## 4 Discussion  
The aim of this study was to explore the effects of external moments and muscle activations on ACL loading using serial FD simulations of single leg, hyperextension landings in OpenSim. The main finding of the study was that external knee moments alone explained much of the variability in ACL forces during single leg landings. Furthermore, the inclusion of muscles in the model increased the model fit by 0.22. The valgus moment was positively correlated with ACL loading, while the internal rotation moment was negatively correlated with ACL loading. This finding somewhat contradicts the results of [PERSON] et al., who showed that multiplanar loading of cadaver knees produced the highest strain on the ACL [8]. These differences may be due to the effects of joint geometry, which was modeled in our study as a flat surface controlled by coordinate limit force actuators. Similar to our findings, [PERSON] et al. found that in a regression, the valgus moment explained more variability in ACL strain than the internal rotation moment [8]. A cadaveric study has found that an internal rotation moment increases ACL forces under hyperextension [28] but without weight bearing or muscle forces included. A post-hoc exploration of the data revealed that the internal rotation moment correlated strongly with all four heads of the Quadriceps muscles. Complex interactions may explain why cadaveric models that produce clinically relevant ACL injury patterns have only recently been created [29]. The high R2 achieved with the BGM model supports the importance of complex interactions between external moments and muscle forces. Figure 1: Prediction profiles for all variables in the generalized boosted model (GBM). Each individual plot shows how the average prediction of ACL load (y-axis) is influenced by a given predictor variable across its range of possible values (x-axis). The risk of ACL injury increases with decreased knee flexion upon landing [5]. The results of our study support this finding, as the knee extension angle had a high partial correlation with ACL forces (Table 3), second only to anterior tibial translation. Combined with the high activation of the quadriceps muscles and the reduced ability of the hamstrings to counteract anterior tibial translation due to the poor moment arm with small knee flexion angles, landing close to full knee extension can result in very high loads on the ACL. These findings are consistent with recent studies using biplane fluoroscopy during in-vivo movements that have found relationships between patellar tendon strain and ACL strain [30] as well as between greater knee extension angles and ACL strain [31]. The present study is not without its limitations. Because the Schmitz model, which includes 16 ligament bundles in addition to the 2 that represent the ACL, was used in this study, it is possible that other ligament bundles were being loaded more under certain conditions, thereby alleviating the loading on the ACL. When preparing knee specimens for cadaver studies related to the ACL, other knee ligaments are typically removed to nullify their influences on the results. Therefore, the Schmitz model was chosen because it is one of the most anatomically complete knee models with 6 degrees of freedom in order to create as realistic of a simulation as possible. Because the use of different models would likely result in different results [16], using the most accurate model is important. Furthermore, because the Schmitz model represents a female, the results of this study may only be generalizable to that population. The inclusion of Coordinate Limit Force actuators and the use of constant values for the moment and muscle activations represent the tradeoff between computation time and biofidelity commonly found in musculoskeletal modeling. These decisions were made in order to reduce the computation time and computer memory needed perform the simulations.