124
Dynamics
of
the Vascular System
Where
uz
and u, are wall movement in the longitudinal and radial
directions respectively.
These equations were later incorporated by
many investigators. Lamb obtained
two
roots for the wave velocity from
a
quadratic equation he derived. One is identical
to
the Moens-Korteweg
formula, or Young's mode velocity
of
propagation, with the propagation
wavelength much greater than the vessel lumen radius, or b>r and
Poisson ratio ~0.5,
or the incompressibility
of
fluid:
c,
=
-
K:
(4.5.14)
The other
is
now know as the Lamb mode velocity for wave propagating
longitudinally
in
the arterial wall:
(4.5.15)
Velocities given in thz longitudinal and radial directions are given by:
4.5.2
Linear Theories of Oscillatory
Blood
Flow in Arteries
In general,
linear
theories
regarding blood flow begin
with the
fundamental Navier-Stokes equations for
a
Newtonian and incompressible
fluid (Attinger, 1964) in cylindrical coordinates, and assuming irrotational
flow. Pulsatile pressure and flow relations, as well as complex velocity
of
wave propagation can be obtained (Li, 1987).
