An extension of Hill's three‐component model to include different fibre types in finite element modelling of muscle

Abstract

SUMMARYMost 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.

A 3D skeletal muscle model coupled with active contraction of muscle fibres and hyperelastic behaviour

“…If these properties are mutually dependent, a numerical algorithm is usually required to determine response of the muscle. In the numerical algorithm proposed by Kojic et al (1998) and later adopted by Tang et al (2005) and Stojanovic et al (2006), the stress calculation for the Hill's model was reduced to the solution of one non-linear equation with respect to the stretch increment of the series elastic element. However, this algorithm was aimed at predicting concentric and isometric contraction of the muscle.…”

Finite element modeling in the musculoskeletal system: generic overview

“…Currently, most of the mathematical representations of muscle contraction mechanics are based on either Hill's model or Huxley's theory (Hatze, 1981b;Riek et al ., 1999;Stojanovic et al ., 2007;Tang et al ., 2007). Hill's model depicts the dynamics of a musculotendon unit using a set of connected discrete mechanical elements.…”

Smeared Multiscale Finite Element Models for Mass Transport and Electrophysiology Coupled to Muscle Mechanics

“…Computational models of skeletal muscles and their implementation to the physiological conditions have been the subject of intensive research within the computational community (e.g., Kojic et al, 1998;Stojanovic et al, 2007;Mijailovich et al, 2010, and references therein).…”