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LEARNING

OBJEC11VES

After reading this article

and taking the test, the

reader will:

. Understand the con-

cept of attenuation prob-

ability and the terms

used to describe it.

. Be aware of the various

factors that affect attenu-

ation and how they affect

it.

. Be familiar with expo-

nential attenuation rela-

tionships and be able to

perform relevant calcu-

lations.

. Know the difference in

attenuation in monochro-

matic versus polychro-

matic beams and know

the effects of added

filtration.

151

The AAPWRSNA PhysicsTutorial for Residents

X-ray Attenuation1Marlene H. McKetty, PhD

Attenuation is the reduction of the intensity of an x-ray beam as it traverses

matter. The reduction may be caused by absorption or by deflection (scat-

ten) of photons from the beam and can be affected by different factors such

as beam energy and atomic number of the absorber. An attenuation coeffi-

cient is a measure of the quantity of radiation attenuation by a given thick-

- ness of absorber Linear and mass attenuation coefficients are the coeffi-

cients used most often The equation I = I e�’ expresses the exponential re-

_J lationship between incident primary photons and transmitted photons for a

monoenergetic beam with respect to the thickness of the absorber and thus

may be used to calculate the attenuation by any thickness of material. The

quality or penetrating ability of an x-ray beam is usually described by stat-

ing its half-value layer (HVL). Another parameter used to describe the pen-

etrating ability of a beam is the homogeneity coefficient. Among other

things, use of added filtration reduces the intensity of the x-ray beam, in-

creases the HVL, decreases patient exposure, and improves image quality

for a given radiation dose.

. INTRODUCTION

In conventional radiography and fluoroscopy, an x-ray beam is passed through the

body section and projects an image onto a receptor. The beam that emerges from

the body varies in intensity. The variation in intensity is caused by x-ray attenua-

tion in the body, which depends on the penetrating characteristics of the beam and

the physical characteristics of the tissues.

This article discusses x-ray attenuation, which represents a logical progression

from the topics of production and interaction of x rays but at the same time is in-

tertwined with them. The principles that apply to x-ray attenuation also apply to

gamma ray attenuation. The article reviews five major areas: (a) the concept of

. Be familiar with the

definition and measure-

ment of half-value layer.

Abbreviations: HVL half-value layer, NCRP National Council on Radiation Protection and Measurements, TVL

tenth value layer

Index terms: Physics #{149}Radiography

RadioGraphics 1998; 18:151-163

‘From the Department of Radiology, Howard University Hospital, 2041 Georgia Aye, NW, Washington, DC 20060.

From the AAPM/RSNA Physics Tutorial at the 1996 RSNA scientific assembly. Received August 21, 1997; revision re-

quested October 9 and received November 11; accepted November 13. Address reprint requests to the author.

�RSNA, 1998

Incident beam

Incident beam, unattenuated

152 U Imaging & Therapeutic Technology Volume 18 Number 1

Figure 1. Diagrams showan unattenuated x-ray beam(top) and an x-ray beam pass-ing through a foil (bottom)into detectors.

Attenuated beam

Foil

Ionization

chamber

Lj

attenuation and the terms used to character-

ize it, (b) the factors that affect attenuation,

(c) exponential attenuation relationships,

(d) concepts involved in the attenuation of

monochromatic and polychromatic x-ray

beams, and (e) half-value layer (HVL) mea-

sunements and their significance.

U DEFINITION OF ATTENUATIONAttenuation is the reduction of the intensity of

an x-ray beam as it traverses matter. The re-

duction may be caused by absorption (in this

process, energy is transferred from the pho-

tons to atoms of the target or irradiated ma-

terial) or by deflection of photons from the

beam (scatter).

In the example of a beam of x rays passing

through a foil and into an x-ray detector,

some of the photons will interact with the foil

and be absorbed completely from the beam

and some photons may be scattered (Fig 1). If

one measures the intensity of the beam (a) af-

ten it has been attenuated by the foil and as it

strikes the detector and then (b) without the

foil and as it strikes the detector, one obtains

a quantitative measurement of the interaction

of the x rays with the material contained in

the foil.

The intensity of an x-ray beam passing

through a layer of attenuating material de-

pends on the thickness and type of material.

The thickness of a material can be expressed

in different units of measure, for example,

meters, kilograms per meter squared, and

electrons pen meter squared.

