Vascular Biology, Structure
and
Function
25
2.2.2
Vusculur Stiffness and Elastic Properties
Vascular stiffness is traditionally expressed in terms of Young’ modulus
of elasticity, which gives a simple description of the elasticity of the
arterial wall. Young’s modulus of elasticity
(E)
is
defined by the ratio
of
tensile stress
(q)
to tensile strain
(EJ.
When the relationship between
stress and strain is a linear one, then the material is said to be Hookian, or
simply, it obeys Hooke’s law of elasticity. This normally applies to a
purely elastic material.
It is only valid for application to a cylindrical
blood vessel when the radial and longitudinal deformations are small
compared to the respective lumen diameter or length of the arterial
segment.
For the following analysis of the physical aspect of an artery, we shall
consider a segment
of
the artery represented by a uniform isotropic
cylinder with radius r, wall thickness h, and segment length
1.
Isotropy
implies the uniform physical properties of the content
of
the arterial wall.
The arterial wall
is
actually
anisotropic,
consisting of various
components discussed above, and the assumption of isotropy can not be
exactly true. Although a gross approximation, this assumption allows
simple descriptions of the mechanical properties of the arterial wall to be
obtained.
Young’s modulus
of
elasticity in terms
of
tensile stress and tensile
strain is:
(2.2.5)
Stress has the dimension of pressure, or force
(F)
per unit area
(A),
F
0
=-=p
‘A
(2.2.6)
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. The
conversion of mmHg to dynes/cm2 follows the formula that expresses the
hydrostatic pressure above atmospheric pressure:
P=hpg
(2.2.7)