Radiation Penetration
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Transcript of Radiation Penetration
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Radiation PenetrationPerry Sprawls, Ph.D.
Online
Textb
ook
Table of
Contents
CHAPTER CONTENTS
INTRODUCTION AND OVERVIEW
PHOTON RANGE
HALF VALUE LAYER
Determining HVL Values
X-RAY BEAM QUALITY
FILTRATION
PENETRATION WITH SCATTER
PENETRATION VALUES
INTRODUCTION AND OVERVIEWCONTEN
TS
One of the characteristics of x- and gamma radiations that makes them useful for
medical imaging is their penetrating ability. When they are directed into an object,
some of the photons are absorbed or scattered, whereas others completely penetrate
the object. The penetration can be expressed as the fraction of radiation passing
through the object. Penetration is the inverse of attenuation. The amount of
penetration depends on the energy of the individual photons and the atomic number,
density, and thickness of the object, as illustrated below.
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Factors That Affect the Penetration of Radiation through a Specific Object
The probability of photons interacting, especially with the photoelectric effect, is
related to their energy. Increasing photon energy generally decreases the probability
of interactions (attenuation) and, therefore, increases penetration. As a rule, high-
energy photons are more penetrating than low-energy photons, although there are
limits and exceptions to this, which we discuss later.
PHOTON RANGECONTENT
S
It might be helpful in understanding the characteristics of radiation penetration tofirst consider the range, or distance, traveled by the individual photons before they are
absorbed or scattered. When photons enter an object, they travel some distance before
interacting. This distance can be considered the range of the individual photons.
A characteristic of radiation is that all photons do not have the same range, even
when they have the same energy. In fact, there is no way to predict the range of a
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specific photon. Let us consider a group of mono-energetic photons entering an
object, as shown below. Some of the photons travel a relatively short distance before
interacting, whereas others pass through or penetrate the object. If we count the
number of photons penetrating through each thickness of material, we begin to see a
fundamental characteristic of photon penetration. The relationship between the
number of photons reaching a specific point and the thickness of the material to that
point is exponential.
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Penetration Range of Individual Photons
The nature of the exponential relationship is that each thickness of material
attenuates the same fraction of photons entering it. This means that the first layer
encountered by the radiation beam attenuates many more photons than the succeeding
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layers.
In a given situation a group of photons have different individual ranges which, when
considered together, produce an average range for the group. The average range is the
average distance traveled by the photons before they interact. Very few photons travel
a distance exactly equal to the average range. The average range of a group of photons
is inversely related to the attenuation rate. Increasing the rate of attenuation by
changing photon energy or the type of material decreases the average range of
photons. Actually, the average photon range is equal to the reciprocal of the
attenuation coefficient ():
Average Range (cm) =1/Attenuation Coefficient (cm-1)
Therefore, the average distance (range) that photons penetrate a material is
determined by the same factors that affect the rate of attenuation: photon energy, typeof material (atomic number), and material density.
Average photon range is a useful concept for visualizing the penetrating
characteristics of radiation photons. It is, however, not the most useful parameter for
measuring and calculating the penetrating ability of radiation.
HALF VALUE LAYERCONTENT
S
Half value layer (HVL) is the most frequently used quantity ore factor for describingboth the penetrating ability of specific radiations and the penetration through specific
objects. HVL is the thickness of material penetrated by one half of the radiation and is
expressed in units of distance (mm or cm).
Increasing the penetrating ability of a radiation increases its HVL. HVL is related to,
but not the same as, average photon range. There is a difference between the two
because of the exponential characteristic of x-ray attenuation and penetration. The
specific relationship is
HVL = 0.693 X Average Range = 0.693/.
This shows that the HVL is inversely proportional to the attenuation coefficient. The
number, 0.693, is the exponent value that gives a penetration of 0.5:
(e-0.693 = 0.5).
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Any factor that changes the rate of interactions and the value of the attenuation
coefficient also changes the HVL. These two quantities are compared for aluminum in
the figure below. Aluminum has two significant applications in an x-ray system. It is
used as a material to filter x-ray beams and also as a reference material for measuring
the penetrating ability (HVL) of x-rays. The value of the attenuation coefficient
decreases rather rapidly with increased photon energy and causes the penetrating
ability to increase.
