Constitutive modelling of arteries

Gerhard Holzapfel, Raymond William Ogden

Research output: Contribution to journalArticle

275 Citations (Scopus)

Abstract

This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thick-walled circular cylindrical tube in order to illustrate its extension–inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.
Original languageEnglish
Pages (from-to)1551-1597
Number of pages47
JournalProceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences
Volume466
Issue number2118
Early online date31 Mar 2010
DOIs
Publication statusPublished - 8 Jun 2010

Fingerprint

Constitutive Modeling
Arteries
arteries
Tissue
Soft Tissue
Mechanical Behavior
Mechanobiology
elastic properties
Modeling
Continuum mechanics
Biomechanics
biodynamics
Smooth muscle
smooth muscle
continuum mechanics
Biological Tissue
Strain energy
Invariant
Collagen
reviewing

Keywords

  • arterial wall mechanics
  • fibrous biological tissues
  • fibre-reinforced materials
  • artery layers
  • finite elasticity

Cite this

Constitutive modelling of arteries. / Holzapfel, Gerhard; Ogden, Raymond William.

In: Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences, Vol. 466, No. 2118, 08.06.2010, p. 1551-1597.

Research output: Contribution to journalArticle

Holzapfel, Gerhard ; Ogden, Raymond William. / Constitutive modelling of arteries. In: Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences. 2010 ; Vol. 466, No. 2118. pp. 1551-1597.
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