Abstract
The robustness of motor outputs to muscle dysfunction has been investigated using musculoskeletal modeling, but with conflicting results owing to differences in model complexity and motor tasks. Our objective was to systematically study how the number of kinematic degrees of freedom, and the number of independent muscle actuators alter the robustness of motor output to muscle dysfunction. We took a detailed musculoskeletal model of the human leg and systematically varied the model complexity to create six models with either 3 or 7 kinematic degrees of freedom and either 14, 26, or 43 muscle actuators. We tested the redundancy of each model by quantifying the reduction in sagittal plane feasible force set area when a single muscle was removed. The robustness of feasible force set area to the loss of any single muscle, i.e. general single muscle loss increased with the number of independent muscles and decreased with the number of kinematic degrees of freedom, with the robust area varying from 1% and 52% of the intact feasible force set area. The maximum sensitivity of the feasible force set to the loss of any single muscle varied from 75% to 26% of the intact feasible force set area as the number of muscles increased. Additionally, the ranges of feasible muscle activation for maximum force production were largely unconstrained in many cases, indicating ample musculoskeletal redundancy even for maximal forces. We propose that ratio of muscles to kinematic degrees of freedom can be used as a rule of thumb for estimating musculoskeletal redundancy in both simulated and real biomechanical systems.
Highlights
Musculoskeletal models have been used to explore motor redundancy, demonstrating how muscle dysfunction impacts motor output
Feasible force set area increased with the number of independent muscles (Fig 1, left to right), and decreased with number of kinematic degrees of freedom (Fig 1, top to bottom); the decrease in Hi- vs. Lo-DoF models was less pronounced in the Int-Muscle and Hi-Muscle models
Effect of model complexity on robustness to general single muscle loss Feasible force set robustness to the loss of any single muscle increased with the number of independent muscles (Fig 1, green areas)
Summary
Musculoskeletal models have been used to explore motor redundancy, demonstrating how muscle dysfunction impacts motor output. Single muscle dysfunction can be compensated for by other muscles, as the upper and lower bounds on feasible muscle activation ranges span 0 to 1 across most of the gait cycle in most muscles. In contrast the feasible muscle activation ranges for a finger model of static force production were tightly bounded [10]. The same study showed that static force production in both the human finger and leg can be dramatically compromised by single muscle loss, as indicated by the vulnerability in the feasible force set that characterizes the maximum endpoint force in all directions [11, 12]
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