Coupling a finite element knee model with musculoskeletal multibody simulations. A case study of ACL force during a change-of-direction movement before and after injury prevention training
Authors: Ebenbichler Maximilian , Heinrich Dieter , Mohr Maurice , Ueno Ryo , Eberle Robert 
Published: September 2024

Introduction & Purpose
Change of direction (COD) movements are a common cause of injuries to the anterior cruciate ligament (ACL), especially in sports such as soccer, basketball, handball (Agel et al., 2016). In Mohr et al., (2024) an 8-week injury prevention training program including COD technique training was investigated. The movements during COD were recorded in an experimental setup with a marker-based system before and after the training program. While Mohr and colleagues observed training effects on the COD movement strategy, it remains unknown whether the ACL forces are actually reduced by the training program. The purpose of this project was to 1) develop a simulation-based approach to estimate ACL forces during COD movements using musculoskeletal simulations (OpenSim) and finite element (FE) knee simulations, and 2) use existing kinematics from a COD movement of one athlete before and after the 8-week injury prevention training program to investigate training effects on ACL force (Mohr et al., 2024).
Methods
The model OKS008 from the publicly-available collection of Open Knee(s) (OKS) FE models (2nd generation) of the Cleveland Clinic (Chokhandre et al., 2023) was implemented in the FE software Abaqus CAE.
In the original OKS008 model (Chokhandre et al., 2023) material parameters and pre-strains were taken from literature. However, the pre-strain of the ligaments is very individual (Lahkar et al., 2021). Therefore, in this study, the pre-strain of the ligaments and four material parameters of the OKS008 model were fit to in vitro kinetic testing data, using an optimization algorithm (interior-point algorithm). The kinetic data from in-vitro tests is available alongside with the OKS knee models, for which all donor knees were mechanically tested during passive flexion experiments (Chokhandre et al., 2023). The optimization was solved based on about 550 FE simulations over the course of one month (AMD Ryzen threadripper 3960 x 24-core processor x 48, 35 cores were used).
The effect of the knee kinematics from Mohr and colleagues (2024) on the loading of the anterior cruciate ligament (ACL) was then investigated with the optimized FE knee model in a post-processing step. Inverse kinematics in OpenSim was used to determine the 3D knee joint kinematics of one athlete during a maximum-speed 135° COD movement before and after the injury prevention training program. This athlete was selected because after the 8-week injury prevention training program, he showed a significant reduction in maximum knee adduction moment. The run-up velocity of the athlete on the COD was 3.97 m/s before the training program (baseline) and 4.09 m/s after the training program (follow-up). To simulate the COD movements in Abaqus, the FE knee model was driven by the measured knee kinematics of the COD, where the secondary kinematics (knee adduction and internal rotation) of the OpenSim model were added to the FE model’s secondary kinematics during passive flexion. The resulting force on the ACL was calculated by a free body cut in Abaqus CAE.
Results
The pre-strain optimized FE knee model closely reproduced the secondary kinematics (abduction, internal rotation) of the donor knee during passive flexion (mean error of 2.1687° before vs. 0.5799° after optimization).
The athlete’s maximum ACL force during the COD before the training program was 457 N, while after the training program a reduction in ACL force during the COD to 246 N was observed (46% reduction). The ACL force during the COD before and after the injury prevention training program is shown in Figure 1.
Discussion
A publicly available FE knee model was successfully optimized based on cadaveric mechanical testing data and implemented into a simulation-based approach to estimate ACL force. The plausibility of the model was checked by a mesh study and comparison with cadaver studies done in Wascher et al. (1993) and Hosseini Nasab et al. (2016). The timing of peak ACL force during a simulated COD movement, between 50 ms and 100 ms after initial contact, is physiologically plausible given that ACL injuries during CODs typically occur around 50 ms after initial contact (Krosshaug et al., 2007). The pre-strain optimization showed that it is necessary to estimate material parameters, e.g. ligament pre-strain, individually for each model to obtain realistic mechanical behaviour.
The case study demonstrated a reduction in ACL force during a COD by 46% following an injury prevention training program. The existing kinematic data from Mohr and colleagues (2024) show that the analyzed athlete performed the COD with decreased knee internal rotation and abduction after the 8-week injury prevention training. It is assumed that the ACL force was reduced due to the lower internal rotation and abduction. Figure 1 show further interesting observations that warrant investigation, e.g. the time-shifted peak ACL force following training. This will be done in future studies including more athletes.
Importantly, ACL forces during change of direction (COD) were calculated by applying only rotational kinematics to the FE model. The next step will be to implement joint reaction forces (JRF) into the FE simulations because they would have an effect on the ACL force (Esrafilian et al., 2022). It is therefore advisable to include the JRF in the subsequent simulations in order to obtain more physiologically relevant results.
Conclusion
We developed a FE simulation model in Abaqus CAE of the OKS008 knee to estimate and compare ACL forces based on the existing kinematics of a COD movement.
However, individual material parameter estimation is required for each model. The material parameter estimation increases the replicability of the specimen specific mechanical cadaver testing. This is an improvement to the original OKS008 model.
For the one analyzed athlete, after the 8-week injury prevention exercise program (Mohr et al., 2024) the ACL force caused by rotational kinematics of a COD is less than before the exercise program. The maximum ACL force during COD is reduced by 46% after the exercise program.
References
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