An attenuation coefficient is a measure of

the quantity of radiation attenuated by a

given thickness of an absorbing material. The

linear attenuation coefficient, symbolized by the

Greek letter �.t, is the fractional change in x-

ray intensity per the thickness of the attenu-

ating material because of interactions in a

given material:

=�N/NAx, (1)

where �N is the number of photons removed

from the x-ray beam in thickness �\x. In

Equation (1), for any given Ii, E�x must be

chosen so that the number of photons re-

moved from the beam is much smaller than

the total number of photons. As the thickness

of the attenuating material increases, the

equation is no longer correct and the rela-

tionship becomes nonlinear.

The linear attenuation coefficient is mea-

sured in units of pen unit length, which is

most commonly expressed in terms of centi-

meters or millimeters. Attenuation rate can

also be expressed in terms of the mass of the

material encountered by photons. The mass

attenuation coefficient is obtained by dividing

the linear attenuation coefficient by the den-

sity of the material through which the pho-

January-February 1998 McKetty U RadioGraphics U 153

Table 1Relationships among the Attenuation Coefficients

Units in Which Thickness isCoefficient Relationship Units of the Coefficients Measured

Linear (li) . . . /cm cm

Mass (l�t/p) J.t/p /g/cm2 g/cm2

Atomic (11a) l1IPZINe /atom/cm2 atom/cm2Electronic (lie) �i/ P4/Ne /electron/cm2 electron/cm2

Note. - Ne number of electrons per gram, Z = atomic number.

Table 2Physical Properties of Selected Materials

Effective Atomic Density 50 keV Linear Attenuation

Material Number (Z) (g/cm3) Coefficient (cm1)

Water 7.4 1.0 0.214Ice 7.4 0.917 0.196Water vapor 7.4 0.000598 0.000128Compact bone 13.8 1.85 0.573

Air 7.64 0.00129 0.00029

Fat 5.92 0.91 0.193

Note. - Data from reference I.

tons pass and thus is represented by the sym-

bol pjp. Mass attenuation coefficient is the

rate of photon interactions per unit area mass

and is independent of the physical state of

the material. The typical unit of the mass at-

tenuation coefficient is per gram per centime-

ten squared (cm2/g), since the unit in which

thickness is measured is gram per centimeter

squared (the mass of a 1-cm2 area of mate-

na!). The coefficient is the inverse of the unit

in which thickness is measured.

Other attenuation coefficients are the elec-

tronic and atomic coefficients, in which the

thickness of the attenuating medium is ex-

pressed as the number of electrons or atoms

per unit area, respectively. The relationship

among the attenuation coefficients is shown

in Table 1.

The atomic attenuation coefficient 1’a is the

fraction of an incident x-ray or gamma ray

beam that is attenuated by a single atom (ie,

the probability that an absorber atom will in-

teract with one of the photons in the beam).

The atomic coefficient is obtained by divid-

ing the mass attenuation coefficient by the

number of atoms per gram. The electronic co-

efficient is obtained by dividing the mass at-

tenuation coefficient by the number of elec-

trons per gram.

U FACTORS AFFECTING ATTENU-ATIONSeveral factors affect attenuation. Some are

related to the x-ray beam or radiation and

the others to properties of the matter through

which the radiation is passing. The factors in-

dude beam energy, the number of photons

traversing the attenuating medium or ab-

sorber, the density of the absorber, and the

atomic number of the absorber. As noted, the

greater the thickness of the attenuating mate-

rial, the greater is the attenuation. Similarly,

as the atomic number or density of the mate-

nial increases, the attenuation produced by a

given thickness increases. Thus, different ma-

terials such as water, fat, bone, and air have

different linear attenuation coefficients, as do

the different physical states or densities of a

material, such as water vapor, ice, and water

(Table 2; Figs 2, 3).

0 5 10

Thickness (cm)

Energy E1

ZA>ZB f

0.5 .� 0.5

a,

0 0

2. 3.

Figures 2, 3. (2) Effect of atomic number on x-ray attenuation. Graph shows the variation in intensity

versus thickness of two materials. Material A has a greater atomic number (Z) than material B; therefore,less thickness of material A is needed to reduce the intensity to any chosen value. (3) Effect of radiation en-ergy on x-ray attenuation. As photon energy increases, the attenuation produced by a given thickness ofabsorber decreases. Graph shows the variation in intensity versus thickness for two beams. Beam I (E1) is

of a greater energy than beam 2 (E,). The lower-energy beam is attenuated more rapidly by a chosen thick-ness of absorber.

Thickness (cm)

I IE1>E2


U,

C

aC

a,>

a,

To understand the relationship between

attenuation and energy, one must be familiar

with three of the basic interactions of x and

gamma nays with matter: photoelectric,

Compton, and pair production interactions.

