Biomechanics and Modeling in Mechanobiology

, Volume 15, Issue 1, pp 245–258 | Cite as

Contraction dynamics and function of the muscle-tendon complex depend on the muscle fibre-tendon length ratio: a simulation study

  • Falk MörlEmail author
  • Tobias Siebert
  • Daniel Häufle
Original Paper


Experimental studies show different muscle-tendon complex (MTC) functions (e.g. motor or spring) depending on the muscle fibre-tendon length ratio. Comparing different MTC of different animals examined experimentally, the extracted MTC functions are biased by, for example, MTC-specific pennation angle and fibre-type distribution or divergent experimental protocols (e.g. influence of temperature or stimulation on MTC force). Thus, a thorough understanding of variation of these inner muscle fibre-tendon length ratios on MTC function is difficult. In this study, we used a hill-type muscle model to simulate MTC. The model consists of a contractile element (CE) simulating muscle fibres, a serial element (SE) as a model for tendon, and a parallel elastic element (PEE) modelling tissue in parallel to the muscle fibres. The simulation examines the impact of length variations of these components on contraction dynamics and MTC function. Ensuring a constant overall length of the MTC by \(L_\mathrm{MTC} = L_\mathrm{SE} + L_\mathrm{CE}\), the SE rest length was varied over a broad physiological range from 0.1 to 0.9 MTC length. Five different MTC functions were investigated by simulating typical physiological experiments: the stabilising function with isometric contractions, the motor function with contractions against a weight, the capability of acceleration with contractions against a small inertial mass, the braking function by decelerating a mass, and the spring function with stretch-shortening cycles. The ratio of SE and CE mainly determines the MTC function. MTC with comparably short tendon generates high force and maximal shortening velocity and is able to produce maximal work and power. MTC with long tendon is suitable to store and release a maximum amount of energy. Variation of muscle fibre-tendon ratio yielded two peaks for MTC’s force response for short and long SE lengths. Further, maximum work storage capacity of the SE is at long \(\mathrm{rel}L_\mathrm{SE,0}\). Impact of fibre-tendon length ratio on MTC functions will be discussed. Considering a constant set of MTC parameters, quantitative changes in MTC performance (work, stiffness, force, energy storage, dissipation) depending on varying muscle fibre-tendon length ratio were provided, which enables classification and grading of different MTC designs.


Tendon length Biomechanics Simulation Direct dynamics Muscle model Energy storage 



The authors thank Michael Günther for the fruitful discussions and his comments on the manuscript. The study was partially supported by the Deutsche Forschungsgemeinschaft (DFG SI841/6,7 to TS and SCH2392/5-1).

Conflict of interest


Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Forschungsgesellschaft für Angewandte Systemsicherheit und Arbeitsmedizin mbH, Zentrum für BewegungstherapieErfurtGermany
  2. 2.Institute of Sport and Motion ScienceUniversity of StuttgartStuttgartGermany
  3. 3.Human Movement Simulation Lab, Institute of Sport and Motion ScienceUniversity of StuttgartStuttgartGermany

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