Elsevier

Journal of Biomechanics

Volume 59, 5 July 2017, Pages 1-8
Journal of Biomechanics

Three-dimensional data-tracking dynamic optimization simulations of human locomotion generated by direct collocation

https://doi.org/10.1016/j.jbiomech.2017.04.038Get rights and content

Abstract

The aim of this study was to perform full-body three-dimensional (3D) dynamic optimization simulations of human locomotion by driving a neuromusculoskeletal model toward in vivo measurements of body-segmental kinematics and ground reaction forces. Gait data were recorded from 5 healthy participants who walked at their preferred speeds and ran at 2 m/s. Participant-specific data-tracking dynamic optimization solutions were generated for one stride cycle using direct collocation in tandem with an OpenSim-MATLAB interface. The body was represented as a 12-segment, 21-degree-of-freedom skeleton actuated by 66 muscle-tendon units. Foot-ground interaction was simulated using six contact spheres under each foot. The dynamic optimization problem was to find the set of muscle excitations needed to reproduce 3D measurements of body-segmental motions and ground reaction forces while minimizing the time integral of muscle activations squared. Direct collocation took on average 2.7 ± 1.0 h and 2.2 ± 1.6 h of CPU time, respectively, to solve the optimization problems for walking and running. Model-computed kinematics and foot-ground forces were in good agreement with corresponding experimental data while the calculated muscle excitation patterns were consistent with measured EMG activity. The results demonstrate the feasibility of implementing direct collocation on a detailed neuromusculoskeletal model with foot-ground contact to accurately and efficiently generate 3D data-tracking dynamic optimization simulations of human locomotion. The proposed method offers a viable tool for creating feasible initial guesses needed to perform predictive simulations of movement using dynamic optimization theory. The source code for implementing the model and computational algorithm may be downloaded at http://simtk.org/home/datatracking.

Introduction

Non-invasive measurement of muscle forces is infeasible thus computational modelling is needed to evaluate these quantities in vivo. Optimization theory is often used to address the mechanically redundant nature of the human locomotor system (Pedotti et al., 1978, Hardt, 1978, Zajac, 1993, Collins, 1995, Pandy, 2001). Computed muscle control (CMC) combines static optimization with linear feedback control to calculate muscle forces by tracking measurements of body-segmental motions (Thelen et al., 2003). CMC has been used in conjunction with OpenSim (Delp et al., 2007), an open-source musculoskeletal modelling and simulation environment, to generate dynamic simulations of walking (Arnold et al., 2007, Liu et al., 2008), running (Hamner et al., 2010) and landing from a jump (Mokhtarzadeh et al., 2014). However, this method is limited in several ways. First, static optimization solves a discrete set of optimization problems along the movement trajectory rather than evaluating the cost function over time (Crowninshield and Brand, 1981, Anderson and Pandy, 2001, Lin et al., 2012). Second, ground reaction forces obtained from experiment are applied directly to the model causing inconsistencies between the model-computed body-segmental motions and the measured ground reaction forces. These inconsistencies in the model dynamics require the application of artificial or residual forces and torques that potentially affect the calculated values of muscle forces. Third, predictive simulations of movement using dynamic optimization theory cannot be pursued because foot-ground contact is not simulated in the model. Finally, a large set of nonlinear differential equations are solved using explicit integration techniques that require small time steps and have poor convergence properties, particularly when the dynamic equations of motion are stiff; for example, when bodies with relatively small masses such as the patella are included in the model.

Muscle forces may also be calculated by using dynamic optimization to solve data-tracking problems in which the model-computed kinematics and kinetics are constrained to reproduce corresponding experimental data. Direct shooting is one of the most common techniques used to track experimental measurements within the framework of dynamic optimization theory. This method is implemented by discretizing the control variables (e.g., muscle excitations) while the state variables are found by integrating the system dynamic equations forward in time (Pandy et al., 1992). Unfortunately, convergence to an optimal solution may require several hours or even days of CPU time (Neptune et al., 2000, McLean et al., 2003). Menegaldo et al. (2006) combined a direct shooting method with inverse dynamics analysis to reproduce desired torque profiles at a lower computational cost. Although a significant advantage of applying dynamic optimization is that the cost function is evaluated over time, the equations for neuromusculoskeletal dynamics are still solved using explicit numerical integration when implementing direct shooting.

Implicit methods such as direct collocation convert the dynamic equations of motion into algebraic constraints by discretizing the state and control variables thus eliminating the need for explicit integration. Direct collocation has been used with relatively simple two-dimensional models to produce data-tracking dynamic optimization simulations of pedaling (Kaplan and Heegaard, 2001), walking (van den Bogert et al., 2011) and running (Miller and Hamill, 2015). De Groote et al. (2016) recently combined direct collocation with a three-dimensional (3D) musculoskeletal model to calculate muscle forces in normal walking, but foot-ground interaction was not explicitly simulated.

The overall goal of the present study was to assess the feasibility of generating accurate, computationally-efficient, data-tracking dynamic optimization solutions for human locomotion by combining the computational power of direct collocation with the flexibility and efficiency of OpenSim. Our specific aim was to implement direct collocation on a 3D neuromusculoskeletal model created in OpenSim to calculate lower-limb muscle forces for walking and running compatible with body-segmental motions and foot-ground forces obtained from experiment.

Section snippets

Human experiments

Gait data were collected from five healthy adult males (age: 26 ± 4 years; height: 178 ± 4 cm; weight: 70 ± 5 kg) at the Biomotion Laboratory of the University of Melbourne. The study was approved by the University’s Human Research Ethics Committee and informed written consent was obtained from each participant prior to data collection. Participants were asked to walk at their preferred speeds (1.4 ± 0.1 m/s) and to run at a prescribed speed of 2 m/s. Marker-trajectory and ground-reaction-force data were

Results

Direct collocation took on average 2.7 ± 1.0 h and 2.2 ± 1.6 h to compute the optimal solutions for walking and running, respectively. CPU time per iteration was similar for the two tasks (0.5 ± 0.0 and 0.5 ± 0.1 min for walking and running, respectively) but the total time taken to solve the walking problem was greater because more iterations were needed to converge to the optimal solution (320 ± 116 iterations for walking compared to 250 ± 171 iterations for running).

Model-predicted body-segmental

Discussion

The aim of this study was to assess the feasibility of generating accurate, computationally-efficient, data-tracking, dynamic optimization simulations of human locomotion by implementing direct collocation on a detailed 3D neuromusculoskeletal model created in OpenSim. Model-predicted body-segmental displacements, ground reaction forces and muscle excitation patterns were consistent with experimental gait data obtained for both walking and running gaits.

Direct collocation is potentially more

Conflict of interest

None of the authors have a conflict of interest in relation to the work reported here.

Acknowledgements

This work was supported by a Discovery Projects Grant from the Australian Research Council (DP160104366).

References (34)

Cited by (55)

  • A review on foot-ground contact modeling strategies for human motion analysis

    2022, Mechanism and Machine Theory
    Citation Excerpt :

    Additionally, the EMG activity was evaluated in eight studies [31,36–40,42,43]. The validation process of the models, which is presented in Table 2, varied across studies and mostly consisted of comparing the numerical and experimental results [5–7,31,32,34–46], or alternatively comparing the results obtained from the simulations with the available literature [6–8,21–31,36,44]. Through these validation processes, the authors were able to verify the performance of the models and identify their potential limitations.

  • Computational performance of musculoskeletal simulation in OpenSim Moco using parallel computing

    2023, International Journal for Numerical Methods in Biomedical Engineering
View all citing articles on Scopus
View full text