Biomedical Engineering Reference
In-Depth Information
Of course this simplistic perturbation analysis ignores important non-linear ef-
fects of wall motion for large artery flows having Reynolds numbers on the order of
hundreds. Nevertheless, early studies seemed to confirm these simplistic analyses.
For example, the author's early CFD studies of flow in distensible vs. rigid 2D by-
pass graft models reported a 15-20 % reduction in WSS variations over the cardiac
cycle for a
4 % distension [6]. Perktold's pioneering CFD studies of a compliant,
idealised compliant 3D carotid bifurcation [7] reported 25 % WSS reductions com-
pared to rigid wall simulations, but pointed out that “global structure of the flow
and stress patterns remains unchanged”, findings later echoed by Zhao et al [8] in
their studies of anatomically realistic carotid bifurcations. Those authors also nicely
summarized the time-varying nature of these effects: “the largest difference occurs
at peak systole with less influence of wall distensibility at diastole. This may be at-
tributed partly to the wall motion which transiently enlarged the cross-sectional area,
causing the instantaneous velocities everywhere in the cross section to decrease in
comparison to the rigid model
7
, in accordance with the conservation of mass.”
Despite the conclusions of the above and other similar studies, the rigid wall as-
sumption is not necessarily reasonable for all large artery flows. Remembering that
it presumes a modest and relatively uniform radial wall motion, the situation is less
clear for vessels that undergo large and/or non-uniform motions. Examples of this
are the ascending aorta and coronary arteries, for which the bulk motion rather than
the compliance alone may have an appreciable impact on the predicted flow pat-
terns [9, 10]. Between these extremes are cases of strong compliance mismatch, such
as artificial grafts or implanted vascular devices such as stents. Plaques or stenoses
also introduce compliance mismatches, although it should be remembered that most
vessels harboring a stenosis, or those requiring some kind of intervention, are prob-
ably stiffer to begin with owing to hypertension or other vascular risk factors, thus
serving in practice to decrease the actual mismatch.
For cases where compliance and/or vessel motion are shown or believed to have
a non-negligible quantitative or qualitative effect, a popular modelling approach is
fluid-structure interaction (FSI), whereby the wall motion must also be solved. In
this case one must confront the practicalities of obtaining the necessary wall struc-
ture and properties, and the pressure boundary conditions, particularly for patient-
specific studies. For example, wall properties and thicknesses are often assumed to
be uniform and based on literature values, which tends to overlook inter- and in-
traindividual variations. Measurement of individual wall properties may be possible
through imaging and inverse modelling approaches, but such non-linear analyses
often introduce appreciable uncertainties. Similarly, although we have shown that
wall
thickness
can be measured and mapped three-dimensionally [11], we have also
shown how imaging can distort wall thickness measurements in a way that can be
difficult to detect or correct [12, 13]. Pressure dynamics, also essential as bound-
ary conditions for FSI, are typically measured at the brachial artery, whereas the
pressures may well be different at other vascular sites of interest [14].
±
7
The italics are mine, and I will return to this point in the next section, as it has implications for
the measurement and prescription of prevailing flow conditions, and for the validation of so-called
“patient-specific” CFD models against in vivo measurements.