Relationship between Attenuation Coefficient and HVL for Aluminum
The figure below illustrates an important aspect of the HVL concept. If the
penetration through a thickness of 1 HVL is 0.5 (50%), the penetration through a
thickness of 2 HVLs will be 0.5 x 0.5 or 25%. Each succeeding layer of material with
a thickness of 1 HVL reduces the number of photons by a factor of 0.5. The
relationship between penetration (P) and thickness of material that is n half value
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layers thick is
P = (0.5 )n.
Relationship between Penetration and Object Thickness Expressed in HVLs
An example using this relationship is determining the penetration through lead
shielding. Photons of 60 keV have an HVL in lead of 0.125 mm. The problem is to
determine the penetration through a lead shield that is 0.5 mm thick. At this particular
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photon energy, 0.5 mm is 4 HVLs, and the penetration is
n = thickness / HVL = 0.5 / 0.125 = 4
P = (0.5)4
= 0.0625.
The following figure summarizes two important characteristics of HVL. In a
specific material, the HVL is affected by photon energy. On the other hand, for a
specific photon energy, the thickness of 1 HVL is related to characteristics of the
material, density, and/or atomic number.
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X-RAY BEAM QUALITYCONTENT
S
The general term "quality" refers to an x-ray beam's penetrating ability. It has been
shown that, for a given material, the penetrating ability of an x-ray beam depends on
the energy of the photons. Up to this point, the discussion has related penetration to
specific photon energies. For x-ray beams that contain a spectrum of photon energies,
the penetration is different for each energy. The overall penetration generally
corresponds to the penetration of a photon energy between the minimum and
maximum energies of the spectrum. This energy is designated the effective energy of
the x-ray spectrum as shown below. The effective energy of an x-ray spectrum is the
energy of a mono-energetic beam of photons that has the same penetrating ability
(HVL) as the spectrum of photons.
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Effective Energy of X-Ray Spectra
The effective energy is generally close to 30% or 40% of peak energy, but its exact
value depends on the shape of the spectrum. For a given KV, two factors that can alter
the spectrum are the amount of filtration in the beam and the high voltage waveform
used to produce the x-rays.
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FILTRATIONCONTEN
TS
As an x-ray beam made up of different photon energies passes through many
materials, photons of certain energies penetrate better than others. This selective
attenuation of photons, according to their energy, is referred to as filtration. The figure
below shows the penetration through two materials of special interest, a 1-cm
thickness of muscle and a 1-mm thickness of aluminum. The penetration through the
muscle, or soft tissue, is considered first. For photons with energies less than 10 keV,
there is virtually no penetration; all the photons are attenuated by the tissue. The low
penetration in tissue by photons of this energy is because of the high value for the
attenuation coefficient. Recall that the high attenuation coefficient value is the result
of photoelectric interactions, which are highly probable at this energy. In the range of
10 keV to 25 keV, penetration rapidly increases with energy. As photon energy
increases to about 40 keV, penetration increases, but much more gradually. Of special
interest is the very low penetrating ability of x-ray photons with energies belowapproximately 20 keV. At this energy, the penetration through 1 cm of tissue is 0.45,
and the penetration through 15 cm of tissue is;
P = (0.45)15 = 0.0000063.
On the other hand, the penetration through 15 cm of tissue for photons with an
energy of 50 keV is
P = (0.8)15 = 0.035.
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Penetration of Soft Tissue and Aluminum for Various Photon Energies
A significant portion (3.5%) of photons with an energy near 50 keV penetrate a 15-
cm-thick patient, whereas virtually no photons with energies of 20 keV or less make it
through. This means that low-energy photons in an x-ray spectrum do not contribute
to image formation; they contribute only to patient exposure. In other words, the
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tissue of the body selectively filters out the low-energy photons.
