Vascular Biology, Structure and Function
an example, the radial strain calculated from an ultrasonic dimension
gage recording of the aortic diameter shown in Fig. 2.2.4 is
In this case, the fractional change in diameter, or
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
curved membrane with a radius of
the case of blood vessel, there are
radii of curvature,
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 vessel has a thin wall or that the ratio of vessel wall
thickness (h) to vessel lumen radius (r) is small, or h/r
the intramural-extramural pressure difference, or the transmural pressure.
When the vessel 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: