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

Handle URI:
http://hdl.handle.net/10754/597310
Title:
A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles
Authors:
Flynn, Cormac; Rubin, M. B.; Nielsen, Poul
Abstract:
The development of 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 discrete fibre model is presented consisting of six weighted fibre-bundles. Each bundle is oriented such that it passes through opposing vertices of a regular icosahedron. A novel aspect is the use of simple analytical distribution functions to simulate undulated collagen fibres. This approach yields closed-form analytical expressions for the strain energy of the collagen fibre-bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a modified neo-Hookean type strain energy function which does not allow for fibre compression. The model accurately simulates biaxial stretching of rabbit-skin (error-of-fit 8.7), uniaxial stretching of pig-skin (error-of-fit 7.6), equibiaxial loading of aortic valve cusp (error-of-fit 0.8), and simple shear of rat septal myocardium (error-of-fit 8.9). It compares favourably with previous soft-tissue models and alternative methods of representing undulated collagen fibres. Predicted collagen fibre stiffnesses range from 8.0thinspaceMPa to 930MPa. Elastin fibre stiffnesses range from 2.0 kPa to 154.4 kPa. © 2011 John Wiley & Sons, Ltd.
Citation:
Flynn C, Rubin MB, Nielsen P (2011) A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles. International Journal for Numerical Methods in Biomedical Engineering 27: 1793–1811. Available: http://dx.doi.org/10.1002/cnm.1440.
Publisher:
Wiley-Blackwell
Journal:
International Journal for Numerical Methods in Biomedical Engineering
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
30-Jun-2011
DOI:
10.1002/cnm.1440
Type:
Article
ISSN:
2040-7939
Sponsors:
This work was in part supported by the New Zealand Foundation for Research, Science and Technology, through grants NERF 139400 and NERF 9077/3608892. This publication is also based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorFlynn, Cormacen
dc.contributor.authorRubin, M. B.en
dc.contributor.authorNielsen, Poulen
dc.date.accessioned2016-02-25T12:30:24Zen
dc.date.available2016-02-25T12:30:24Zen
dc.date.issued2011-06-30en
dc.identifier.citationFlynn C, Rubin MB, Nielsen P (2011) A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles. International Journal for Numerical Methods in Biomedical Engineering 27: 1793–1811. Available: http://dx.doi.org/10.1002/cnm.1440.en
dc.identifier.issn2040-7939en
dc.identifier.doi10.1002/cnm.1440en
dc.identifier.urihttp://hdl.handle.net/10754/597310en
dc.description.abstractThe development of 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 discrete fibre model is presented consisting of six weighted fibre-bundles. Each bundle is oriented such that it passes through opposing vertices of a regular icosahedron. A novel aspect is the use of simple analytical distribution functions to simulate undulated collagen fibres. This approach yields closed-form analytical expressions for the strain energy of the collagen fibre-bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a modified neo-Hookean type strain energy function which does not allow for fibre compression. The model accurately simulates biaxial stretching of rabbit-skin (error-of-fit 8.7), uniaxial stretching of pig-skin (error-of-fit 7.6), equibiaxial loading of aortic valve cusp (error-of-fit 0.8), and simple shear of rat septal myocardium (error-of-fit 8.9). It compares favourably with previous soft-tissue models and alternative methods of representing undulated collagen fibres. Predicted collagen fibre stiffnesses range from 8.0thinspaceMPa to 930MPa. Elastin fibre stiffnesses range from 2.0 kPa to 154.4 kPa. © 2011 John Wiley & Sons, Ltd.en
dc.description.sponsorshipThis work was in part supported by the New Zealand Foundation for Research, Science and Technology, through grants NERF 139400 and NERF 9077/3608892. This publication is also based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.subjectAnalytical distribution functionsen
dc.subjectAnisotropyen
dc.subjectConstitutive modelen
dc.subjectSoft tissue mechanicsen
dc.titleA model for the anisotropic response of fibrous soft tissues using six discrete fibre bundlesen
dc.typeArticleen
dc.identifier.journalInternational Journal for Numerical Methods in Biomedical Engineeringen
dc.contributor.institutionThe University of British Columbia, Vancouver, Canadaen
dc.contributor.institutionTechnion - Israel Institute of Technology, Haifa, Israelen
dc.contributor.institutionUniversity of Auckland, Auckland, New Zealanden
kaust.grant.numberKUK-C1-013-04en
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