Cardiovascular Physiology
363
Resistance cannot be measured directly, but it can be
calculated from the directly measured
F
and
P
. For example,
in Figure 12–4 the resistances in both tubes can be calculated
to be 90 mmHg
÷
10 ml/min = 9 mmHg/ml per minute.
This example illustrates how resistance can be calculated,
but what is it that actually determines the resistance? The dis-
tinction between how a thing is calculated or measured and
its determinants may seem confusing, but consider the fol-
lowing: By standing on a scale you
measure
your weight, but
your weight is not
determined
by the scale but rather by how
much you eat and exercise, and so on. One determinant of
resistance is the fl uid property known as
viscosity,
which is a
function of the friction between molecules of a fl owing fl
uid;
the greater the friction, the greater the viscosity. The other
determinants of resistance are the length and radius of the
tube through which the fl uid is fl owing, because these charac-
teristics affect the surface area inside the tube and thus deter-
mine the amount of friction between the fl uid and the wall of
the tube. The following equation defi nes the contributions of
these three determinants:
R
=
8
L
η
π
r
4
(12–2)
where
η
= fl
uid viscosity
L
= length of the tube
r
= inside radius of the tube
8/
π
= a mathematical constant
In other words, resistance is directly proportional to both the
fl uid viscosity and the vessel’s length, and inversely propor-
tional to the fourth power of the vessel’s radius.
Blood viscosity is not fi xed but increases as hematocrit
increases. Changes in hematocrit, therefore, can have signifi cant
effects on resistance to fl ow in certain situations. In extreme
dehydration, for example, the reduction in body water leads to
a relative increase in hematocrit and thus, in the viscosity of
the blood. Under most physiological conditions, however, the
hematocrit and, thus, the viscosity of blood is relatively con-
stant and does not play a role in controlling resistance.
Similarly, because the lengths of the blood vessels remain
constant in the body, length is also not a factor in the control
of resistance along these vessels. In contrast, the radii of the
blood vessels do not remain constant, and so vessel radius—
the 1/
r
4
term in our equation—is the most important determi-
nant of changes in resistance along the blood vessels.
Figure
12–5
demonstrates how radius infl uences the frictional resis-
tance and thus the fl ow of fl uids through a tube. Decreasing
the radius of a tube twofold increases its resistance sixteenfold.
If
P
is held constant in this example, fl ow through the tube
decreases 16-fold because
F
=
P
/
R
.
Note that the equation relating pressure, fl ow, and resis-
tance applies not only to fl ow through blood vessels, but also
to the fl ows into and out of the various chambers of the heart.
These fl ows occur through valves, and the resistance a valvu-
lar opening offers determines the fl ow through the valve at
any given pressure difference across it.
As you read on, remember that
the ultimate function
of the cardiovascular system is to ensure adequate blood fl
ow
through the capillaries of various organs.
Refer to the summary
in
Table 12–1
as you read the description of each component
to focus on how they contribute to this goal.
Figure 12–5
Effect of tube radius (
r
) on resistance (
R
) and fl ow. (a) A given
volume of fl uid is exposed to far more surface friction against the
walls of a smaller tube. (b) Given the same pressure gradient, fl ow
through a tube decreases 16-fold when the radius is halved.
Figure 12–5
physiological
inquiry
If outlet B in Figure 12–5b had two individual outlet tubes, each
with a radius of 1, would the fl ow be equal to side A?
Answer can be found at end of chapter.
15
10
5
15
10
5
(a)
(b)
5 ml of fluid
radius = 2
radius of
A
(
r
A
) = 2
radius of
B
(
r
B
) = 1
A
B
radius = 1
R
Since flow =
and
R
B
= 16 x
R
A
,
1
_
r
4
R
A
=
1
__
2
4
=
1
__
16
1
__
16
P
___
R
Flow in
B
=
of flow in
A.
1
___
(
r
A
)
4
R
B
=
1
__
1
4
==
1
1
__
1
1
___
(
r
B
)
4
previous page 391 Vander's Human Physiology The Mechanisms of Body Function read online next page 393 Vander's Human Physiology The Mechanisms of Body Function read online Home Toggle text on/off