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

Authors: Laura A. Frey-Law; Frank K. Urban III

Addresses: Department of Physical Therapy and Rehabilitation Science, Carver College of Medicine, The University of Iowa, 1-252 Medical Education Bldg., Iowa City, IA 52242, USA ' Electrical and Computer Engineering, Florida International University, University Park Campus, Miami Florida, 33199, USA

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.

Keywords: muscle fatigue; mathematical models; fatigue models; numerical techniques; numerical analyses; optimisation; gradient-based optimisation; parameter identification; parameter estimation; Levenberg-Marquardt method; least squares.

DOI: 10.1504/IJHFMS.2019.102171

International Journal of Human Factors Modelling and Simulation, 2019 Vol.7 No.1, pp.34 - 46

Received: 29 Jun 2018
Accepted: 01 Apr 2019
Published online: 09 Sep 2019 *

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