title: Comparative Sensitivity Analysis of Muscle Activation Dynamics.
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.
authors.affiliation: Institut für Mathematik, Universität Koblenz, 56070 Koblenz, Germany.
authors.forename: Robert
authors.initials: R
authors.lastname: Rockenfeller
authors.affiliation: Institut für Sport- und Bewegungswissenschaft, Universität Stuttgart, Allmandring 28, 70569 Stuttgart, Germany ; Institut für Sportwissenschaft, Lehrstuhl für Bewegungswissenschaft, Friedrich-Schiller-Universität, Seidelstraße 20, 07749 Jena, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Günther
authors.affiliation: Institut für Sport- und Bewegungswissenschaft, Universität Stuttgart, Allmandring 28, 70569 Stuttgart, Germany ; Stuttgart Research Centre for Simulation Technology, Pfaffenwaldring 7a, 70569 Stuttgart, Germany.
authors.forename: Syn
authors.initials: S
authors.lastname: Schmitt
authors.affiliation: Institut für Mathematik, Universität Koblenz, 56070 Koblenz, Germany.
authors.forename: Thomas
authors.initials: T
authors.lastname: Götz
mesh_terms: D000818:Animals; D001696:Biomechanical Phenomena; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D009119:Muscle Contraction / Q000502:physiology*; D018482:Muscle, Skeletal / Q000502:physiology*; D017711:Nonlinear Dynamics