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Scatter Factors and Peak Scatter Factors for Cobalt-60,6 MV, 10 MV,
and 18 MV Photon Beams
Wamied Abdel-Rahman Medical Physics Unit
McGill University, Mon treal September, 1999
A thesis submitted to the Faculty of Graduate Studies and Research In partial fulfillment of the requirements for the degree of
Master of Science in Medical Radiation Physics
O Wamied Abdel-Rahman
National Liirary 1+1 of- BiMiithèque nationale du Canada
Acquisitions and Acquisitions et Bibliiraphic Senrices services bibiiiraphiques
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Abstract
The aim of external beam radiotherapy is to deliver a prescribed dose to a target
volume accurately and uniformiy while sparing the surrounding healthy tissue. In
radiation dosimetry calculations, many tùnctions are employed to achieve this goal, and
the Peak Scatter Factor (PSF) is one of the fimdamental functions used in dosimetry.
A brief background of some of the basic physics employed in external beam
radiotherapy is given, illustrating some of the applications of the PSF in dosimetry. Also,
the evolution of the definition of the PSF is discussed by presenting the PSF definitions
quoted in several dosimetric references. In addition, concems debated arnong physicists
regarding the consistency of tabulated values of the PSF in dosimetric references with the
definition of the PSF are presented.
A practical method for measuring the PSF for megavoltage photon beams is
developed. The method is applied to Co-60,6 MV, 10 MV, and 18 MV photon beams
using water, polytyrene, and solid water phantoms. The measured PSFs arc compared to
tabulated PSF and Normalized Peak Scatter Factors (NPSF) published in the British
Journal of Radiology (BJR), supplement 25.
Résumé
La radiothérapie a pour but de donner une dose précise et uniforme au volume
cible tout en minimisant la dose aux tissus sains. Les calculs de dosimétrie utilisent
plusieurs paramètres semi-empiriques dont le "Peak Scatter Factor" ( P M ) qui est un
paramètre de base en dosimétrie. La définition actuelle du PSF a évolué depuis sa
première utilisation.
Un résumé des principes de physique employés pour la dosimétrie des rayons
externes en radiothérapie est d o ~ é pour illustrer l'application du PSF. L'évolution de la
définition du PSF est présentée par la description des différents protocoles de dosimétrie.
Une discussion de la non-uniformité des valeurs de PSF ainsi que ses différentes
définitions sont aussi présentées.
Une méthode expérimentale pour mesurer le PSF pour les rayons de photons à
hautes énergies (méga voltage) a été développée. Elle a été appliquée aux rayons de
photons Co-60,6 MV, 10 MV et 18 MV en effectuant des mesures dans divers fantômes.
Les valeurs de PSF obtenues sont comparées aux valeurs tabulées de PSF et de PSF
normalisées (NPSF) publiées dans "British Journal of Radiology" (BIR) supplément 25.
Acknowledgements
1 would like to thank my supervisor, Dr. Emin B. Podgorsak, for his guidance and
support throughout the completion of this work. He has always allowed me to work
independently while maintaining his open door policy.
1 would also like to thank the entire Medical Physics staff who have always been
eager to help. In particular, 1 am grateful to William Parker for helping me writing parts
of this thesis. 1 would also like to thank a fellow student Francois Deblois for his patience
in showing me how to work efficientiy with the BEAM software.
Finally, I would like to thank my parents, Dr. Tarig Abdel-Rahman and Zeinab
Abdel-Rahim for their love and support. This thesis is dedicated to them.
Table of Contents
Chapter 1: Background
BASIC CONCEPTS IN RADIOTHERAPY ................ .......................*... 1
1.1.1 PRIMARY AND SCATTERED PHOTONS ......................................... 1
MEASUREMENT OF DOSE ................... ...............o............................. 7
GOALS OF THE THESIS ................... ................................................... 20
Chapter 2: Definition of Peak Scatter Factors
THE: BRITISH JOURNAL OF RADIOLOGY, SUPPLEMENT 11 .... 26
INTERNATIONAL COMMISSION ON RADIATION UNITS AND MEASUREMENTS, REPORT 23 ....., .... . ...... ........................................... 28
PSF VERSUS TAR ................... ......................................o.......................... 32 THE BRITISH JOURNAL OF RADIOLOGY, SUPPLEMENT 17 .... 34
THE: BRITISH JOURNAL OF RADIOLOGY, SUPPLEMENT 25 .... 10
Chapter 3: Materials and Methods
THEORY .................................................................................................... 45
................... MATERLUS AND EXPERIMENTAL TECHNIQUES ... 51
............ 3.2.1 ATTENUATION .... ......................................................... 53
3.2.2 COLLIMATOR FACTOR (CF) ....................................................... 55
........................ ....................... 3 .2.3 TISSUE OUTPUT RATIO (TOR) .. 57
Chapter 4: Results and Discussion
................................................ MEASUREMENT OF ATTENUATION 63
............. MEASUREMENT OF COLLIMATOR FACTOR ............... 72
MEASUREMENT OF TISSUE-OUTPUT-RATIO ............................... 73
2 ................................................... EXTRACTION OF SF(5. 10x 10 cm 71
SF AND PSF R E S U L T S . ~ ~ ~ ~ ~ ~ ~ ~ ~ a ~ ~ ~ ~ ~ ~ * ~ ~ ~ ~ ~ ~ o ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ - a 79
4.5.1 PSF FOR CO-60 ......................................................................... 81
4.5.2 PSF ~ S U L T S FOR LINACS ......................................................... 82
PSF AND ENERGY ................................................................................... 85
SUMMARY ................................................................................................ 92
Chapter 5: Conclusions
SUMMARY ................................................................................................ 94
FUTURE WORK ....................................................................................... 96
vii
The objective of radiotherapy is to deliver a prescnbed dose unifomly and
accurately to a target volume while minirnizing the dose to tissues smunding the target.
This goal is achieved by coliecting a set of dosimetric data for a clinical radiation beam.
perfonning a dose distribution calculation for a given patient, prescnbhg the appropriate
target dose, and then delivering the prescribed target dose. The dosimetric data, which
allows us to set the radiation beam parameters, consists of beam outputs under various
conditions, dose profiles, depth dose curves, and other dosimetric functions. Because the
human body is composed of approximately 75% of water by weight, water or water
equivalent phantoms are used for coIlecting the dosimetric data. The choice of water as a
phantom material is indicated by the recommendations of many calibration protocols and
by the abundance of dosimetric data measwed in water in most dosimetric data
references. Nowadays, solid phantoms that have physical properties very similar, yet not
identical, to water have replaced water for daily dosimetric measurements in many
radiotherapy clinics. Compared to water, these materials are more practical, easier for
setting up a specific assembly, and safer to use with ionization chambers. Polystyrene and
solid water phantoms are two examples of solid phantoms, and they are used for
dosimetric data acquisition in many radiotherapy clinics.
