Ganong's Review of Medical Physiology, 23rd Edition

542 SECTION VICardiovascular Physiology

vivo are markedly affected by small changes in the caliber of
the vessels. Thus, for example, flow through a vessel is dou-
bled by an increase of only 19% in its radius; and when the
radius is doubled, resistance is reduced to 6% of its previous
value. This is why organ blood flow is so effectively regulated
by small changes in the caliber of the arterioles and why varia-
tions in arteriolar diameter have such a pronounced effect on
systemic arterial pressure.

VISCOSITY & RESISTANCE

The resistance to blood flow is determined not only by the ra-
dius of the blood vessels (vascular hindrance) but also by the
viscosity of the blood. Plasma is about 1.8 times as viscous as
water, whereas whole blood is 3 to 4 times as viscous as water.
Thus, viscosity depends for the most part on the hematocrit,
that is, the percentage of the volume of blood occupied by red
blood cells. The effect of viscosity in vivo deviates from that
predicted by the Poiseuille–Hagen formula. In large vessels,
increases in hematocrit cause appreciable increases in viscosi-
ty. However, in vessels smaller than 100 μm in diameter—that
is, in arterioles, capillaries, and venules—the viscosity change
per unit change in hematocrit is much less than it is in large-
bore vessels. This is due to a difference in the nature of flow
through the small vessels. Therefore, the net change in viscos-
ity per unit change in hematocrit is considerably smaller in the
body than it is in vitro (Figure 32–24). This is why hematocrit
changes have relatively little effect on the peripheral resistance
except when the changes are large. In severe polycythemia, the
increase in resistance does increase the work of the heart. Con-

versely, in marked anemia, peripheral resistance is decreased,

in part because of the decline in viscosity. Of course, the de-

crease in hemoglobin decreases the O 2 -carrying ability of the

blood, but the improved blood flow due to the decrease in vis-

cosity partially compensates for this.

Viscosity is also affected by the composition of the plasma

and the resistance of the cells to deformation. Clinically sig-

nificant increases in viscosity are seen in diseases in which

plasma proteins such as the immunoglobulins are markedly

elevated as well as when red blood cells are abnormally rigid

(hereditary spherocytosis).

CRITICAL CLOSING PRESSURE

In rigid tubes, the relationship between pressure and flow of ho-

mogeneous fluids is linear, but in thin-walled blood vessels in

vivo it is not. When the pressure in a small blood vessel is re-

duced, a point is reached at which no blood flows, even though

the pressure is not zero (Figure 32–25). This is because the ves-

sels are surrounded by tissues that exert a small but definite

pressure on them, and when the intraluminal pressure falls be-

low the tissue pressure, they collapse. In inactive tissues, for ex-

ample, the pressure in many capillaries is low because the

precapillary sphincters and metarterioles are constricted, and

many of these capillaries are collapsed. The pressure at which

flow ceases is called the critical closing pressure.

LAW OF LAPLACE

The relationship between distending pressure and tension is

shown diagrammatically in Figure 32–26. It is perhaps surpris-

ing that structures as thin-walled and delicate as the capillaries

are not more prone to rupture. The principal reason for their rel-

ative invulnerability is their small diameter. The protective effect

of small size in this case is an example of the operation of the law

of Laplace, an important physical principle with several other

applications in physiology. This law states that tension in the

wall of a cylinder (T) is equal to the product of the transmural

pressure (P) and the radius (r) divided by the wall thickness (w):

T = Pr/w

FIGURE 32–24 Effect of changes in hematocrit on the
relative viscosity of blood measured in a glass viscometer and in
the hind leg of a dog. In each case, the middle line represents the
mean and the upper and lower lines the standard deviation.
(Reproduced with permission from Whittaker SRF, Winton FR: The apparent viscosity
of blood flowing in the isolated hind limb of the dog, and its variation with
corpuscular concentration. J Physiol [Lond] 1933;78:338.)

14

12

10

8

6

4

2

20 40 60 80%

Hematocrit

Glass

viscometer

Hind

Relative viscosity limb

FIGURE 32–25 Relation of pressure to flow in thin-walled

blood vessels.

Pressure

Critical

closing pressure

Blood vessels

Flow