The AAPWRSNA
Physics
Tutorial
for Residents
I
X-ray
article meets the
criteriafor
1.0 credit
hour in category
I of
f/ic AMA
Plnjsician’s
Recognition
Award.
To obtain credit,see
the questionnaire
on
Marlene
pp
as
H. McKetty,
Attenuation
The
ten)
LEARNING
reading
this
and taking
reader
article
the test,
the
the
con-
used
may
will:
be
Understand
cept
of attenuation
ability
and
used
.
prob-
the
Be aware
factors
ation
it.
of the
that
and
various
affect
they
Be
familiar
with
use
of added
the
HVL,
a given
factors
attenuation
by
coefficients
are
expresses
to the
attenuation
of an
by
x-ray
Another
beam
used
intensity
and
by
the
Among
statpen-
other
x-ray
improves
a
thus
The
described
of the
and
refor
to describe
coefficient.
the
exponential
of material.
is usually
exposure,
thick-
coeffi-
absorber
thickness
parameter
reduces
the
photons
of the
any
homogeneity
patient
the
coeffi-
a given
transmitted
thickness
such
attenuation
attenuation
and
filtration
decreases
radiation
INTRODUCTION
In conventional
expo-
attenuation
tionships
and
perform
relevant
beam,
image
in-
quality
dose.
be
able
radiography
and
fluoroscopy,
an x-ray
body
section
and projects
an image
onto a receptor.
the body
varies
in intensity.
The variation
in intensity
tion in the body,
which
depends
on the penetrating
relato
calcu-
lations.
the
difference
in
in monochro-
matic
versus
polychro-
matic
beams
and
effects
know
physical
characteristics
of the tissues.
This article
discusses
x-ray
attenuation,
from
the topics
of production
and interaction
beam
is passed
The beam
is caused
characteristics
through
the
that emerges
from
by x-ray
attenuaof the beam
and
the
Know
attenuation
the
things,
An
I = I e’
is the
(scat-
different
absorber.
photons
(HVL).
it traverses
of radiation
respect
of a beam
by
as
deflection
.
nential
.
ability
affected
primary
ability
layer
be
of the
beam
or by
equation
the
penetrating
half-value
x-ray
absorption
affect
it.
.
with
to calculate
creases
for
attenu-
how
its
etrating
terms
to describe
or
ing
can
mass
The
beam
used
and
quantity
incident
of an
by
number
and
often
between
intensity
caused
beam
of the
monoenergetic
be
atomic
Linear
most
lationship
the
and
of absorber
quality
.
from
energy
of the
may
is a measure
ness
cients
_J
OBJEC11VES
reduction
reduction
of photons
beam
cient
-
PhD
is the
matter.
145-150.
After
Attenuation1
tertwined
with
gamma
of added
ray
them.
attenuation.
The
principles
The
article
that
which
represents
of x rays but
apply
reviews
to x-ray
five
major
a logical
progression
at the same
time is in-
attenuation
areas:
also
(a) the
apply
concept
to
of
filtration.
.
Be familiar
definition
ment
with
and
of half-value
the
measurelayer.
Abbreviations:
tenth
Index
value
HVL
terms:
RadioGraphics
‘From
From
half-value
layer,
NCRP
National
Council
on
Radiation
Protection
and
Measurements,
TVL
layer
Physics
1998;
the Department
the AAPM/RSNA
quested
October
RSNA,
1998
9 and
Radiography
#{149}
18:151-163
of Radiology,
Howard
University
Hospital,
Physics
Tutorial
at the 1996 RSNA
scientific
received
November
11; accepted
November
2041 Georgia
assembly.
13.
Address
Aye, NW, Washington,
DC 20060.
Received
August
21, 1997; revision
reprint
requests
to the
re-
author.
151
Incident
beam,
unattenuated
Ionization
Incident
beam
Attenuated
beam
chamber
Lj
Figure
1. Diagrams
show
an unattenuated
x-ray beam
(top) and an x-ray beam passing through
a foil (bottom)
into detectors.
attenuation
and the
ize it, (b) the factors
(c)
(d)
exponential
concepts
monochromatic
beams,
and
sunements
terms
used
that affect
and
their
The thickness
in different
meters,
the
OF ATTENUATION
is the
reduction
of the
intensity
beam
as it traverses
matter.
may be caused
by absorption
process,
energy
is transferred
tons to atoms
of the target
or by deflection
beam
(scatter).
In the example
of photons
of
The re(in this
from
the
or irradiated
from
of x rays
x rays
with
foil.
The intensity
through
a layer
the
passing
then
(b) without
the
detector,
one obtains
of the interaction
material
contained
in
the
pends
on the
of an x-ray
of attenuating
thickness
and
beam
passing
material
detype
U
Imaging
& Therapeutic
Technology
for
meter
of radiation
be expressed
example,
squared,
thickness
attenuation
coefficient,
symbolized
letter
.t, is the
fractional
change
intensity
ating
given
of an absorbing
per
material
material:
the
thickness
because
of
by a
linear
Greek
ray
and
is a measure
attenuated
given
material.
of the
The
by the
in x-
attenu-
of interactions
in a
=N/NAx,
of material.
N
from the
Equation
chosen
is the
number
x-ray
beam
(1), for any
so that
the
moved
from
the
the total number
(1)
of photons
in thickness
given
Ii, Ex
number
removed
\x. In
must
be
of photons
The linear
sured
in units
most
commonly
re-
beam
is much
smaller
than
of photons.
