(Overview of the Circulation (Physics of Pressure and Flow and resistance pdf - The Circulation

Figure 14–1 gives an

Volumes of Blood in the Different Parts of the Circulation.

controllable reservoir for the extra blood, either a small or a large amount,

Even so, they are muscular enough to contract or expand and thereby act as a

Because the pressure in the venous system is very low, the venous walls are thin.

to the heart; equally important, they serve as a major reservoir of extra blood.

The

into progressively larger veins.

collect blood from the capillaries, and they gradually coalesce

The

permeable to water and other small molecular substances.

To serve this role, the capillary walls are very thin and have numerous minute

hormones, and other substances between the blood and the interstitial fluid.

is to exchange fluid, nutrients, electrolytes,

The function of the

blood flow in each tissue bed in response to the need of the tissue.

by relaxing, dilate it severalfold, thus having the capability of vastly altering

through which blood is released into the capillaries. The arte-

are the last small branches of the arterial system; they act as

The

at a high velocity in the arteries.

tissues. For this reason, the arteries have strong vascular walls, and blood flows

The function of the

tion, it is important to understand the role of each part of the circulation.

flow to all the tissues of the body except the lungs, it is also called the

The circulation, shown in Figure 14–1, is divided into the

Physical Characteristics of the Circulation

functions of the circulation? These are some of the topics and questions that we

trolling blood volume and blood flow, and how does this relate to all the other

sure to cause the needed tissue blood flow. What are the mechanisms for con-

controlled in response to tissue need for nutrients. The heart and circulation in

The rate of blood flow through most tissues is

optimal survival and function of the cells.

another, and, in general, to maintain an appropriate

the body tissues, to transport waste products away,

The function of the circulation is to service the

Flow, and Resistance

Medical Physics of Pressure,

161

Overview of the Circulation;

needs of the body tissues—to transport nutrients to

to conduct hormones from one part of the body to

environment in all the tissue fluids of the body for

turn are controlled to provide the necessary cardiac output and arterial pres-

discuss in this section on the circulation.

systemic circulation

and the pulmonary circulation. Because the systemic circulation supplies blood

greater

circulation or peripheral circulation.

Functional Parts of the Circulation.

Before discussing the details of circulatory func-

arteries is to transport blood under high pressure to the

arterioles

control conduits
riole has a strong muscular wall that can close the arteriole completely or can,

capillaries

capillary pores

venules

veins function as conduits for transport of blood from the venules back

depending on the needs of the circulation.

overview of the circulation and lists the percentage of the total blood volume

are in accord with the needs of the lungs, because

culation. The low pressures of the pulmonary system

7 mm Hg. Yet the total blood flow through the lungs

The mean pulmonary capillary pressure averages only

a mean pulmonary arterial pressure of only 16 mm Hg.

8 mm Hg, with

about 25 mm Hg and

pulmonary artery systolic pressure

pulsatile, just as in the aorta, but the pressure level is

In the pulmonary arteries, the pressure is

Note at the far right side of Figure 14–2 the respec-

these same pores to the outlying tissue cells.

walls, even though nutrients can

17 mm Hg, a pressure low enough that little of the

“functional” pressure in most vascular beds is about

as 10 mm Hg near the venous ends, but their average

as high as 35 mm Hg near the arteriolar ends to as low

The pressure in the systemic capillaries varies from

its mean pressure falls progressively to about 0 mm Hg

of 80 mm Hg, as shown on the left side of Figure 14–2.

of 120 mm Hg and a

100 mm Hg. Also, because heart pumping is pulsatile,

the mean pressure in the aorta is high, averaging about

Pressures in the Various Portions of the Circulation.

ingly short time.

remains in the capillaries for only 1 to 3 seconds. This

typical length of only 0.3 to 1 millimeter, the blood

0.3 mm/sec. However, because the capillaries have a

aorta but only 1/1000 as rapidly in the capillaries, about

ditions, the velocity averages about 33 cm/sec in the

vascular cross-sectional area. Thus, under resting con-

through each segment of the circulation each minute,

four times those of the corresponding arteries. This

areas of the veins than of the arteries, averaging about

of each type were put side by side,

Cross-Sectional Areas and Velocities of Blood Flow.

tissues. This function is discussed in detail in Chapter

function of the circulation occurs, diffusion of sub-

illaries. It is here, however, that the most important

and the pulmonary vessels, 9 per cent.

capillaries. The heart contains 7 per cent of the blood,

arteries, and 7 per cent in the systemic arterioles and

culation, 64 per cent is in the veins, 13 per cent in the

heart and lungs. Of the 84 per cent in the systemic cir-

body is in the systemic circulation, and 16 per cent in

in major segments of the circulation. For instance,

162

Unit IV

The Circulation

about 84 per cent of the entire blood volume of the

Most surprising is the low blood volume in the cap-

stances back and forth between the blood and the

16.

