title: Modelling non-symmetric collagen fibre dispersion in arterial walls.
abstract: New experimental results on collagen fibre dispersion in human arterial layers have shown that the dispersion in the tangential plane is more significant than that out of plane. A rotationally symmetric dispersion model is not able to capture this distinction. For this reason, we introduce a new non-symmetric dispersion model, based on the bivariate von Mises distribution, which is used to construct a new structure tensor. The latter is incorporated in a strain-energy function that accommodates both the mechanical and structural features of the material, extending our rotationally symmetric dispersion model (Gasser et al. 2006 J. R. Soc. Interface 3, 15-35. (doi:10.1098/rsif.2005.0073)). We provide specific ranges for the dispersion parameters and show how previous models can be deduced as special cases. We also provide explicit expressions for the stress and elasticity tensors in the Lagrangian description that are needed for a finite-element implementation. Material and structural parameters were obtained by fitting predictions of the model to experimental data obtained from human abdominal aortic adventitia. In a finite-element example, we analyse the influence of the fibre dispersion on the homogeneous biaxial mechanical response of aortic strips, and in a final example the non-homogeneous stress distribution is obtained for circumferential and axial strips under fixed extension. It has recently become apparent that this more general model is needed for describing the mechanical behaviour of a variety of fibrous tissues.
authors: Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria holzapfel@tugraz.at.
authors: Gerhard A
authors: GA
authors: Holzapfel
authors: Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria.
authors: Justyna A
authors: JA
authors: Niestrawska
authors: School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK.
authors: Ray W
authors: RW
authors: Ogden
authors: Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria.
authors: Andreas J
authors: AJ
authors: Reinisch
authors: Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria.
authors: Andreas J
authors: AJ
authors: Schriefl
mesh_terms: D000818:Animals; D001158:Arteries / Q000737:chemistry* / Q000502:physiology*; D003198:Computer Simulation; D055119:Elastic Modulus / Q000502:physiology; D024022:Fibrillar Collagens / Q000737:chemistry* / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular; D008956:Models, Chemical; D013314:Stress, Mechanical; D014018:Tissue Distribution; D059289:Vascular Stiffness / Q000502:physiology*
chemical_list: D024022:Fibrillar Collagens
keywords: anisotropy; arterial wall mechanics; collagen fibre dispersion; constitutive modelling; fibre orientation