The Peak Scatter Factor (PSF) and the Tissue Air Ratio (TAR) are two exarnples
of dosimetric functions used in dose calculations for photon bearns. Their definitions
have gone through a series of changes since their initial implementation. In the early days
of radiotherapy, only low energy photon beams were available for extemal beam
radiotherapy treatment of cancer lesions and, as a result, treatments were limited to
viii
targets located close to the skin. Initially, physicists used exposure to quantifi the
interaction of photon beams with matter, and the surface of phantoms was used as a
reference point for the functions used in dosimetry. The PSF, which was then known as
the Back Scatter Factor (BSF), was used to represent the increase of the exposure at the
surface of a phantom caused by to back scattered photons produced in the phantom.
Sirnilarly, when the concept of TAR was introduced, it was used to represent the exposure
measured under full scattering conditions in the phantom compared tu the exposure in air
at the same distance fiorn the source. Therefore, the PSF equaled the TA R at the surface.
With the introduction of high energy X rays and y rays into radiotherapy, the
definitions of both the PSF and the TAR went through a series of changes prirnarily
because of two reasons. First, the quantities of kerma and absorbed dose replaced
exposure for describing the interaction of ionizing radiation with matter. Moreover, the
depth of maximum dose d,, was used as the dose reference point, replacing the reference
point on the surface.
The current, generally accepted definition of the PSF was given in the
International Commission on Radiation Units and Measurements (KRU), report 23,
which was released in 1973. The report introduced a quantity cdled the Scatter Factor
(SF) which accounted for pnmary and scattered dose components, and defined the PSF as
the SF at dm. On the other hand, in the KRU report 23, the definition of the TAR took a
different path as it was based on the dose in the phantom compared to the dose in a small
m a s of tissue in air at the same distance fkom the source. Meanwhile, PSF data available
in dosimetric references was gathered by defining the PSF as a special case of the TAR,
equaiing to the TAR at dm=. Recently, the British Journal of Radiology (BJR),
supplement 25, which was pubüshed in 1996, proposed a new dennition of the TAR,
which assures the equality of the TAR at d,, to the PSF as defined by the ICRU report 23
regardless of the beam energy.
Additionally, PSF measurement techniques were based on the measurement of the
dose in a small m a s of tissue in air, which is the concept used in the definition of the
TAR quoted by the ICRU report 23. The PSF values for low energy photon beams
obtained using such methods are very close to values which would be obtained if a
method based on measuring primary and scattered doses is used. However, for high
energy photon beams, these methods fail to provide accurate results consistent with the
ICRU report 23 definition of the PSF. Recently, a method based on results from Monte
Car10 simulations, was used to obtain the SF for a megavoltage photon beam.
The aim of this thesis is to determine the SFand the PSF for severai megavoltage
photon beams using solid water and polystyrene phantoms, and to compare our measured
PSFs to those listed in the BJR supplement 25.
Chapter One
CHAPTER 1 BACKGROUND
BASIC CONCEPTS IN RADIOTHERAPY ..................... ............................................. 1
........................................................... 1.1.1 PRIMARY AND SCATÏERED PHOTONS 1
..................................................................................... 1.1.2 A ~ U A T I O N LAW 3
................................................................................ 1.1.3 THE CONCEPT OF DOSE 5
1.2 MEASUREMENT OF DOSE .............................................. .................................. 7
............................................................ 1.3 GOALS OF THE THESIS ...................... ..... 2 0
This chapter presents a review of basic physics concepts as applied to radiotherapy,
mainly the attenuation law and the concept of dose. It also discusses the role of the peak
scatter factor in dose determination and treatment delivery. The chapter concludes with a
discussion of the airns and goals of the work described in this thesis.
1.1 Basic concepts in radiotherapy
I . 1. I P rimary and scattered photons
When a radiation beam passes through tissue, some of the energy canied by the
beam is deposited in the medium where it might cause biologicai damage. For a photon
beam, the initial step involves the interaction of a photon with an orbital electron and in
some cases with a nucleus of the attenuating material.
There are three main processes by which photons interact and transfer energy to
the medium'. In the photoelectric orocess2, a photon interacts with a bound orbital
electron. If the photon energy is greater than the binding energy of the electron, the
Chapter One
electron absorbs the photon energy and is ejected fiom the atom with a kinetic energy
equal to the photon energy less the electron binding energy.
Photons can also interact with matter through a process known as Corn~ton
scatterin& whereby a photon is scattered by an electron and the result is a less energetic
scattered photon and a recoil electron. Because this process becomes dominant at
relatively high photon energies that are much greater than the electron binding energy,
Compton scattering relations are derived assuming the electron to be free and stationary.
The third possible photon interaction with matter is the pair vroduction2, a process
in which a photon interacts with the Coulomb field of an atomic nucleus creating an
electron-positron pair. The photon must have an energy of at least 1 .O22 MeV, and any
excess energy is converted to kinetic energy, mainly shared between the electron and the
positron with a negligible amount of energy transferred to the nucleus. The positron, after
losing its energy to electrons in the medium, is annihilated by one of the fÏee electrons in
matter. The annihilation of the positron-electron pair results in the emission of two
photons each with an energy of 0.5 1 1 MeV, moving in opposite direction.
For the three photon interactions discussed above, the energetic electrons released
through these interactions travel through the medium and cause ionization and excitation
of atoms in the medium and breakage of molecular bonds which may subsequently result
in biological damage1. Some of the high speed electrons may interact with a nucleus of
the attenuator and radiate and lose some of their kinetic energy through producing X rays,
known as bremsstrahiung. The scattered photons and bremsstrahlung X rays may then
interact with the medium in the same way as the original photon did. Consequently, we
can associate the biological damage with two groups of photons, depending on their
origin. The fmt group is called "primarv ho tons", consisting of photons that originate
Chapter One
fiom the radiation source and interact in the medium for the first t k e . Photons interacting
in the medium which were produced by previous interactions of primary photons in the
medium are referred to as "scattered ho tons" or secondary photons. The dose deposited
in the medium by the former group is called 'bprïmarv dose" while the dose deposited by
the latter group is "scattered dose".
