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This study aimed to test whether adding a rest recovery parameter, r, to the analytical three-compartment controller (3CC) fatigue model (Xia and Frey Law, 2008) will improve fatigue estimates during intermittent contractions. The 3CC muscle fatigue model uses differential equations to predict the flow of muscle between three muscle states: Resting (M(R)), Active (M(A)), and Fatigued (M(F)). This model uses a feedback controller to match the active state to target loads and two joint-specific parameters: F, fatigue rate controlling flow from active to fatigued compartments) and R, the recovery rate controlling flow from the fatigued to the resting compartments. This model does well to predict intensity-endurance time curves for sustained isometric tasks. However, previous studies find when rest intervals are present that the model over predicts fatigue. Intermittent rest periods would allow for the occurrence of subsequent reactive vasodilation and post-contraction hyperemia. We hypothesize a modified 3CC-r fatigue model will improve predictions of force decay during intermittent contractions with the addition of a rest recovery parameter, r, to augment recovery during rest intervals, representing muscle re-perfusion. A meta-analysis compiling intermittent fatigue data from 63 publications reporting decline in peak torque (% torque decline) were used for comparison. The original model over-predicted fatigue development from 19 – 29% torque decline; the addition of a rest multiplier significantly improved fatigue estimates to 6 – 10% torque decline. We conclude the addition of a rest multiplier to the three-compartment controller fatigue model provides a physiologically consistent modification for tasks involving rest intervals, resulting in improved estimates of muscle fatigue.

Although the rotator cuff muscles are susceptible to fatigue, shoulder fatigue studies reporting torque decline during intermittent tasks are relatively uncommon in the literature. A previous modification to the three-compartment controller (3CC) fatigue model incorporated a rest recovery multiplier (3CC-r model) to represent augmented blood flow to muscle during rest intervals ( Looft et al., 2018 ). A rest recovery value of r = 15 was optimal for ankle, knee, and elbow joint regions, whereas r = 30 was better for hand/grip muscles. However, shoulder torque decline data was unavailable in the literature for comparison. Thus, the purpose of this study was to collect fatigue data for two different intermittent, isometric shoulder flexion fatiguing tasks and assess the 3CC-r model with r = 15 or 30 compared to the original 3CC model. Twenty healthy participants (9 M) completed two fatigue tasks: 50% maximum voluntary contraction (MVC) with 50% duty cycle (DC) and 70% MVC with 70% DC. MVCs were assessed at discrete time points (1, 3, 5, 10, and 15 min) until endurance time (MET). Mean observed percent torque decline (%TD) for the two tasks were compared to three model estimates: 3CC-r (using r = 15 and r = 30) and 3CC. Using these data, we confirmed that the addition of a rest multiplier (r = 15 somewhat better than r = 30) substantially improved predictions of shoulder fatigue using a previously validated analytical fatigue model (3CC). The relatively large reduction in model errors over the original model suggests the importance of representing augmented recovery during rest periods.

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.