The Mathematical Institute, University of Oxford, Eprints Archive

A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles

Flynn, C. and Rubin, M. B. and Nielsen, P. (2010) A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles. International Journal for Numerical Methods in Biomedical Engineering . (Submitted)

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Abstract

The development of accurate constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A novel discrete fibre model is presented consisting of six weighted fibre bundles. Each bundle is oriented such that they pass through opposing vertices of a regular icosahedron. A novel aspect of the model is the use of simple analytical distribution functions to simulate the undulated collagen fibres. This approach yields a closed form analytical expression for the strain energy function for the collagen fibre bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a neo-Hookean strain energy function. The model accurately simulates the biaxial stretching of rabbit-skin (error-of-fit 8.7%), the uniaxial stretching of pig-skin (error-of-fit 7.6%), equibiaxial loading of aortic valve cusp (error-of-fit 0.8%), and the simple shear of rat septal myocardium (error-of-fit 9.1%). The proposed model compares favourably with previously published soft-tissue models and alternative methods of representing undulated collagen fibres. The stiffness of collagen fibres predicted by the model ranges from 8.0 MPa to 0.93 GPa. The stiffness of elastin fibres ranges from 2.5 kPa to 154.4 kPa. The anisotropy of model resulting from the representation of the fibre field with a discrete number of fibres is also explored.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1027
Deposited By:Peter Hudston
Deposited On:07 Jan 2011 08:42
Last Modified:09 Feb 2012 15:52

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