In clinical radiation machines, there are two sources of scattered photons. In
addition to the phantom scattering, scattering may take place in the collimator of the
machine and the photon beam emerging fiom the machine contains both ptimary photons
emitted by the source and photons scattered by the collimator. Practically, it is dificult to
separate the collimator scattered photons fiom the primary bearn, and for megavoltage
photon bearns it is reasonably accutate to consider collimator scatter as part of the
prïmary beam. Therefore, it is customary to use the term "primarv ho tons" the primary
photons and the collirnator-scattered photons combined, and the term "scattered photons"
is then reserved for the phantom-scattered photons.
1.1.2 Attenuation law
Each photon may interact with the medium through only one process, but, when
considering a photon beam consisting of a large number of photons and traversing a
material of thickness hx, al1 of the possible interactions occur with a relative probability
proportional to the cross section for that process. The sum of the relative probabilities is
called the total or linear attenuation coefficient p and represents the probability per unit
distance traveled in the medium that a photon will interact through one process or
another. The linear attenuation coefficient depends on the photon energy and on the
Chapter One
medium being traversed. In many references the rnass attenuation coefficient d p , which
is obtained by dividing the iinear coefficient p by the density p of the attenuating
materiai, is quoted for various attenuating materials. Figure 1-1 gives Np in various
materiais of interest in medical physics for photons with energies fiom l keV to
100 MeV.
Figure 1-1: Mass attenuation coefficient for various materials published by the National Institute of Standards and Technology (NET) (reference 3).
For a photon beam traveling in a matenal some photons are scattered through the
Compton effect and some are absorbed through photoelectric effect, pair production, or
some other more rare effect. If the beam is monoenergetic, the number of "uncollided
photons" N after traversing a thickness x of the attenuator is given by the attenuation law
as follows:
where No is the total number of incident photons.
Chapter One
The tenn Half Value Laver (HVL) is defined as the thickness of an attenuator of
specified composition required to reduce the intensity of the photon beam to half its
iv 1 original value. That means that when the attenuator thickness x = HYL, then - = -
No 2 by
definition. Therefore, fiom Eq. (1-1) it can be shown that:
The W L is often used as a crude but simple means to specify the quality of a
photon beam. The rnethod is crude because it tells very little about the number and energy
of the photons present in the beam. A complete specification of the quality of an X ray
beam requires the knowiedge of the X ray spectrum emitted by the source; however, such
a complete specification is not necessary for most purposes in radiotherapy because the
biological effects of radiation are not very sensitive to the energy of the radiation, and in
radiotherapy one is ofien interested primarily in the penetration of the beam into the
patient rather than in a detailed energy spectrum.
1.1.3 The concept of dose
Tt is essential to quantitatively relate specific measurements for a radiation beam
to chernical and biological changes produced in tissue. Initially, e ~ ~ o s u r e ' " * ~ was used as
a quantity for rneaswing ionizing radiation. Exposure is defined for gamma rays and
X rays in terms of the amount of ionization they produce in air. The unit of exposure is
called the roentgen R (1 R = 2 . 5 8 ~ lo4 Clkg) and was first introduced at the Radiological
Congress in Stockholm in 1928. Suice 1962, exposure has been deiïned for photons with
Chapter One
energies below 3 MeV by the International Commission on Radiological Units and
Measurements (KRU) as the quotient A Q / h , where A Q is the surn of al1 charges of one
sign produced in air when ail the electrons liberated by the photons in a mass h of air
are cornpletely stopped in air.
Aithough exposure provides a practical and measurable standard for photon beams
in air, additional concepts are required for quantifjring ionizing radiation to include other
Ends of ionizing radiation, such as photons with energies above 3 MeV, electrons and
alpha particles, and also to be applied to materials other than air, particularly tissue.
Nowadays, absorbed dose1"', ofien referred to sirnply as dose, is the primary physicai
quantity used in radiation dosimetry. It is defined as the energy absorbed per unit mass
fiom any kind of ionizing radiation in any material, and its SI unit, Jkg", is called the
Gray (Gy) and it is treated as a point function, having a value at every position in the
irradiated object.
Another important dosimetric quantity used today is the kema4*', which is an
acronym for "kinetic enerav released in matter". This quantity is used for describing the
initial interaction of photons and neutrons in mattcr. Kerma is defmed as the initial kinetic
energy of al1 charged particles liberated by radiation per unit mass. Although the
dimension of kerma is identicai to the dimension of dose, j-kg-' is used with kerma, while
Gy is generally reserved for absorbed dose.
C hapter One
1.2 Measurement of dose
In clinical radiation dosimetry it is customary to determine the dose to a reference
point in an irradiated phantom. In radiotherapy clinics this is usually achieved by using a
calibrated ionization chamber to measure the ionhtion at the reference point. The
exposure or dose calibration factor of the ionization chamber must be traceable to a
national standards laboratory, such as the National Research Council (NRC) in Ottawa,
Canada or the National Institute of Standards and Technology (NIST) in the United
States. The dose at the reference point is then determined by applying cumbersome
correction factorsS to the measured ionization. These factors are discussed in detail in
various protocols devoted to procedures for calibrahg radiation beams in an absolute
manner. The dose to any other point in the phantom is then determined by using various
dosimetric functions, which are defined such as to relate the dose at an arbitrary point to
the dose at the reference point.
Percentage d e ~ t h dose
One of the fimdamental dosimetric functions is the percentage depth d ~ s e ~ * ~
(PDD). Figure 1-2 provides a schematic diagram illustrating the parameters used for the
definition of the PDD function. For a given field size A defined at the surface of the
phantom and a fixed source-surfacedistance (SSD) 1; the PDD, expressed as a
percentage, is defined as the ratio of the dose at depth d o n the central axis of the beam to
the maximum dose also on the beam central axis.
Chapter One
Figure 1-2: Schematic representation of the definition of the PDD.
The PDD depends on the field size, depth in phantom, SSD, and the beam energy
E ( references 4 and 5). Referring to figure 1-2, PDDMAJE) is defined as;
where De is the dose at the arbitrary point Q and Dp is the dose at the reference point P,
which is on the beam centrai axis at the depth of maximum dose d-.
The energy of the beam E was included as a parameter for the PDD in Eq. (1-3).
In fact, al1 dosimeûic fùnctions are energy dependent, but this parameter will be dropped
in the following equations for simplicity and the reader has to understand that these
dosimetric equations contain the energy E implicitly.
