A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

Abstract

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

“…To describe the interaction between blood and vessel wall, different approaches can be used. 31 , 89 , 113 In the simplest case, the fluid pressure is related to the cross-section of the vessel via a linear function with respect to the luminal diameter ( D = ) where is the external pressure from the surrounding tissue, is a parameter representing the wall elasticity and is the unstressed cross-section area. However, modeling reactive hyperemia requires a vessel wall model able to describe the hyperpolarization-induced dilation and then the resulting (compliant) structural response to hyperemic flow.…”

Multiscale constitutive framework of 1D blood flow modeling: Asymptotic limits and numerical methods

“…To model the FSI occurring between blood and vessel walls, an appropriate constitutive model, which relates pressure to area variations, needs to be considered. To this end, it must be remembered that the smooth muscle cells that constitute the intermediate layer of vessels impart a viscoelastic behavior to the wall, which assumes a key role when high frequencies are dominant [3,13]. In contrast, when stress is applied very slowly, viscous aspects do not occur, and the wall behaves mostly elastically.…”

Uncertainty quantification of a three-dimensional in-stent restenosis model with surrogate modelling

“…The construction of a surrogate model can be categorized into three types: simplified models, projection-based methods and data-fit methods [ 18 ]. Simplified models refer to a rough approximation based on simplifications of the simulated system such as spatial dimensionality reduction [ 19 , 20 ] or coarse-grid discretizations [ 21 , 22 ]. The projection-based methods proceed by identifying a low-dimensional subspace that is constructed to retain the essential character of the system input–output mapping.…”