Computational and Mathematical Methods in Medicine
Volume 2017 (2017), Article ID 6752731, 2 pages
https://doi.org/10.1155/2017/6752731

Corrigendum

Corrigendum to “Comparative Sensitivity Analysis of Muscle Activation Dynamics”

Robert Rockenfeller,¹ Michael Günther,2,3 Syn Schmitt,2,4 and Thomas Götz¹

¹Institut für Mathematik, Universität Koblenz, 56070 Koblenz, Germany
²Institut für Sport- und Bewegungswissenschaft, Universität Stuttgart, Allmandring 28, 70569 Stuttgart, Germany
³Institut für Sportwissenschaft, Lehrstuhl für Bewegungswissenschaft, Friedrich-Schiller-Universität, Seidelstraße 20, 07749 Jena, Germany
⁴Stuttgart Research Centre for Simulation Technology, Pfaffenwaldring 7a, 70569 Stuttgart, Germany

Correspondence should be addressed to Michael Günther; s7gumi@uni-jena.de

Received 13 July 2017; Accepted 10 August 2017; Published 20 September 2017

Copyright © 2017 Robert Rockenfeller et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We provide a comment to our paper “Comparative Sensitivity Analysis of Muscle Activation Dynamics,” Computational and Mathematical Methods in Medicine (2015), 16 pages, Article ID 585409, DOI 10.1155/2015/585409 [1], where we stated an erroneous form of Hatze’s activation dynamics that is not applicable to non-steady-state muscle processes. However, as we only considered steady-state situations, all results and consequences still hold true. The authors would like to apologize for any inconvenience caused.

In his consecutive work [2–4], Hatze introduced the dynamics of changes in activity (activation dynamics) for skeletal muscle fibers in response to neural stimulation as a multilevel process, with being the relative free calcium ion concentration and the length of the contractile element (CE). In [4, Eqns. , , and ], this process is summarized as follows:

In our main article [1, Eqn. ], we had reformulated the above equation system (1) as

in an effort to eliminate the state variable in favor of . However, the specific formulation in (2) holds only true in the steady-state case . This is because the transformation [5, Eqns. –] was erroneously done by

rather than properly taking the total derivative

for the total time derivative of .

In our framework only steady-state muscle conditions were investigated; that is, , such that the second term of the right hand side in (4) vanishes. Hence, the situation from (2) holds throughout the article. In non-steady-state isometric contractions, this second term seems to be of reversed sign to the first, but with a considerably smaller absolute value; compare [6].

Acknowledgments

The authors would like to thank Maria Hammer for drawing attention to their computational error.

References

R. Rockenfeller, M. Günther, S. Schmitt, and T. Götz, “Comparative sensitivity analysis of muscle activation dynamics,” Computational and Mathematical Methods in Medicine, vol. 2015, Article ID 585409, 2015.

H. Hatze, “A myocybernetic control model of skeletal muscle,” Biological Cybernetics, vol. 25, no. 2, pp. 103–119, 1977.

H. Hatze, “A general myocybernetic control model of skeletal muscle,” Biological Cybernetics, vol. 28, no. 3, pp. 143–157, 1978.

H. Hatze, Myocybernetic control models of skeletal muscle, University of South Africa, 1981.

M. Günther, Computersimulation zur Synthetisierung des muskulär erzeugten menschlichen Gehens unter Verwendung eines biomechanischen Mehrkörpermodells [Ph.D. thesis], Universität Tübingen, Tübingen, Germany, 1997.

R. Rockenfeller and M. Günther, “Extracting low-velocity concentric and eccentric dynamic muscle properties from isometric contraction experiments,” Mathematical Biosciences, vol. 278, pp. 77–93, 2016.