A three-compartment muscle fatigue model accurately predicts joint-specific maximum endurance times for sustained isometric tasks
Introduction
Muscle fatigue is considered a risk factor for musculoskeletal injury (Ding et al., 2000), yet few predictive tools are available to model this ubiquitous phenomenon. The development of localized muscle fatigue has classically been described by the intensity – endurance time (ET) curve in the ergonomics literature (Rohmert, 1960). In the past 50+ years, several authors have proposed updated versions of this classic nonlinear curve (Monod and Scherrer, 1965, Hagberg, 1981, Huijgens, 1981, Rose et al., 2000, Garg et al., 2002). More recently, comparisons between several of these models show that equations varied by joint region (El Ahrache et al., 2006, Ma et al., 2009, Ma et al., 2011). Likewise, a large meta-analysis of 194 publications involving experimental fatigue data confirmed joint-specific intensity–ET relationships (Frey Law and Avin, 2010). Thus, ETs vary as a function of task intensity, but also based on the joint region involved.
These intensity–ET statistical relationships have been well documented and provide one practical tool to predict maximum ET. However this statistical approach is unable to predict fatigue outcomes beyond this single measure, such as the time course of fatigue development, the relative decline in force producing capability for a given task duration, or force recovery during rest periods. Thus more comprehensive, flexible models are needed to represent the complexity of localized muscle fatigue behavior.
We recently proposed a three-compartment, predictive fatigue model, consisting of active (MA), fatigued (MF), and resting (MR) muscle states, to predict the decay and recovery of muscle force (Xia and Frey Law, 2008). We adapted this approach from a similar model first proposed by Liu et al., (2002) with the addition of a feedback controller, C(t), and a variation of the “flow patterns” between muscle states. These adaptations allow sub-maximal contractions and rest intervals to be modeled, yet preserve the use of only two constant parameters to define overall model behavior (fatigue, F, and recovery, R). While this model was shown to qualitatively reproduce expected curvilinear intensity–ET relationships (Xia and Frey Law, 2008), it is yet to be validated against experimental data.
There are many possible fatigue measures that could be used to test the accuracy of this model for predicting localized muscle fatigue. However, well-characterized intensity–ET models (Frey Law and Avin, 2010) provide useful metrics as a first step in evaluating fatigue during simple, sustained isometric contractions. Further, sustained isometric tasks are commonly used to study fatigue behavior in humans, e.g., (Bystrom and Sjogaard, 1991, Shahidi and Mathieu, 1995, Hunter et al., 2002), as they provide a well-defined methodology. Thus, the primary purposes of this study were to: 1) determine a single set of optimal model parameter values, F and R, to predict several joint-specific intensity–ET curves for sustained isometric contractions, and 2) assess the accuracy of the model using these parameter values.
Section snippets
Methods
A global optimization search strategy was used to determine one set of optimal parameter values for the three-compartment, biophysical fatigue model for each joint region, based on joint-specific empirical intensity–ET curves (Frey Law and Avin, 2010). A series of nine relative task intensities were considered, referred to as “optimization intensities”. After determining these joint-specific optimal F and R parameter values, the biophysical model was then evaluated using a new set of task
Results
Optimal, joint specific, F and R parameters were found as a result of the global optimization strategy (Table 1). The resulting model predictions for ET well surpassed our minimum criterion for each joint, with a minimum of 7 out of 9 ET predictions falling within the expected 95% prediction intervals (using the ‘optimization task intensities’). Across each joint, the highest intensities (> ∼80% max) were the most challenging to maintain within the 95% prediction intervals, typically
Discussion
The main finding of this study is that a parsimonious three-compartment biophysical fatigue model can accurately predict fatigue, i.e., maximum ETs, for sustained isometric contractions across a wide range of task intensities for several distinct joint regions. While this fatigue model is inherently able to predict multiple aspects of muscle fatigue, including the time course of fatigue development and recovery, we were able to validate the model using the outcome variable, ET, due to the
Conflict of interest statement
None.
Acknowledgments
This research was supported in part by the United States Council for Automotive Research, Southfield, MI; the National Institutes of Health, K01 AR056134 and a University of Iowa Heartland Center Graduate Student Fellowship.
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