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A comparison of hyperelastic constitutive models applicable to brain and fat tissues.

ABSTRACT: 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.

SUBMITTER: Mihai LA

PROVIDER: S-EPMC4614457 | biostudies-literature | 2015 Sep

REPOSITORIES: biostudies-literature

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A comparison of hyperelastic constitutive models applicable to brain and fat tissues.

Mihai L Angela LA Chin LiKang L Janmey Paul A PA Goriely Alain A

Journal of the Royal Society, Interface 20150901 110

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 quali ...[more]

PMID: 26354826

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Project description:The mechanical function of the uterine cervix is critical for a healthy pregnancy. During pregnancy, the cervix undergoes significant softening to allow for a successful delivery. Abnormal cervical remodeling is suspected to contribute to preterm birth. Material constitutive models describing known biological shifts in pregnancy are essential to predict the mechanical integrity of the cervix. In this work, the material response of human cervical tissue under spherical indentation and uniaxial tensile tests loaded along different anatomical directions is experimentally measured. A deep-learning segmentation tool is applied to capture the tissue deformation during the uniaxial tensile tests. A 3-dimensional, equilibrium anisotropic continuous fiber constitutive model is formulated, considering collagen fiber directionality, fiber bundle dispersion, and the entropic nature of wavy cross-linked collagen molecules. Additionally, the universality of the material model is demonstrated by characterizing previously published mouse cervix mechanical data. Overall, the proposed material model captures the tension-compression asymmetric material responses and the remodeling characteristics of both human and mouse cervical tissue. The pregnant (PG) human cervix (mean locking stretch ζ=2.4, mean initial stiffness ξ=12 kPa, mean bulk modulus κ=0.26 kPa, mean dispersion b=1.0) is more compliant compared with the nonpregnant (NP) cervix (mean ζ=1.3, mean ξ=32 kPa, mean κ=1.4 kPa, mean b=1.4). Creating a validated material model, which describes the role of collagen fiber directionality, dispersion, and crosslinking, enables tissue-level biomechanical simulations to determine which material and anatomical factors drive the cervix to open prematurely. STATEMENT OF SIGNIFICANCE: In this study, we report a 3D anisotropic hyperelastic constitutive model based on Langevin statistical mechanics and successfully describe the material behavior of both human and mouse cervical tissue using this model. This model bridges the connection between the extracellular matrix (ECM) microstructure remodeling and the macro mechanical properties change of the cervix during pregnancy via microstructure-associated material parameters. This is the first model, to our knowledge, to connect the the entropic nature of wavy cross-linked collagen molecules with the mechanical behavior of the cervix. Inspired by microstructure, this model provides a foundation to understand further the relationship between abnormal cervical ECM remodeling and preterm birth. Furthermore, with a relatively simple form, the proposed model can be applied to other fibrous tissues in the future.

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A comparison of hyperelastic constitutive models applicable to brain and fat tissues.

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A comparison of hyperelastic constitutive models applicable to brain and fat tissues.

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