An obvious solution is to place some material in the x-ray beam, before it enters the
patient, to filter out the low-energy photons. In diagnostic x-ray equipment, aluminum
is normally used for this purpose. The figure above shows the penetration through a 1-
mm thickness of aluminum. Typically, most x-ray machines contain the equivalent ofseveral millimeters of aluminum filtration. This might not always be in the form of
aluminum because several objects contribute to x-ray beam filtration: the x-ray tube
window, the x-ray beam collimator mirror, and the table top in fluoroscopic
equipment. The total amount of filtration in a given x-ray machine is generally
specified in terms of an equivalent aluminum thickness.
The addition of filtration significantly alters the shape of the x-ray spectrum, as
shown below. Since filtration selectively absorbs the lower energy photons, it
produces a shift in the effective energy of an x-ray beam. The figure below compares
an unfiltered spectrum to spectra that passed through 1-mm and 3-mm filters. It isapparent that increasing the filtration from 1 mm to 3 mm of aluminum produces a
noticeable decrease in the number of x-ray photons. It should be observed, however,
that most of this decrease is in photons with energies less than approximately 40 keV.
These are the photons with a low probability of penetrating a typical patient and
contributing to image formation. They do, however, contribute to patient exposure.
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X-Ray Spectra After Filtration
Adding filtration increases the penetration (HVL) of an x-ray beam by removing the
low-energy photons. HVL values are used to judge the adequacy of the filtration.
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Regulations that specify filtration requirements generally state a minimum acceptable
HVL value. Typical values are shown in the table below. It is assumed that if an x-ray
beam has the minimum specified HVL value at a stated KV, the filtration is adequate.
Recommended Minimum Penetration (HVL) for Various KV Values
KVM inimum penetration (HVL)
forAluminum (mm)
30 0.3
50 1.2
70 1.5
90 2.5
110 3.0
PENETRATION WITH SCATTERCONTENT
S
Up to this point, the x-ray photons that penetrate an object were assumed to be those
that had escaped both photoelectric and Compton interactions. In situations in which
Compton interactions are significant, it is necessary to modify this concept because
some of the radiation removed from the primary beam by Compton interactions is
scattered in the forward direction and creates the appearance of increased penetration.
A prime example is an x-ray beam passing through the larger portions of the human
body, as illustrated below. When significant forward-scattered radiation combines
with the penetrated portion of the primary beam, the effective penetration, Pe, is given
by:
Pe=P x S
where S is the scatter factor. Its value ranges from 1 (no scatter) to approximately 6
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for conditions encountered in some diagnostic examinations.
Scattered Radiation Adds to the Primary Radiation That Penetrates an Object
Several factors contribute to the amount of radiation scattered in the forward
direction and hence to the value of S. One of the most significant factors is the x-ray
beam area, or field size. Since the source of the scattered radiation is the volume of
the patient within the primary x-ray beam, the source size is proportional to the beam
area. Within limits, the value of S increases from a value of 1 (no scatter), more or
less, in proportion to field size. Another important factor is body section thickness,
which affects the size of the scattered radiation source. A third significant factor is
KV. As the KV is increased over the diagnostic range, several changes occur. Agreater proportion of the photons that interact with the body are involved in Compton
interactions, and a greater proportion of the photons created in Compton interactions
scatters in the forward direction. Perhaps the most significant factor is that the
scattered radiation produced at the higher KV values is more penetrating. A larger
proportion of it leaves the body before being absorbed. When the scattered radiation
is more penetrating, there is a larger effective source within the patient. At low KV
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values, most of the scattered radiation created near the entrance surface of the x-ray
beam does not penetrate the body; at higher KV values, this scattered radiation
contributes more to the radiation passing through the body.
PENETRATION VALUESCONTEN
TS
We have seen that the amount of radiation that penetrates through a specific
thickness of material is determined by the energy of the individual photons and the
characteristics (density and atomic number) of the material. HVL values provide
useful information about the penetration of a specific radiation in a specific material.
When an HVL value is known, the penetration through other thicknesses can be easily
determined. The table below gives HVL values for several materials related to
diagnostic imaging.
HVL Values for Certain Materials
aterialHVL (mm)
30 keV 60 keV 120 keV
Tissue 20.0 35.0 45.0
luminum 2.3 9.3 16.6
Lead 0.02 0.13 0.15
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