Functionality indexes assessed through a simple model of muscle activation, fatigue and recovery

A nonlinear dynamical system is proposed as a qualitative mathematical model with the twofold aim to reasonably describe the force behavior in a fatiguing sub-maximal contraction and to be possibly employed in assessing muscular activation indexes. The model's properties are studied in terms of its equilibria and their stability properties and the existence of the fatigue equilibrium is ensured as the only system's attractor in the feasibility range of the parameters. Suitable mathematical indicators - related to the dynamical properties of resilience and reactivity - are introduced to characterize the asymptotic and the transient system's behavior. The practical impact of the analytical results is elucidated and a connection is established between the introduced mathematical indicators and muscle functionality indexes as rate of force development, task failure time and complete restore time. Experimental validation with handgrip force signal at high load and possible practical applications are also presented.