Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms - Mathematical Methods and Models in Biomedicine - page 143

Blood is a concentrated suspension of formed cellular elements that includes red
blood cells (RBC or erythrocytes), white blood cells (or leukocytes), and platelets
(or thrombocytes), suspended in an aqueous polymer solution, the plasma. RBC
have been shown to exert the most significant influence on the mechanical properties
of blood, mainly due to their high concentration (hematocrit H t ≈

40-45%).
Consequently, the rheology of blood is largely affected by the behavior of the RBC,
which can range from 3D microstructures to dispersed individual cells, depending
predominantly on the shear rates [ 24 ]. Hemodynamics is not only related to the fluid
properties but also to other mechanical factors, including the forces exerted on the
fluid, the fluid motion, and the vessel geometry.
According to the circulatory region of interest and the desired level of accuracy,
blood flow may be modeled as steady or pulsatile, Newtonian or non-Newtonian,
and laminar or turbulent. In medium to large vessels, blood flow has pulsatile behav-
ior, due to the repeated, rhythmic mechanical pumping of the heart [ 15 ]. However,
in small arteries sufficiently distant from the heart the flow is predominantly steady.
In this work, the importance of including the pulsatility of blood is studied, and both
steady and unsteady simulations are considered.
As mentioned above, the RBC play an important role in the blood rheol-
ogy. While plasma exhibits a nearly Newtonian behavior, whole blood has non-
Newtonian characteristics [ 22 ]. This is mainly due to the RBC's tendency to form
3D microstructures at low shear rates and to their deformability and alignment with
the flow field at high shear rates. Experimental studies suggest that in most part of
the arterial system the viscosity of blood can be considered as a constant, and blood
can be modeled as a Newtonian fluid. However, the complex processes related to
the formation and breakup of the 3D microstructures, as well as the elongation
and recovery of individual RBC, contribute in particular to blood shear-thinning
viscosity, corresponding to a decrease in the apparent viscosity with increasing
shear rate. It has also been observed that blood can present viscoelastic behavior
[ 1 , 22 ]. The variability of the blood viscosity leads to differences in perceived shear
stress along the arterial wall. Indeed, in large arteries the instantaneous shear rate
over a cardiac cycle has drastic variations, up to two orders of magnitude [ 25 ].
Despite these findings, as referred, it is often reasonable to simulate blood flow as
a Newtonian fluid, since in sufficiently large nonpathological arteries it experiences
high shear rates, over 100 s − 1 . Many authors adopt this argument however this
assumption is not valid when the shear rate is lower than 100 s − 1 , which is the case
of small arteries, veins, capillaries, and aneurysms or in recirculation regions down-
stream of a stenosis [ 27 ]. In these cases the flow is slower and the non-Newtonian
models are better suited. Nevertheless, hemodynamics in intracranial aneurysms has
been argued to be accurately modeled using the Newtonian assumption [ 4 ]. Here,
both Newtonian and non-Newtonian fluid mathematical models will be adopted and
compared.
Variations in the mathematical modeling of blood rheology lead to modeling
uncertainties, which might compromise the reproducibility of the clinical data. The
present work also focuses on the uncertainties that arise from considering different
boundary conditions at the outflow sections of the computational domain, as well