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Session: Vascular - II
Session starts: Friday 27 January, 11:30
Presentation starts: 12:30
Room: Room 559

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Alessandro Giudici (Maastricht University)
Koen van der Laan (Maastricht University)
Myrthe van der Bruggen (Maastricht University)
Shaiv Parikh (Maastricht University)
Eline Berends (Maastricht University)
Sébastien Foulquier (Maastricht University)
Tammo Delhaas (Maastricht University)
Koen Reesink (Maastricht University)
Bart Spronck (Maastricht University)

Abstract:
Arteries exhibit complex viscoelastic behaviours, which are highly non-linear both in terms of elasticity and viscosity. Previous works have proposed different solutions to model elastic non-linearity, which capture well the arterial wall response to quasi-static deformations. However, in vivo the arterial wall is subjected to pulsatile loads for which viscoelastic phenomena cannot be neglected. Unlike for elasticity, effective solutions to model non-linear viscoelasticity are lacking. On the one hand, quasi-linear viscoelasticity (QLV) offers a practical solution to viscoelastic modelling, but its linear viscosity assumption is unsuitable for whole-wall vascular application. On the other hand, deformation-dependent parameters make fully non-linear viscoelastic models impractical. Indeed, their application to experimental data often leads to identifying specific solutions for each tested loading condition. In the present study, we address this issue by applying QLV theory at the wall constituent rather than at the whole-wall level. Five murine common carotid arteries were subjected to an experimental protocol of quasi-static and harmonic biaxial loading conditions for viscoelastic mechanical characterisation. In our constituent-based QLV (cbQLV) framework, the arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres in which collagen and elastin were assigned different stress relaxation functions. Non-linearity in viscoelasticity was quantified in terms of dependency of the dynamic-to-quasi-static stiffness ratio on pressure, and the performance of our model was compared to that of standard QLV (sQLV). The experimentally measured dynamic-to-quasi-static stiffness ratio was negligible at low pressures (1.03±0.03 at a pressure range 40–80 mmHg; mean±standard deviation) and rose with increasing pressure (1.58±0.22 at 120–160 mmHg, Figure 1A). By assigning viscoelastic behaviour to collagen and almost purely elastic behaviour to elastin, cbQLV captured well the pressure dependency of this ratio (Figure 1B). Conversely, sQLV failed to capture this complex behaviour (Figure 1C). In conclusion, constituent-based QLV offers a practical solution to model complex non-linear viscoelastic behaviours using a unique set of deformation-independent viscous parameters.