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A two-muscle, continuum-mechanical forward simulation of the upper limb

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Abstract

By following the common definition of forward-dynamics simulations, i.e. predicting movement based on (neural) muscle activity, this work describes, for the first time, a forward-dynamics simulation framework of a musculoskeletal system, in which all components are represented as continuous, three-dimensional, volumetric objects. Within this framework, the mechanical behaviour of the entire muscle–tendon complex is modelled as a nonlinear hyperelastic material undergoing finite deformations. The feasibility and the full potential of the proposed forward-dynamics simulation framework is demonstrated on a two-muscle, three-dimensional, continuum-mechanical model of the upper limb. The musculoskeletal model consists of three bones, i.e. humerus, ulna, and radius, an one-degree-of-freedom elbow joint, and an antagonistic muscle pair, i.e. the biceps and triceps brachii, and takes into consideration the contact between the skeletal muscles and the humerus. Numerical studies have shown that the proposed upper limb model is capable of predicting realistic moment arms and muscle forces for the entire range of activation and motion. Within the limitations of the model, the presented simulations provide, for the first time, insights into existing contact forces and their influence on the muscle fibre stretch. Based on the presented simulations, the overall change in fibre stretch is typically less than 3%, despite the fact that the contact forces reach up to 71% of the exerted muscle force. Movement-predicting simulations are achieved by minimising a nonlinear moment equilibrium equation. Based on the forward-dynamics simulation approach, an iterative solution procedures for position-driven (inverse dynamics) and force-driven scenarios have been proposed accordingly. Applying these methodologies to time-dependent scenarios demonstrates that the proposed methods can be linked to state-of-the-art control algorithms predicting time-dependent muscle activation levels based on principles of forward dynamics.

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Notes

  1. An interactive computer program for Continuum Mechanics, Image analysis, Signal processing and System Identification (http://www.cmiss.org).

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Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement No. 306757 (LEAD).

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Authors and Affiliations

  1. Institute of Applied Mechanics (CE), University of Stuttgart, Pfaffenwaldring 7, 70569, Stuttgart, Germany

    O. Röhrle & M. Sprenger

  2. Institut für Sport- und Bewegungswissenschaft, University of Stuttgart, Allmandring 28, 70569, Stuttgart, Germany

    S. Schmitt

  3. Cluster of Excellence for Simulation Technology, University of Stuttgart, Pfaffenwaldring 5a, 70569 , Stuttgart, Germany

    O. Röhrle, M. Sprenger & S. Schmitt

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  1. O. Röhrle
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Correspondence to O. Röhrle.

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Röhrle, O., Sprenger, M. & Schmitt, S. A two-muscle, continuum-mechanical forward simulation of the upper limb. Biomech Model Mechanobiol 16, 743–762 (2017). https://doi.org/10.1007/s10237-016-0850-x

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