Chapter One
Several PDD c w e s for various photon beams are shown in figure 1-3. For a low
energy photon bearn such as an orthovoltage X-ray beam with a HVL of 2.0 mm of
copper shown in figure 1-3, the maximum dose occurs at the surface; meanwhile, the
maximum dose for the higher energy beams occurs deeper inside the phantom, at a depth
defined as the depth of maximum dose dm For the high energy beams, the "build up"
region between the surface and d,, provides skin sparing when delivering a required
dose to a target volume located deep inside the patient. Figure 1-3 also shows that the
PDD decreases beyond the depth of maximum dose dm=. The decrease of the PDD with
depth in phantom is governed by three effects: the inverse square law, exponentiai decay,
and scattering.
Figure 1-3: Seveml PDD curves in water for various photon beams for a field size of 1Ox IO cm2 and source-surface distance (SSD) as indicated.
Chapter One
D e ~ t h of dose maximum
The depth of maxiaiun dose d, is an important parameter for characterizhg
PDD distributions. For megavoltage linac beams d,, depends on two parameters: beam
energy and field size. The primary dependence is on barn energy, and d,, is often
quoted only as a function of beam energy without much regard for field size. Thus, in the
first approximation the d,, depths for 4,6, 10, 18 and 25 MV X-ray beams are quoted as
10, 1 5, 25, 35, and 40 mm, respectively. However, as shown by various investigatorsH,
d,, of flattened lioac beams also depends on field size. This dependence is illustrated for
6, 1 0, and 18 MV X-ray beams8 in figure 1 -4. At al1 beam energies d,, increases rapidly
in the field size range fiom 1 x 1 to about 5x5 cm2, reaches a saturation for fields around
5x5 cm2, and then decreases gradually with an increasing field size, until, around
3 0 x 3 0 cm2, it reiums to a value about equal to that for a 1 x 1 cm2 field. For the small
fields used in radiosurgery, the d,, increase with field size is attributed to in-phantom
scatter, while for large fields the d,, decrease with field size is attributed to
contamination electronss which originated in the flattening filter and are M e r scattered
by the coIlimator jaws and air.
Chapter One
Figure 1-4: The variation of d,, with square fields for 6, 10, and 18 M V X-ray beams8.
sixe18 has shown that, in contrast to the behavior of flattened bearns, an
unflattened 10 MV X-ray beam shows not only a diminished d,, for al1 fields, but also
an increase in d,, with increasing field size at small fields and a constant d,, for al1
fields larger than 5x5 cm2. The higher value of d,, for flattened beams of the same field
sizes was attributed to beam hardening effects produced by the copper flattening filter on
the 1 O MV radiation beam. The increase in d,, in the field size range fiom 1 x 1 to 5x5
cm2 for both the flattened and unflattened bearns is caused by in-phantom scatter which
for small fields is independent of the flattening filter. The independence of d,, on the
field size for unflattened beams at sizes larger than 5 x 5 cm2 suggested that the observed
field size dependence for large flattened beams is caused by the flattening filter itself
which directly or indirectly produces high energy scattered electrons.
Chapter One ~~~~~
Typical d,, values listed in the British Journal of Radiology (BJR),
supplement 25 for various photon beams are listeâ in table 1-1.
Table 1-1: Typical values of d,, listed in the British Journal of Radiology (BJR), supplement 25 (reference 9) for various photon beams.
Beam profiles
Beam profiles are a representation of the variation of the dose across the field at
various depths in the phantom. They are measured by scanning dong the field axis at
various depths in water or a water equivalent matenal. In clinics several beam profiies for
various field sizes are measured at various depths covering typicai patient thicknesses and
are used by the treatment planning system in conjunction with the PDD to calculate the
dose distribution of a treatment plan in the patient. In addition, the beam profiles at d,,
and 10 cm depths may be used also for venfication of cornpliance with specifications of
the radiation unit. The profile values are usuaily normaiized to the value at the central
beam axis at the same depth in phantom and cailed the off axis ratios (OARs). Often a Ml
set of beam profiles at various depths is shown normalized to the value at d,, at the
Chapter One
central axis. The profile values given for the central axis then represent the PDDs for the
particular s k . Figure 1-5 shows a full set of beam profiles for a 10 MV bearn for
10x10 and 30x30 cm2 fields.
Figure 1-5: Beam profile sets of 1 Ox 1 O and 30x30 cm2 tields for a 10 MV beam.
Relative dose factors
Calibration protocols are used to determine the dose to d,, for a reference field
(usually 1Ox 10 cm2). To determine the dose at d,, for field sizes other than the reference
field, the Relative Dose Factor (RDF) is used. Simply stated, the RDF is defmed as the
ratio of the dose rate at d,, for a given field A to the dose rate at d,, for a reference field
A, . Refemng to figure 1-6 the RDF is given mathematically as:
C hapter One
0
where DP stands for the dose rate at point P where the field size is A at the surface of the
O
phantom and D P ~ stands for the dose rate at point PM for field size A, .
Figure 1-6: Schematic illustration of the definition of the RDF.
The RDF is used dong with the PDD to calculate the treatment times or monitor
units MU required for each field used in patient treatment. Because the collimator setting
affects both the rate of radiation output fiom the unit and the dose rate deposited at d,,
by photons scattered nom the medium, the RDF can be decomposed into two independent
factors, narnely, the Collimator Factor (CF) which describes the change in the rate of
radiation output and depends on the collimator setting Ac, and a phantom scatter factor
( S,), which describes the change in the scattered dose at d,, and depends on the field
size A on the surface of the medium. Therefore, the RDF c m be decomposed as:
RDF(A) = CF(A,) x S, ( A ) (1 -5)
Peak scatter factor
Chapter One
If we were able to prevent the production of scattered photons within the phantom,
then the dose at d, would equal to the dose delivered by the p h a r y photons only. The
ratio of the total dose to the primary dose at d,, is called the peak scatter factor (PSF)
(reference 10) . Thus we can write:
where Dp and Pp are the total and primary doses at d,, for field size Ad- defined at d,,
The PSF is usually used with low energy photon bearns and it is reasonable to assume
that the field sim A at the surface of the phantom is equal to the field size A, Il*P at d,, for
low energy photon bearns. For this reason, the PSF is ofien quoted for the field size A
defined at the surface of the phantom. Also, because it is difficult to determine the
primary dose P p in Eq. 1-6, physicists have defined the PSF as a special case of the
Tissue Air Ratio (TAR), and this will be discussed in a greater detaii in chapter 2.
The PSF may be used to determine the Sp for field size A with the following
relationship:
where Are/ is the reference field. The ratio of the PSF in Eq. (1-7) is also known as the
Normalized Peak Scatter Factor (NPSF).
