Using computed muscle control to generate forward dynamic simulations of human walking from experimental data
Introduction
Forward dynamic simulation offers a potentially powerful methodology for characterizing the causal relationship between muscle excitations and multi-joint movement during gait. For example, recent studies have used simulations of normal walking to quantify the contributions of lower extremity muscles to vertical support, forward progression, and swing leg kinematics (Neptune et al., 2001; Anderson and Pandy, 2003; Anderson et al., 2004; Goldberg et al., 2004; Neptune et al., 2004). Unfortunately, conventional approaches for generating dynamic simulations of gait require inordinate amounts of computation time (Anderson and Pandy, 2001; Neptune et al., 2001) making the wide-spread use of forward dynamic simulation, particularly on a subject-specific basis, impractical.
Computed muscle control (CMC) is a new approach for generating forward dynamic simulations that offers substantial performance benefits over conventional dynamic optimization techniques. Dynamic optimization typically require thousands of complete integrations of the model state equations to converge to a solution (Neptune, 1999; Anderson and Pandy, 2001), which translates into days, weeks or even months of computer time depending on the complexity of the model. Even then, numerical difficulties are endemic to dynamic optimization of complex nonlinear problems, which can lead to sub-optimal solutions (Neptune, 1999). In contrast, CMC, by employing feedforward and feedback control, is able to closely track experimental kinematics using only a single integration of the model state equations. We previously demonstrated that CMC could generate an accurate, coordinated simulation of bicycle pedaling with less than 10 min of computer processing time (Thelen et al., 2003).
CMC is well suited for simulating movements in which all degrees-of-freedom can be independently controlled via muscle actions. However, during gait, the motion of the center-of-mass is dictated by intermittent foot–floor reaction forces. While both foot–floor forces and whole-body motion can be recorded experimentally, they generally are not dynamically consistent due to measurement errors and modeling assumptions (Vaughan et al., 1982; Kuo, 1998; Cahouet et al., 2002). As a result, it is not possible to use CMC to vary muscle excitations to drive a forward dynamic model to replicate both experimental kinematic and kinetic measures without the application of additional external forces, often referred to as residual forces. Furthermore, the original formulation of CMC did not explicitly account for delays in force production due to muscle activation and muscle–tendon contraction dynamics. Although the motions of the body segments are relatively slow during gait, ground reaction forces do change rapidly during loading and push off. As a consequence, failure to account for delays involved in the production of muscle forces can lead to substantial tracking errors.
The objective of this study was to develop a methodology for efficiently generating simulations of human walking that closely track experimental measures of body kinematics and ground reaction forces without the application of residual forces. In this paper, we first describe a technique for ensuring consistency between whole-body dynamics and measured ground reaction forces. We then introduce a modified version of CMC that explicitly accounts for delays in muscle force production. This approach is shown to generate accurate subject-specific forward simulations of normal gait with relatively little computer processing time.
Section snippets
Forward dynamic musculoskeletal model
The body was modeled as an 8-segment, 21-degree-of-freedom articulated linkage actuated by 92 Hill-type muscle–tendon units. Major aspects of this musculoskeletal model have been described elsewhere (Delp et al., 1990; Delp and Loan, 2000) and previously used to reproduce the salient features of normal gait in the sagittal, transverse, and frontal planes (Anderson and Pandy, 2001). The coupling of muscle excitation (u) to activation (a) was modeled as a first-order process with rise and decay
Results
The residual elimination algorithm introduced relatively small changes in the pelvis translations. Average root-mean-squared (RMS) differences of less than 5 mm were introduced into the pelvis translations to achieve dynamic balance (Table 3). Slightly larger variations of the low back angles from the kinematically derived values were required to achieve dynamic consistency. Mean RMS differences ranged from 1° in the sagittal plane to 5° in the transverse plane (Table 3). The use of nonlinear
Discussion
In this study we sought to develop a computationally feasible method for generating forward dynamic simulations of gait that closely track experimental data. We achieved this goal by first using a residual elimination algorithm (REA) to generate a set of desired kinematic trajectories that were dynamically consistent with ground reactions. We then applied a computed muscle control algorithm to determine muscle excitations that drive a forward dynamic simulation to track the desired kinematics.
Acknowledgements
We gratefully acknowledge the financial support provided by the National Institutes of Health (NIH grants HD45109, HD38962 and HD33929) and the experimental gait data provided by the Center for Motion Analysis (Connecticut Children's Medical Center).
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