C h a p t e r 1 7
Control of Cardiovascular Function
379
Wall Tension, Radius, and Pressure
In a blood vessel,
wall tension
is the force in the ves-
sel wall that opposes the distending pressure inside the
vessel. French astronomer and mathematician Pierre de
Laplace described the relationship between wall tension,
pressure, and the radius of a vessel or sphere more than
200 years ago. This relationship, which has come to be
known as the
law of Laplace,
can be expressed by the
Equation P = T/r, in which T is the wall tension, P is
the intraluminal pressure or pressure within the vessel,
and r is the vessel radius (Fig. 17-3A). Accordingly, the
internal pressure expands the vessel until it is exactly
balanced by the tension in the vessel wall. The smaller
the radius, the greater is the pressure needed to balance
the wall tension. The law of Laplace can also be used
to express the effect of the vessel radius on wall tension
(T = P × r). This correlation can be compared with a
partially inflated balloon (Fig. 17-3B). Because the pres-
sure is equal throughout, the tension in the part of the
balloon with the smaller radius is less than the tension in
the section with the larger radius. The same holds true
for an arterial aneurysm in which the tension and risk
of rupture increase as the aneurysm grows in size (see
Chapter 18).
The law of Laplace was later expanded to include
wall thickness (T = P × r/wall thickness). Wall tension is
inversely related to wall thickness, such that the thicker
the vessel wall, the lower the tension, and vice versa. In
hypertension, for example, arterial vessel walls hyper-
trophy and become thicker, thereby reducing the ten-
sion and minimizing wall stress. The law of Laplace can
also be applied to the pressure required to maintain the
patency of small blood vessels. Provided that the thick-
ness of a vessel wall remains constant, it takes more pres-
sure to overcome wall tension and keep a vessel open
as its radius decreases in size. The
critical closing pres-
sure
refers to the point at which vessels collapse so that
blood can no longer flow through them. In circulatory
shock, for example, there is a decrease in blood volume
and vessel radii, along with a drop in blood pressure. As
a result, many of the small vessels collapse as the blood
pressure drops to the point where it can no longer over-
come the wall tension. The collapse of peripheral veins
often makes it difficult to insert venous lines that are
needed for fluid and blood replacement.
Vascular Distensibility
Distensibility
refers to the ability of a blood vessel to
be stretched and accommodate an increased volume of
blood. It is normally expressed as the fractional increase
in volume for each millimeter of mercury (mm Hg)
increase in pressure.
Vascular compliance
or
capacitance
refers to the
total quantity
of blood that can be stored in
a given portion of the circulation for each millimeter of
mercury rise in pressure. Both compliance and capaci-
tance can be used to as a measure of the distensibility
or flexibility of a blood vessel. The most distensible of
all vessels are the veins, which can increase their vol-
ume with only slight changes in pressure, allowing them
to function as a reservoir for storing large quantities of
blood that can be returned to the circulation when it is
needed. Although arteries have a thicker muscular wall
than veins, their distensibility allows them to store some
of the blood that is ejected from the heart during systole,
providing for continuous flow through the capillaries as
the heart relaxes during diastole.
P
P
T
T
Radius
Tension = Pressure × radius
A
B
FIGURE 17-3.
The law of Laplace relates pressure (P), tension
(T), and radius (r) to a cylindrical blood vessel.
(A)
The pressure
expanding the vessel is equal to the wall tension divided by the
vessel radius.
(B)
Effect of the radius on tension in a cylindrical
balloon. In a balloon, the tension in the wall is proportional to
the radius because the pressure is the same everywhere inside
the balloon.The tension is lower in the portion of the balloon
with the smaller radius. (From Rhoades RA,Tanner GA. Medical
Physiology. Boston, MA: Little, Brown; 1996:627.)
SUMMARY CONCEPTS
■■
Blood flow is determined largely by the pressure
difference between the two ends of a vessel or
group of vessels and the resistance that the blood
must overcome as it moves through the vessel
or vessels.The resistance or opposition to blood
flow, which is directly related to the viscosity of
the blood as determined by the percentage of
red blood cells and inversely related to the fourth
power of the vessel radius, increases as the
viscosity of the blood increases and decreases as
the radius of a vessel increases and vice versa.
■■
The relationship between the wall tension of a
vessel, its intraluminal pressure, and its radius
can be described using the law of Laplace (wall
tension = pressure × radius).Thus, at any given
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