The decomposition of the RDF into a change of the primary dose component
described by the CF and a change of the scatter dose component described by the S, has
many usefiil and simple applications in dosirnetry. For example, shielding blocks are used
Chapter One -- - -
reguiarly in radiotherapy treatment to produce inegular fields. Assuming that the surfice
of the phantom is at the isocenter, the RDF of the irregular field A' can be calculated
using the CF for the collimator setting A, and the PSF for the A ' and Amy The relation is:
RDF ( A ' ) = CF ( A , ) x PSF ( A ' )
PSF (A,, -
Tissue air ratio
The tissue air ratio (TAR) is another important fiinction used in dosimetry. It was
first defined as the ratio of the exposure in phantom to the exposure in air with the same
field size and at the same distance fiom the source. The definition of the TAR was later
modified to the ratio of the dose at a given point in a phantom and the dose at the same
point in fiee air within a small mass of phantom matenal large enough to provide the
maximum electronic build-up . Using the geometry iilustrated in figure 1-7, the TAR is
expressed as:
where Dp is the dose at point Q in the phantom, Dp. is the dose at Q' in the small mass of
tissue, and AQ is the field size defined at depth d.
Figure 1-7: Schematic illustration of the definition of the TAR.
Chapter One
As demonstrated by Johns and ~unnùi~ham~ who defhed the PSF to equal the
TAR at dm, the TAR may be calculated fiom the PDD using the following relationship:
where f stands for the SSD, A is the field size on the surface of the phantom, and AQ is the
field size at depth d. The relation between AQ and A is:
It is aiways advantageous to have a table of TAR values because, in contrast to the
PDD, the TAR is independent of the SSD and thus a single TAR table replaces the
individual PDD tables needed for different SSD. These TAR tables are especially useful
for isocentric setups.
Tissue phantom ratio and tissue maximum ratio
When the definition of the TAR is applied to high energy photon beams, a large
volume of mass is required to establish the maximum electronic build-up at the point in
air. The size of the mass may be so large that not al1 of it will be irradiated by small field
sizes. ~amnark" suggested replacing the reference dose in air in the definition of the
TAR by a dose determined in a phantom at a specified depth and called the ratio tissue
phantom ratio (TPR). Therefore, the TPR is defined as the ratio of the dose in phantom for
a chosen depth d and field size AQ defined at depth d to the dose at a reference point in the
same phantom and same field size AQ but at some reference depth d4 The defkition of
the TPR is shown schematically in figure 1-8 and the TPR is given by:
Chapter One
DC? TPR ( d , A , ) = -, De=,
where De is the dose at point Q in the phantom, Dpn, is the dose at the reference point
Qw which is at depth d,/. If the reference depth is equal to d-, the TPR is called the
tissue maximum ratio (TMR) and the point Q@notation is replaced by Q,. The TMR
can be denved fiom TAR data in those cases where TARs are accurately known using the
following relationship :
Figure 1-8: Schematic illustration o f the definition of the TPR.
Enerw de~endence of PSFs
Equations (1 -8), (1 - 1 O), and (1 - 1 3) are examples illustrating various applications
of the PSF in dosimetry. The PSFs are quoted for various photon beams in many
dosimetric references and figure 1 -9 is a plot of the PSF for several square fields (5x5,
10x 10, 20x20 cm2) versus beam energy12. The plot shows that the PSF. for a given
constant field size, increases with the barn energy reaching a maximum at beams with
W . around 0.6 mm Cu before it drops to values close to 1 .O at higher energies. At low
Chapter One
photon energies, because the dominant interaction of photons in the medium is the
photoeffect, the number of scattered photons produced by other interactions is minimal.
Therefore, we expect that the total dose at d, will be very close to the primary dose.
However, as the energy of the beam is increased, more Compton scattering interactions
take place in the phantom, resulting in an increasing scattered dose at d,, and thus an
increasing total dose. The decrease of the PSF values as the beam energy M e r
increases is associated with the direction in which the scattered photons are produced. As
the beam energy increases, more of the Compton scattered photons'"*s are produfed in the
forward direction which results in reducing the phantom volume that contributes to the
scattered dose at d,, and a corresponding reduction in the PSF.
. 1 .O
o. I 1 .O 10.0
HVL (mm o f Cu)
Figure 1-9: Variation of PSF with HVL in copper for various square fields".
Chapter One
1.3 Goals of the tbesis
The goal of this work is to determine PSF values in solid phantoms for photon
beams with enagies greater than cobalt40 (Co-60). The PSF values obtained for
megavoltage photon beams wouid be usefùl for irnproving the accuracy of dose
distribution calcuIations and in treatment planning when using high energy radiation
beams. In addition, obtaining PSF values in different materials would provide some
justification for using water dosimetric parameters with measurements conducted in
contemporary solid phantoms.
The specific goals of this thesis are:
i ) to provide a historic development of the definition of the PSF and to understand
the difficulty in obtaining PSF values for photon beams with energies greater than
cobalt-60 gamma ray energies,
ii) to derive a practical method for measuring PSFs for megavoltage photon beams,
iii) to apply this method to PSF measurements in a Co-60 beam and to compare
results obtained for various phantoms to the PSF values for Co-60 quoted in the
British Journal of Radiology (BJR), supplement 25, and
iv) to measure PSF values for 6 MV, 10 M V and 18 MV X-ray photon beams in
various phantoms and compare the resuits to normalized peak scatter factors
quoted in the BJR, supplement 25.
Chapter One
References
Turner J. E.: Atoms, Radiation, and Radiation Protection. 2nd edition. John Wiley
& Sons, New York, New York, U.S.A. (1995).
Krane K. S.: Imoductory NucZem Physics. John Wiley & Sons, New York, New
York, U.S.A. (1988).
Hubbell J. H. and Seltzer S. M. "Tables of X-Ray Mass Attenuation Coefficients
and Mass Energy-Absorption Coefficients nom 1 keV to 20 MeV for Elements
Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest" NISTIR 5632,
National Institute of Standards and Technology (NIST).
Khan F.M.: n e Physics of Radiation Therapy. 2nd edition. Williams & Wilkins,
Baltimore, Maryland, U.S.A. (1994).
Johns H. E. and Cunningham J. R.: The Physics of Radiology. 4th edition. Charles
C. Thomas, Springfield, Illinois, U.S.A. (1983).
Biggs P.J and Ling C.C. "Electrons as the cause of the observed d,, shift with
field size in high energy photon beams", Med Phys. 6 : 29 1 -295 (1 979).
Arcovito G., Pieramattei A., D'Abram0 G., and Ancireassi R. "Dose measurement
and calculation of small fields for 9 MV X-rays", Med Phys. 12 : 779-784 (1994).