In a photoelectric interaction, a photon col-

lides with an atom and causes an electron to

be ejected from one of the electron orbital

shells around the nucleus of the atom. The

energy of the ejected electron is equal to the

energy of the incoming photon minus the

binding energy of the electron. The more

closely bound the electron, the higher is its

binding energy; consequently, the energy of

the ejected electron is lower. The probability

that a photoelectric interaction will occur is

most likely when the energy of the incoming

photon and the binding energy of the elec-

tron are nearly the same. The probability of a

photoelectric interaction varies with photon

energy approximately as l/E3 and varies

with atomic number (Z) approximately as Z3.

Thus, as photon energy is increased, the pho-

toelectric interaction decreases.

A Compton interaction on scattering oc-

curs when an incident photon collides with a

free electron and causes it to move from its

orbital shell. The photon is deflected at an

angle and therefore travels in a new direc-

tion. The deflected on scattered photon has

reduced energy. The remainder of the energy

of the incident photon is transferred to the

electron, which is called a recoil electron. The

distribution of energy between the recoil

electron and scattered photon depends on

the energy of the incident photon and the

angle of emission of the scattered photon.

The probability that a Compton interaction

will occur decreases with an increase in en-

ergy.

Pair production involves an interaction be-

tween a photon and an atomic nucleus, but it

can occur only if the energy of the incident

photon is greater than 1.02 MeV. Therefore,

this interaction does not occur in the energy

range of x-ray beams used for diagnostic ra-

diology.

Photoelectric and Compton interactions

produce attenuation in the diagnostic energy

range. The probability that either interaction

will occur decreases as photon energy in-

creases, but the decrease in the photoelectric

effect is more rapid than the decrease in

Compton scattering. Although beam attenua-

tion caused by the photoelectric effect rap-

idly decreases with increasing energy, there

may be periodic increases in the attenuation.

The jumps on increases in attenuation cone-

spond to the orbital shells in which electrons

are bound. The highest energy at which the

attenuation jumps or increases is known as

the K absorption edge, which corresponds to

the binding energy of the K-shell electrons.

Additional absorption edges exist at lower

energies that correspond to the binding ener-

gies of more loosely bound electrons in outer

shells. At each absorption edge, there is an

abrupt increase in attenuation.

I

Lead

Nal - . -.

Water- - - -

Air

- 100C5)

0

a)8 10C

0

Ca

C

a)Ca

U)U)Ca

E 0.1Ca

0

0.010.01

4.

.�

0.

Photoelectric

- - - Compton

Rayleigh

- . - . Pair

C’,

0)

EC)

5.

Energy (MeV)

10

Energy (MeV)

Figures 4, 5. (4) Mass attenuation coefficients for selected materials as a function of photon energy.

Graph shows the variation of si/p for sodium iodide, lead, water, and air. (5) Mass attenuation coefficientsfor photons in air. Graph displays the mass attenuation coefficient for air (with an effective atomic number

of about 7.6) for specific interactions with x rays and the total attenuation as a function of energy.


Photoelectric interactions are important

for a low-energy range (up to 50 keV) and

materials with large atomic numbers. Pair

production interaction is important only for a

very high energy range (5-100 MeV) and ma-

terials with large atomic numbers. Compton

interaction is predominant in the intermedi-

ate energy range (60 keV-2 MeV) for all ma-

tenials, regardless of atomic number (1). The

relative probability of each type of interac-

tion is proportional to the cross section for

that process. Cross section is defined as the

probability that a particular reaction will oc-

cur. The total linear attenuation coefficient is

equal to the sum of the individual interac-

tions and their cross-sectional values:

�totaI = � � c� + K,

where t = photoelectric, � Compton and

classical, and x pair production interac-

tions. This equation with the appropriate

subscripts applies to the mass, electronic, and

atomic coefficients.

In radiography performed with low ener-

gies (<30 keV), photoelectric effect is most

important in soft tissue and bone. As the x-

ray energy is increased, Compton scattering

becomes the predominant interaction. If �t is

plotted versus photon energy for air, soft tis-

sue, and lead, the curves fall rapidly with in-

creases in energy because of the rapid de-

crease of the photoelectric effect. However, at

the K absorption edge, there will be an in-

crease in the attenuation coefficient. For ex-

ample, the attenuation curve for sodium io-

dide will show an increase at 33 keV because

the K electron binding energy is 33 keV for

iodine (Figs 4, 5). The attenuation curve for

lead will show an increase at 88 keV (Figs 4,

5). The curves decrease more slowly in the

region in which the Compton effect is impor-

tant. Because the mass attenuation coeffi-

cients do not depend on density and the

physical state of the absorber, numeric data

are often expressed in terms of these coeffi-

cients, rather than linear attenuation coeffi-

cients.

