Physical Concepts and Basic Fluid Mechanics
47
the length-tension relation is curvilinear. Many experiments, however,
were done in-vitro situations, having the advantage of well-controlled
experimental conditions, but the disadvantage
of
extending the results to
equate with in-vivo parametric changes.
A
material that obeys Young’s modulus of elasticity in terms of
tensile stress and tensile strain is:
(3.1
.
1
4)
Stress has the dimension of pressure, or force
(F)
per unit area
(A),
F
0
=-=p
‘A
(3.1.1
5)
where
P
is pressure, in mmHg or dynes/cm2.
Thus, stress has the
dimension of mmHg or dynes/cm2 in cm-gm-sec or
CGS
units.
Strain in the longitudinal direction, or along the length of the blood
vessel is expressed as the ratio of extension per unit length, or the ratio of
the amount stretched longitudinally to the length of the original vessel
segment,
A1
ll
&
=-
(3.1
.
1
6)
Strain in the radial direction, or perpendicular to the vessel segment
length, is the fraction of distention of the vessel lumen radius or
diameter. It is given by
Ar
r
&
=-
r
(3.1
.
1
7)
For a blood vessel considered to be purely elastic, Hooke’s law
applies. To find the tension
(T)
exerted on the arterial wall due to intra-
luminal 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,
