Biomedical Engineering Reference
In-Depth Information
In short, uncertainties or inaccuracies in the data needed to model the effects of
compliance may mask any perceived benefit of doing so, especially in light of the
extra conceptual and computational effort required for including the effects of com-
pliance. This is especially true for patient-specific studies, where these uncertainties
may well be subsumed by the uncertainties associated with the reconstruction of the
(rigid) geometry itself [15]. If the
effects
of compliance on flow are to be included,
one way to do this without resorting to full-blown FSI simulations would be to im-
pose the wall motion directly (e.g., based on time-resolved images, as is often done
for coronary arteries). Alternatively, for cases with relatively small motions, one may
employ transpiration (normal wall velocity) boundary conditions [16], based on the
premise that the effects of compliance are mainly due to the storage and release of
fluid at the wall, rather than the wall deformations themselves.
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In summary, for predicting flow and WSS patterns in finite segments of large
arteries, rigid wall CFD models are probably a reasonable approximation to that
which occurs in a compliant vessel. This is not to imply, by the way, that structural
(wall) stresses are unworthy of investigation, for undoubtedly they play a central role
in regulating normal and pathological vascular responses, alone or in concert with
WSS [17]. Rather, the reader is encouraged to contextualize the effects of compli-
ance with the effect of other sources of error/imprecision. As will be seen in the next
section, however, the effects of compliance must be confronted when imposing
in
vivo
flow boundary conditions, necessarily measured from compliant vessels, onto
rigid CFD models.
1.3 Compliance and flow boundary conditions
Notwithstanding Moore's law and the development of increasingly clever computa-
tional modelling techniques, 3D CFD models of large arteries must still be isolated
from the entirety of the circulatory system. This means that assumptions must be
made about the nature of the velocity profile at the truncated inlet(s) and outlet(s),
irrespective of whether these profiles are derived form measured or assumed flow
rates, or indeed multiscale models. The most common assumption, especially for
inlets, is a fully developed (Womersley) velocity profile, which implicitly assumes
that the upstream vasculature is straight enough for the prevailing flow to be approx-
imately fully-developed, or that the CFD model has been truncated sufficiently far
upstream so that the effect of the assumed velocity profile shape is negligible. At the
carotid bifurcation, for example, we have shown that it is not always clear what con-
stitutes “straight enough” when it comes to fully-developed flow (or lack thereof) in
the upstream common carotid artery [18]. On the other hand, we have demonstrated
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This was the principle used by Womersley to derive his famous analytic solution for flow in
compliant tubes. It was later exploited by the author for his so-called “hybrid” implicit-explicit 2D
FSI approach [6], which solved for the transpiration velocities simultaneously with the rest of the
velocity field, and then iteratively updated the wall position based on those wall velocities.
