Vascular Biology, Structure and Function
27
As
an example, the radial strain calculated from an ultrasonic dimension
gage recording of the aortic diameter shown in Fig. 2.2.4 is
=
0.1
1.93
E,
=-
19.3
(2.2.1
1)
In this case, the fractional change in diameter, or
AD/D,
represents the
radial strain.
For
a blood vessel considered to be purely elastic, Hooke's law
applies. To find the tension (T) exerted on the vessel wall due to
intraluminal blood pressure distention, Laplace's law is useful. Laplace's
law describes the tension exerted on
a
curved membrane with a radius of
curvature.
In
the case of blood vessel, there are
two
radii of curvature,
one that
is
infinite in the longitudinal direction along the blood vessel
axis and the other is in the radial direction.
Thus, Laplace's law for an
artery can be written as:
T=p.r
(2.2.12)
This assumes the vessel has a thin wall or that the ratio of vessel wall
thickness (h) to vessel lumen radius (r) is small, or h/r
I
1/10.
Here
p
is
the intramural-extramural pressure difference, or the transmural pressure.
When the vessel wall thickness is taken into account, the Lame equation
becomes relevant:
P'
ot
=
-
h
(2.2.13)
Arteries have been assumed to be incompressible. Although not
exactly
so,
this is in general a good approximation.
To assess the
compressibility
of
a material, the Poisson ratio is defined. It is the ratio
of
radial strain to longitudinal strain.
We obtain from the above
definitions, the Poisson ratio as:
