A comparison of optimisation methods and knee joint degrees of freedom on muscle force predictions during single-leg hop landings
Introduction
Accurate knowledge of lower-limb muscle forces is important in understanding how muscles function during normal and pathological gait. Reliable estimations of muscle forces can improve predictions of joint contact forces and stresses (Kim et al., 2009) as well as ligament forces (Kernozek and Ragan, 2008, Laughlin et al., 2011, Mokhtarzadeh et al., 2013). A collective understanding of these biomechanical variables can provide insight into the causes or consequences of different joint diseases. For example, accurate knowledge of knee muscle forces can be utilised to improve our understanding of changes in medial and lateral tibiofemoral contact forces after an anterior cruciate ligament injury, which has been suggested to be precursor to knee osteoarthritis (Fregly et al., 2012).
Musculoskeletal modelling has recently become a powerful biomechanical tool used to predict muscle forces in which optimisation methods are commonly utilised to solve the muscle-moment redundancy problem (i.e. a net joint moment can be produced from an infinite number of muscle force combinations; Crowninshield, 1978). Static optimisation (SO) and computed muscle control (CMC) are two popular optimisation methods used for predicting muscle forces and are accessible for use in the freely available musculoskeletal modelling software, OpenSim (Delp et al., 2007, Thelen and Anderson, 2006). SO is an inverse dynamics-based method that partitions the net joint moment amongst individual muscles by minimising a given performance criterion (e.g. sum of squares of muscle activations; Erdemir et al., 2007). On the other hand, CMC is a forward dynamics-based approach that utilises feedback control theory to predict a set of muscle excitations that will produce kinematics that closely match the kinematics calculated from inverse kinematics (Thelen and Anderson, 2006, Thelen et al., 2003). Whilst these methods provide a means for obtaining otherwise unattainable in vivo muscle forces, these predictions are limited in that it is challenging to know how valid or accurate these methods are in predicting individual muscle forces given that no direct measures are available.
A previous study has shown that the muscle forces predicted by SO can produce accurate joint contact forces during walking by comparing the predicted contact forces to those measured in a person with an instrumented knee implant (Kim et al., 2009). Previous studies have also shown that SO and CMC produce similar muscle force predictions during walking and running in terms of timing and magnitude (Anderson and Pandy, 2001a, Lin et al., 2011). However, these studies have cautioned against the use of SO for ballistic movements such as jumping as SO may produce muscle activation patterns that are inconsistent with electromyographic (EMG) recordings (Lin et al., 2011). In addition, the ability of SO to predict co-contraction of antagonistic muscles has been criticised because this method excludes muscle activation dynamics. However, several studies have mathematically proven that multi-jointed models containing joints with multiple degrees of freedom (i.e. non-planar joints) can predict co-contraction of antagonistic muscles (Ait-Haddou et al., 2000, Jinha et al., 2006a, Jinha et al., 2006b). Given that many past studies have used planar knee joint models i.e. 1 degree of freedom (DOF) when predicting muscle forces (Dorn et al., 2012, Fok et al., 2013, Mokhtarzadeh et al., 2013), the current study aims to evaluate the forces generated by the lower-limb muscles using different optimisation methods and knee degrees of freedom.
Therefore, our study proposes to compare the individual lower-limb muscle force results produced by SO and CMC using both planar and non-planar knee joint models during a ballistic movement (i.e., hopping). We hypothesise that the muscle force results based on the SO method using a 3 degree-of-freedom (DOF) knee joint will be similar to those based on the CMC method from both a 1 and 3 DOF knee joint (H1). On the other hand, we estimate that SO results from a 1 DOF knee joint will be significantly lower than the results obtained from other combinations of knee joint types and optimisation methods (H2).
Section snippets
Methods
Nineteen healthy and physically active subjects with no history of knee injury (height=1.74±0.08 m, body mass=74.2±10.8 kg) participated in this study after providing informed consent. Ethical approval was provided by the University of Melbourne׳s Behavioural and Social Sciences Human Ethics sub-committee (ethics ID 1136167). Data were collected in the Physiotherapy Movement Laboratory at The University of Melbourne.
Participants performed an initial static trial by standing in a neutral position
Results
All sagittal and transverse plane joint angles calculated using inverse kinematics or CMC in a 1 DOF or 3 DOF knee were well-matched (RMS error<3°; Fig. 1). Residual moments and forces across all participants were also within an acceptable range (RMS<0.2 BW for residual forces and RMS<0.05 BW-HT for residual moments; Fig. 2). Finally, muscle force profiles were qualitatively consistent with EMG measurements using all four muscle force prediction approaches (Fig. 3).
Discussion
The aim of this study was to compare the muscle force predictions given from two different optimisation methods (SO and CMC) during a single-leg hopping movement in musculoskeletal models with planar knee joints and models with non-planar knee joints. In general, all four approaches predicted similar muscle force time histories/profiles. However, the magnitude of muscle forces predicted by CMC tended to be higher than SO in most of the major muscles for a given type of knee joint. Also, the use
Conflict of interest statement
None of the authors above has any financial or personal relationship with other people or organisations that could inappropriately influence this work, including employment, consultancies, stock ownership, honoraria, paid expert testimony, patent applications/registrations, and grants or other funding.
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