108
Dynamics
of
the
Vascular
System
Y
2,
=-
@la
(4.3.18)
Knowing these relationships, the measurement of pressure and flow
together with their gradients permit determination of the propagation
constant. Thus, one can apply this method by measuring two pressures
and two flows, or by measuring two pressures,
a
few centimeters apart, a
flow midway between them, and the pulsatile change in diameter.
Alternatively, the transverse impedance, which is related to vessel wall
properties, can be obtained from the dynamic pressure-area relationship.
If two pressures and flows are measured simultaneously at two sites
along a uniform vessel, the propagation constant can be obtained from:
(4.3.19)
where Az denotes the distance between the
two
sites. Subscript
1
refers
to the upstream site and
2,
the downstream site.
Another method utilizes the simultaneous recording of three pressures
along
a
uniform vessel. The propagation constant is obtained as:
(4.3.20)
when differential pressures are measured, Ap1
=
p1-p2; Ap3
=
p3-p2. The
three pressures p1
,
p2,
p3, are simultaneously measured at an equal
distance (Az) apart.
The three-point pressure method was extensively evaluated by Li et
al.
(1980) in
a
hydrodynamic model. Subsequently, this method was
applied to investigate pulse wave propagation in dogs
(Li
et al., 1981)
with respect to contributions by vascular wall elastic and geometric
properties, vessel wall and blood viscosity, and nonlinearities in system
parameters and in the equations of motion.
Discrepancies in results
obtained with different experimental methods and theory were discussed
and resolved. Measurements were obtained from the abdominal aorta,
as
