126
Dynamics
of
the
Vascular
System
where
Jo
and
J1
are the zero and first order Bessel functions of the first
kind, and
Al
and
C1
are constants.
By using Lamb's equations for the wall and applying the boundary
condition that fluid and wall velocities are equal at the wall, i.e.
and
a complex velocity of propagation is obtained as
c1
=
kF
2P
(4.5.23)
(4.5.24)
(4.5.25)
where k contains Bessel functions
Jo
and
J1.
For
k
=
1, as in the case
when the fluid is ideal, i.e. the kinematic viscosity
q/p
=
0,
this equation
reduces to the familiar Moens-Korteweg formula for pulse wave
velocity.
Differences in linearized theories are mostly in the description of
arterial
wall
properties and
arterial wall motion. More accurate
descriptions of the blood-arterial wall interactions can be achieved by
additions or improvements in the equations describing the wall and
blood, or the so-called blood-wall interactions. These latter arise because
of the fluid-tissue interface and the differences in mechanical behaviors.
Indeed, modern clinical analysis has placed more emphasis on the blood-
endothelial
interface and on the blood flow and
elastin-collagen
interactions.
Morgan and Kiely (1954) added viscous fluid stress terms to the
Lamb equations (4.5.12 and 4.5.13):
(4.5.26)
