166
Dynamics
of
the
Vascular
System
impedances of junction vessels. By using measured and calculated
vascular parameters (Table
5.3.1)
obtained from measurements in dog
aorto-iliac junction (a trifurcation with the abdominal aorta branching
into its continuation branch and left and right iliac arteries)
,
the local
reflection was found to be just
0.07
(Li,
1984, 1986).
Fig.
5.3.3
shows that the local reflection coefficient is significantly
increased when the vessel lumen radius is progressively decreased
downstream from the junction
(daughter vessels).
But when the
branching vessels become stiffer with increased elastic modulus, such
changes in local reflection coefficient is rather moderate (Fig.
5.3.4).
This indicates that junction geometry is more dominant in determining
pulse transmission through vascular branching than elastic factors.
-3t
2s
50%
75%
loox
I!iX
2oox
AB-
Fig.
5.3.4:
Local reflection coefficient
is
plotted against the reduction in elastic modulus.
Reflection is increased with increased branching vessel stiffness,
but
the increase
is
less
pronounced as compared with corresponding percentage reduction in lumen radius.
5.4
Optimization Aspects Applicable to Vascular Branching
5.4.1
Optimizing
Vessel Radius
and
the Cube
Law
To overcome the resistance to blood flow, the power required will be
inversely proportional to the fourth power of radius, or r4, according to
Poiseuille’s law governing steady flow through
a
rigid cylindrical vessel:
