# Model-based analysis of fatigued human knee extensors

### Abstract

This study investigated the effect of isometrically induced fatigue on Hill-type muscle model parameters and related task-dependent effects. Parameter identification methods were used to extract fatigue-related parameter trends from isometric and ballistic dynamic maximum voluntary knee extensions. Nine subjects, who completed ten fatiguing sets, each consisting of nine 3 s isometric maximum voluntary contractions with 3 s rest plus two ballistic contractions with different loads, were analyzed. Only at the isometric task, the identified optimized model parameter values of muscle activation rate and maximum force generating capacity of the contractile element decreased from $$20.8 \pm 8.4$$ to $$11.2 \pm 4.1$$ Hz and from $$18{,}137 \pm 150$$ to $$10{,}666 \pm 2139$$ N, respectively. For all tasks, the maximum efficiency of the contractile element, mathematically related to the curvature of the force–velocity relation, increased from $$0.35 \pm 0.04$$ to $$0.42 \pm 0.05$$ . The model parameter maximum contraction velocity decreased from $$0.93 \pm 0.1$$ to $$0.9 \pm 0.1$$ m/s and the stiffness of the serial elastic element from $$1936 \pm 227$$ to $$1432 \pm 245$$ N/mm. Thus, models of fatigue should consider fatigue dependencies in active as well as in passive elements, and muscle activation dynamics should account for the task dependency of fatigue.

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