Now showing 1 - 4 of 4
  • Publication
    Automated Estimation of Collagen Fibre Dispersion in the Dermis and its Contribution to the Anisotropic Behaviour of Skin
    Collagen fibres play an important role in the mechanical behaviour of many soft tissues. Modelling of such tissues now often incorporates a collagen fibre distribution. However, the availability of accurate structural data has so far lagged behind the progress of anisotropic constitutive modelling. Here, an automated process is developed to identify the orientation of collagen fibres using inexpensive and relatively simple techniques. The method uses established histological techniques and an algorithm implemented in the MATLAB image processing toolbox. It takes an average of 15 s to evaluate one image, compared to several hours if assessed visually. The technique was applied to histological sections of human skin with different Langer line orientations and a definite correlation between the orientation of Langer lines and the preferred orientation of collagen fibres in the dermis (p<0.001,R2=0.95) was observed. The structural parameters of the Gasser–Ogden–Holzapfel (GOH) model were all successfully evaluated. The mean dispersion factor for the dermis was κ=0.1404±0.0028. The constitutive parameters μ, k 1 and k 2 were evaluated through physically-based, least squares curve-fitting of experimental test data. The values found for μ, k 1 and k 2 were 0.2014 MPa, 243.6 and 0.1327, respectively. Finally, the above model was implemented in ABAQUS/Standard and a finite element (FE) computation was performed of uniaxial extension tests on human skin. It is expected that the results of this study will assist those wishing to model skin, and that the algorithm described will be of benefit to those who wish to evaluate the collagen dispersion of other soft tissues.
      350Scopus© Citations 152
  • Publication
    Deficiencies in numerical models of anisotropic nonlinearly elastic materials
    Incompressible nonlinearly hyperelastic materials are rarely simulated in finite element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial finite element packages therefore assume that the material is slightly compressible. It is then further assumed that the corresponding strain-energy function can be decomposed additively into volumetric and deviatoric parts. We show that this decomposition is not physically realistic, especially for anisotropic materials, which are of particular interest for simulating the mechanical response of biological soft tissue. The most striking illustration of the shortcoming is that with this decomposition, an anisotropic cube under hydrostatic tension deforms into another cube instead of a hexahedron with non-parallel faces. Furthermore, commercial numerical codes require the specification of a 'compressibility parameter' (or 'penalty factor'), which arises naturally from the flawed additive decomposition of the strain-energy function. This parameter is often linked to a 'bulk modulus', although this notion makes no sense for anisotropic solids; we show that it is essentially an arbitrary parameter and that infinitesimal changes to it result in significant changes in the predicted stress response. This is illustrated with numerical simulations for biaxial tension experiments of arteries, where the magnitude of the stress response is found to change by several orders of magnitude when infinitesimal changes in 'Poisson’s ratio' close to the perfect incompressibility limit of 1/2 are made.
      622Scopus© Citations 35
  • Publication
    Automated Estimation of Collagen Fibre Dispersion in the Dermis and its Contribution to the Anisotropic Behaviour of Skin
    Collagen fibres play an important role in the mechanical behaviour of many soft tissues. Modelling of such tissues now often incorporates a collagen fibre distribution. However, the availability of accurate structural data has so far lagged behind the progress of anisotropic constitutive modelling. Here, an automated process is developed to identify the orientation of collagen fibres using inexpensive and relatively simple techniques. The method uses established histological techniques and an algorithm implemented in the MATLAB image processing toolbox. It takes an average of 15 s to evaluate one image, compared to several hours if assessed visually. The technique was applied to histological sections of human skin with different Langer line orientations and a definite correlation between the orientation of Langer lines and the preferred orientation of collagen fibres in the dermis (p<0.001,R 2 =0.95) was observed. The structural parameters of the Gasser–Ogden–Holzapfel (GOH) model were all successfully evaluated. The mean dispersion factor for the dermis was κ=0.1404±0.0028. The constitutive parameters μ, k 1 and k 2 were evaluated through physically-based, least squares curve-fitting of experimental test data. The values found for μ, k 1 and k 2 were 0.2014 MPa, 243.6 and 0.1327, respectively. Finally, the above model was implemented in ABAQUS/Standard and a finite element (FE) computation was performed of uniaxial extension tests on human skin. It is expected that the results of this study will assist those wishing to model skin, and that the algorithm described will be of benefit to those who wish to evaluate the collagen dispersion of other soft tissues.
      709Scopus© Citations 152