164
Dynamics
of
the
Vascular
System
(5.3.26)
This assumes that the wall thickness-to-radius ratio or h/r
is
relatively
constant for the branching vessels.
Since
2
A, =n-[$]
(5.3.27)
it is clear that alterations in branching vessel lumen radii could exert
a
more
significant
effect on wave reflections at vascular
branching
junction,
TI,
than changes in their respective elastic moduli.
For constant elasticity for all vessels involved at vascular branching,,
i.e. c,/cl=l, the wave reflections due to vascular branching becomes
dependent only on area ratio, i.e.
1
-
A,
I-,
=-
1
+
A,
(5.3.28)
5.3.3
Minimum Local Reflections at Vascular Branching Junctions
By examination of the characteristic impedances of mother and daughter
vessels, that pulse wave reflection due to vascular branching
is
minimal
(Li, 1984). Since reflection is energetically wasteful, this means little
energy
is
lost due to pulse transmission through vascular branching
junctions. This has been attributed to close to optimal area ratios and
branching angles.
Also
geometric effect rather than elastic effect
dominants pulse propagation through vascular branching junctions (Li,
1986).
The
area
ratio
concept
has
received
continued
attention.
Experimental results showed that minimum reflection is obtained when
area ratio equals 1.23 for an equi-bifurcation. This correlates closely to
that given by Womersley's theory (minimum reflection when area ratio
equals 1.26). In small muscular vessels, viscous damping is appreciably
more important than in large vessels.
In these vessels, the point of
