1. Introduction
Ruptures of the anterior cruciate ligament (ACL), one of the most serious injuries in sports, affect female athletes at an incidence rate 2.2 times higher than males [
1]. Prevention of ACL injuries is the ideal goal as fewer than half of competitive athletes return to the same or higher activity level two years post-surgery following an ACL rupture [
2]. ACL tears often occur in a non-contact manner when an individual quickly decelerates to change direction or lands from a jump [
3]. About two thirds of ACL injuries occur during a knee valgus or varus injury mechanism [
3], and the mechanics of the landing and cutting maneuvers that may result in these injuries are thoroughly studied [
4,
5,
6]. However, almost one-third of the injuries occur during a hyperextension event [
3], and this kind of injury has hardly been studied at all.
The forces that tear the ACL are well understood from cadaveric studies that apply various loads to knee specimens in order to assess their effects on ACL strain [
7]. Such studies are valuable as measurements taken from strain transducers implanted in the ACL allow for the effects of potential loading mechanisms to be studied directly. As a result, the multi-planar loading of the knee with abduction and internal rotation moments has been shown to result in higher ACL strains compared to that of uni-planar loading [
8]. These findings have been used in motion capture studies to identify potential risk factors for ACL injury [
5,
6,
9]. However, both cadaver and motion capture studies have inherent limitations. Cadaver studies are limited in the number of tests that can be conducted due to wear on the specimens and the struggle to account for the role of the muscles during dynamic loading. Motion capture studies are limited to studying movements where no ACL injury occurs, and the forces acting on the ACL are largely unknown. Computer simulation studies (in silico) are well suited to exploring the complex interactions of external moments and muscle forces that produce high ACL strain values during injurious situations such as a single leg hyperextension landing.
Through programs such as OpenSim, forward dynamic (FD) simulations can be used to study various aspects of gait under conditions not typically available in experimental approaches [
10]. Model parameters such as ligament properties and muscle activations can be manipulated at will, and the number of tests that can be performed is limited only by computation time. As a result, the interest in musculoskeletal modeling has increased in recent years, with researchers advancing towards anatomically correct knee models [
11,
12,
13].
Although previous studies have used OpenSim modeling to assess knee kinematics under various conditions [
14,
15,
16], no study has used these models for dynamic serial simulations to assess multi-planar loading during knee hyperextension on the ACL despite having been identified as a potential injury mechanism and a predictive tool for ACL injuries [
17]. Therefore, the aim of this study was to explore the effects of various external moments and muscle activations on ACL loading using serial FD simulations of single leg, hyperextension landings in OpenSim.
3. Results
Descriptive statistics for the model outputs are shown in
Table 3. Positive values for kinematics represent knee extension, adduction, internal rotation, and anterior translation. The combination of 0 N*m of internal rotation moment and 150 N*m of valgus moment resulted in the highest mean loading for both bundles (a: 667.0 ± 99.1 N, p: 1382.1 ± 168.5 N), while the combination of 90 N*m of rotation and 0 N*m of valgus resulted in the lowest mean loading for both bundles (a: 369.9 ± 65.9 N, p: 921.1 ± 118.1 N).
The ACL was modeled as two bundles in OpenSim: the anterior and posterior bundles. There was no difference in magnitude or direction between each independent variable and the load on each respective bundle. For simplicity, results of the regression analysis are therefore presented only for the anterior bundle.
The results of the generalized linear regression using only knee kinematics are presented in
Table 4. The model R2 was 0.91 and of the kinematic variables the anterior tibial translation had the greatest partial correlation (0.86).
The results of the generalized linear regression using only external moments are presented in
Table 5. The model R2 was 0.37, and the rotation moment had a greater partial correlation than the valgus moment.
The results of the generalized linear regression for all forces are presented in
Table 6. The model R2 was 0.59, and the muscle with the highest partial correlation was the Vastus Lateralis muscle at −0.30.
The results of the GBM are presented in
Figure 1 and the last column of
Table 6. The model R2 was 0.9. The most important variable (
Table 6, last column) was the internal rotation moment followed by the Vastus Medialis muscle.
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 Kiapour 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, Kiapour 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.
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. However, the authors acknowledge that they may also underscore the full effect of the interactions within the musculoskeletal system when exposed to external moments.
Lastly, in order to limit the focus of this study to only knee kinematics/kinetics, all other model coordinates, including the coordinate governing the patellofemoral joint, were locked during the simulations. As a result, musculotendinous structures attached to this joint, namely the patella tendon and the quadriceps muscles, would have had no contribution to knee kinematics/kinetics during the simulations. In order to maintain their biomechanical function as the knee extensor, the attachment points of the quadriceps muscles were extended to include the path of the patella tendon. While not anatomically accurate, this change represents a close approximation, which the authors believe minimally impacts the results of this study.