As the thickness
of the attenuating
material
increases,
equation
is no longer
correct
and the
tionship
becomes
nonlinear.
attenuation
of pen unit
expressed
the
rela-
coefficient
is mealength,
which
is
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
sity of the material
152
can
the
and some
photons
may be scattered
(Fig 1). If
one measures
the intensity
of the beam
(a) aften it has been attenuated
by the foil and as it
of the
per
phoma-
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
strikes
the detector
and
foil and as it strikes
the
a quantitative
measurement
kilograms
quantity
where
of a beam
of a material
units
of measure,
electrons
pen meter
squared.
An attenuation
coefficient
significance.
U DEFINITION
terial)
to characterattenuation,
attenuation
relationships,
involved
in the attenuation
of
and polychromatic
x-ray
(e) half-value
layer
(HVL)
mea-
Attenuation
an x-ray
duction
Foil
coefficient
by the denthrough
which
the pho-
Volume
18
Number
1
Table 1
Relationships
among
the
Attenuation
Coefficients
Units
Coefficient
Relationship
Linear
(li)
Mass
(11a)
number
Ne
-
Table 2
Physical
/atom/cm2
atom/cm2
/electron/cm2
electron/cm2
of Selected
Effective
Number
Material
Water
Ice
Water
bone
=
Data
-
pass
from
and
reference
thus
bol pjp. Mass
rate of photon
Atomic
(Z)
is independent
50 keV Linear
Coefficient
1.0
0.917
0.000598
0.214
0.196
0.000128
1.85
0.00129
0.573
0.00029
0.91
0.193
by the
sym-
is the
area mass
physical
state
efficient
FACTORS
ATION
ten squared
Several
related
coefficient
thickness
Other
thickness
pressed
per unit
unit
is the inverse
is measured.
attenuation
and
in which
of the
are
coefficients,
attenuating
as the number
area,
respectively.
atomic
of the
coefficients
atomic
among
the attenuation
in Table
1.
The
the
is measured
is gram
per centimeter
(the mass
of a 1-cm2 area of mate-
na!). The
in which
tronic
since
attenuation
fraction
of an incident
beam
that is attenuated
the
the
unit
coefficient
January-February
mass
attenuation
of atoms
per
1998
mass
at-
of elec-
AFFECTING
factors
to the
others
affect
attenuation.
Some
are
x-ray
beam
or radiation
and
to properties
which
the
dude
beam
ATTENU-
of the
radiation
matter
is passing.
energy,
the
The
number
through
factors
in-
of photons
traversing
sorber,
the
is ex-
atomic
greater
number
of the absorber.
As noted,
the
the thickness
of the attenuating
mate-
rial,
is shown
1’a
is the
x-ray
or gamma
ray
by a single
atom
(ie,
coefficient
by the
gram.
The electronic
the
the
attenuating
density
greater
as the atomic
nial increases,
the probability
that an absorber
atom
will interact
with
one of the photons
in the beam).
The atomic
coefficient
is obtained
by dividing the
number
the
number
elec-
of electrons
or atoms
The relationship
coefficients
by the
the
in which
medium
by dividing
coefficient
gram.
of
U
(cm2/g),
is obtained
tenuation
trons
per
the material.
The typical
unit of the mass
attenuation
coefficient
is per gram
per centimethickness
squared
Attenuation
(cm1)
I.
coefficient
per unit
of the
number.
Density
(g/cm3)
is represented
attenuation
interactions
atomic
Materials
5.92
Note.
and
Z
13.8
7.64
Fat
tons
gram,
7.4
7.4
7.4
vapor
Compact
Air
per
is
cm
g/cm2
P4/Ne
of electrons
Properties
Thickness
Measured
l1IPZINe
i/
(lie)
in Which
Coefficients
/cm
/g/cm2
J.t/p
Electronic
Note.
of the
. . .
(lt/p)
Atomic
Units
medium
of the
is the
absorber,
attenuation.
or aband
Similarly,
number
or density
of the
the attenuation
produced
given
thickness
terials
different
such as water,
fat,
linear
attenuation
increases.
Thus,
different
2; Figs
mateby a
ma-
bone,
and air have
coefficients,
as do
the different
physical
states
or densities
material,
such
as water
vapor,
ice, and
(Table
the
of a
water
2, 3).
co-
McKetty
U
RadioGraphics
U
153
I
f
ZA>ZB
U,
I
E1>E2
C
a
C
a, 0.5
0.5
.
>
Energy
E1
a,
a,
0
0
5
0
10
Thickness
Thickness
(cm)
2.
(cm)
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
energy on x-ray attenuation.
As photon
energy
increases,
the attenuation
produced
by a given thickness
of
absorber
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
thickness of absorber.
To understand
the relationship
attenuation
and energy,
one must
with
three
of the basic
interactions
gamma
Compton,
distribution
of energy
between
the recoil
electron
and scattered
photon
depends
on
the energy
of the incident
photon
and the
nays with
matter:
photoelectric,
and pair production
interactions.
In a photoelectric
lides
between
be familiar
of x and
with
interaction,
an atom
and
angle
of emission
The probability
a photon
causes
col-
will
to
ergy.
an electron
occur
with
in en-
can
of the incoming
energy
of the
photon
is greater
than 1.02 MeV.
