A Dynamical Model of Muscle Activation, Fatigue, and Recovery

Abstract

A dynamical model is presented as a framework for muscle activation, fatigue, and recovery. By describing the effects of muscle fatigue and recovery in terms of two phenomenological parameters (F, R), we develop a set of dynamical equations to describe the behavior of muscles as a group of motor units activated by voluntary effort. This model provides a macroscopic view for understanding biophysical mechanisms of voluntary drive, fatigue effect, and recovery in stimulating, limiting, and modulating the force output from muscles. The model is investigated under the condition in which brain effort is assumed to be constant. Experimental validation of the model is performed by fitting force data measured from healthy human subjects during a 3-min sustained maximal voluntary handgrip contraction. The experimental results confirm a theoretical inference from the model regarding the possibility of maximal muscle force production, and suggest that only 97% of the true maximal force can be reached under maximal voluntary effort, assuming that all motor units can be recruited voluntarily. The effects of different motor unit types, time-dependent brain effort, sources of artifacts, and other factors that could affect the model are discussed. The applications of the model are also discussed.

A Finite Element Approach for the Modelling of Skeletal Muscle Fatigue

“…Therefore, the displacement decreases at most for R 1 = 0.0 s −1 . The aforementioned results cordially agree with models describing the fatigue behaviour at fibre/muscle level, see [13]. However, in comparison to this model, which is implemented in terms of a stand-alone programme for one-dimensional problems, we present an approach implemented into the finite element framework which is consequently applicable to threedimensional muscle structures.…”

“…As aforementioned, these parameters control the number of fibres that are in the remaining state during muscle activation. In contrast to the model developed by Liu et al [13], which is implemented as so-called stand-alone programme, we aim to implement the behaviour as described before into a three-dimensional framework, see next section. …”

An integrated exercise response and muscle fatigue model for performance decrement estimates of workloads in oxygen-limiting environments

“…The process of muscle fatiguing is dependent not only on the mechanical aspect but also on a number of factors such as neural signaling, oxygen and fuel availability, and byproduct generation. Liu et al (2002) were able to create a phenomenological model to explain macroscopic muscle endurance curves by reducing the complexities of muscle fatigue into a series of first-order differential equations that utilized a recovery parameter R, a fatigue parameter F, and maximal force generation capacity M 0 . However, the formulation required brain input to be known.…”

Movement Variability and Digital Human Models: Development of a Demonstrator Taking the Effects of Muscular Fatigue into Account

“…Since the start of this century, this field of research has undergone a revival and new models have now been published. For example, Ding et al [14] use a biochemical approach, Böl et al [15] apply a "finite elements" approach, and a biophysical approach is developed by Liu et al [16] in their three-compartment model. Of all these approaches, the three-compartment model appears the best adapted to integration into DHM-type tools, and the literature presents several studies of this type of model with virtual humans in specific conditions (static effort, estimation of MET) [12,17,18].…”