If all the

systemic vessels
their approximate total cross-sectional areas for the
average human being would be as follows:

Note particularly the much larger cross-sectional

explains the large storage of blood in the venous
system in comparison with the arterial system.

Because the same volume of blood must flow

the velocity of blood flow is inversely proportional to

short time is surprising because all diffusion of
nutrient food substances and electrolytes that occurs
through the capillary walls must do so in this exceed-

Because

the heart pumps blood continually into the aorta,

the arterial pressure alternates between a systolic pres-
sure level

diastolic pressure level

As the blood flows through the systemic circulation,

by the time it reaches the termination of the venae
cavae where they empty into the right atrium of the
heart.

plasma leaks through the minute pores of the capillary

diffuse easily through

tive pressures in the different parts of the pulmonary
circulation.

far less:

averages

diastolic pressure

each minute is the same as through the systemic cir-

all that is required is to expose the blood in the

Systemic

vessels

Veins, venules,

Arteries–13%

Arterioles
and
capillaries–7%

Heart–7%

Aorta

Pulmonary circulation–9%

and venous

sinuses–64%

Inferior

vena cava

Superior

vena cava

parts of the circulatory system.

Distribution of blood (in percentage of total blood) in the different

Figure 14–1

Small veins

Venules

250

Capillaries

2500

Arterioles

Small arteries

Aorta

2.5

Vessel

Cross-Sectional Area (cm

)

Venae cavae

control of cardiac output and arterial pressure.

remainder of this chapter, we begin to discuss the basic

are served specifically by the circulation. In the

Thus, in summary, the needs of the individual tissues

and by regulating the blood volume.

prolonged periods, hours and days, the kidneys

increase the arterial pressure. Then, over more

heart, and (c) cause generalized constriction of

heart pumping, (b) cause contraction of the large

raise the pressure back toward normal. The

100 mm Hg, within seconds a barrage of nervous

For instance, if at any time the pressure falls

controlling the arterial blood pressure.

The circulatory

independently of either local blood flow control

3. In general the arterial pressure is controlled

pump the required amounts of blood flow.

the tissues. The heart, however, often needs help

as an automaton, responding to the demands of

whence it had originally come. Thus, the heart acts

the veins to the heart. The heart responds

through a tissue, it immediately returns by way of

When blood flows

sum of all the local tissue flows.

2. The cardiac output is controlled mainly by the

flow.

activity. Also, nervous control of the circulation

constricting them, to control local blood flow

act directly on the local blood vessels, dilating or

and other tissue waste products, and these in turn

of each tissue continuously monitor tissue needs,

demands increased flow. Instead, the microvessels

seven times greater than resting levels. Therefore,

the resting level. Yet the heart normally cannot

When tissues are active, they need

is almost always precisely controlled in relation to

1. The rate of blood flow to each tissue of the body

complex, there are three basic principles that underlie

Basic Theory of Circulatory

Overview of the Circulation; Medical Physics of Pressure, Flow, and Resistance

Chapter 14

163

pulmonary capillaries to oxygen and other gases in the
pulmonary alveoli.

Function

Although the details of circulatory function are

all functions of the system.

the tissue need.
greatly increased supply of nutrients and
therefore much more blood flow than when at
rest—occasionally as much as 20 to 30 times

increase its cardiac output more than four to

it is not possible simply to increase blood flow
everywhere in the body when a particular tissue

such as the availability of oxygen and other
nutrients and the accumulation of carbon dioxide

precisely to that level required for the tissue

from the central nervous system provides
additional help in controlling tissue blood

automatically to this increased inflow of blood by
pumping it immediately into the arteries from

in the form of special nerve signals to make it

or cardiac output control.
system is provided with an extensive system for

significantly below the normal level of about

reflexes elicits a series of circulatory changes to

nervous signals especially (a) increase the force of

venous reservoirs to provide more blood to the

most of the arterioles throughout the body so that
more blood accumulates in the large arteries to

play an additional major role in pressure control
both by secreting pressure-controlling hormones

details of the management of tissue blood flow and

Systemic

Pulmonary

Pressure (mm Hg)

100

120

Aorta

Large arteries

Small arteries

Arterioles

Capillaries

Venules

Small veins

Large veins

Venae cavae

Pulmonary arteries

Arterioles

Capillaries

Venules

Pulmonary veins

Normal blood pressures in the different portions of the circulatory system when a person is lying in the horizontal position.

