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Nonlinear 2D arm dynamics in response to continuous and pulse-shaped force perturbations

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Abstract

Ample evidence exists regarding the nonlinearity of the neuromuscular system but linear models are widely applied to capture postural dynamics. This study quantifies the nonlinearity of human arm postural dynamics applying 2D continuous force perturbations (0.2–40 Hz) inducing three levels of hand displacement (5, 15, 45 mm RMS) followed by force-pulse perturbations inducing large hand displacements (up to 250 mm) in a position task (PT) and a relax task (RT) recording activity of eight shoulder and elbow muscles. The continuous perturbation data were used to analyze the 2D endpoint dynamics in the frequency domain and to identify reflexive and intrinsic parameters of a linear neuromuscular shoulder-elbow model. Subsequently, it was assessed to what extent the large displacements in response to force pulses could be predicted from the ‘small amplitude’ linear neuromuscular model. Continuous and pulse perturbation responses with varying amplitudes disclosed highly nonlinear effects. In PT, a larger continuous perturbation induced stiffening with a factor of 1.5 attributed to task adaptation evidenced by increased co-contraction and reflexive activity. This task adaptation was even more profound in the pulse responses where reflexes and displacements were strongly affected by the presence and amplitude of preceding continuous perturbations. In RT, a larger continuous perturbation resulted in yielding with a factor of 3.8 attributed to nonlinear mechanical properties as no significant reflexive activity was found. Pulse perturbations always resulted in yielding where a model fitted to the preceding 5-mm continuous perturbations predicted only 37 % of the recorded peak displacements in RT and 79 % in PT. This demonstrates that linear neuromuscular models, identified using continuous perturbations with small amplitudes, strongly underestimate displacements in pulse-shaped (e.g., impact) loading conditions. The data will be used to validate neuromuscular models including nonlinear muscular (e.g., Hill and Huxley) and reflexive components.

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Authors and Affiliations

  1. Department of Biomechanical Engineering, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands

    Riender Happee, Erwin de Vlugt & Bart van Vliet

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  1. Riender Happee
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  2. Erwin de Vlugt
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  3. Bart van Vliet
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Correspondence to Riender Happee.

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Appendix

See Fig. 8.

Fig. 8
figure 8

Model fits for one specific trial in condition PT5 in the frequency domain (upper four graphs) and the time domain (lower two graphs). Two model fits are presented using a criterion in the frequency domain (MFRF) and the time domain (velocity)

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Happee, R., de Vlugt, E. & van Vliet, B. Nonlinear 2D arm dynamics in response to continuous and pulse-shaped force perturbations. Exp Brain Res 233, 39–52 (2015). https://doi.org/10.1007/s00221-014-4083-x

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