The range of energies used in x-ray imag-

ing is chosen to optimize the diagnostic x-ray

information and to minimize the radiation

absorbed by the patient. Both these factors

depend on the mass attenuation coefficients

of various materials and tissues.

The importance of linear and mass attenu-

ation coefficients can be demonstrated in sev-

eral clinical situations. Contrast agents that

contain iodine and barium are used because

of their large attenuation coefficients, which

increase the visibility of anatomic structures

that contain the contrast agent. The increased

attenuation is caused by the atomic number

and K absorption edge of the contrast agent

being greater than those of the surrounding

tissue. In cases in which the penetration

of x rays must be reduced, a shielding mate-

rial with a large attenuation coefficient is

Figure 6. Exponential attenuationrelationships. Each absorber re-

duces the transmission of x rays by20%. if one starts with 1,000 pho-

tons, the first absorber will reducethe number of photons to 800; thesecond, from 800 to 640; the next,from 640 to 512; and so on to an ex-ponentially diminishing number ofphotons.

640� N� ‘5

�a,.��a,� “.

20%

512 ...

N(x)=N0e�

Thickness of tissue


Transmission-.�l000 800.�n ____

� . �� ,- a,..a,. . _____

� ______� ____p:-.� :5

�,,

� .; . �-

.�. ____

Attenuation � 20% 20%

required. Shielding is achieved by using ma-

tenials with a high atomic number, such as

lead.

U EXPONENTIAL ATTENUATIONRELATIONSHIPSAttenuation measurements of a monoener-

getic (monochromatic) beam of x or gamma

rays depend on the number of photons inci-

dent on an absorber, the number of photons

transmitted through the absorber, and the

absorber thickness. The expression j.t =

L�x previously discussed must be trans-

formed into a more convenient form. If �N

and E�x are very small, they are known as dif-

ferentials and the differential equation is

solved by using calculus to give the follow-

ing equations:

and

I = I e�t0

N = N e�,0

where I� = beam intensity at an absorber

thickness of zero, x absorber thickness, I

beam intensity transmitted through an ab-

sonben of thickness of x, e base of the natu-

nal logarithm system, �.t attenuation coeffi-

cient, N = number of transmitted photons,

and N0 = number of incident photons.

These equations may be used to calculate

attenuation by any thickness of material

when the incident and transmitted photon in-

tensity or photon number is measured. In di-

agnostic radiology, photon intensity (ie, the

number of photons in a beam weighted by its

energy) is the quantity that is most often

measured. Exponential reduction in the num-

ben of photons is demonstrated in Figure 6. If

I/Jo �5 plotted as a function of x on linear

graph paper, an exponential curve will be ob-

tamed (Fig 7). The logarithm of the number

of photons transmitted varies linearly with

the thickness of the attenuating material;

therefore, if the logarithm of I/I,, is plotted

against x, a straight line graph will result.

This plot is referred to as a semilogarithmic

plot because one axis is logarithmic and the

other linear.

Polychromatic beams contain a spectrum

of photon energies. With an x-ray beam, the

maximum photon energy is determined by

the peak kilovoltage (kVp) used to generate

the beam. Because of the spectrum of photon

(2) energies, the transmission of a polychromatic

beam through an absorber does not strictly

(3) follow Equation (3). When a polychromatic

beam passes through an absorber, photons of

low energy are attenuated more rapidly than

the higher energy photons; therefore, both

the number of transmitted photons and the

quality of the beam change with increasing

amounts of an absorber. A semilogarithmic

plot of the number of photons in a polychro-

matic beam as a function of the thickness

of the attenuating materials will not be a

straight line but will be a curve (Fig 8). The

initial slope of the curve is steep because the

low-energy photons are attenuated, but, as

the beam becomes more monochromatic, the

slope decreases. A comparison of the curves

for polychromatic and monochromatic radia-

tion is shown in Figure 9.

Linear Scale Semi-log Scale1000

800

800

400

200

0

1000

100

10

cm of water

0 4 8 12 16 20 0 4 8 12 16

cm of water

Figure 7. Attenuation ofmonochromatic radiation

20 plotted on a linear scale andsemilogarithmic scale.

U,C00

EU,C

C-

1000

100

10

0 ��1�I�20

cm of water

I 00 kVp

�polychromatic


U,

C

a0

E#{149}1Ca,

I-

U,

C

20

EU,Ca,

100 kVp spectrum Semi-log Scale2.5 mm Al Inherent filtration

I mmAlinciema,ts 100

C0U,

CeEU,Ca,

I-

Ca,U

a,0.

