A Finite Element Approach for the Modelling of Skeletal Muscle Fatigue

Abstract

Key words Finite element method, skeletal muscle, muscle fatigue, muscle activation, muscle recovery. MSC (2000) 74L15, 74S05, 74F99, 92C10Skeletal muscles are the primary unit for the movement of the human body, they serve as shock absorber and protect the skeleton system against external loads. By maintaining a certain force level, muscle show fatigue effects, expressed by a decrease of the retentive force. To incorporate such effects in a finite element framework, we use a fatigue model that allows us to describe the dynamical processes between active, fatigued, and recovered fibres. The chosen modelling strategy facilitates the efficient transport of the known information about physiological processes in the single fibre to the three-dimensional macroscopic level where e. g. the dependence of muscle contraction on fatigue effects is studied. Besides the theoretical derivation of the modelling approach, simulations at fibre as well as at muscle level have been investigated.

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

“…introducing a muscle compartment model, whose states can be controlled to match desired data trajectories (Hawkins and Hull, 1993;Freund and Takala, 2001;Liu et al, 2002;Xia and Frey-Law, 2008;Böl, 2009;Frey-Law et al, 2012;Sih et al, 2012). For computational simplification, Wiener-Hammerstein models (Wiener, 1942;Narendra and Gallman, 1966;Wills et al, 2013) are also used (Cai et al, 2009).…”

“…Several state-of-the-art muscle models do not comprise the physiologically well-observed force decay over time, especially in fast-twitch fibers under high neural stimulation (Brown and Loeb, 2000;Rode et al, 2009;Blümel et al, 2012;Millard et al, 2013;Haeufle et al, 2014b;Schappacher-Tilp et al, 2015;Mörl et al, 2016). Moreover, literature terminology is vaguely summarizing any possible force-decay mechanism under the umbrella of fatigue, which is discussed throughout disciplines, such as biology (Enoka and Stuart, 1992;Fitts, 1994), biomechanics (Bergström and Hultman, 1985;MacIntosh et al, 2012), engineering (Böl, 2009), medicine (Chen et al, 1999;Cardozo et al, 2011), physiology (Lindström et al, 1977;Allen and Westerblad, 2001;Allen et al, 2008), and sports science (Komi, 2000;Brown et al, 2017). One of the first books addressing (muscle as well as whole body) fatigue was published at the beginning of the 20th century (Mosso, 1904) and a multitude of research has followed since, see Gandevia (2001) for a thorough review.…”