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Title: An extension of Hill's three-component model to include different fibre types in finite element modelling of muscle
Authors: Stojanovic, B
Kojic, M
Rosic, M
Tsui, CP 
Tang, CY 
Keywords: Biceps muscle
Finite element method
Functionally graded materials
Hill's muscle model
Muscle modelling
Issue Date: 2007
Publisher: John Wiley & Sons Ltd
Source: International journal for numerical methods in engineering, 2007, v. 71, no. 7, p. 801-817 How to cite?
Journal: International Journal for Numerical Methods in Engineering 
Abstract: Most of the proposed versions of the Hill's model use a sliding-element theory, considering a single sarcomere. However, a muscle represents a collection of different fibre types with a large range in contractile properties among them. An extension of Hill's three-component model is proposed here to take into account different fibre types. We present a model consisting of a number of sarcomeras of different types coupled in parallel with the connective tissue. Each sarcomere is modelled by one non-linear elastic element connected in series with one non-linear contractile element. Using the finite element method, in an incremental-iterative scheme of calculating equilibrium configurations of a muscle, the key step is the determination of stresses corresponding to strain increments. The stress calculation procedure for the extended Hill's model is reduced to the solution of a number of independent non-linear equations with respect to the stretch increments of the serial elastic elements in each sarcomere. Since the distribution of the specific fibre type is non-uniform over the muscle volume, we have material heterogeneity which we modelled by using the so-called 'Generalized Isoparametric Element Formulation' for functionally graded materials (FGMs). The proposed computational scheme is built in our FE package PAK, so that muscles of complex three-dimensional shapes can be modelled. In numerical examples, we illustrate the main characteristics of the developed numerical model and some possibilities of realistic modelling of muscle functioning.
DOI: 10.1002/nme.1963
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