30 40 50 80 70 80 90 100 10Energy(keV) 0 1 2 3 4 5

Increase in effective energy (keV): Absorbflr thickness (mm Al)48.5. 50.2.51.7, 53.0, 54.1

Figure 8. Attenuation of polychromatic radiation. Photons of low en-

ergy are attenuated more rapidly than the higher-energy photons, result-ing in a change in the number of photons with increasing amounts of ab-

sorber and a change in the quality of the x-ray beam. This is illustrated inthe left graph of a bremsstrahlung spectrum, progressively attenuated by1 mm aluminum filters. A semilogarithmic plot of the number of photonsin a polychromatic beam as a function of thickness of the attenuating ma-terial will be a curve, as shown in the right graph.

- 100 keVmonochromatic

Figure 9. Graph shows a comparison of the curves

for polychromatic and monochromatic radiation. An

important point here is the comparison between kilo-electron volt and peak kilovoltage. A monoenergetic

x-ray photon beam at 100 keV (effective energy, 100

keV) is substantially more penetrating than a compa-rable x-ray photon beam produced at 100 kVp (effec-

tive energy, -40 keV, depending on filtration of thebeam). Most of the x-ray photons in a bremsstrah-lung spectrum are composed of substantially lower

energies than the peak energy, thus resulting in a sig-

nificant increase in attenuation, which is nonlinear

on the semilogarithmic graph illustrated. (Redrawnfrom reference 2 and reprinted with permission.)

50 cm

or more(Cu or Al)

Detector:

ionization

chamber

Narrow beam geometry


Figure 10. Diagram demonstrates

the ideal setup for measurement ofHVL. The sensitive volume of theexposure meter is positioned onthe axis of the x-ray beam, at aminimum of 50 cm from the colli-mator and from the walls andfloor. The x-ray beam should becollimated tightly around but to-tally include the sensitive volume

of the radiation detector.

U HVL MEASUREMENTSThe penetrating ability or quality of an x-ray

beam is described explicitly by its spectral

distribution, which indicates the energy

present in each energy interval. However, the

HVL or half-value thickness is the concept

used most often to describe the penetrating

ability of x-ray beams of different energy 1ev-

els and the penetration through specific ma-

tenials. The HVL is defined as the thickness of

a standard material that reduces the beam in-

tensity to one-half. At energy levels below

120 kV, HVLs are usually measured in mlii-

meters of aluminum; at energy levels of 120-

400 kV, HVLs may be expressed in millime-

tens of copper.

The HVL of an x-ray beam is obtained by

measuring the exposure rate from the x-ray

generator for a series of attenuating materials

or attenuators placed in the beam. The first

measurement is made with no attenuator be-

tween the x-ray source and detector, and

then measurements are made for succes-

sively thicker attenuating materials. The at-

tenuators should have constant composition

and should not contain impurities. The setup

for HVL measurements is shown in Figure

10.

The sensitive volume of the exposure

meter is positioned on the axis of the x-ray

beam. It should be at least 50 cm from the

collimator or beam-defining system of the x-

ray unit so that radiation scattered from the

added absorbers is avoided. There should be

no scattering material in the vicinity of the

detector, which should be at least 50 cm from

the walls or floor. The x-ray beam should be

about 5 x 5 cm at the detector and should

completely include the sensitive volume of

the detector.

The conditions just described under which

the HVL measurements should be made are

referred to as narrow-beani conditions or con-

ditions of good geometry. This is in contrast

to broad-beam conditions, in which a large x-

ray beam is used and only a small distance

exists between the absorber and detector.

With broad-beam geometry, a large number

of photons from the absorber are scattered

into the detector.

HVL measurements should always be

made under narrow-beam geometry condi-

tions to ensure that the only photons that

reach the detector are primary photons trans-

mitted by the attenuating material. Figure 11

shows the two types of measurement condi-

tions.

A graph is made of exposure readings (or-

dinate or y axis) versus thickness of the at-

tenuating material (abscissa or x axis). The x-

ray intensity equal to one-half the original in-

tensity and the corresponding thickness of

the attenuating material (ie, HVL) are deter-

mined. Results of a typical measurement se-

nies are shown in Figure 12.