Therefore,
this interaction
does not occur
in the energy
closely
bound
the
photon
electron.
electron,
the
higher
is its
the energy
The probability
that a photoelectric
most
likely
when
will
of the
and
interaction
the energy
the
binding
energy
energy
approximately
with
Thus,
and
when
free electron
orbital
shell.
angle
tion.
and
varies
The
as Z3.
the pho-
decreases.
and
The
causes
photon
therefore
energy.
incident
electron,
which
from
its
at an
in a new
on scattered
The
photon
a
direc-
photon
has
remainder
of the energy
is transferred
to the
is called
a recoil
electron.
The
Technology
used
and
attenuation
The probability
occur
decreases
be periodic
of the
for
are
bound.
diagnostic
interactions
in the
that
diagnostic
energy
either
interaction
as photon
energy
the
K absorption
beam
attenuaeffect
rapenergy,
there
in the
the
binding
Additional
energies
gies
energy
which
of the
absorption
that correspond
of more
At
each
increase
energy
attenuation.
loosely
coneelectrons
at which
or increases
edge,
in-
in the photoelectric
the decrease
in
Although
photoelectric
increasing
highest
jumps
beit
ra-
Compton
increases
The
attenuation
but
incident
The jumps
on increases
in attenuation
spond
to the orbital
shells
in which
abrupt
& Therapeutic
beams
Compton
scattering.
tion caused
by the
idly decreases
with
shells.
Imaging
energy
creases,
but the decrease
effect
is more
rapid
than
may
it to move
is deflected
travels
deflected
reduced
of the
will
ocwith
if the
of x-ray
produce
range.
elec-
interaction
on scattering
an incident
photon
collides
only
involves
an interaction
an atomic
nucleus,
and
diology.
Photoelectric
The probability
of a
varies
with photon
as l/E3
interaction
A Compton
curs
of the
occur
range
of
occur
is
incoming
atomic
number
(Z) approximately
as photon
energy
is increased,
toelectric
Pair
tween
minus
the
The more
binding
energy;
consequently,
the ejected
electron
is lower.
production
a photon
an increase
energy
binding
tron are nearly
the same.
photoelectric
interaction
U
decreases
photon.
interaction
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
photon
154
of the scattered
that a Compton
the
is known
as
corresponds
K-shell
to
electrons.
edges
exist at lower
to the binding
enerbound
absorption
electrons
edge,
in outer
there
is an
in attenuation.
Volume
18
Number
1
100
0
Lead
Nal
a)
Water-
C
5)
8
10
I
C
0
Ca
C
-
. -.
Photoelectric
-
-
-
Air
-
-
Compton
-
Rayleigh
C’,
0)
-
a)
. -
Pair
.
E
Ca
U)
U)
Ca
C)
E
0.1
.
Ca
0
0.01
0.01
0.
10
Energy
Energy
(MeV)
Figures
4, 5.
Graph
(4) Mass
shows
of about
attenuation
the variation
for photons
in air.
Photoelectric
coefficients
of si/p
Graph
the
interactions
interactions
production
interaction
very high energy
terials
with
large
interaction
and
important
only
in the
(60 keV-2
of atomic
of each
for
a
intermedi-
and
their
coefficient
interac-
cross-sectional
as a function
and
coefficient
the total
for
5). The
region
tant.
is
where
t
=
classical,
tions.
x
equation
(<30
ray
energy
becomes
plotted
keV),
to the
mass,
electronic,
with
photoelectric
in soft
tissue
is increased,
the predominant
versus
photon
the K absorption
edge,
crease
in the attenuation
1998
effect
and
bone.
Compton
energy
curve
low
and
ener-
is most
As the
If
soft
t
the
mass
there
will
coefficient.
slowly
effect
io-
in the
is impor-
attenuation
coeffi-
range
of energies
used
in x-ray
to optimize
the
diagnostic
and
by the
to minimize
the
patient.
these
importance
of their
large
increase
the
Both
of linear
and
the
data
coefficoeffiimagx-ray
radiation
attenuation
and tissues.
contain
attenuation
visibility
the
factors
coefficients
mass
attenu-
coefficients,
which
of anatomic
contrast
agent.
structures
The
increased
attenuation
is caused
by the atomic
number
and K absorption
edge
of the contrast
agent
is
tis-
being
in-
of x rays
must
rial
a large
fall rapidly
with
of the rapid
deeffect.
However,
sodium
ation
coefficients
can be demonstrated
in several clinical
situations.
Contrast
agents
that
contain
iodine
and barium
are used
because
that
x-
scattering
interaction.
for air,
for
is chosen
The
appropriate
number
of energy.
curves
decrease
more
in which
the Compton
cients.
The
and
interac-
performed
sue, and lead,
the curves
creases
in energy
because
crease
of the photoelectric
January-February
the
coefficients
atomic
an increase
at 33 keV because
binding
energy
is 33 keV for
depend
on the mass
of various
materials
K,
production
with
attenuation
information
Compton
pair
subscripts
applies
atomic
coefficients.
In radiography
important
+
photoelectric,
and
This
c
an effective
as a function
Because
ing
values:
=
(with
energy.
attenuation
iodine
(Figs 4, 5). The attenuation
curve
for
lead will show
an increase
at 88 keV (Figs 4,
absorbed
totaI
air
attenuation
the
of photon
air. (5) Mass
cients
do not depend
on density
and
physical
state
of the absorber,
numeric
are often
expressed
in terms
of these
cients,
rather
than
linear
attenuation
tion is proportional
to the cross
section
for
that process.
Cross section
is defined
as the
probability
that a particular
reaction
will oc-
tions
water,
dide will show
the K electron
MeV)
for all manumber
(1). The
type of interac-
cur. The total linear
attenuation
equal
to the sum of the individual
materials
lead,
ample,
and
Pair
(5-100
MeV)
and manumbers.
Compton
is predominant
ate energy
range
tenials,
regardless
relative
probability
attenuation
x rays
to 50 keV)
numbers.
is important
range
atomic
selected
iodide,
mass
with
are
range
(up
large
atomic
for
for sodium
displays
7.6) for specific
for a low-energy
materials
with
gies
(MeV)
5.
4.
tissue.
greater
than those
In cases
in which
with
of the surrounding
the penetration
be reduced,
a shielding
attenuation
coefficient
mateis
at
be an inFor ex-
McKetty
U
RadioGraphics
U
155
Transmission-.l000
800
.n
.
,-
a,.
640
____
_____
______
____
512
a,..
.
p:-.
...
N
‘5
a,.
:5
,,
Figure
6.
Exponential
relationships.
duces
Each
absorber
the transmission
20%.
if one
starts
.; .
attenuation
re-
of x rays
with
1,000
Attenuation
by
____
Shielding
tenials
lead.
with
atomic
U EXPONENTIAL
getic
rays
ma-
number
of photons
as
energy)
measured.
is the quantity
Exponential
by using
number,
such
of a monoener-
beam
number
dent on an absorber,
transmitted
through
the
the
and
into
Ex
ing
a more
are
ferentials
solved
very
of photons
and the
expression
j.t
must
be trans-
convenient
small,
=
plot
form.
they
are
If N
known
as dif-
=
paper,
I et
(2)
N e,
(3)
0
where
I
=
thickness
beam
beam
of zero,
intensity
sonben
x
equations
attenuation
tensity
agnostic
by any
the
incident
or photon
radiology,
& Therapeutic
thickness,
through
of x, e
base
.t
attenuation
system,
cient,
N = number
and N0 = number
These
absorber
I
be used
thickness
and
natucoeffi-
number
of material
photon
is measured.
photon
intensity
Technology
inIn di-
(ie,
logarithm
the
be ob-
of the number
linearly
with
material;
of I/I,,
is plotted
line graph
will result.
to as a semilogarithmic
axis
is logarithmic
beams
energies.
photon
6. If
and
contain
With
energy
the
a spectrum
an x-ray
beam,
is determined
the
by
kilovoltage
(kVp)
used
to generate
Because
of the spectrum
of photon
the transmission
of a polychromatic
an absorber
Equation
higher
does
(3). When
not
through
an absorber,
are attenuated
more
energy
strictly
a polychromatic
photons;
photons
of
rapidly
than
therefore,
both
photons
and the
with
increasing
amounts
of an absorber.
A semilogarithmic
plot of the number
of photons
in a polychro-
to calculate
transmitted
will
the number
of transmitted
quality
of the beam
change
of transmitted
photons,
of incident
photons.
may
curve
through
follow
the
an abof the
an exponential
one
beam
passes
low energy
at an absorber
transmitted
of thickness
nal logarithm
when
0
intensity
linear
other
linear.
Polychromatic
beam
=
of x on
its
num-
in Figure
7). The logarithm
transmitted
varies
of the attenuating
because
by
as a function
if the
the peak
the beam.
energies,
weighted
that is most
often
reduction
in the
is demonstrated
plotted
of photon
maximum
equations:
N
Imaging
5
in a beam
against
x, a straight
This plot is referred
and the differential
equation
is
by using
calculus
to give the follow-
I
U
I/Jo
therefore,
and
156
of photons
tamed
(Fig
of photons
the thickness
of x or gamma
of photons
inci-
number
absorber,
absorber
thickness.
The
Lx previously
discussed
formed
ben
graph
measurements
of tissue
Thickness
ATTENUATION
(monochromatic)
depend
on the
“.
20%
N(x)=N0e
RELATIONSHIPS
Attenuation
20%
pho-
is achieved
a high
a,
20%
tons, the first absorber
will reduce
the number
of photons
to 800; the
second,
from 800 to 640; the next,
from 640 to 512; and so on to an exponentially
diminishing
number
of
photons.
required.
-
..
matic
beam
of the
straight
initial
attenuating
materials
will not be a
line but will be a curve
(Fig 8). The
slope
of the curve
is steep
because
the
low-energy
as a function
photons
the beam
becomes
slope
decreases.
for
polychromatic
tion
is shown
are
of the
thickness
attenuated,
but,
more
monochromatic,
A comparison
of the
and
in Figure
as
the
curves
monochromatic
radia-
9.
Volume
18
Number
1
Linear
Scale
Semi-log
1000
U,
U,
C
a
Scale
1000
800
C
2
0
0
800
100
E
E
400
U,
C
#{149}1
C
a,
a,
I-
200
Figure
0
10
0
4
8
12
16
20
0
4
8
cm of water
12
16
20
Attenuation
Semi-log
4
5
of
radiation
plotted
on a linear scale
semilogarithmic
scale.
cm of water
100 kVp spectrum
2.5 mm Al Inherent
I mmAlinciema,ts
7.
monochromatic
and
Scale
filtration
100
C
0
U,
Ce
E
U,
C
a,
IC
a,
U
a,
0.
30
40
50
80
70
80
90
10
100
Energy(keV)
0
Increase
in effective
energy (keV):
48.5. 50.2.51.7,
53.0, 54.1
Figure
8.
Attenuation
1
2
Absorbflr
of polychromatic
radiation.
3
(mm Al)
thickness
Photons
of low
en-
ergy are attenuated
more rapidly
than the higher-energy
photons,
resulting in a change
in the number
of photons
with increasing
amounts
of absorber
and a change
in the quality
of the x-ray beam. This is illustrated
in
the left graph of a bremsstrahlung
spectrum,
progressively
attenuated
by
1 mm aluminum
filters. A semilogarithmic
plot of the number
of photons
in a polychromatic
beam as a function
of thickness
of the attenuating
material
will
be a curve,
as shown
in the
right
graph.
1000
-
U,
C
100
keV
monochromatic
0
0
100
important
U,
10
I 00
C-
kVp
polychromatic
0
1I20
cm of water
shows
a comparison
and monochromatic
point
electron
volt
x-ray
photon
E
C
Figure
9.
Graph
for polychromatic
here
is substantially
rable
x-ray
photon
1998
more
beam
produced
lung spectrum
are composed
energies
than the peak
energy,
nificant
increase
in attenuation,
reference
between
penetrating
tive energy,
-40 keV, depending
beam).
Most of the x-ray photons
on the semilogarithmic
January-February
is the comparison
kilo-
and peak
kilovoltage.
A monoenergetic
beam
at 100 keV (effective
energy,
keV)
from
of the curves
radiation.
An
2 and
graph
reprinted
McKetty
than
at 100
100
a compakVp
(effec-
on filtration
of the
in a bremsstrah-
of substantially
lower
thus resulting
in a sigwhich
is nonlinear
illustrated.
with
(Redrawn
permission.)
U
RadioGraphics
U
157
Narrow
Figure
10.
Diagram
beam
geometry
demonstrates
the ideal setup for measurement
of
HVL. The sensitive
volume
of the
exposure
meter is positioned
on
the axis of the x-ray beam, at a
minimum
of 50 cm from the collimator and from the walls and
floor. The x-ray beam should
be
collimated
tightly
around
but totally
include
the
of the radiation
U HVL
sensitive
50 cm
HVL
used
Detector:
volume
chamber
detector.
MEASUREMENTS
collimator
in each energy
interval.
However,
or half-value
thickness
is the concept
most
often
to describe
the penetrating
or beam-defining
unit
so that
system
radiation
added
absorbers
is avoided.
no scattering
material
in the
the
of the
scattered
x-
from
There
vicinity
detector,
which
should
be at least
the walls
or floor.
The x-ray
beam
about
5 x 5 cm at the detector
and
the
should
be
of the
50 cm
should
should
from
be
completely
include
the detector.
The conditions
a standard
the HVL measurements
referred
to as narrow-beani
ditions
of good
geometry.
should
be made
are
conditions
or conThis is in contrast
to broad-beam
in which
material
that
for
or attenuators
measurement
tween
the
x-ray
the
at energy
be expressed
The HVL of an x-ray
measuring
the exposure
generator
reduces
At energy
levels
usually
measured
meters
of aluminum;
400 kV, HVLs
may
tens of copper.
beam
rate
beam
levels
of 120in millimeis obtained
by
from
the x-ray
a series
of attenuating
placed
is made
in the beam.
The
with
no attenuator
source
and
and should
not contain
for HVL measurements
materials
detector,
first
beand
impurities.
is shown
It should
be at least
& Therapeutic
exposure
of the x-ray
50 cm
Technology
from
the
just
sensitive
described
conditions,
of photons
from
into the detector.
the
to ensure
reach
mitted
shows
that
the
two
tions.
A graph
types
is made
or y axis)
and
the
of
under
which
a large
are
scattered
be
condi-
only
that
photons
primary
photons
transmaterial.
Figure
11
of measurement
of exposure
readings
thickness
(abscissa
to one-half
corresponding
condi-
of the
(orat-
or x axis).
The xthe original
inthickness
of
the attenuating
mined.
Results
material
(ie, HVL)
are
of a typical
measurement
nies are
in Figure
shown
x-
should
always
geometry
versus
tenuating
material
ray intensity
equal
tensity
the
the detector
are
by the attenuating
volume
a small
distance
and detector.
a large
number
absorber
HVL measurements
made
under
narrow-beam
dinate
The sensitive
volume
of the
meter
is positioned
on the axis
Imaging
at-
the
ray beam
is used
and only
exists
between
the absorber
With
broad-beam
geometry,
tions
The setup
in Figure
10.
beam.
in-
below
in mlii-
then measurements
are made
for successively
thicker
attenuating
materials.
The
tenuators
should
have
constant
composition
U
ray
ability
of x-ray
beams
of different
energy
1evels and the penetration
through
specific
matenials.
The HVL
is defined
as the thickness
of
tensity
to one-half.
120 kV, HVLs
are
158
or Al)
ionization
The penetrating
ability
or quality
of an x-ray
beam
is described
explicitly
by its spectral
distribution,
which
indicates
the energy
present
(Cu
or more
deterse-
12.
Volume
18
Number
1
Collimator
Collimator
Attenuator
I,
Source
Source
----p
Scattered
not
Detector
Detector
IN
Narrow-Beam
photons
Absorber
detected
Broad-Beam
X-ray
mmCu
3
.1
0
100
I iS
82
63
51
to en(unat-
permission.)
Filtration
exposure
conditions
only primary
tenuated)
photons
reach the
detector.
(Redrawn
from reference
3 and reprinted
with
Geometry
(mm)
0
geometry
sure that
arc
scattered into the
detector
Geometry
thickness
Figure 11.
Diagrams
illustrate the geometry
for narrow-beam
and broad-beam
conditions.
HVL measurements should
always
be
made under
narrow-beam
Attenuator
3
.1
Exposure
rate
R man
UVI.
mm
Cu
0.35
1.3
1.8
68
20
11.4
7.6
5.5
2.3
2.7
38
29
120
E
E
100
10
;8o
Ce
0
0.
60
‘C
a,
>.
a,
*
20
0
I
0
1
Absorber
2
thickness
3
4
(mm
5
01234567
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
mdicated
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
redrawn
from
reference
1 and reprinted
with permission;
left graph
redrawn
from
reference 4 and reprinted
with permission.)
January-February
1998
McKetty
U
RadioGraphics
U
159
I 00
I 00
75
‘I)
E
a
Broad
50
11)
25
0
rge
Filter
deor
sotwce
Ui
0
(A)
tector
near
(B)field
‘Small
field
10
0
1
01234567
2345
Thickness
(cm)
(mm Cu)
Filtration
13.
Attenuation
curves
and HVLs
for narrowand broad-beam
geometry.
Broad-beam
conditions
will indicate
a greater
penetrating
power
of the beam (ie, a
greater
HVL or haif-value
thickness),
which
is not truly representative
of the actual
value. This result
is chiefly
due to attenuation
caused
by scatter,
which
reaches
the detector in broad-beam
or poor geometry
conditions
because
either the field area is too
large or the attenuating
material
is too close to the detector,
as shown
in the right graph
Figure
and
diagram.
Right
graph
shows
the
results
for
the
filter
near
near the source for a small field and a large field. (Values
SI units with the factor 10 R/min
2.58 x 10 C/kg/mm.)
ment conditions
are varied,
one can obtain four different
=
dicates
an HVL
ditions.
A complete
tial
for
routine
of 2 cm
(Modified
attenuation
curve
dosimetry;
rather,
with
from
reference
is not
essen-
thicknesses
of the attenuating
material
exposure
rate to slightly
that reduce
the
more
than haif and
to slightly
are
less
than
half
narrow-beam
required.
The
difference
in apparent
attenuation
for broad
and narrow
beams
is seen in Figure
13. Unden broad-beam
conditions,
the beam
will appear to have
greater
penetrating
power
(ie, a
greater
HVL
were
measured
or half-value
thickness)
with
narrow-beam
than
if it
geometry.
1 and
geometry
reprinted
(ie, if the
detector
and
the
filter
2.8 cm
with
broad-beam
to
incon-
permission.)
thickness
of the
absorber
is 1 HVL),
then:
1/10
-
0.5;
1/10
=
0.5
therefore,
If the
natural
of the
exponential)
of the
equality,
U RELATIONSHIP
LINEAR
CIENT
and
with
the
for R/min
can be converted
Note that as four measureapparent
HVLs. Left graph
OF HVL AND
ATTENUATION
COEFFI-
e’-
=
logarithm
(inverse
function
is calculated
for
each
side
in [0.5]
=
in
-0.693
=
jiHVL
=
0.693/si
(4)
0.693/I-IVL.
(5)
HVL
For a monoenergetic
beam
of x-ray
or gamma ray photons,
it was already
determined
in Equation
(2) that I
I0e.
When
x
HVL
l
[e”-]
=
Thus,
knowledge
calculation
of the
of the
HYL
“effective”
allows
ficient,
and similarly,
knowledge
tive attenuation
coefficient
allows
nation
of the HVL of the radiation
is particularly
160
U
Imaging
& Therapeutic
Technology
important
the
attenuation
for
coef-
of the effecthe determibeam.
This
polychromatic
Volume
18
Number
1
given:
HVL
2.4
mm
cm
= 0.24
=
t
Al
0.693
I
HVL
0.693/0.24
=
cm
Al
Figure
Energy
(keV)
interpolate
10
70.74
15
21.33
20
9.153
values
table
to estimate
Energj
3.024
2.888
30
40
Eff:
(keV)
30
30.9
?
ear
0.748
80
0.543
I 00
1.525
spectra
with
pends
on the
a variable
attenuation
energy
intensity
that
and
Energy
of
the
be easily
calculated
from
coefficient
for a monoen-
the
0.459/cm,
then using
0.693/j.t,
the HVL for
or 1.51 cm.
x-ray
ray
For a polychromatic
tube),
the attenuation
explicitly
known.
ment
etry
of the
HVL
methods
with
allows
fective
attenuation
ing material
for
situation,
a measure-
narrow-beam
determination
coefficient
the specific
geomof the
VALUE
The tenth-value
of a material
ef-
of the attenuatpolychromatic
tensity
by a factor
10%
(TVL)
reduce
of 10 (90%
in-
attenuation,
transmission):
TVL
is often
=
0.1
=
eMW
TVL
= 2.303/si.
used
for
shielding
calcula-
tions,
in which
barriers
can be specified
in
the number
of TVLs.
The shielding
calculations
determine
material
working
ray
the
amount
that
beams
(which
effective
energy
of a monoenergetic
is attenuated
in other
spectrum
energy
the
contain
penetrafor each
of an x-ray
beam
at the
same
en-
beam
is
of pho-
rate
as the
words,
that has the same
of photons
in the beam.
is about
30%-50%
of peak
energy.
if the HVL and mass
cients
or linear
attenuation
material
are
of a polychromatic
(Fig 14). First, the
attenuation
coefficients
known,
the
beam
can
“effective”
coeffifor a
effective
energy
be calculated
linear
attenua-
discussed.
tabulated
energy
This
value
is then
values.
To detervalue,
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 interpolation
I/I,
energy.
OF EFFECTIVE
x-ray
HVL
previously
compared
with
mine
an accurate
is the thickness
the incident
valji
tion coefficient
is determined
on the basis of
the HVL through
the relationship
of .t and
LAYER
layer
will
that
tons
given
beam.
U TENTH
versus
of photon
energies),
thus the HVL is different
beam,
HVL
as the
The effective
beam
(eg, from
an xcoefficient
is not
In this
keV
polychromatic
a spectrum
tion and
ergy. The
the energy
HVL
is 0.693/0.459
is determined
ENERGY
ergetic
photon
beam
and vice versa.
For example,
if the linear
attenuation
coefficient
for
aluminum
at an energy
level of 100 keV is
the equation
aluminum
coeffi-
from interpolating
ues in the table of
U DETERMINATION
de-
filtration
For
beam.
The HVL can
linear
attenuation
30.9
=
attenuation
energy
40
Effective
0.459
Illustra-
cient j.t with Equations
(4) and (5). Effective
50
60
14.
tion shows how effective energy
can be determined
by measuring HVL (eg in millimeters
of aluminum)
and calculating
the lin-
is “automatically”
determined
by using
the effective
mass
case, the effective
attenuation
value.
In this
energy
value
is determined
at the
of the
intersection
the effective
(Fig 15).
mass
attenuation
attenuation
curve
coefficient
and
value
of attenuating
required
to protect
individuals
with
or near
radiation
sources
or x-
units.
January-February
1998
McKetty
U
RadioGraphics
U
161
U HOMOGENEITY
The
homogeneity
used
coefficient
in addition
of beam
to the
quality
for
A monoenergetic
cording
if the
first
C
U
5
spectra.
is attenuated
attenuation
reduces
the
aclaw.
beam
U
2
C
0
getic
equal.
low
a second
HVL
to one-quarter.
beam,
the
first
will reduce
it by oneWith
a monoenen-
and
second
With
a polychromatic
energy
are attenuated
photons
of higher
HVLs
beam,
more
energy.
The
are
photons
rapidly
0.5
second
-
cient
for
the
the
homogeneity
coef-
homogeneity
a polychromatic
beam
coeffi-
is less
than
iii
=
=
=
=
=
-
-
-
-
-
10
20
i:
ii
=
-
ii
iii
iii
=
EEE
=
=
=
-
=
-
-
-
-
15.
30
40
Energy (key)
Illustration
shows
can be determined
terpolation.
-
HVL
is called
It follows
that
0.1
Figure
the thickness
required
to reduce
the penetration
to one-quarter)
is larger
than
the first
HVL.
The ratio of the two HVLs
first HVL/
ii
0.2
U,
U,
ergy
(ie,
second
ficient.
a,
E
HVL
T1 S
-
a,
of
than
ii
I
a,
to
C
one-half,
half again
attenuation
I I I I I I I I
10
a,
as a descriptor
polychromatic
HVL
20
is sometimes
HVL
beam
exponential
to the
Thus,
Aluminum
COEFFICIENT
HVL
50
how
with
‘
60
effective
en-
use of graphical
is measured
in the
same
inway
as
in Figure
14 (eg, in millimeters
of aluminum),
and
the linear attenuation
coefficient
is calculated
with
Equations
(4) and (5). The correct
energy
is determined
from the graph at the intersection
of the attenuation
curve and the effective
mass attenuation
coefficient
value.
one.
U EFFECTS
Diagnostic
and
OF ADDED
x-ray
the
mean
beams
energy
FILTRATION
are
polychromatic,
is approximately
30%-
50% of the peak
energy.
As a polychromatic
beam
passes
through
matter,
the low-energy
photons
are
attenuated
high-energy
photons
of the
increases.
tive
ness
beam
energy
that
of attenuating
hardening.
the patient
more
and
The
tient.
purpose
tion
primary
is to remove
the
the
filtra-
photons
that
are not energetic
enough
to reach
the film.
these
photons
are not removed
by a filter,
they
will
will expose
the patient
to radiation
but
not arrive
at the film to form
the radio-
graph.
oil,
the
If
U
Imaging
deliberately
added
filtration.
In diagnostic
is usually
Technology
consists
the x-ray
envelope
sunin the x-ray
exit
to the
used
window
of absorbers
beam
to
radiology,
for
added
filtra-
but compound
filters
containing
copper
aluminum
or other
materials
may be
used.
The filter is positioned
of the x-ray
tube between
the
collimator
also adds
assembly.
The
to the filtration.
collimator
The total
of added
filtration
is specified
in the exit port
housing
and
assembly
amount
in terms
of
aluminum
equivalent
thickness
and, in a
typical
x-ray
unit,
is about
2-3 mm aluminum
equivalent
thickness,
1 mm of which
from
the
tion adds
lent.
Added
& Therapeutic
the
that
are
filtration
and
Added
is
collimator
assembly.
Inherent
filtraabout
0.5 mm aluminum
equivafiltration
tages:
(a) it alters
trum,
(b) it causes
ergy of the x-ray
162
and
insulating
when
glass
cathode
or port.
tion,
and
by (a) inherent
and (c) the pa-
low-energy
tube,
aluminum
thickbeam
whether
cause
the
of added
occurs
by the
provide
energy
in effec-
increasing
is called
Therefore,
any absorber,
or an added
filter,
will
is filtered
filtration,
than
effective
increase
occurs
with
material
beam
to harden.
The x-ray
beam
filtration,
(b) added
The
rapidly
the
Inherentfiltration
beam
is attenuated
rounding
the anode
provides
several
advan-
the shape
of the x-ray
speca shift in the effective
enbeam
by selectively
remov-
Volume
18
Number
1
tages.
The
NCRP
values
are
shown
in Table
>.
3. HVL
indicate
U,
C
a,
measurements
and values
if these
filtration
criteria
are used
are met.
to
C
Figure
16 demonstrates
filtration
a,
on
the
effect
a polychromatic
of added
x-ray
beam.
a,
U CONCLUSIONS
One
a,
of the
technical
principles
on which
radi-
a,
ography
0
20
40
60
Photon
Figure
16.
added
filtration
Graph
ence
x-ray
2 and
reprinted
Tube
Potential
(kVp)
Below
the effect
energy
and
(Modified
with
permission.)
Total
from
essential.
penetrating
refer-
ferent
0.5 mm
Filtration
1.5
-
mm
1.
Mo for
target
2.5 mm
Recommended
by
NCRP
beam
the
ray
beam),
beam,
and
(f)
dose.
(ie, the
total
number
(d) it increases
(e) it decreases
it improves
A disadvantage
that it necessitates
factors
(kilovolts
compensate
for the reduction
the beam.
The National
Council
on
tion and
mended
mandated
ray
tubes
Measurements
and other
minimum
operating
for
filtration
at certain
values
to
of
1998
figures.
HE,
Cunningham
radiation
of radiology.
JR. The
with
4th
interaction
matter.
ed.
In: The
Springfield,
of
phys-
Ill: Tho-
4.
5.
JE, Murry
RC Jr. Attenu-
of radiation
with
physics
of medical
matimag-
protection.
3rd ed. St Louis,
1984; 173-181.
National
Council
Measurements.
and
gamma-ray
on Radiation
Medical
x-ray,
protection
50 MeV (equipment
use).
NCRP
report
NCRP,
1989.
design,
no. 102.
Mo:
Protection
electron
for energies
performance,
Bethesda,
1994;
Mosby,
and
beam,
up to
and
Md:
Protecrecomhave
for
x-
kilovol-
This article meets the criteria for I .0 credit hour in category
To obtain credit, see the questionnaire
on pp 145-150.
January-February
of
nar-
ing. Baltimore,
Md: Williams
& Wilkins,
17-38.
Bushong
SC. X-ray
emission.
In: Radiologic
science
for technologists:
physics,
biology,
and
is
in intensity
peak
concept
under
3.
a given
filtration
Radiation
the
Boone JM. Interaction
ter. In: The essential
in
of exposure
seconds)
(NCRP)
has
regulatory
bodies
the
be measured
conditions.
ation.
In: Christensen’s
physics
of diagnostic
radiology.
4th ed. Philadelphia,
Pa: Lea &
Febiger,
1990; 70-92.
Bushberg
JT, Seibert
JA, Leidholdt
EM Jr.
(7).
of photons
of added
the increase
or milliampere
is by using
the
dif-
2.
aluminum
quality
underthe units
affecting
it is
mas, 1983; 133-164.
Curry
TS III, Dowdy
the H\TL of an xpatient
exposure,
image
Johns
ics
ing more
low-energy
photons
than high-energy photons,
(c) it reduces
the intensity
of
the
tubes
an
way of expressing
of x-ray
beams
from
in preparing
ionizing
mo-
aluminum
70
in attenua-
U REFERENCES
aluminum
tubes)
50-70
difference
Acknowledgments:
The author thanks Diana M.
Roach for her assistance
in the preparation
of the
manuscript,
and J. Anthony
Seibert,
PhD, for as-
for
(0.03 mm
lybdenum
Note.
x-ray
sistance
50
Above
A practical
ability
HVL,
which
must
row-beam
geometry
Filtration
Total
is the
tion by different
materials;
thus,
standing
of attenuation
probability,
for describing
it, and the factors
of a
of
intensity
beam.
Table 3
Required
Minimum
X-ray Tubes
Operating
(key)
demonstrates
on the
polychromatic
Energy
100
80
is based
I of
f/ic
AMA
Physician
McKetty
‘s Recognition
U
Award.
RadioGraphics
U
163