A three-compartment muscle fatigue model accurately predicts joint-specific maximum endurance times for sustained isometric tasks

The development of localized muscle fatigue has classically been described by the nonlinear intensity-endurance time (ET) curve (Rohmert, 1960; El Ahrache et al., 2006). These empirical intensity-ET relationships have been well-documented and vary between joint regions. We previously proposed a three-compartment biophysical fatigue model, consisting of compartments (i.e. states) for active (M(A)), fatigued (M(F)), and resting (M(R)) muscles, to predict the decay and recovery of muscle force (Xia and Frey Law, 2008). The purpose of this investigation was to determine optimal model parameter values, fatigue (F) and recovery (R), which define the "flow rate" between muscle states and to evaluate the model's accuracy for estimating expected intensity-ET curves. Using a grid-search approach with modified Monte Carlo simulations, over 1 million F and R permutations were used to predict the maximum ET for sustained isometric tasks at 9 intensities ranging from 10% to 90% of maximum in 10% increments (over 9 million simulations total). Optimal F and R values ranged from 0.00589 (F(ankle)) and 0.0182 (R(ankle)) to 0.00058 (F(shoulder)) and 0.00168 (R(shoulder)), reproducing the intensity-ET curves with low mean RMS errors: shoulder (2.7s), hand/grip (5.6s), knee (6.7s), trunk (9.3s), elbow (9.9s), and ankle (11.2s). Testing the model at different task intensities (15-95% maximum in 10% increments) produced slightly higher errors, but largely within the 95% prediction intervals expected for the intensity-ET curves. We conclude that this three-compartment fatigue model can be used to accurately represent joint-specific intensity-ET curves, which may be useful for ergonomic analyses and/or digital human modeling applications.