Biomedical Engineering Reference
In-Depth Information
Fig. 1.2.
Changes in pressure waveform shape and timing along the aorta [5]. Reproduced with
permission from the American Physiological Society
wavelength,
, of several metres. When looked at “from a distance”, any long seg-
ment of the vascular tree may harbor an appreciable fraction of a pulse cycle. This is
manifested as a temporal shift in the peak of the propagating pulse along the vessel
length,
6
and changes in amplitude and shape due to attenuation, dispersion and wave
reflection (Fig. 1.2).
For studies of local hemodynamics and their relationship to focal vascular disease,
vessel segments of interest are typically of lengths, L, on the order of cm. It then
follows that the segment harbors only small fraction of a pressure pulse (i.e., L/
λ
λ
1, the long wavelength approximation), meaning that the entire segment essentially
pulses in synchrony. While there may be some wave propagation - as noted above
this is the principle of measuring PWV - the effects of any differential compliance
are assumed to be relatively minor.
What remains then is the question of whether the “uniform” pulsation is large
enough to warrant consideration of the flow effects. Considering that wall shear
stress (WSS, often denoted
τ
w
), the target of many of these studies, is thought to
scale with the cube of the lumen radius, at least according to Poiseuille's epony-
mous law, one can deduce via Taylor expansion that a diameter pulsation of
±
Δ
D/D
will result in a WSS variation of approximately
±
3
Δτ
w
/
τ
w
relative to the nominal
rigid-wall values. In other words, for a
5 % deformation, rigid wall simulations
should overestimate peak systolic WSS by roughly 15 %; however, when averaged
over the cardiac cycle these differences are muted or cancelled out depending on the
nature of the presumed pressure pulse and inertial flow (i.e., Womersley number)
effects.
±
6
In fact, PWV is often measured in vivo by measuring this shift at two or more locations spaced a
known distance apart [4].
