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Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 585409, 16 pages
http://dx.doi.org/10.1155/2015/585409
Research Article

Comparative Sensitivity Analysis of Muscle Activation Dynamics

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

Received 15 December 2014; Accepted 5 February 2015

Academic Editor: Eduardo Soudah

Copyright © 2015 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.

Abstract

We mathematically compared two models of mammalian striated muscle activation dynamics proposed by Hatze and Zajac. Both models are representative for a broad variety of biomechanical models formulated as ordinary differential equations (ODEs). These models incorporate parameters that directly represent known physiological properties. Other parameters have been introduced to reproduce empirical observations. We used sensitivity analysis to investigate the influence of model parameters on the ODE solutions. In addition, we expanded an existing approach to treating initial conditions as parameters and to calculating second-order sensitivities. Furthermore, we used a global sensitivity analysis approach to include finite ranges of parameter values. Hence, a theoretician striving for model reduction could use the method for identifying particularly low sensitivities to detect superfluous parameters. An experimenter could use it for identifying particularly high sensitivities to improve parameter estimation. Hatze’s nonlinear model incorporates some parameters to which activation dynamics is clearly more sensitive than to any parameter in Zajac’s linear model. Other than Zajac’s model, Hatze’s model can, however, reproduce measured shifts in optimal muscle length with varied muscle activity. Accordingly we extracted a specific parameter set for Hatze’s model that combines best with a particular muscle force-length relation.