28
Dynamics
of
the Vascular System
(2.2.1 4)
When radial strain is half that of longitudinal strain, or when
o
=
0.5,
the material is said to be incompressible. This means that when
a
cylindrical material is stretched, its volume remains unchanged. Or, in
the case
of
an artery, when it is stretched,
its
lumen volume remains
unchanged. Experimental measurements to obtain the Poisson ratio for
arteries have shown
o
to be close to 0.5. Arteries, therefore, can be
considered to be close to being incompressible.
The above analysis assumes an isotropic arterial wall. The non-
isotropy, or anisotropy is seen in the various differences in the relative
content and physical properties
of
the arterial wall. Collagen is the
stiffest wall component, with an elastic modulus of
10'
-
lo9
dynes/cm2.
This is some
two
orders of magnitude larger than those of elastin, 1-6
x
lo6
dynes/cm2
,
and smooth muscle, 0.1-2.5 x lo6 dynes/cm2.
Elastin
is
relatively extensible, but
is
not a purely Hookean material.
Collagen on the other hand is relatively inextensible, because of its high
stiffness. Much more is
known about
vascular
smooth
muscle.
Mechanical properties of arterial vessel walls can also be altered by
neural
mechanisms and by circulating
catecholamines,
such as
norepinephrine. The composite of the arterial wall components operates
in such a manner that at low pressures, elastin dominates the composite
behavior. At high pressures, collagen becomes more important. Elastic
modulus is
a
nonlinear function
of
pressure. The pressure dependence of
the mechanical properties of arteries has been reported by several
investigators (e.g., Cox, 1975; Weizsacker and Pascal, 1982; Drzewiecki
et al, 1997).
Fig. 2.2.5 illustrates how arterial lumen diameter and
compliance vary with changing transmural pressure.
With increasing
positive
transmural
pressure,
arterial vessel
diameter is distended
(Weizsacker and Pascal,
1982), as expected, the corresponding
compliance however, declines. With negative transmural pressure, the
arterial area compliance decreases as the artery is under collapse. The
decrease in compliance with increasing transmural pressure follows a
negative exponential function.
