22
Dynamics
of
the Vascular System
differential effects on large and small arteries, changes in taper factors
from normal can be quite pronounced.
Fig. 2.2.1
:
Schematic diagram illustrating a blood vessel with geometric taper. The vessel
diameter narrows with increasing distance
(z)
away from the origin. Geometric taper, an
exponential function
of
distance, is normally calculated from the change in cross-
sectional areas
(A)
as shown.
Alternative formula to calculate taper factor per unit length, or
k,,
is
~(z)
=
A(O)e-"'
(2.2.4)
expressed as follows:
The reported values of
k,
obtained for the abdominal aorta, the iliac,
femoral and carotid arteries are shown in Table 2.2.1. These are
measured in vivo at a mean arterial pressure of about 90 mmHg. The
average body weights of dogs used are about
20
kg.
It is obvious from
these data that the taper factor is smaller for smaller vessels.
Carotid
arteries have the least taper. They are thus the best approximation to a
geometrically uniform cylindrical vessel.
Area ratios calculated for vascular branching junctions were about
1.08
at the aortic arch, and 1.05 at the aorto-iliac junction (Li et al.,
1984). These values are slightly larger than
1.0.
The hemodynamic
consequences of these are discussed in Chapter
5.
