Biomedical Engineering Reference
In-Depth Information
that blood viscosity changes instantaneously with shear rate. While disaggregation
of RBC rouleaux with increasing shear is thought to occur more or less instanta-
neously, the kinetics of RBC aggregation are slower and more complex. The end re-
sult is that simple shear-thinning rheology models may be reasonable for flow fields
that have persistent recirculation regions (e.g., aneurysms), but may
overestimate
non-Newtonian effects when recirculation zones are transient (e.g., carotid bulb),
such that rouleaux may not have time to form within a periodic cardiac cycle. As
we pointed out in [30], the implication of this is the truth of non-Newtonian effects
may fall somewhere between the already-narrow space between constant viscosity
and instantaneously shear-thinning models.
One final assumption that is inevitably made for large artery CFD studies is that
blood may be treated as if it were a homogeneous fluid, which is usually justified by
the orders of magnitude difference in the length scales of large arteries (e.g., lumen
diameters) vs. RBC.
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This presumes that the length scales of the
flow features
are
similarly large, an implicit assumption that may well be violated under conditions
of pathological flow, as shall be discussed in the next and final section.
1.5 Rheology and turbulence
It is generally accepted that blood flow in large arteries is laminar under normal
physiological conditions, except perhaps distal to heart valves and in the ascending
aorta [39]. It is also widely considered that turbulence occurs only under severe
pathological conditions, notably downstream of severe constrictions or stenoses,
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although there is some evidence that mild stenoses may induce turbulence [41].
Until relatively recently, CFD studies have focused almost exclusively on nom-
inally turbulent flows through idealized stenoses, for which detailed experimental
data are available (e.g., [42]). We have found, for example, that so-called two-
equation turbulence models may be satisfactory for modelling steady turbulent
flows, but tend to be overly dissipative for the transitional, relaminarizing flows ex-
perienced under physiological conditions [43]. More recent investigations by others
have focused on large-eddy simulation (LES) and even direct numerical simulation
(DNS) methods [44], the latter essentially a brute force solution of the Navier-Stokes
equations resolved down to the anticipated length scales of the smallest (i.e., Kol-
mogorov) eddies at which viscous dissipation occurs. Irrespective of CFD methodol-
ogy, there is ongoing debate about the nature of physiological “turbulence”, namely,
whether it is turbulence in the strict fluid mechanical sense of random and uncorre-
lated flow exhibiting a classical cascade of energy, or indeed whether in some cases it
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m RBC-free plasma layer adjacent to the arterial wall has an appreciable
effect on the apparent viscosity of blood (i.e., the Fahraeus-Lindqvist effect) for arteries below
∼
For example, the
∼
3-
μ
25 mm radius [28], namely a two-order-of-magnitude scale difference.
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Turbulence caused by the external compression of an artery is thought to give rise to the so-called
Korotkoff sounds used for blood pressure measurement. Noises (“bruits”) can also be detected
by a stethoscope placed over a stenosed superficial vessel like the carotid artery, or intracranial
aneurysms, which may also harbor turbulent flow [40].
0
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