Sixel K.E. and Podgorsak E.B. "Build-up region and depth of dose maximum of
megavoltage X-ray beams", Med. Phys. 21 : 4 1 1-4 16 (1 994).
The British Journal of Radiology, Supplement 25. Br. J. Radiol., Supplement 25
(1 996).
ICRU 1973 "Measurement of absorbed dose in a phantom irradiated by a single
beam of X or gamma rays", Report 23, International Commission on Radiation
Units and Measurements (ICRU).
Kamnark C. J., Deubert A., and Loevhger R. "Tissue phantom ratios an aid to
treatment planning", Br. J Radiol. 38 : 158-1 65 (1 956).
Bradshow A. L. "The variation of percentage depth dose and scatter factor with
beam quality", Br. J , Radiol., Sup~lement 25, Amendix D : 125-130 (1996).
Chapter Two
CHAPTER 2
DEFINITION OF PEAK SCATTER FACTOR
INTRODUCTION ................... ... ....................................................................................... 22
THE BRITISH JOURNAL OF RADIOLOGY, SUPPLEMENT 11 ....................... ........ -26
INTERNATIONAL COMMISSION ON RADIATION UNITS AND MEASUREMENTS (KRU), REPORT 23 ..................................................................... 28
PSF VERSUS TAR.. .................. .. ........... .. ...................................................................... .32
.............................. THE BRJTISH JOURNAL O F RADIOLOGY, SUPPLEMENT 17 -34
VARIOUS TECHNIQUES FOR THE DETERMINATION OF THE PSF .................... 37 ............................... THE BRITISH JOURNAL O F RADIOLOGY, SUPPLEMENT 25 -40
CONCLUSION .................. ......... .................................................................................... 4 1
2.1 Introduction
For many years the PSF was assurned to be a special case of the TAR. Thus, to
provide a historical development of the defuiition of the PSF, one must first discuss the
definition of the TAR. In this chapter, the evolution of the definition of both functions are
discussed in parailel. Their definitions in the early days of radiotherapy, in the
International Commission on Radiation Units and Measurement (ICRU), report 10
(reference l), and in the ICRU report 23 (reference 2) are presented. Physicists, since the
release of the KRU report 23, have raised many questions concerning the consistency of
the PSF data tabulated in dosimetry references, such as the British Journal of Radiology
(BJR) supplements, with special attention to PSF values for Co-60 beams. For these
Cbapter Two
beams, physicists have debated PSF and TAR values published in the BIR supplement 17
(reference 3) and this resulted in changing these values in the recently published BIR
supplement 25 (reference 4).
The PSF is an important quantity in radiation dosimetry and its values for various
common radiation beams have k e n tabulated in many articles and dosimetry reference
books. These values become refined when more data fkom various therapy units are
gathered or, in some cases, are replaced with newer values.
In the past, the PSF was referred to as the Back Scatter Factor (BSF) and was
definedl as the ratio of the exposure X on the surface of an irradiated phantom to the
exposure X, in air at the same distance f fiom the source, as illustrated schernatically in
figure 2-1. Because calibration protocols for radiotherapy beams were based on
measuring the exposure in air, the PSF was mainly used for determining the exposure at
the surface of a phantorn fiom the known exposure in air at the same distance fiom the
source. With the aid of PSF and other dosimetric functions, such as PDD and TAR, the
exposure at any other point on the central beam axis in the phantom could be calculated.
Figure 2-1: A schematic diagram illustrating the definition of PSF in the eady days of radiotherapy.
Chapter Two . .
johns et al.' introduced the TAR concept in 1953. The TAR was defmedas the
ratio of the exposure Xp at a depth d in phantom to the exposure X, in air at the same
distance f+d fiom the source, as illustrated schematically in figure 2-2. Although the TAR
was &t introduced for use in rotational therapy, it has also been applied since then in
conventional stationary beam therapy because of its independence of SSD.
Figure 2-2: A schematic diagram illustrating the definition of the TAR as introduced by Johns and colleagues5.
The definitions of the PSF and the TAR apply for equal irradiations (equal
exposwe times for a constant output of a source and equd field sizes at the position of the
chamber), thus one may conclude that the PSF is just a special case of the TAR, equaling
the value of the TAR at the surface of the phantom (d = 0).
In 1963, the ICRU released report 10 (reference 1) and introduced a new function
calIed the Scatter Factor (Sn, defined as "the ratio of the exwswe at a reference mint in
the phantom to the exwsure at the same wint in sriace under similar conditions cf
irradiation in the absence of the phantom". The PSF for X-ray beams greater than 400
kVp was then defined as the SF at d,, on the central axis. For radiation of lower energy,
the SF at the phantom surface on the central axis was called the BSF.
Chapter Two -
In the same report, the TAR was defined as '%e ratio of the absorbed dose at a
piven mint in a phantom to the absorbed dose which wodd be measured at the same
point in fiee air within a volume of phantom material iust large enouah to ~rovide the
maximum electronic build-ui, at the wint". Using the geometry illustrated in figure 2-3,
the TAR at depth d and for field size AQ can be expressed as:
D~ TAR(d, A,) = -, Dè
where Dp is the absorbed dose in a phantom at depth d and field size AQ defined at depth
d on the central beam axis and DQ. is the absorbed dose measured at the same point in air
within a volume of phantom material just large enough to provide the maximum
electronic build-up.
Figure 2-3: A schematic diagram illustrating the definition of the TAR as introduced by the K R U report 10 (reference 2).
The definition of the SF presented by the KRU report 10 (reference 1) was
ambiguous because some physicists interpreted this definition as implying that the
prirnary contribution should be established for a beam that has not k e n attenuated. In
Chapter Two
fact, a group of physicists intmduced an attenuation factor to existing PSF values to
remove the attenuation of the primary beam2.
2.2 The British Journal of Radiology, Supplement 11
The BIR supplements, published by the British Institute of Radiology, contain
dosimetric data for various radiation beams used for therapeutic purposes. Data for these
beams were gathered fiom different centers around the world, and average values of a
specific dosimetric parameter were published in these supplements. Examples of
published data are: the linear attenuation coefficient p in various materials, as well as
PSFs, TARs, and PDDs for various radiation beams . The supplements are used as a guide
or reference for expected vaiues that should be obtained when measuring beam
parameters for similar radiation beams. In some cases where there are insufficient
resources for measuring a particular dosimetric parameter, data fkom the supplements
may be used directly. For this reason, the supplements are updated when additional
measured dosimetric data become available or when modifications of the previous
tabulated data are required.
