A comparison of hyperelastic constitutive models applicable to brain and fat tissues.
In some soft biological structures such as brain and fat tissues, strong experimental evidence suggests that the shear modulus increases significantly under increasing compressive strain, but not under tensile strain, whereas the apparent Young's elastic modulus increases or remains almost constant when compressive strain increases. These tissues also exhibit a predominantly isotropic, incompressible behaviour. Our aim is to capture these seemingly contradictory mechanical behaviours, both qualitatively and quantitatively, within the framework of finite elasticity, by modelling a soft tissue as a homogeneous, isotropic, incompressible, hyperelastic material and comparing our results with available experimental data. Our analysis reveals that the Fung and Gent models, which are typically used to model soft tissues, are inadequate for the modelling of brain or fat under combined stretch and shear, and so are the classical neo-Hookean and Mooney-Rivlin models used for elastomers. However, a subclass of Ogden hyperelastic models are found to be in excellent agreement with the experiments. Our findings provide explicit models suitable for integration in large-scale finite-element computations.
School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK mihaila@cardiff.ac.uk.
L Angela
LA
Mihai
Institute for Medicine and Engineering, University of Pennsylvania, 3340 Smith Walk, Philadelphia, PA, USA.
LiKang
L
Chin
Departments of Physiology and Physics and Astronomy, Institute for Medicine and Engineering, University of Pennsylvania, 3340 Smith Walk, Philadelphia, PA, USA.
Paul A
PA
Janmey
Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK.
Alain
A
Goriely
D000273:Adipose Tissue; D001921:Brain; D055119:Elastic Modulus; D006801:Humans; D008959:Models, Neurological
brain tissue; brain tumours; constitutive models; elastic moduli; fat tissue; large strain