CHAPTER 5 • VASCULAR FUNCTION
105
FIGURE 5.11
Model of the circulation within an organ showing the series arrangement of multiple
segments of parallel vessels.
likewise flows through each of the other
vascular segments. Within each of the series
elements, many parallel components may exist
(e.g., several parallel capillaries may arise from
a single arteriole). Each vascular element (e.g.,
the arterioles) will have a resistance value that
is determined by vessel length, radius, and
number of parallel vessels.
For an in-series resistance network, the
total resistance (Rj.) equals the sum of the indi-
vidual segmental resistances. The total resist-
ance for the model depicted in Figure 5.11 is
Eq. 5-9
RT =RA+Ra+Rc+Rv+Rv
(A = artery; a = arterioles; c = capillary;
v = venules; V = vein)
The resistance of each segment relative to
the total resistance of all the segments deter-
mines how changing the resistance of one seg-
ment affects total resistance. To illustrate this
principle, assign a relative resistance value to
each of the five resistance segments in this
model. The relative resistances are similar to
what is observed in a typical vascular bed.
Assume Ra =1, Ra = 70, Rc = 20,
(e.g., renal artery), and Ra represents the small
arteries and arterioles within the organ, which
are the primary site of vascular resistance.
Therefore, this empirical example demon-
strates that
changes in large artery resistance
have relatively little effect on total resistance,
compared to changes in small artery and arteri-
olar resistances that have a large affect on total
resistance.
This is why small arteries and arte-
rioles are the principal vessels regulating organ
blood flow and systemic vascular resistance.
The
above
analysis
explains
why
the
radius of a large, distributing artery must be
decreased by more than 60% or 70% to have a
significant effect on organ blood flow. This is
referred to as a critical stenosis. The concept
of a critical stenosis can be confusing because
Poiseuille equation indicates that resistance to
flow is inversely related to radius to the fourth
power. Therefore, a 50% reduction in radius
should increase resistance 16-fold (a 1500%
increase). Indeed, within that single vessel
segment, resistance will increase
16-fold;
however, total resistance will increase only by
about 15% if the large artery resistance is nor-
mally 1% of the total resistance.
Rv = 8, Rv = lj
Therefore, Rr=l + 70 + 20 + 8+ l = 100
If Ra were to increase fourfold (to a value of 4),
Rj. would increase to 103, a 3% increase. In
contrast, if Ra were to increase fourfold (to a
value of 280), the Rj. would increase to 310, a
210% increase. In this model, RA
represents a
large artery distributing blood flow to an organ
PROBLEM 5-2
A parent arteriole branches into two
smaller arterioles. In relative terms, the
resistance of the parent arteriole is 1,
and the resistance of each daughter
vessel is 4. What is the combined
resistance of the parent vessel and its
branches?