Figure 14–2

tance of this formula, the reader should also become

ics of the circulation. Because of the extreme impor-

Ohm’s law, illustrated in Equation 1, expresses the

pressure.

will be no flow despite the presence of 100 mm Hg

yet no difference exists between the two ends, there

the pressure at both ends of a vessel is 100 mm Hg and

vessel, that determines rate of flow. For example, if

two ends of the vessel, not the absolute pressure in the

ference but inversely proportional to the resistance.

the resistance. This formula states, in effect, that the

) between the two ends of the vessel, and R is

in which F is blood flow,

Ohm’s law

culated by the following formula, which is called

the vessel. The flow through the vessel can be cal-

. Resistance occurs

at the other end, the pressure is P

these relationships, showing a blood vessel segment

Figure 14–3 demonstrates

vascular resistance.

impediment to blood flow through the vessel, which is

that pushes the blood through the vessel, and (2) the

“pressure gradient” along the vessel, which is the force

tween the two ends of the vessel, also sometimes called

two factors: (1)

Pressure, Flow, and

Interrelationships Among

164

Unit IV

The Circulation

Resistance

Blood flow through a blood vessel is determined by

pressure difference of the blood be-

called

located anywhere in the circulatory system.

represents the pressure at the origin of the vessel;

as a result of friction between the flowing blood and
the intravascular endothelium all along the inside of

DP is the pressure difference

- P

blood flow is directly proportional to the pressure dif-

Note that it is the difference in pressure between the

most important of all the relations that the reader
needs to understand to comprehend the hemodynam-

familiar with its other algebraic forms:

Blood Flow

Blood flow means simply the quantity of blood that
passes a given point in the circulation in a given period

D =

ed greatly by the electronic apparatus. Another

frequency ultrasound wave is intermittently cut off, and

5, the high-

owmeter shown in Figure 14

For the

approaching.)

by the person, the pitch of the sound from the whistle

while blowing its whistle. Once the whistle has passed

is called the Doppler effect. (It is the same effect that

cells are moving away from the transmitter crystal. This

frequency than the transmitted wave because the red

ected waves have a lower

toward the crystal. These re

owing blood. The re

owing blood. A portion of the sound is re

dred thousand cycles per second downstream along the

transmits ultrasound at a frequency of several hun-

energized with an appropriate electronic apparatus,

at one end in the wall of the device. This crystal, when

5. A minute piezoelectric crystal is mounted

Figure 14

ultrasonic Doppler flowmeter,

Ultrasonic Doppler Flowmeter.

ow.

of a second, allowing accurate recording of pulsatile

magnet and the electrodes.

ow. The probe contains both the strong

recording apparatus. Figure 14

ow is generated between the two electrodes, and this

lines of force. When blood

of a strong magnet, and electrodes are placed on the

this case, a blood vessel is placed between the poles

eld. In

electric generator. Figure 14

eld. This is the well-

4. Figure 14

of which are illustrated in Figure 14

owmeter, the principles

Electromagnetic Flowmeter.

flowmeters.

ow. They are called

a blood vessel or, in some instances, applied to the

Methods for Measuring Blood Flow.

pumped into the aorta by the heart each minute.

cardiac output

adult person at rest is about 5000 ml/min. This is called

The overall blood

ow.

liters per minute,

ow is expressed in

of time. Ordinarily, blood fl

milliliters

per minute or

but it can be expressed

in milliliters per second or in any other unit of fl

flow in the total circulation of an

the

because it is the amount of blood

Many mechanical and

mechanoelectrical devices can be inserted in series with

outside of the vessel to measure fl

One of the most important

devices for measuring blood flow without opening the
vessel is the electromagnetic fl

–

–4A

shows the generation of electromotive force (electrical
voltage) in a wire that is moved rapidly in a cross-wise
direction through a magnetic fi
known principle for production of electricity by the

–4B shows that the same

principle applies for generation of electromotive force
in blood that is moving through a magnetic fi

two sides of the vessel perpendicular to the magnetic

flows through the vessel,

an electrical voltage proportional to the rate of blood
fl
is recorded using an appropriate voltmeter or electronic

–4C shows an actual

“probe” that is placed on a large blood vessel to record
its blood fl

A special advantage of the electromagnetic flowme-

ter is that it can record changes in flow in less than 1/100

changes in flow as well as steady fl

Another type of flowmeter

that can be applied to the outside of the vessel and that
has many of the same advantages as the electromagnetic
flowmeter is the

shown in

–

flected by the

red blood cells in the fl

flected ultra-

sound waves then travel backward from the blood cells

one experiences when a train approaches and passes by

suddenly becomes much lower than when the train is

–

the reflected wave is received back onto the crystal and
amplifi
portion of the electronic apparatus determines the

Pressure gradient

Resistance

Blood flow

Interrelationships among pressure, resistance, and blood flow.

Figure 14–3

le is the following:The

The cause of the parabolic pro

ow.

long distance. This effect is called the

slightly away from the wall has moved a small distance,

cent to the vessel wall has hardly moved, the portion

; the portion of

1 second later in Figure 14

a parabolic interface develops between them, as shown

ow,

ow in the vessel. When the

uid, but there is

uids, the one at the left colored by

6. In Figure 14

This is demonstrated in Figure 14

vessel is far greater than that toward the outer edges.

ow occurs, the velocity of

When laminar

Parabolic Velocity Profile During Laminar Flow.

subsequently.

continually mixing within the vessel, as discussed

, which

turbulent flow

, and it is the opposite of

line flow

laminar flow

vessel. This type of

same distance from the vessel wall. Also, the central

, with each layer of blood remaining the

steady rate through a long, smooth blood vessel, it

When blood

Laminar Flow of Blood in Vessels.

ow.

owmeter is capable of recording rapid, pul-

owmeter, the ultrasonic

ow.

ected wave, thus determining the velocity of

frequency difference between the transmitted wave and

Overview of the Circulation; Medical Physics of Pressure, Flow, and Resistance

Chapter 14

165

the refl
blood fl

Like the electromagnetic fl

Doppler fl
satile changes in flow as well as steady fl

flows at a

flows

in streamlines

most portion of the blood stays in the center of the

flow is called

or stream-

is blood flowing in all directions in the vessel and

flow in the center of the

–

–6A, a

vessel contains two fl
a dye and the one at the right a clear fl
no fl

fluids are made to fl

–6B

fluid adja-

and the portion in the center of the vessel has moved a

“parabolic profile

for velocity of blood fl

”

fluid molecules touching the wall barely move because

–

for chronic implantation around

electromagnetic flowmeter probe

); and a modern

field and blood flows through

is placed in a strong magnetic

electrical voltage in electrodes on

passes through an electromag-

electrical voltage in a wire as it

Flowmeter of the electromagnetic

Figure 14–4

type, showing generation of an

netic field (A); generation of an

a blood vessel when the vessel

the vessel (B

blood vessels (C).

Crystal

Reflected

wave

Transmitted

wave

Ultrasonic Doppler flowmeter.

Figure 14–5

lent flow, with elements of the fluid moving in a disorderly pattern.

, Two fluids (one dyed red, and the other clear) before flow

Figure 14–6

A
begins; B, the same fluids 1 second after flow begins; C, turbu-

because the mercury manometer (shown in Figure

is measured in millimeters of mercury (mm Hg)

turbulence.

number is almost never high enough to cause

(4) large vessel diameter. However, in small vessels,

ow, (3) sudden change in vessel diameter, and

ow, (2) pulsatile nature of

ejection by the ventricles; this causes considerable tur-

number

of the aorta and pulmonary artery, Reynolds

the branches of these vessels. In the proximal portions

even normally rises to 200 to 400 in large arteries; as a

number for

straight, smooth vessel.

imately 2000, turbulence will usually occur even in a

number rises above approx-

However, when Reynolds

will die out along the smooth portions of the vessels.

number rises above 200 to 400,

than 1. When Reynolds

about 1/30 poise, and the density is only slightly greater

cosity (in poise). The viscosity of blood is normally

is density, and

, r

ow (in centimeters/second), d is the vessel

tendency for turbulence to occur,

inversely proportional to the viscosity of the blood, in

the blood vessel, and the density of the blood, and is

ow, the diameter of

The tendency for turbulent

When eddy currents are present, the blood

. These are similar to the whirlpools that one

). Turbulent

(see Figure 14

, or disorderly, rather than streamline

when it passes over a rough surface, the

obstruction in a vessel, when it makes a sharp turn, or

ow becomes too great, when it passes by an

When the rate

Turbulent Flow of Blood Under Some Conditions.