Attenuator

Source I,Attenuator

�----p Detector

Source

INScattered photons

not detected

Detector

Narrow-Beam Geometry

arcscattered into the

detector

Broad-Beam Geometry

Absorber

thickness (mm)

0

3

.1

X-ray exposure

I iS

82

63

51

38

29

100

Filtration

mmCu

0

3

.1

Exposure rate

R man

68

20

11.4

7.6

5.5

UVI.

mm Cu

0.35

1.3

1.8

2.32.7

10

0 1 2 3 4 5I

120

E 100E;8o

Ce0 600.‘C

a,>.

a,* 20

0

01234567Absorber thickness (mm Al)

Filtration (mm Cu)

Figure 12. Results of a typical measurement series for HVL determination are shown

for a lower-energy beam (left) measured with aluminum and a higher-energy beam

(right) measured with copper. The graph on the right has several sequential HVLs mdi-

cated below the curve. For example, the first HVL is the thickness required to reduce the

original intensity of the beam from 68 R/min (1.75 x 102 C/kg/mm) to 34 R/min (8.77 x

10-s C/kg/mm), which graphically is determined as 0.35 mm copper. After the addition

of 1 mm copper, the beam is now reduced to 20 R/min (5.16 x 10� C/kg/mm). The HVL

of the beam including the 1 mm copper is the thickness required to reduce the beam to

10 R/min (2.58 x 10� C/kg/mm). The thickness is graphically determined as 1.3 mm

copper, indicating the greater penetrability of the beam with added filtration. Several

other HVLs indicated on the graph are determined in a similar fashion. (Right graph re-

drawn from reference 1 and reprinted with permission; left graph redrawn from refer-

ence 4 and reprinted with permission.)

Collimator Collimator


Figure 11. Diagrams illus-trate the geometry for nar-row-beam and broad-beamconditions. HVL measure-ments should always bemade under narrow-beamgeometry conditions to en-

sure that only primary (unat-

tenuated) photons reach thedetector. (Redrawn from ref-erence 3 and reprinted withpermission.)

I 00

75

50

25

0

Broad

I 00

10

E

a

11)

0

Ui

��rge fieldtectorFilter neard�e�or (B)

sotwce (A) ‘�Small field

0 1 2345

Thickness (cm)

01234567

Filtration (mm Cu)

Figure 13. Attenuation curves and HVLs for narrow- and broad-beam geometry.Broad-beam conditions will indicate a greater penetrating power of the beam (ie, agreater HVL or haif-value thickness), which is not truly representative of the actualvalue. This result is chiefly due to attenuation caused by scatter, which reaches the de-

tector in broad-beam or poor geometry conditions because either the field area is toolarge or the attenuating material is too close to the detector, as shown in the right graphand diagram. Right graph shows the results for the filter near the detector and the filter

near the source for a small field and a large field. (Values for R/min can be converted to

SI units with the factor 10 R/min = 2.58 x 10� C/kg/mm.) Note that as four measure-ment conditions are varied, one can obtain four different apparent HVLs. Left graph in-dicates an HVL of 2 cm with narrow-beam geometry and 2.8 cm with broad-beam con-

ditions. (Modified from reference 1 and reprinted with permission.)


‘I)

A complete attenuation curve is not essen-

tial for routine dosimetry; rather, thicknesses

of the attenuating material that reduce the

exposure rate to slightly more than haif and

to slightly less than half are required. The

difference in apparent attenuation for broad

and narrow beams is seen in Figure 13. Un-

den broad-beam conditions, the beam will ap-

pear to have greater penetrating power (ie, a

greater HVL or half-value thickness) than if it

were measured with narrow-beam geometry.

U RELATIONSHIP OF HVL ANDLINEAR ATTENUATION COEFFI-CIENTFor a monoenergetic beam of x-ray or gam-

ma ray photons, it was already determined

in Equation (2) that I I0e�. When x = HVL

(ie, if the thickness of the absorber is 1 HVL),

then:

therefore,

1/10 - 0.5;

1/10 = 0.5 = e��’�-

If the natural logarithm (inverse function

of the exponential) is calculated for each side

of the equality,

in [0.5] = in [e�”-]

-0.693 = jiHVL

HVL = 0.693/si

l� 0.693/I-IVL.

(4)

(5)

Thus, knowledge of the HYL allows the

calculation of the “effective” attenuation coef-

ficient, and similarly, knowledge of the effec-

tive attenuation coefficient allows the determi-

nation of the HVL of the radiation beam. This

is particularly important for polychromatic

70.74

21.33

9.153

Energy (keV)

10

15

20

30

40

50

60

80

I 00

interpolate table values to estimate E�ff:

Energj (keV)

0.748

0.543

0.459

1.525 40

Effective Energy = 30.9 keV

�t = 0.693 I HVL = 0.693/0.24 cm


given: HVL 2.4 mm Al

= 0.24 cm Al

3.024 30

2.888 ? � 30.9

Figure 14. Illustra-

tion shows how effec-tive energy can be de-termined by measur-

ing HVL (eg� in mil-limeters of aluminum)and calculating the lin-ear attenuation coeffi-

cient j.t with Equations(4) and (5). Effective

energy is determined

from interpolating val-ues in the table of ji

versus energy.

spectra with a variable attenuation that de-

pends on the energy intensity and filtration of

the beam.

