Comparing different muscle activation dynamics using sensitivity analysis

Abstract

In this paper, we mathematically compared two models of mammalian striated muscle activation dynamics proposed by Hatze and Zajac. Both models are representative of a broad variety of biomechanical models formulated as ordinary differential equations (ODEs). The models incorporate some parameters that directly represent known physiological properties. Other parameters have been introduced to reproduce empirical observations. We used sensitivity analysis as a mathematical tool for investigating the influence of model parameters on the solution of the ODEs. That is, we adopted a former approach for calculating such (first order) sensitivities. Additionally, we expanded it to treating initial conditions as parameters and to calculating second order sensitivities. The latter quantify the non-linearly coupled effect of any combination of two parameters. As a completion we used a global sensitivity analysis approach to take the variability of parameters into account. The method we suggest has numerous uses. A theoretician striving for model reduction may use it for identifying particularly low sensitivities to detect superfluous parameters. An experimenter may use it for identifying particularly high sensitivities to facilitate determining the parameter value with maximised precision.