378
U N I T 5
Circulatory Function
Principles of Blood Flow
The term
hemodynamics
refers to the principles that gov-
ern the flow of blood in the vascular system. The physics
of fluid flow through rigid tubes provides the basis for
understanding the flow of blood through blood vessels,
even though blood vessels are not rigid tubes (they are
distensible) and blood is not a simple homogenous fluid.
Pressure, Resistance, and Flow
Flow through the blood vessels in the circulatory system
is determined almost entirely by two factors: the pressure
difference (
Δ
P) between the two ends of a vessel or group
of vessels and the resistance (R) that the blood must over-
come as it moves through the vessel or vessels. Thus, the
flow of blood through a vessel can be calculated using the
equation: flow =
Δ
P/R. In the circulatory system, blood
flow is represented by the cardiac output. Resistance is
the opposition to flow caused by friction between the
moving blood components and the stationary vessel wall.
In the peripheral circulation, the collective resistance of
all the vessels in that part of the circulation is referred to
as the
total peripheral vascular resistance.
The relationship between pressure and resistance can be
quantified by what has become known as
Poiseuille’s law
.
In the 1840s, Louis Poiseuille determined that the flow of
fluid was determined by the pressure difference between
the two ends of a tube (P
1
− P
2
), the fourth power of the
radius (r
4
) of the tube, the viscosity (
η
) of the fluid, the tube
length (l), and two constants (
π
and 8) using the following
equation: flow =
πΔ
P r
4
/8
η
l. Simplifying the equation (i.e.,
flow =
Δ
P r
4
/
η
) by deleting the constants
π
and 8 along
with the length, which usually does not change, makes it
clear that flow will increase as the pressure gradient and
vessel radius increase and decrease as the blood viscosity
increases. Note particularly that the rate of flow is directly
related to the
fourth power of the radius,
emphasizing
the importance of vessel diameter in determining the rate
of flow through the vessel. For example, if the pressure
remains constant, the rate of flow is 16 times greater in a
vessel with a radius of 2 mm (2 × 2 × 2 × 2 = 16) than in a
vessel with a radius of 1 mm (1 × 1 × 1 × 1 = 1).
Viscosity generates resistance to flow by producing
friction between the molecules of a liquid. Unlike water
that flows through plumbing pipes, blood is a nonho-
mogeneous liquid. It contains blood cells, platelets, fat
globules, and plasma proteins that increase its viscosity.
It is mainly the hematocrit or percentage of suspended
red cells in the blood that determines viscosity.
Flow in Series and Parallel Vessels
The interaction between pressure and resistance is deter-
mined by whether blood vessels are arranged in series or
in parallel. In vessels such as arteries, arterioles, capillar-
ies, venules, and veins, which are collectively arranged
in series, flow through each vessel at any given pressure
is the same; therefore, the total resistance is equal to the
sum of the resistances (R) of each vessel (R
1
+ R
2
+ R
3
).
In segments of the circulation where blood vessels
branch extensively to form parallel circuits, as in those
that supply blood to the many organs and tissues of
the body, greater amounts of blood will flow through
parallel vessels than through any of the individual ves-
sels. Thus, for any given pressure, the total resistance to
blood flow will be equal to the sum of the reciprocals of
the individual resistances (1/R
1
+ 1/R
2
+ 1/R
3
).
Velocity, Cross-Sectional Area, and Flow
In addition to the amount of blood flowing through a
given organ or tissue, the rate or velocity at which the
blood is moving is also important.
Flow
is a volume
measurement (milliliters [mL] per second [sec]) that is
determined by the cross-sectional area of a vessel and
the velocity of flow.
Velocity
is a distance measurement;
it refers to the speed or linear movement per unit time
of blood as it flows through a vessel. When the flow
through a given segment of the circulatory system is
constant—as it must be for continuous flow—the veloc-
ity is inversely proportional to the cross-sectional area
of the vessel (i.e., the smaller the cross-sectional area,
the greater is the velocity of flow).
The linear velocity of blood flow in the circulatory
system varies widely from 30 to 35 cm/second in the
aorta to 0.2 to 0.3 mm/second in the capillaries. This
is because even though each individual capillary is very
small, the total cross-sectional area of all the systemic
capillaries greatly exceeds the cross-sectional area of
other parts of the circulation. As a result of this large
surface area, the slower movement of blood allows
ample time for exchange of nutrients, gases, and metab-
olites between the tissues and the blood.
Laminar VersusTurbulent Flow
Ideally, blood flow should be
laminar
or
streamlined,
with the blood components arranged in layers so that the
plasma is adjacent to the smooth, slippery endothelial
lining of the blood vessel, and the blood elements, includ-
ing the platelets, are in the center or
axis
of the blood-
stream. This arrangement reduces friction by allowing
the blood layers to slide smoothly over one another, with
the axial layer having the most rapid rate of flow.
Under certain conditions, however, blood flow can
switch from laminar to turbulent. In
turbulent flow
the laminar stream is disrupted and the flow becomes
mixed, moving both radially (crosswise) and axially
(lengthwise). Turbulent flow can be caused by a number
of factors, including high velocity of flow, change in ves-
sel diameter, and low blood viscosity. The tendency for
turbulence to occur is increased in direct proportion to
the velocity of flow.
Because energy is used in propelling blood both radi-
ally and axially, more energy (pressure) is required to
drive turbulent flow than laminar flow. Turbulence is
often accompanied by vibrations of the blood and sur-
rounding cardiovascular structures. Some of these vibra-
tions are in the audible range and can be heard using a
stethoscope. For example, a heart murmur results from
turbulent flow through a diseased heart valve.