more rapidly than the outer layers.

thus, each layer toward the center

the fourth layer over the third, and so forth. Therefore,

ecules slips over these, the third layer over the second,

of adherence to the vessel wall. The next layer of mol-

166

Unit IV

The Circulation

the fluid in the middle of the vessel can move rapidly
because many layers of slipping molecules exist
between the middle of the vessel and the vessel wall;

flows progressively

of blood fl

flow may then

become turbulent

–6C

flow means that the blood

flows crosswise in the vessel as well as along the vessel,
usually forming whorls in the blood called eddy cur-
rents
frequently sees in a rapidly flowing river at a point of
obstruction.

flows with

much greater resistance than when the flow is stream-
line because eddies add tremendously to the overall
friction of flow in the vessel.

flow increases in direct

proportion to the velocity of blood fl

accordance with the following equation:

where Re is Reynolds’ number and is the measure of the

n is the mean velocity

of blood fl
diameter (in centimeters)

h is the vis-

’

turbulent flow will occur at some branches of vessels but

’

Reynolds’

flow in the vascular system

result there is almost always some turbulence of flow at

’

can rise to several thousand during the rapid phase of

bulence in the proximal aorta and pulmonary artery
where many conditions are appropriate for turbulence:
(1) high velocity of blood fl
the fl

Reynolds’

Blood Pressure

Standard Units of Pressure.

Blood pressure almost always

14–7) has been used since antiquity as the standard

◊ ◊

is low, it returns toward its resting position.

sure is high, the membrane bulges slightly, and when it

in which the pressure is to be measured. When the pres-

uid chamber. The

cal recorder. Each of these transducers uses a very thin,

recorder is needed. Figure 14

changing pressures, some other type of pressure

3 seconds. Whenever it is desired to record rapidly

that occur more rapidly than about one cycle every 2 to

steady pressures, cannot respond to pressure changes

mercury manometer, although excellent for recording

that it cannot rise and fall rapidly. For this reason, the

The

1 millimeter.

that of water, and 1 centimeter is 10 times as great as

gravity to a height of 10 centimeters.

. A pressure of 10 cm H

Occasionally, pressure is measured in

up to 100 millimeters.

sure is 100 mm Hg, it will push the column of mercury

against gravity up to a level 50 mm high. If the pres-

pressure in a vessel is 50 mm Hg, one means that the

. When one says that the

force exerted by the blood against any

reference for measuring pressure. Actually, blood pres-
sure means the
unit area of the vessel wall

force exerted is sufficient to push a column of mercury

centimeters of

water (cm H

O means a

pressure sufficient to raise a column of water against

One millimeter of

mercury pressure equals 1.36 cm water pressure
because the specific gravity of mercury is 13.6 times

High-Fidelity Methods for Measuring Blood Pressure.

mercury in the mercury manometer has so much inertia

–8 demonstrates the basic

principles of three electronic pressure transducers com-
monly used for converting blood pressure and/or rapid
changes in pressure into electrical signals and then
recording the electrical signals on a high-speed electri-

highly stretched metal membrane that forms one wall
of the fl

fluid chamber in turn is con-

nected through a needle or catheter to the blood vessel

Anticoagulant

solution

Float

0 pressure

Mercury

manometer

Moving sooted

paper

100 mm Hg pressure

throughout the history of physiology.

that has been used in the manner shown for recording pressure

Recording arterial pressure with a mercury manometer, a method

Figure 14–7

of the vessels. Although the diameters of these vessels

sure difference of 100 mm Hg between the two ends

relative diameters of 1, 2, and 4 but with the same pres-

trated in Figure 14

lined. This is demonstrated by the experiment illus-

Conductance Tremendously!

Very Slight Changes in Diameter of a Vessel Can Change Its

pressure.

per millimeter of mercury pressure, but it can also be

through a vessel for a given pressure difference. This

“Conductance” of Blood in a Vessel and Its Relation to Resis-

0.14 PRU (about one seventh that in the systemic

output is normal at about 100 ml/sec, the

sure difference of 14 mm. Therefore, when the cardiac

atrial pressure averages 2 mm Hg, giving a net pres-

rial pressure averages 16 mm Hg and the mean left

In the pulmonary system, the mean pulmonary arte-

dilated, the resistance can fall to as little as 0.2 PRU.

