}^{\circ}\), 135\({}^{\circ}\) and 180\({}^{\circ}\), respectively, before conducting the IR testing; (**D–F**) indicate the correlation between ACL strain and force in the knee joint while performing CM of 90\({}^{\circ}\), 135\({}^{\circ}\) and 180\({}^{\circ}\), respectively, post conducting the IR testing. Abbreviations: The intensity of the dots corresponds to the strength of the relationship between the two variables, with darker dots indicating a closer association. Figure 5: The results of the SNPM1d test for ACL strain, as well as the heatmap results depicting mean clustering pre- and post-IR in various CM directions, were obtained. (**A–C**) demonstrates a comparison of ACL strain pre- and post-IR training during CM at 90\({}^{\circ}\), 135\({}^{\circ}\) and 180\({}^{\circ}\), respectively; (**D**) Displays the alterations in mean ACL strain values pre-IR training during CM at 90\({}^{\circ}\) (1), 135\({}^{\circ}\) (2) and 180\({}^{\circ}\) (3), as well as the changes in mean ACL strain values after IR training during CM at 90\({}^{\circ}\) (4), 135\({}^{\circ}\) (5) and 180\({}^{\circ}\) (6). For the sake of brevity, the comparison of knee joint angle, moment, and contact force was only reported for 90\({}^{\circ}\) CM, as depicted in Figure 6. Before and after running training comparison of the external rotation moment of the knee revealed significantly lower moment at 65-97% (\(p\) = 0.010) of the stance phase (Figure 6B).