Impact of blood rheology on wall shear stress in a model of the middle cerebral artery

Abstract

Perturbations to the homeostatic distribution of mechanical forces exerted by blood on the endothelial layer have been correlated with vascular pathologies, including intracranial aneurysms and atherosclerosis. Recent computational work suggests that, in order to correctly characterize such forces, the shear-thinning properties of blood must be taken into account. To the best of our knowledge, these findings have never been compared against experimentally observed pathological thresholds. In this work, we apply the three-band diagram (TBD) analysis due to Gizzi et al. (Gizzi et al. 2011 Three-band decomposition analysis of wall shear stress in pulsatile flows. Phys. Rev. E 83, 031902. (doi:10.1103/PhysRevE.83.031902)) to assess the impact of the choice of blood rheology model on a computational model of the right middle cerebral artery. Our results show that, in the model under study, the differences between the wall shear stress predicted by a Newtonian model and the well-known Carreau-Yasuda generalized Newtonian model are only significant if the vascular pathology under study is associated with a pathological threshold in the range 0.94-1.56 Pa, where the results of the TBD analysis of the rheology models considered differs. Otherwise, we observe no significant differences.

Keywords: blood flow modelling; lattice Boltzmann; multi-scale modelling; rheology; three-band diagram analysis.

Figure 1.

Three-dimensional model of a subset of the right MCA used in this work. Geometry segments are labelled A–E for later reference. The arrows indicate flow direction. (Online version in colour.)

Figure 2.

Dynamic viscosity η as a function of shear rate for the CY and the Newtonian models. (Online version in colour.)

Figure 3.

One-dimensional model of the main arteries in the upper body. Each segment (solid line) represents a different part of a human arterial system including characterization of the three-dimensional model of the right MCA in figure 1 (see top right arrow). Segment lengths are not to scale. The dots represent (i) bifurcations, when found at the intersection of two or more segments, (ii) zero-dimensional representations of the peripheral vasculature, when found at the end of an open-ended segment, or (iii) the heart in the case labelled with H. (Online version in colour.)

Figure 4.

Pressure differentials, relative to outlet D, obtained from the one-dimensional model at the inlet and outlets. Simulations were run for a total of three cardiac cycles. Inlet A, solid line; outlet C, dashed line; outlet E, dotted line. (Online version in colour.)

Figure 5.

Traction vector t (estimated with the CY rheology model) at the upstream bifurcation of the three-dimensional model. Vectors are scaled according to their magnitude. Points x₃ and x₄ in table 2 are shown in green and magenta, respectively. Visualizations generated with the open source software package ParaView [29]. (a) End of diastole t = 1.82 s; (b) peak flow during systole t = 1.97 s.

Figure 6.

TBD analysis at points x₃, x₄ and x₅. The values of N^−,0,+(σ) are presented as a stacked histogram. (a) Newtonian TBD at x₃, (b) CY TBD at x₃, (c) Newtonian TBD at x₄, (d) CY TBD at x₄, (e) Newtonian TBD at x₅, and (f) CY TBD at x₅.