Parameter Identification for a Four-Compartment Controller Muscle Fatigue Model

Abstract

Abstract. Localized muscle fatigue arises from interacting central and peripheral mechanisms whose contributions vary with contraction intensity and joint velocity. The four-compartment controller with enhanced recovery (4CCr) model captures these processes but its practical use is limited by parameter identifiability and sensitivity to optimization settings. This study systematically evaluates the robustness of 4CCr parameters across joints, velocities, optimization algorithms, and sample-size subsets. Residual capacity (RC) is extracted from peak isometric torque across five isometric–isokinetic cycles in 32 participants, and the three unknown 4CCr parameters—baseline peripheral fatigue (FPi0), baseline peripheral recovery (RPi0), and velocity coefficient (ki)—are estimated using genetic algorithm (GA) and particle swarm optimization (PSO). Comprehensive GA hyperparameter sweeps and PSO validation reveal strong equifinality in (RPi0, ki) and unexpectedly high stability in FPi0 across subjects, velocities, and solvers. Sample-size analyses (N = 10, 14, 18) further confirm that FPi0 converges rapidly with increasing dataset, whereas RPi0 and ki fluctuate substantially across datasets and therefore do not yield consistent physiological interpretations. The recovery analysis indicates that the 4CCr model reflects realistic two-phase recovery, unlike the three-compartment controller with enhanced recovery (3CCr) model which recovers rapidly. These findings demonstrate that peripheral fatigue rate is the only well-constrained parameter in the 4CCr muscle fatigue model, and that fixing FPi0 enables more reliable optimization of the remaining parameters. This work clarifies parameter identifiability within the 4CCr model and supports the development of a more stable, generalizable fatigue model for digital human simulations and velocity-dependent strength prediction.