128
Dynamics
of
the
Vascular
System
Many linear theories
of
oscillating blood flow in arteries have been
proposed, but that of Womersley remains the most commonly used.
A
frequency dependent parameter not originally defined by him, but later
known as the Womersley's parameter was introduced, as shown in eqn.
(4.5.28).
Womersley
(1
957) also utilized a linearized Navier-Stokes
equation, and an equation
of
motion of
a
freely moving elastic tube with
homogeneous and isotropic wall material.
He also made assumptions
that the pulse propagation wavelength is much greater than that
of
the
arterial lumen radius, or b>r, and that the propagating pressure pulse
takes the form of
where
A
is
the amplitude of the pressure pulse (p) and
c
is
pulse wave
velocity. He obtained
r
(4.5.34)
An
equation for the pulse wave velocity was derived, assuming
arterial wall and blood densities are equal,
where k, is
a
function
of
the Bessel function
(4.5.36)
(4.5.3 7)
where
Jo
and
J,,
are zero and first order Bessel functions of the first
kind.
Solutions for
Jo
and
J,,
are tabulated by Womersley and van
