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:
This assumes the artery has a thin-wall or that the ratio of arterial wall
thickness (h) to arterial lumen radius (r) is small, or h/r
1/10. Here p is
the intramural-extramural pressure difference, or the transmural pressure.
When the arterial wall thickness is taken into account, the Lame equation
Arteries have been assumed to be incompressible. Although not
this is in general a good approximation.
To assess the
a material, the Poisson ratio is defined. It is the ratio
radial strain to longitudinal strain.
We obtain from the above
definitions, the Poisson ratio as:
When radial strain is half that of longitudinal strain, or when
the material is said to be incompressible. This means that when
stretched, its volume remains unchanged.
the case of an artery, when it is stretched, its lumenal volume remains
obtain the Poisson ratio for
arteries have shown
to be close
Arteries, therefore, can be
considered to be close to being incompressible.
purely elastic material differs from a viscoelastic material. The
former depends only on strain (eqns. 3.1.16 and 3.1.17) while the latter
depends on the rate of change of strain, or strain rate (dddt) also. The
artery as a viscoelastic material exhibits stress-relaxation, creep, and
hysteresis phenomena (Fig. 3.1.1).