PRU. Conversely, when the vessels become greatly

out the body become strongly constricted, the total

100/100, or 1 PRU.

total peripheral resistance,

lation, called the

Therefore, the resistance of the entire systemic circu-

arteries to the systemic veins is about 100 mm Hg.

100 ml/sec. The pressure difference from the systemic

output. In the adult human being, this is approximately

that is, it is equal to the cardiac

The rate of blood

Total Peripheral Vascular Resistance and Total Pulmonary Vas-

. Resistance in these units can

seconds) unit is used to express resistance. This unit is

basic physical unit called the CGS (centimeters, grams,

Occasionally, a

PRU

, usually abbreviated

ow is 1 ml/sec, the resistance is said to be 1

pressure difference between two points is 1 mm Hg

difference between two points in the vessel. If the

any direct means. Instead, resistance must be calcu-

ow in a vessel, but it cannot be measured by

Resistance to Blood Flow

manner shown on the recording paper in Figure 14

occur as rapidly as 20 to 100 cycles per second, in the

have been recorded accurately. In common use are

systems, pressure cycles up to 500 cycles per second

With some of these high-

too, can be recorded by an electronic system.

stretched less, its resistance decreases. These changes,

is stretched greatly, its resistance increases; when it is

ance wire is connected to the membrane. When this wire

a very thin, stretched resist-

Finally, in Figure 14

and this, too, can be recorded electronically.

space inside an electrical wire coil. Movement of the

brane, and this can be displaced upward into a center

In Figure 14

between these two, and this change in capacitance can

the plate, which increases the

the membrane bulges, the membrane comes closer to

hundredths of a centimeter above the membrane. When

In Figure 14

Overview of the Circulation; Medical Physics of Pressure, Flow, and Resistance

Chapter 14

167

–8A, a simple metal plate is placed a few

electrical capacitance

be recorded using an appropriate electronic system.

–8B, a small iron slug rests on the mem-

iron into the coil increases the inductance of the coil,

–8C,

fidelity types of recording

recorders capable of registering pressure changes that

–8C.

Units of Resistance.

Resistance is the impediment to

blood fl

lated from measurements of blood flow and pressure

and the fl
peripheral resistance unit

Expression of Resistance in CGS Units.

dyne seconds/centimeters

be calculated by the following formula:

cular Resistance.

flow through the

entire circulatory system is equal to the rate of blood
pumping by the heart—

is about

In conditions in which all the blood vessels through-

peripheral resistance occasionally rises to as high as 4

total

pulmonary vascular resistance calculates to be about

circulation).

tance.

Conductance is a measure of the blood flow

is generally expressed in terms of milliliters per second

expressed in terms of liters per second per millimeter
of mercury or in any other units of blood flow and

It is evident that conductance is the exact reciprocal

of resistance in accord with the following equation:

Slight changes in the diame-

ter of a vessel cause tremendous changes in the vessel’s
ability to conduct blood when the blood flow is stream-

–9A, which shows three vessels with

Conductance

Resistance

ml sec

mm Hg

R in

dyne

sec

1333

¯ =

rapidly changing blood pressures (explained in the text).

Principles of three types of electronic transducers for recording

Figure 14–8

of the vessel, l is length of the vessel, and

difference between the ends of the vessel, r is the radius

ow,

derive the following formula, known as Poiseuille

multiplying them by the areas of the rings, one can

stream of blood simply does not exist. By integrating the

wall, so that the extremely rapidly

In the small vessel, essentially all the blood is near the

ows extremely rapidly.

ows extremely slowly, whereas that in the

velocities. Thus, the blood that is near the wall of the

fth, and

ows more rapidly. The third, fourth,

therefore,

the vascular endothelium. The next ring of blood toward

That is, the blood in the ring touching the wall of the

ow, which was discussed earlier in the chapter.

of a large and a small vessel. The concentric rings inside

by referring to Figure 14

The cause of this great increase in con-

Poiseuille’s Law.

fourth power of the diameter,

Thus, the conductance of the vessel increases in pro-

ow.

and 256 ml/mm, which is a 256-fold increase in

ows are 1, 16,

increase only fourfold, the respective

168

Unit IV

The Circulation

portion to the

in accor-

dance with the following formula:

ductance when the diameter increases can be explained

–9B, which shows cross sections

the vessels indicate that the velocity of flow in each ring
is different from that in the adjacent rings because of
laminar fl

vessel is barely flowing because of its adherence to

the center of the vessel slips past the first ring and,

sixth rings likewise flow at progressively increasing

vessel fl
middle of the vessel fl

flowing central

velocities of all the concentric rings of flowing blood and

’s law:

in which F is the rate of blood fl

DP is the pressure

h is viscosity

of the blood.