The HVL can be easily calculated from the

linear attenuation coefficient for a monoen-

ergetic photon beam and vice versa. For ex-

ample, if the linear attenuation coefficient for

aluminum at an energy level of 100 keV is

0.459/cm, then using the equation HVL

0.693/j.t, the HVL for aluminum is 0.693/0.459

or 1.51 cm.

For a polychromatic beam (eg, from an x-

ray tube), the attenuation coefficient is not

explicitly known. In this situation, a measure-

ment of the HVL with narrow-beam geom-

etry methods allows determination of the ef-

fective attenuation coefficient of the attenuat-

ing material for the specific polychromatic

beam.

U TENTH VALUE LAYERThe tenth-value layer (TVL) is the thickness

of a material that will reduce the incident in-

tensity by a factor of 10 (90% attenuation,

10% transmission):

I/I, = 0.1 = eMW��

TVL = 2.303/si.

TVL is often used for shielding calcula-

tions, in which barriers can be specified in

the number of TVLs. The shielding calcula-

tions determine the amount of attenuating

material required to protect individuals

working with or near radiation sources or x-

ray units.

U DETERMINATION OF EFFECTIVEENERGYFor polychromatic x-ray beams (which contain

a spectrum of photon energies), the penetra-

tion and thus the HVL is different for each en-

ergy. The effective energy of an x-ray beam is

the energy of a monoenergetic beam of pho-

tons that is attenuated at the same rate as the

x-ray beam, in other words, that has the same

HVL as the spectrum of photons in the beam.

The effective energy is about 30%-50% of peak

energy.

if the HVL and mass attenuation coeffi-

cients or linear attenuation coefficients for a

given material are known, the effective energy

of a polychromatic beam can be calculated

(Fig 14). First, the “effective” linear attenua-

tion coefficient is determined on the basis of

the HVL through the relationship of �.t and

HVL previously discussed. This value is then

compared with tabulated values. To deter-

mine an accurate energy value, interpolation

of the values in the table is performed. If a

mass attenuation curve is available for a given

material as a function of energy, the interpola-

tion is “automatically” determined by using

the effective mass attenuation value. In this

case, the effective energy value is determined

at the intersection of the attenuation curve and

the effective mass attenuation coefficient value

(Fig 15).

Aluminum attenuation20

10

5

2

I

Ca,U

U

C0

a,

C

a,

U,U,a,

E


U HOMOGENEITY COEFFICIENT

The homogeneity coefficient is sometimes

used in addition to the HVL as a descriptor

of beam quality for polychromatic spectra.

A monoenergetic beam is attenuated ac-

cording to the exponential attenuation law.

Thus, if the first HVL reduces the beam to

one-half, a second HVL will reduce it by one-

half again to one-quarter. With a monoenen-

getic beam, the first and second HVLs are

equal.

With a polychromatic beam, photons of

low energy are attenuated more rapidly than

photons of higher energy. The second HVL

(ie, the thickness required to reduce the pen-

etration to one-quarter) is larger than the first

HVL. The ratio of the two HVLs - first HVL/

second HVL - is called the homogeneity coef-

ficient. It follows that the homogeneity coeffi-

cient for a polychromatic beam is less than

one.

U EFFECTS OF ADDED FILTRATIONDiagnostic x-ray beams are polychromatic,

and the mean energy is approximately 30%-

50% of the peak energy. As a polychromatic

beam passes through matter, the low-energy

photons are attenuated more rapidly than the

high-energy photons and the effective energy

of the beam increases. The increase in effec-

tive energy that occurs with increasing thick-

ness of attenuating material is called beam

hardening. Therefore, any absorber, whether

the patient or an added filter, will cause the

beam to harden.

The x-ray beam is filtered by (a) inherent

filtration, (b) added filtration, and (c) the pa-

tient. The primary purpose of added filtra-

tion is to remove the low-energy photons that

are not energetic enough to reach the film. If

these photons are not removed by a filter,

they will expose the patient to radiation but

will not arrive at the film to form the radio-

graph.

0.5

0.2

I I I I I I I I

ii T1 �S ii iii i: ii ii iii iii

= = = = = ===

EEE=

==

--

--

--

--

--

-- -

-�

--

--

- - �

0.1 � ‘�10 20 30 40 50 60

Energy (key)

Figure 15. Illustration shows how effective en-

ergy can be determined with use of graphical in-terpolation. HVL is measured in the same way as

in Figure 14 (eg, in millimeters of aluminum), andthe linear attenuation coefficient is calculated withEquations (4) and (5). The correct energy is deter-mined from the graph at the intersection of the at-tenuation curve and the effective mass attenuationcoefficient value.

