Radiation Penetration

7/29/2019 Radiation Penetration

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Radiation PenetrationPerry Sprawls, Ph.D.

Online

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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.
http://www.sprawls.org/ppmi2http://www.sprawls.org/ppmi2http://www.sprawls.org/ppmi2http://www.sprawls.org/ppmi2/RADPEN/#INTRODUCTION%20AND%20OVERVIEWhttp://www.sprawls.org/ppmi2/RADPEN/#INTRODUCTION%20AND%20OVERVIEWhttp://www.sprawls.org/ppmi2/RADPEN/#PHOTON%20RANGEhttp://www.sprawls.org/ppmi2/RADPEN/#HALF%20VALUE%20LAYERhttp://www.sprawls.org/ppmi2/RADPEN/#Determining%20HVL%20Valueshttp://www.sprawls.org/ppmi2/RADPEN/#Determining%20HVL%20Valueshttp://www.sprawls.org/ppmi2/RADPEN/#X-RAY%20BEAM%20QUALITYhttp://www.sprawls.org/ppmi2/RADPEN/#FILTRATIONhttp://www.sprawls.org/ppmi2/RADPEN/#PENETRATION%20WITH%20SCATTERhttp://www.sprawls.org/ppmi2/RADPEN/#PENETRATION%20VALUEShttp://www.sprawls.org/ppmi2/RADPEN/#CHAPTER%20CONTENTShttp://www.sprawls.org/ppmi2/RADPEN/#CHAPTER%20CONTENTShttp://www.sprawls.org/ppmi2/RADPEN/#CHAPTER%20CONTENTShttp://www.sprawls.org/ppmi2/RADPEN/#CHAPTER%20CONTENTShttp://www.sprawls.org/ppmi2/RADPEN/#CHAPTER%20CONTENTShttp://www.sprawls.org/ppmi2/RADPEN/#PENETRATION%20VALUEShttp://www.sprawls.org/ppmi2/RADPEN/#PENETRATION%20WITH%20SCATTERhttp://www.sprawls.org/ppmi2/RADPEN/#FILTRATIONhttp://www.sprawls.org/ppmi2/RADPEN/#X-RAY%20BEAM%20QUALITYhttp://www.sprawls.org/ppmi2/RADPEN/#Determining%20HVL%20Valueshttp://www.sprawls.org/ppmi2/RADPEN/#HALF%20VALUE%20LAYERhttp://www.sprawls.org/ppmi2/RADPEN/#PHOTON%20RANGEhttp://www.sprawls.org/ppmi2/RADPEN/#INTRODUCTION%20AND%20OVERVIEWhttp://www.sprawls.org/ppmi2http://www.sprawls.org/ppmi2


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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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Radiation Penetration