Prediction of ground reaction forces and moments during various activities of daily living
Introduction
Inverse dynamics based simulations on musculoskeletal models are a commonly used method for the analysis of human movement. Despite widespread use, it is well known that solutions obtained with inverse dynamics are sensitive to inaccuracies in the various input variables (Pamies-Vila et al., 2012, Riemer et al., 2008). Errors can stem from estimating body segment parameters (Pearsall and Costigan, 1999, Rao et al., 2006), estimating joint parameters (Schwartz and Rozumalski, 2005), skin movement artifacts (Leardini et al., 2005), noise on skin-mounted marker data (Richards, 1999), estimating the center of pressure (Schmiedmayer and Kastner, 1999) or force plate calibration (Collins et al., 2009). Consequently, when solving the inverse dynamics problem, the equations of motion are violated, resulting in dynamic inconsistency, a condition with residual forces and moments (Kuo, 1998).
Several algorithms have been proposed that reduce or eliminate the residual forces and moments, such as the least-squared optimization (Kuo, 1998), the residual elimination algorithm (REA) (Thelen and Anderson, 2006) and the residual reduction algorithm (RRA) (Delp et al., 2007). These algorithms adjust the kinematics, ground reaction forces (GRFs) and/or body segment parameters, thereby improving the dynamic consistency. Unfortunately, they have shortcomings too: the REA was shown to dramatically change torso angles for movements longer than 0.5 s (John et al., 2007). For the RRA, an adjustment in the joint angles of up to five degrees is considered reasonable (OpenSim User׳s Guide). Since these differences are larger than the minimal detectable change for most of the joint angles (Wilken et al., 2012), these adjustments may not be defendable.
Alternatively, dynamic consistency can be improved by deriving the ground reaction forces and moments (GRF&Ms) from three-dimensional full-body motion using the equations of motion (Audu et al., 2007, Choi et al., 2013, Oh et al., 2013, Ren et al., 2008, Robert et al., 2013). An additional advantage of this method is that it enables inverse dynamic analysis for studies without force plate data, for example ambulatory measurements with inertial measurements only (e.g. Luinge and Veltink, 2005) or motion capture during treadmill walking (e.g. Hesse et al., 1999). A difficulty of this method is the indeterminacy problem during a double contact phase when the system defines a closed kinetic chain. To overcome this problem, Audu et al. (2003) used optimization techniques to compute the GRF&Ms for different static postures of a standing bipedal model, which were later validated against measured data (Audu et al., 2007). However, it is unknown whether this method is valid for dynamic movements. Ren et al. (2008) introduced a smooth transition assumption to solve the indeterminacy problem. The smoothing functions were based on empirical data and, therefore, the smooth transition assumption may not be applicable for movements other than those present in the empirical data. Oh et al. (2013) and Choi et al. (2013) solved the indeterminacy problem using an artificial neural network. Also their method requires training data, which is not always present. Robert et al. (2013) tested several optimization methods to predict the external contact loads during sit-to-stand movements. Although their method does not require empirical or training data, their contact configurations are simplified and the method was validated for sit-to-stand motion only.
Therefore, the purpose of this paper is to demonstrate a universal method for predicting the GRF&Ms based on measured kinematic data only, which is applicable to a variety of Activities of Daily Living (ADLs), and in which the indeterminacy problem during the double contact phase of gait and gait-related ADLs is solved without the use of empirical or training data. The predicted GRF&Ms were evaluated with simultaneously measured force plate data. For the trials where subjects walked at self-selected comfortable walking speed, a sensitivity study was performed to evaluate the effects of the chosen muscle recruitment strategy and parameters of the ground contact model on the accuracy of the predictions.
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Subjects
Nine healthy subjects (4 males and 5 females; age: 41.6±15.9 yr; height: 1.74±0.12 m; weight: 73.0±11.1 kg, Body Mass Index: 23.9±2.0 kg/m2) with no history of musculoskeletal disorders volunteered for the study at the Rehabilitation Department of the Radboud University Medical Centre, Nijmegen, the Netherlands. The local ethics committee approved the study protocol and informed consent was obtained from all subjects prior to the study.
Instrumentation
A six-camera digital optical motion capture system (Vicon MX,
Results
The model showed excellent predictions for the vertical GRF (ρ ranging from , median ) and the antero-posterior GRF (ρ ranging from , median ) for almost all activities (Table 1, Fig. 3). The magnitude of the vertical GRF was slightly but consistently underestimated (M ranging from −1.2% to −4.0%, median ), whereas the magnitude of the antero-posterior GRF was consistently overestimated (M ranging from median ). Nevertheless, no significant
Discussion
In this paper, we demonstrated a universal method to predict the GRF&Ms using kinematic data and a scaled musculoskeletal model only, applied to a variety of ADLs. The method entails a dynamic contact model and optimization techniques to solve the indeterminacy problem during a double contact phase.
In general, reasonably good results were obtained for all analyzed activities. However, weak or even negative correlations were found for the transverse GRM for multiple activities. Averaging over
Conflict of interest
None of the authors have any financial or personal conflict of interest with regard to this study.
Acknowledgments
The authors gratefully acknowledge the financial support provided by the European Commission FP7 Programme for the TLEMsafe project (www.tlemsafe.eu) (Grant no. FP7-ICT-247860).
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