History effect and timing of force production introduced in a skeletal muscle model

Skeletal muscle modelling requires a detailed description of muscular force production. We have performed a series of experiments on mouse skeletal muscles to give a basis for an improved description of the muscular force production. Our previous work introduced a force modification in isometric phases, which was based on the work performed by or on the muscle during transient-length-varying contractions. Here, state-space diagrams were used to investigate the timing aspects of the force production. These show a dominant exponential nature of the force development in isometric phases of the contractions, reached after a non-exponential phase, assumed as an activation or deactivation stage and not further analysed here. The time constants of the exponential functions describing isometric force redevelopment after length variations appear to be related to the one for an initial isometric contraction, but depending on the previous history. The timing of force production calculated from the state-space diagrams was in agreement with the generally accepted muscle properties, thereby demonstrating the reliability of the method. A macroscopic muscular model consisting of a contractile element, parallel and series elastic elements was developed. The parameters from the experiment analysis, particularly the force modification after non-isometric contractions and the time constants, were reproduced by the simulations. The relationship between time constants introduced in a mechanistic model and the measured macroscale timings is discussed.