Inherentfiltration occurs when the x-ray

beam is attenuated by the glass envelope sun-

rounding the anode and cathode in the x-ray

tube, the insulating oil, and the exit window

or port. Added filtration consists of absorbers

that are deliberately added to the beam to

provide filtration. In diagnostic radiology,

aluminum is usually used for added filtra-

tion, but compound filters containing copper

and aluminum or other materials may be

used. The filter is positioned in the exit port

of the x-ray tube between the housing and

collimator assembly. The collimator assembly

also adds to the filtration. The total amount

of added filtration is specified in terms of

aluminum equivalent thickness and, in a

typical x-ray unit, is about 2-3 mm alumi-

num equivalent thickness, 1 mm of which is

from the collimator assembly. Inherent filtra-

tion adds about 0.5 mm aluminum equiva-

lent.

Added filtration provides several advan-

tages: (a) it alters the shape of the x-ray spec-

trum, (b) it causes a shift in the effective en-

ergy of the x-ray beam by selectively remov-

0 20 40 60 80 100

Photon Energy (key)

This article meets the criteria for I .0 credit hour in category I of f/ic AMA Physician ‘s Recognition Award.

To obtain credit, see the questionnaire on pp 145-150.


>.

U,Ca,

C

a,

a,

a,

a,

Figure 16. Graph demonstrates the effect ofadded filtration on the energy and intensity of a

polychromatic x-ray beam. (Modified from refer-

ence 2 and reprinted with permission.)

Table 3Required Minimum Total Filtration forX-ray Tubes

Operating Tube

Potential (kVp) Total Filtration

Below 50 0.5 mm aluminum(0.03 mm Mo for mo-

lybdenum target

tubes)50-70 1.5 mm aluminum

Above 70 2.5 mm aluminum

Note. - Recommended by NCRP (7).

ing more low-energy photons than high-en-

ergy photons, (c) it reduces the intensity of

the beam (ie, the total number of photons in

the beam), (d) it increases the H\TL of an x-

ray beam, (e) it decreases patient exposure,

and (f) it improves image quality for a given

dose. A disadvantage of added filtration is

that it necessitates the increase of exposure

factors (kilovolts or milliampere seconds) to

compensate for the reduction in intensity of

the beam.

The National Council on Radiation Protec-

tion and Measurements (NCRP) has recom-

mended and other regulatory bodies have

mandated minimum filtration values for x-

ray tubes operating at certain peak kilovol-

tages. The NCRP values are shown in Table

3. HVL measurements and values are used to

indicate if these filtration criteria are met.

Figure 16 demonstrates the effect of added

filtration on a polychromatic x-ray beam.

U CONCLUSIONSOne of the technical principles on which radi-

ography is based is the difference in attenua-

tion by different materials; thus, an under-

standing of attenuation probability, the units

for describing it, and the factors affecting it is

essential. A practical way of expressing the

penetrating ability of x-ray beams from dif-

ferent x-ray tubes is by using the concept of

HVL, which must be measured under nar-

row-beam geometry conditions.

Acknowledgments: The author thanks Diana M.Roach for her assistance in the preparation of themanuscript, and J. Anthony Seibert, PhD, for as-sistance in preparing the figures.

U REFERENCES1. Johns HE, Cunningham JR. The interaction of

ionizing radiation with matter. In: The phys-ics of radiology. 4th ed. Springfield, Ill: Tho-

mas, 1983; 133-164.2. Curry TS III, Dowdy JE, Murry RC Jr. Attenu-

ation. In: Christensen’s physics of diagnostic

radiology. 4th ed. Philadelphia, Pa: Lea &

Febiger, 1990; 70-92.

3. Bushberg JT, Seibert JA, Leidholdt EM Jr.

Boone JM. Interaction of radiation with mat-ter. In: The essential physics of medical imag-ing. Baltimore, Md: Williams & Wilkins, 1994;

17-38.

4. Bushong SC. X-ray emission. In: Radiologic

science for technologists: physics, biology,

and protection. 3rd ed. St Louis, Mo: Mosby,1984; 173-181.

5. National Council on Radiation Protection and

Measurements. Medical x-ray, electron beam,

and gamma-ray protection for energies up to50 MeV (equipment design, performance, and

use). NCRP report no. 102. Bethesda, Md:

NCRP, 1989.

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