Constitutive modelling of arteries
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.
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The arterial wall is often treated as incompressible, so internal pressure changes translate to vessel wall dilation while total wall volume is conserved.
“The arterial wall is often treated as incompressible44,51, pressure changes applied internally translates to vessel wall dilation, but the total wall volume is conserved.”
From Synthetic photoplethysmography (PPG) of the radial artery through parallelized Monte Carlo and its correlation to body mass index (BMI) (2021) · cites this paper as [51]
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Boonya-ananta, T., Rodriguez, A. J., Ajmal, A., Du Le, V. N., Hansen, A. K., Hutcheson, J. D., & Ramella-Roman, J. C. (2021) · Scientific Reports · doi:10.1038/s41598-021-82124-4 · Cited by 70 · see citing works
- Authors
- Holzapfel, G. A., & Ogden, R. W.
- Affiliations
- Graz University of Technology (AT)
- University of Glasgow (GB)
- Corresponding author
- Holzapfel, Gerhard A.
- Venue
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 2010-03-31
- Volume
- 466
- Issue
- 2118
- Pages
- 1551-1597
- ISSN
- 1364-5021 (ISSN-L)
- 1471-2946
- OpenAlex
- W2164783843
- Cited by
- 528
- References
- 147
- Citations by year
- 2026: 24 · 2025: 34 · 2024: 27 · 2023: 18 · 2022: 32 · 2021: 37 · 2020: 40 · 2019: 29 · 2018: 32 · 2017: 45 · 2016: 38 · 2015: 32 · 2014: 48 · 2013: 32 · 2012: 33
- FWCI
- 17.18
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences (publishedVersion)
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Elasticity and Material Modeling
- Physical Sciences › Engineering › Biomedical Engineering › Soft Robotics and Applications
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Cell Biology › Cellular Mechanics and Interactions
- Keywords
- arterial wall mechanics, constitutive modeling, collagen fiber orientation, deformation invariants, strain energy function, thick-walled cylinders, mechanobiology, arterial biomechanics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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