Vascular Branching
157
1999).
It has been shown that the pulsatile blood flow characteristics, as
we discussed in earlier chapters, cannot be neglected, particularly in the
evolution of vortex structures downstream from the stenosis.
It is
essential
to
determine
the
wall
shear
stress
temporal
evolution
downstream from a stenosis.
The
close
relation
of
atherosclerosis and stenosis
and
their
morphological resemblance have indeed generated much interest in
analyzing common fluid mechanical factors and consequences. In many
instances, particularly in modeling studies, these
two
pathological
conditions cannot be separated. Their importance in the manifestation of
eventual diseases of the vascular system, however, is well recognized.
5.3 Pulse Transmission Characteristics at Vascular Branching
5.3.1
Impedance Matching and Wave Refections
One consequence
of
vascular branching is the pronounced changes in
pressure and flow waveforms. To this end, analysis of pulse transmission
characteristics at vascular branching has been limited. Pulse transmission
at branching junction, unlike that along a single continuous vessel,
depends on the mechanical and geometric properties of the source or
mother vessel as well as on the branching or daughter vessels. Impedance
is an effective means to embrace all these properties. If the combined
impedances
of
the daughter vessel match that
of
the mother vessel, then,
the transmission will simply be ideal and there will be no wave
reflections, nor energetic losses at the branching junction.
The relations for the pressure and flow pulse waveforms expressed as
magnitude and phase are, as defined previously, for the nth harmonic:
(5.3.1)
(5.3.2)
The vascular impedance obtained for the nth harmonic is therefore,
