Mathematical modeling of exercise fatigability in the severe domain: A unifying integrative framework in isokinetic condition

Abstract

Muscle fatigue is the decay in the ability of muscles to generate force, and results from neural and metabolic perturbations. This article presents an integrative mathematical model that describes the decrease in maximal force capacity (i.e. fatigue) over exercises performed at intensities above the critical force F_c (i.e. severe domain). The model unifies the previous Critical Power Model and All-Out Model and can be applied to any exercise described by a changing force F over time. The assumptions of the model are (i) isokinetic conditions, an intensity domain of F_c<F, (ii) constant individual parameters of F_c, and τ, (iii) fatigability proportional to the accumulation of impulse J_AC above the critical force F_c. The present study adjusted the parameters to fit previous experimental observations from three types of exercises: constant intensity, all-out, and increasing ramp exercise. This integrative model establishes a connection between the previous individual models and provides an excellent description of exercise fatigability in the severe domain. With this new integrative model, the maximal force production of the muscle can be predicted over time during both maximal and submaximal exercises.

Keywords: All-out; Anaerobic capacities; Critical power; Endurance; Exercise fatigability; Fatigue; Maximal force capacity; Muscular capacities; Power-time relationship; Time to exhaustion.