Hemodynamics
of
Large Arteries
103
where
E
is the elastic modulus of the artery, h and
r
are the wall
thickness and radius of the artery and
p
is the density of blood. This
formula is applicable to a single vessel, while foot-to-foot velocity has
been obtained either for a single artery or over the pulse propagation
path, e.g. over several arteries.
4.3.3
Apparent Propagation Constant and Transfer Function
Vascular
tree
structure and neuro-humoral influences,
there
are
considerable differences in the amount of wave reflections that arise in
different parts of the circulation. In the presence of reflected waves, one
can define an apparent propagation constant where
and
-YoppZ
P2
=
Ple
(4.3.7)
(4.3.8)
(4.3.9)
The apparent propagation constant
so
defined
is
dependent on wave
reflections and reflects local propagation characteristics. In this case, the
separation
(Az)
between p2 and
p1
needs to be small,
so
that caPp
is more
representative of the underlying artery. When the separation is large, say
from the ascending aorta to the abdominal aorta, the apparent wave
velocity obtained may contain interactions resulting from branching
vessels with their vascular beds.
On the other hand, the larger the
distance of separation, gives much better accuracy or resolution of the
attenuation and phase shift.
The apparent propagation constant at any point along the vessel
is
defined by:
(4.3.10)
