Nonlinearities make a difference: comparison of two common Hill-type models with real muscle |
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Authors: | Tobias Siebert Christian Rode Walter Herzog Olaf Till Reinhard Blickhan |
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Institution: | Institute of Motion Science, Friedrich Schiller University, Seidelstrasse 20, 07749 Jena, Germany. tobias.siebert@uni-jena.de |
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Abstract: | Compared to complex structural Huxley-type models, Hill-type models phenomenologically describe muscle contraction using only
few state variables. The Hill-type models dominate in the ever expanding field of musculoskeletal simulations for simplicity
and low computational cost. Reasonable parameters are required to gain insight into mechanics of movement. The two most common
Hill-type muscle models used contain three components. The series elastic component is connected in series to the contractile
component. A parallel elastic component is either connected in parallel to both the contractile and the series elastic component
(model CC+SEC]), or is connected in parallel only with the contractile component (model CC]). As soon as at least one of
the components exhibits substantial nonlinearities, as, e.g., the contractile component by the ability to turn on and off,
the two models are mechanically different. We tested which model (CC+SEC] or CC]) represents the cat soleus better. Ramp
experiments consisting of an isometric and an isokinetic part were performed with an in situ cat soleus preparation using
supramaximal nerve stimulation. Hill-type models containing force–length and force–velocity relationship, excitation–contraction
coupling and series and parallel elastic force–elongation relations were fitted to the data. To test which model might represent
the muscle better, the obtained parameters were compared with experimentally determined parameters. Determined in situations
with negligible passive force, the force–velocity relation and the series elastic component relation are independent of the
chosen model. In contrast to model CC+SEC], these relations predicted by model CC] were in accordance with experimental
relations. In conclusion model CC] seemed to better represent the cat soleus contraction dynamics and should be preferred
in the nonlinear regression of muscle parameters and in musculoskeletal modeling. |
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