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Constituent-based quasi-linear viscoelasticity: a revised quasi-linear modelling framework to capture nonlinear viscoelasticity in arteries.
- Source :
-
Biomechanics & Modeling in Mechanobiology . Oct2023, Vol. 22 Issue 5, p1607-1623. 17p. - Publication Year :
- 2023
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Abstract
- Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 ± 0.03 (mean ± standard deviation) at 80–40 mmHg to 1.58 ± 0.22 at 160–120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity. [ABSTRACT FROM AUTHOR]
- Subjects :
- *VISCOELASTICITY
*CAROTID artery
*ARTERIES
*ELASTIN
*STANDARD deviations
*VISCOSITY
Subjects
Details
- Language :
- English
- ISSN :
- 16177959
- Volume :
- 22
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Biomechanics & Modeling in Mechanobiology
- Publication Type :
- Academic Journal
- Accession number :
- 172041376
- Full Text :
- https://doi.org/10.1007/s10237-023-01711-8