122
Dynamics
of
the
Vascular System
Using the Lame equation for stress
Pr
‘h
0
=-
and write strain as:
dr
r
E
=-
we obtain a similar wave equation:
d2v,
-
Eh
d2v,
at2
2rp
az2
which gives the pulse wave velocity as:
(4.5.7)
(4.5.8)
(4.5.9)
(4.5.10)
This
is
the well-known Moens-Korteweg formula for pulse wave
velocity (Li,
2000).
Moens in 1878 obtained this formula through
experimentation and obtained
C,
=
k,,,
-
dz
(4.5.1 1)
Where
k,
is a constant. Korteweg, also in 1878, approached from
a
theoretical perspective by assuming a flat velocity profile, ignoring
viscosity, fluid compressibility, and vessel wall constraints and obtained
an identical formula (Noordergraaf, 1969; Li, 1987)
The flat velocity profile implies that the blood flow velocity across
the artery is uniform.
In
a parabolic velocity profile, the centerline
velocity is the highest and the velocity declines in a parabolic fashion
