Optimisation-based identification of parameters in a mathematical model of muscle fatigue

Abstract

A number of mathematical muscle fatigue models have been developed; however, the determination of optimal parameter values defining model behaviour is not trivial. Typically, parameter identification relied on estimates of endurance time (ET) for sustained static contractions. However, this is not feasible for more complex tasks, such as intermittent contractions, in which ET is not achieved or reported due to long task durations. Here we present numerical methods, which use multiple time-varying measures of fatigue development to find best-fit fatigue (F) and recovery (R) parameter values for one fatigue model. While we used the three-compartment controller model (3CC), the approach using the Levenberg-Marquardt algorithm could be applied to other fatigue models. This method determines best-fit parameter solutions as those resulting in a minimum least squares difference between measured and modelled data. We present a summary of this approach with two extreme examples with multiple on/off cycle repetitions from the literature to demonstrate determination of the two model parameters, F and R, for each dataset. Thus, the method works with repetitive contractions, utilising multiple data points over time, not just a single endurance time point, as in previous studies.