D Pr

Conductance

Diameter

ow is expressed

), the total resistance to blood

For blood vessels arranged in parallel (Figure

ow to other tissues.

extent, independently of

ow, to a great

tissues of the body. This parallel arrangement permits

, the total vascular resistance

shown in Figure 14

oles, capillaries, venules, and veins. In the example

equal to the sum of resistances of the arteries, arteri-

The total peripheral vascular resistance is therefore

vessels are arranged in series,

veins are collectively arranged in series. When blood

lel. The arteries, arterioles, capillaries, venules, and

the low pressure side (i.e., vena cava) through many

pressure part of the systemic circulation (i.e., aorta) to

Resistance to Blood Flow in Series and Parallel Vascular Cir-

ow. Indeed, ranges of blood

signals, either to turn off almost completely the blood

the arterioles, responding with only small changes in

Thus, this fourth power law makes it possible for

the vessel, one can see that a fourfold increase in vessel

often as much as fourfold. From the fourth power law

allow the internal diameters to change tremendously,

25 micrometers. However, their strong vascular walls

arterioles. The internal diameters of the arterioles

tion, about two thirds of the total systemic resistance

Importance of the Vessel Diameter “Fourth Power Law” in

of the vessel, which demonstrates once

fourth power

Note particularly in this equation that the rate of

blood flow is directly proportional to the
of the radius
again that the diameter of a blood vessel (which is equal
to twice the radius) plays by far the greatest role of all
factors in determining the rate of blood flow through a
vessel.

Determining Arteriolar Resistance.

In the systemic circula-

to blood flow is arteriolar resistance in the small

range from as little as 4 micrometers to as great as

discussed above that relates blood flow to diameter of

diameter can increase the flow as much as 256-fold.

diameter to nervous signals or local tissue chemical

flow to the tissue or at the other extreme to cause a
vast increase in fl

flow of

more than 100-fold in separate tissue areas have been
recorded between the limits of maximum arteriolar
constriction and maximum arteriolar dilatation.

cuits.

Blood pumped by the heart flows from the high

miles of blood vessels arranged in series and in paral-

flow through each blood

vessel is the same and the total resistance to blood flow
(R

total

) is equal to the sum of the resistances of each

vessel:

–10A

is equal to the sum of R

and R

Blood vessels branch extensively to form parallel

circuits that supply blood to the many organs and

each tissue to regulate its own blood fl

14–10B

as:

It is obvious that for a given pressure gradient,

far greater amounts of blood will flow through this

total

. . .

R . . .

total

P =

100 mm

d = 1

d = 2

d = 4

1 ml/min

16 ml/min

256 ml/min

Large vessel

Small vessel

farther away from the vessel wall, the faster the flow.

, Concentric rings of blood flowing at different velocities; the

, Demonstration of the effect of vessel diameter on blood flow.

Figure 14–9

A
B

the viscosity of water.

if all other factors are constant. Furthermore,

ow in a vessel

The greater the viscosity, the less the

in Poiseuille

Viscosity on Vascular Resistance and

Effect of Blood Hematocrit and Blood

increasing total peripheral vascular resistance.

ow (i.e., cardiac output) while

well as the pressure gradient. Therefore, amputation of

ow in the tissue, as

tance of the systemic circulation. Blood

lel, and each tissue contributes to the overall conduc-

skin, and coronary circulations are arranged in paral-

For example, brain, kidney, muscle, gastrointestinal,

ow. The total conductance (C

, for blood

each parallel vessel provides another pathway, or

ance. Many parallel blood vessels, however, make it

resistance.