The BJR supplement 1 1 was published in 1972. Although dosimetric data were
published in previous supplements FJR supplement 5 (1 953) and BJR supplement 10
(1 96 1 )], the BIR supplement 1 1 became a reference for central axis depth dose data for
radiation beams used in radiotherapy6. It contained centrai axis depth dose data for
nominal photon beam energies as low as 6 kVp up to beams produced by betatrons with
energies as high as 35 MV. Values of p for water for various photon beams were quoted
26
Chapter Two - -
in the supplement, for example, the authors7 posted a value of 0.0632 cm-' for Co-60
beams. These values are used for calcdating the primary TAR cornponent [also known as
TAR(d, O)] using the following relationship:
TAR(d,O) = e-"(J-d-' . (2-2)
TAR(4 O) is an important parameter, because it allows the caiculation of the scatter air
ratio (SAR) or the scatter-to-primary ratio (SPR); both ratios are used in irregular field
calculations, and are calculated fiom the TAR using the following equations :
SAR(d, r , ) = TAR(d, r, ) - TAR(d,O) ,
and
SPR(d, r, ) =
where d stands for the depth in the phantorn and rp stands for the radius of the radiation
field at depth d. Data for clinical electron beams ranging in energy fiom 2 MeV to 30
MeV were also tabulated. The BJR supplement 1 1 also contained data for fast neutron
beams. Additionally, specific topics, such as the equivalent field method and the variation
of percentage depth dose with beam quality, were discussed in appendices attached to the
supplement6.
There are two main concems regarding PSF and TAR data published in the
supplement. First, PSF and TAR data were limited to photon beams with energies less
than or equal to a Co-60 beam even though central avis data, such as the PDDs were
tabulated for megavoltage photon bearns. Also, PSF values equaied to the value of the
TAR at d,,.
Chapter Two
2.3 International Commission on Radiation Units and Measurements (ICRU), Report 23
The currently accepted definition of the PSF was published by the KRU in
report 23 (reference 2) in 1973. In the report, a new definition of the SF was given to
avoid the ambiguity in the SF definition presented in the ICRU report 10. It was redized
that the fluence rate of primary photons at depth is independent of the field size, whereas
the fluence rate of scattered photons depends on the field size and the dimensions of the
phantom. Therefore, the SF was defined as 'Vhe ratio of the exwsure (or the absorbed
dose) at a point in a phantom to the part of that exwsure (or absorbed dose) which is due
to ~rimarv ho tons". When a photon intefâcts at a point in the phantom, it sets electrons
in motion and, in some cases, a scattered photon is generated. Considering figure 2-4, the
exposure or absorbed dose deposited at a point in a phantom results nom photons
interacting in the medium for the first time (primary photons) and photons which have
interacted in the medium more than once (scattered photons). The SF is thus given by:
where DQ is the total absorbed dose and Pa is the primary dose at point Q in the phantom.
Similarly to the ICRU report 10, the SF of the point at the intersection of the surface
dong the central axis is called the BSF for X-rays generated at potentials less than
400 kVp and, for higher energies, the reference point is taken at dm on the central axis
and the SF is then called the PSF. The report also noted that the BSF for X-rays less than
400 kVp was a specid case of the TAR at the surface.
Chapter Two - -
Another important issue addressed by the report was that TAR values could be
derived nom depth dose data by using the BSF and removing the inverse square factor.
The relationship between the TAR and the PDD is:
where f is the SSD and d is the depth of the point of interest in the phantom.
Equation (2-6) shows the cornmon practice of reporting TAR values as a function of the
field size Ag at depth d, in contrast to the PDD which is reported as a fûnction of the field
size A at the surface of the phantom.2
Because there are many applications for the PSF in dosimetry, it was necessary to
obtain PSF values for the various photon beams used in radiotherapy. However, the PSF
is alrnost impossible to measure directly using the definition given in the KRU report 23.
Meanwhile, the TAR is very simple to measure as will be discussed in the following
paragraph, and physicists used these simple techniques for measuring the TAR and
assumed that the TAR at d,, equals to the PSF.
Chapter Two
Source
Figure 2-4: A schematic diagram of primary and scattered photons contributing to the exposure or absorbed dose at point Q in a phantom.
Johns and ~unnin~harn* addressed a practical problem in dosimetq ivhen
absorbed dose is calculated fiom exposure. As defined by the ICRU report 23, the TAR
requires determining the dose at a point in phantom and at a point in air within a smail
mass of phantom material. First, considering the point Q in phantom on the central axis of
the radiation beam, the dose DQ calculated fiom the measured exposure in the phantom is
given as:
q, =R*N,=f,-A,, (2-7)
where R is the chamber reading afler irradiation, corrected for temperature, pressure, and
collection efficiency; N, is the exposure calibration factor of the chamber; f,d is the
30
Chapter Two
roentgen-to-rad conversion factor; and A, is the displacement factor. The displacement
factor is used to account for the attenuation that would have taken place in medium in the
absence of the chamber. For point Q ' in the small mass of tissue in air, the procedure of
determinhg the dose is illustrated in figure 2-5. Assuming the chamber bas an exposure
calibration factor of N , the exposure Xe-- in air at Qui, for a chamber readhg of R *,
corrected for temperature and pressure is given by:
XQa, = R'- Ni.
Small mass of phantom Calibrated chamber.
t 2 req
Qair
Figure 2-5: Determination of the absorbed dose to a point in air within a small m a s of tissue material.
Since the effects of the chamber wall are included in N i , XQmr is the exposure in
air in the absence of the chamber. If the exposure at point Q ' in a small mass of tissue
could be measured it would be less than the exposure at point Qay in air because of the
attenuation produced by the thickness req of the small mas. To correct for the attenuation,
the exposure Xea, in air is multiplied by a factor A,. The absorbed dose Dpm to Q ' in the
small mass of tissue is then given by:
Chapter Two
If we f.urther assume that the beam spectnun in the phantom is very similar to the
beam spectnun in the small mass of tissue (Ni = Nx and f md = fm.), Eqs. (2-l), (2-7) and
(2-9) can be combined and the TAR is then given by:
DQ - R - A , TAR(d, A,) =- -- .
Dg R8* Aey
Values of A, for various photon beam energies were calculated using the mean
and the maximum ranges of electrons produced by the mean energy of the photon beam.
The value calculated by Johns and ~unain~harn~ for Co40 is 0.985, which is very close
to the Ac value for typical thimble ionization chambers. Therefore, for Co-60 beams, the
TAR can be calculated by taking the ratio of the exposures (or the readings if the same
chamber was used for measuring the exposure in air and in phantom) directly without
applying any correction factors.
