52
Dynamics of the Vascular System
4a2b
P(w)
E(w)
=
b2
-a2
D(w)
(3.1.24)
where
a
and
b
are inner and outer arterial diameters, respectively.
P(w)
and D(w)are frequency domain pressure and diameter, respectively.
Fig.
3.1.3:
Dynamic elastic modulus
(Edyn)
plotted as a function of frequency for the
thoracic aorta, abdominal aorta, femoral and carotid arteries. Notice the
Edyn
is essentially
unchanged above
2
Hz.
Experimental
results
show that the viscous modulus is
small
compared with the elastic modulus (Li et al., 1981; Li, 1987; Nichols and
O'Rourke, 1998). It
is
of the order of
10%.
The dynamic modulus has
also been found
to
be essentially constant above
2
Hz
(Li,
2000).
A
complex Young's modulus was considered by Westerhof and
Noordergraaf
(1
970) to describe arterial wall viscoelasticity and also
utilized frequency dependent parameters.
They define the complex
elastic modulus as the ratio of complex stress to complex strain:
