Biomedical Engineering Reference
In-Depth Information
that this has little impact if the inlet is truncated at least three diameters upstream of
bifurcation [19].
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Setting aside the technicalities of what kind of velocity profile to impose onto such
3D CFD models, the section turns its attention to subtler, but potentially more dele-
terious effects of the rigid-wall assumption on large artery CFD models. As noted
earlier, compliance results in the alternating storage and release of flow caused by the
periodic expansion and contraction of the artery walls in response to the pulse pres-
sure. Although periodicity of the cardiac cycle presumes that inlet and outlet flow
rates must match in a time-averaged sense, there is no such requirement of instanta-
neous conservation of flow rates. On the other hand, for rigid-wall CFD simulations,
the continuity equation requires that mass/flow be conserved at each instant of time.
This sets up the potential for a fundamental incompatibility between inlet and outlet
flow rates derived from in vivo measurements on compliant vessels, which must be
reconciled with the use of rigid-wall CFD models at the potential cost of accuracy.
One obvious example of this arises from CFD simulation of long arterial do-
mains, where the local effects of compliance might be relatively small, but over
long distances may result in appreciable discrepancies between the inlet and out-
let flow rates. This is an issue we were first forced to confront in our PIV vs. CFD
studies of aneurysm flows, which employed silicone-based flow models for the PIV
measurements [20]. As shown in Fig. 1.3, there was a significant delay between the
outlet vs. inlet flow rates, owing to the small but non-negligible compliance of the
silicone, coupled with the placement of the flow meters necessarily far upstream
and downstream. Although the (rigid-walled) CFD domain included these long in-
let and outlet segments, we were focused on flow within the aneurysm sac, and thus
we could simply align the inlet and outlet flow waveforms temporally (i.e., reflecting
their actual relative timings close to the aneurysm sac) without penalty, as suggested
by the good agreement between the CFD simulations and PIV measurements [20].
Less clear cut is our recent study of retrograde flow in the mouse aorta and its role
in accelerating plaque formation [21]. Doppler ultrasound measurements obtained
previously suggested that flow rate dynamics might be appreciably attenuated along
the length of the descending aorta [22], which constituted our (rigid-walled) CFD
domain. In this case we chose to impose a flow waveform appropriate to the proxi-
mal descending aorta inlet, and accepted the fact that flow at the (traction-free) distal
descending aorta outlet would not match the actual flow rate dynamics as measured
by Doppler ultrasound. This precluded any robust quantitative analyses, but we con-
sidered it a reasonable first order approximation in light of our goal to qualitatively
associate patterns of hemodynamic extrema with patterns of plaque distribution.
Finally, and to demonstrate that the effects of compliance on flow waveforms are
not restricted to long CFD domains, consider the left panel of Fig. 1.4, which illus-
trates the observation that flow rate waveforms at the internal and external (ICA and
ECA) outlets of the carotid bifurcation do not necessarily align temporally. As part
of a magnetic resonance imaging (MRI) study of carotid artery flow rates in older
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Different conclusions may be drawn for other vascular territories depending on, say, the curvature
of the inlet or the Reynolds number (i.e., entrance length), so the interested reader is encouraged to
review the literature and/or perform their own tests specific to their application of interest.
