158
Dynamics
of
the
Vascular System
z,
=
lznIeJOn
(5.3.3)
where the magnitude of impedance is simply the ratio of the pressure
amplitude to the flow amplitude, and for the nth harmonic:
(5.3.4)
with the phase lag
Characteristic impedance that reflect the vessel properties alone,
irrespective of wave reflections can then be approximated from the high
frequency average of the impedance modulus. Characteristic impedance,
like input impedance, is complex, although its dependence on frequency
is
only weakly
so
in large vessels.
In order to isolate the contributions of vascular branching to overall
pulse
transmission
characteristics, it
is necessary to define local
characteristic impedances that reflect the mechanical and geometric
properties of the vessels at vascular junction.
A
local reflection coefficient can be defined for vascular branching
only:
(5.3.6)
where
ZOd
represents the resultant
parallel
combination of the
characteristic impedance of branching daughter vessels, and
Z,
is the
mother vessel's characteristic impedance. For instance, for a bifurcation
with daughter branch characteristic impedances of
Z,
and
Z02,
we have:
(5.3.7)
For an equi-bifurcation (Fig.
5.3.
l),
one obtains:
