A biophysically guided constitutive law of the musculotendon-complex: modelling and numerical implementation in...

Many biomedical, clinical, and industrial applications may benefit from musculoskeletal simulations. Three-dimensional macroscopic muscle models (3D models) can more accurately represent muscle architecture than their 1D (line-segment) counterparts. Nevertheless, 3D models remain underutilised in academic, clinical, and commercial environments. Among the reasons for this is a lack of modelling and simulation standardisation, verification, and validation. Here, we strive towards a solution by providing an open-access, characterised, constitutive relation (CR) for 3D musculotendon models.

The musculotendon complex is modelled following the state-of-the-art active stress approach and is treated as hyperelastic, transversely isotropic, and nearly incompressible. Furthermore, force-length and -velocity relationships are incorporated, and muscle activation is derived from motor-unit information. The CR was implemented within the commercial finite-element software package Abaqus as a user-subroutine. A masticatory system model with left and right masseters was used to demonstrate active and passive movement.

The CR was characterised by various experimental data sets and was able to capture a wide variety of passive and active behaviours. Furthermore, the masticatory simulations revealed that joint movement was sensitive to the muscle's in-fibre passive response.

This user-material provides a "plug and play" template for 3D neuro-musculoskeletal finite element modelling. We hope that this reduces modelling effort, fosters exchange, and contributes to the standardisation of such models.