Finite element modelling of skeletal muscles coupled with fatigue

In this study, Hill's muscle theory coupled with fatigue was proposed to describe mechanical behaviours of skeletal muscles. The force developed by a fatigued muscle was described by a muscle fatigue formula which was a time function of the activation α_a and the stretch λ. The modified Hill's muscle theory was hence incorporated into a three-dimensional (3D) finite element model using the PAK finite element code. In this paper, the theoretical derivation of the 3D muscle model was firstly described. After presenting the method of establishing the finite element programme, a case example of studying the mechanical response of a frog gastrocnemius muscle was used to illustrate the applicability of the proposed methodology. The effects of the muscle fatigue on the deformation as well as the stress and strain distribution of the frog muscle subject to a cyclic activation function have been determined. An experiment capturing the real-time shape change of a frog muscle was also conducted to assess the applicability of the proposed method. A comparison between the deformed shapes of the predictive model and the frog muscles was also made. It was shown that the method is capable of providing a reasonable model for describing the mechanical behaviour of skeletal muscles.