120
Dynamics
of
the
Vascular
System
individual contributions to global reflection phenomenon a demanding
task.
Reflection
sites have generally been determined from the first
impedance minimum, and subsequent calculation:
C
&.
=-
fmin
in
and
Amin
LR
=-
4
(4.4.14)
(4.4.15)
hmin
and fmin are the wavelength and frequency corresponding to the
impedance minimum.
LR
is
the distance of the effective reflection site
from the point of measurement.
Some investigators have used the zero-
phase crossing of impedance for the calculation of effective reflection
sites.
4.5 Modeling Aspects
of
the Arterial System
4.5,
I
Mathematical Formulations
There
are
three equations
generally thought to be sufficient to
characterize the propagation of the pulse wave.
The first of these
equations describes fluid motion,
av
1
ap
at
p
az
2
-_-
(4.5.1)
where v, is the blood velocity in the longitudinal
z
direction or along the
blood vessel from proximal to distal locations, p is pressure and
p
is the
density
of
blood, The left side of the equation represents the rate of
change of velocity,
or
flow
acceleration. This equation implies that
blood flow acceleration
is
proportional to the pressure gradient. For this