blood vessels. However, increasing the resistance of

resistance, not the resistance of the other parallel

through each of the parallel vessels in Figure 14

than the resistance of any single blood vessel. Flow

blood vessels. Therefore, the total resistance is far less

Overview of the Circulation; Medical Physics of Pressure, Flow, and Resistance

Chapter 14

169

parallel system than through any of the individual

–10B

is determined by the pressure gradient and its own

any of the blood vessels increases the total vascular

It may seem paradoxical that adding more blood

vessels to a circuit reduces the total vascular resist-

easier for blood to flow through the circuit because

con-

ductance

total

)

for blood flow is the sum of the conductance of each
parallel pathway:

flow through

each tissue is a fraction of the total blood flow (cardiac
output) and is determined by the resistance (the recip-
rocal of conductance) for blood fl

a limb or surgical removal of a kidney also removes a
parallel circuit and reduces the total vascular conduc-
tance and total blood fl

Blood Flow

Note especially that another of the important factors

’s equation is the viscosity of the blood.

the vis-

cosity of normal blood is about three times as great as

But what makes the blood so viscous? It is mainly

the large numbers of suspended red cells in the blood,

C . . .

total

the plasma, but these effects are so much less than

as great as 10 times that of water, and its

, the blood viscosity can become

When the hematocrit rises to 60 or 70, which it often

at normal hematocrit is about 3; this means that three

12. The viscosity of whole blood

as shown in Figure 14

blood increases drastically as the hematocrit increases,

The viscosity of

Effect of Hematocrit on Blood Viscosity.

bration allows direct reading of the percentage of cells.

11. The cali-

a calibrated tube, as shown in Figure 14

the person resides. These changes in hematocrit are

degree of bodily activity, and on the altitude at which

depending on whether the person has anemia, on the

averages about 38. These values vary tremendously,

tocrit of men averages about 42, while that of women

volume is cells and the remainder is plasma.The hema-

ocrit of 40, this means that 40 per cent of the blood

Thus, if a person has a hemat-

The percentage of the blood that is cells is

each of which exerts frictional drag against adjacent
cells and against the wall of the blood vessel.

Hematocrit.

called the hematocrit.

discussed in relation to the red blood cells and their
oxygen transport function in Chapter 32.

Hematocrit is determined by centrifuging blood in

–

times as much pressure is required to force whole
blood as to force water through the same blood vessel.

does in polycythemia

flow through

blood vessels is greatly retarded.

Other factors that affect blood viscosity are the

plasma protein concentration and types of proteins in

the effect of hematocrit that they are not significant

Vascular resistances:

Figure 14–10

A, in series and B, in parallel.

Normal

Anemia

Polycythemia

100

Hematocrits in a healthy (normal) person and in patients with

Figure 14–11

anemia and polycythemia.

despite high arterial pressure.

more. Conversely, very strong sympathetic stimulation

gure,

peripheral blood vessels. Thus, as shown in the

13 the large changes in

Note also in Figure 14

to increase vascular diameter.

ow at 50 mm Hg instead of two times as would

ow at 100 mm Hg

Therefore, for most tissues, blood

ow in both of these ways.

which decreases vascular resistance. Thus, greater

vessels but also distends the vessels at the same time,

13. The reason for

upward curving lines in Figure 14

ow is greater than one would expect, as shown by the

the body. However, the effect of pressure on blood

From the discussion thus far, one might expect an

Resistance and Tissue Blood Flow

Effects of Pressure on Vascular

cosity of blood plasma is about 1.5 times that of water.

considerations in most hemodynamic studies. The vis-

170

Unit IV

The Circulation

increase in arterial pressure to cause a proportionate
increase in blood flow through the various tissues of

–

this is that an increase in arterial pressure not only
increases the force that pushes blood through the

pressure increases the fl

arterial pressure is usually four to six times as great as
blood fl
be true if there were no effect of increasing pressure

–

blood flow that can be caused by either increased
or decreased sympathetic nerve stimulation of the

inhibition of sympathetic activity greatly dilates the
vessels and can increase the blood flow twofold or

can constrict the vessels so much that blood flow occa-
sionally decreases to as low as zero for a few seconds

References

See references for Chapter 15.

Viscosity (water = 1)

Hematocrit

Viscosity of whole blood

Viscosity of plasma

Viscosity of water

Normal blood

Effect of hematocrit on blood viscosity. (Water viscosity

Figure 14–12

= 1.)

80 100 120 140 160 180 200

Blood flow (ml/min)

Arterial pressure (mm Hg)

Sympathetic
inhibition

Normal

Sympathetic
stimulation

Critical
closing

pressure

decreased sympathetic stimulation of the vessel.

different degrees of vascular tone caused by increased or

Effect of arterial pressure on blood flow through a blood vessel at

Figure 14–13