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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
154 U Imaging & Therapeutic Technology Volume 18 Number 1
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.
January-February 1998 McKetty U RadioGraphics U 155
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
156 U Imaging & Therapeutic Technology Volume 18 Number 1
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
January-February 1998 McKetty U RadioGraphics U 157
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
158 U Imaging & Therapeutic Technology Volume 18 Number 1
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
January-February 1998 McKetty U RadioGraphics U 159
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.)
160 U Imaging & Therapeutic Technology Volume 18 Number 1
‘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
January-February 1998 McKetty U RadioGraphics U 161
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
162 U Imaging & Therapeutic Technology Volume 18 Number 1
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.
January-February 1998 McKetty U RadioGraphics U 163
>.
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.
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3. Bushberg JT, Seibert JA, Leidholdt EM Jr.
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