Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

Abstract

Modelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function--a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.

Mechanical behavior of bovine pericardium treated with hyaluronic acid derivative for bioprosthetic aortic valves

“…However, some of these biomaterials exhibit a nonlinear deformation behavior. The theory of nonlinear elasticity based on hyperelastic models describes the elastic nonlinear tissue response under large strains . In the hyperelastic approach, the strain energy function correlates the displacement with the respective stress values.…”

“…The theory of nonlinear elasticity based on hyperelastic models describes the elastic nonlinear tissue response under large strains. 23 In the hyperelastic approach, the strain energy function correlates the displacement with the respective stress values. In the present work, the strain energy function was described by the Ogden function, which is defined strictly in terms of stretch ratios and material fit coefficients.…”

Breast magnetic resonance elastography: a review of clinical work and future perspectives

“…We can conclude from this literature overview that the biomechanical models used for breast MRE thus far mainly focus on viscoelasticity, with some attention to tissue (an)isotropy and tensor imaging. Other potentially powerful comprehensive biomechanical models include poroelastic, hyperelastic, nonlinear and orthotropic models, [28][29][30][31][32][33][34] although a further theoretical disquisition falls outside the scope of this article.…”

Efficient isogeometric thin shell formulations for soft biological materials

“…(Chagnon et al, 2015). This section discusses a few isotropic constitutive models that are commonly used for biomaterials and soft tissues (Martins et al, 2006;Wex et al, 2015). Both kinds of constitutive laws, i.e.…”

“…In literature, this model is mostly called as "Fung" model while it is also named "Fung-Demiray" (e.g. byWex et al, 2015) or "Demiray" model (e.g. byGasser et al, 2006).…”