2.4 PSF versus TAR
A question of consistency arises when the PSF is viewed fkom the standpoints of
the SF and the TAR. While the PSF is defined as the ratio of the total dose received at d,,
to the dose due to primary photons, it is assurned that it is equal to the TAR at cimm. To
justify this assumption, we need to consider how the dose fiom the primary photons is
delivered at a point in phantom.
When photons interact in the medium, they generate energetic electrons. The
electmns are set in motion and interact in the medium by transferring part of their kinetic
32
Chapter Two
energy to other electrons in the medium or losing some energy to bremsstrahlung X rays.
Eventually, these electrons corne to rest after traveling a certain distance having lost al1 of
their kinetic energy. If we consider a point in the phantom, electrons that were created
elsewhere in the phantom may deposit a dose at our point of interest. Because electrons
have a certain range in the medium, which depends on their initial kinetic energy and the
medium, the primary dose delivered at the point of interest is produced by interactions of
primary photons within a certain radius from the point. This defmes the term "dose in a
small mass of hant tom" used in the definition of the TAR as given in the ICRU report 23.
But is this consistent with the definition of the PSF in the sarne report? As shown below,
many physicists tried to answer the question.
The definition of the TAR is based on the dose absorbed at a reference point in a
small mass of phantom in air. Scattered photons are generated within the small mass of
phantom material and some of these scattered photons will interact a second time within
the smail mass and contribute to the dose absorbed at the reference point. The question
raised by physicists was whether or not to include this amount of dose in the dose Dp in
the small mass of tissue in air used in the definition of the TAR. As a common practice in
clinics, DQ* is determined by taking a direct measurement using an ionization chamber
with an appropriate build-up cap added. As a result, the exposure measured includes the
contribution of scattered photons fiom the build-up cap. If we accept that there is an
implicit assumption that the scattered contribution is to be included in the definition of the
TAR, there is an inconsistency with the definition of PSF given by the KRU report 23.
In 1973, en$ estirnated the relative absorbed dose due to scattered photons in a
small mass of phantom matenal in air by calculating the fkactional energy fluence of
photons scattered by the small mass to the primary photons in a sphencal mass of
33
Chapter Two - - - - - - -
material of radius r. For a 1.2 MeV photon beam (very close to the average energy of
Co-60 beams), the fiactional absorbed dose for a 0.5 cm radius of spherical small mass of
phantom material is approximately 0.01. To avoid any inconsistency of the TAR with the
PSF, the TAR was used with low energy photon beams up to Co-60, which explains the
lack of TAR data for megavoltage photon bearns in the BIR supplement 1 1, and the TPR
and the TMR were used with higher energy beams.
2.4 The British Journal of Radiology, Supplement 17
In 1983, the British Institute of Radiology released the BJR supplement 17 as a
revision of the BIR supplement 1 1, with some expansion. For example, data published for
photon beams were extended to include photon energies up to 43 MV. In addition, data
obtained fiom a variety of units manufactured by different companies were taken into
account when the supplement was published in order to establish data usable at centers
where there are insufficient resources for obtaining them by direct meas~rements'~.
For Co-60 beams, no changes were made to the PDD and the PSF values posted
in the BJR supplement 1 1. Similarly, the TAR values have remained unaltered because
they were calculated nom PDD and PSF data using Eq. (1 - 10). However, the value of p
for water was changed fiom 0.0632 cm-' to 0.0657 cm-' determined by extrapolation of
the TAR data to zero field size. ' ' ~ a ~ ' ~ proposed using the NPSF with high-energy photon beams replacing the
PSF because of the difficulty of measuring the PSF directly. Many dosimetric relations
Chapter Two - - -
contain ratios of PSFs and Day showed that they can be replaced by ratios of NPSFs, as
follows. For low energy photon beams, physicists determined the PSF measuring the dose
in the phantom at d,, and by measuring the dose in a small mass of tissue in air at the
same point using an appropriate build-up cap. As the bearn energy increases, a large
build-up cap has to be used for the measurement in air to establish the maximum
electronic equilibriurn at the point in air. The larger the size of the phantom material, the
greater the possibility for a photon to interact more than once in the build-up cap which
increases the total measured dose. Therefore, the measured dose in air is greater than the
primary dose and the increase was described as a factor given by (1 +B). For this reason,
the term "apparent PSF" is used to describe the ratio of the totai dose at d,, to the dose
to a small mass of phantorn material. It is given by 12:
apparent P SF(A) = PSF(A)
l + B
Values of B were estimated to range fiom 0.0 1 to 0.10 for beams between 2 and 30 MV,
depending on the shape and size of the small mas, whereas the field size is unlikely to
have any affect on B.
The NPSF is the ratio of the "apparent PSF' of field size A to the "apparent PSF'
of a reference field size A,. As a direct consequence of the fact that B is independent of
the field size, any ratio of PSF can be replaced by the ratio of NPSF, as shown by the
foilowing relations 12:
NPSF(A) = apparent PSF(A) - PSF(A) - apparent PSF( A,, ) PSF(AmJ ) '
Chapter Two
and
~ a ~ ' * also proposed a method to estimate the PSF using measured NPSFs. If the
NPSF is ploîted as a function of the field size (figure 2-6), the NPSF of zero field size
may be obtained by extrapolating the curve to zero field size. Because the definition of
the PSF in the ICRU report 23 sets the PSF of a zero field size equal to 1 .O, the PSF for
field size A could be estimated using:
1 .O2
1 .O0 NPSF
0.98
I I 1 I
5 10 15 20 Side of square field (cm)
Figure 2-6: Estimation of the PSF by extrapolating the NPSF to zero field size to obtain NPSF(0) (reference 12).
Chapter Two
In the BJR supplement 17, the NPSF data were &en for several high energy
photon beams and, according to the tabulated values, it appears that the NPSF is
independent of the beam energy. Applying Day's method to the NPSF for these beams
would then result in calculating PSFs that are aiso independent of the beam energy. One
might argue that the independence of the PSF of the bearn energy in the megavoltage
range contradicts the fact that, as the photon energy increases, more photons are scattered
in the fonvard direction resulting in reducing the laterai scattered dose to d,, and we
should expect the PSF to decrease with the beam energy. However, as the beam energy
increases, the length of the build-up region becomes greater and, as a result, there is more
material above d- where more "focward" scattered photons as produced. The increased
scattering fiom the build-up region might compensate for the reduction in the
laterally-scattered photons.
2.5 Various techniques for the determination of the PSF
In order to obtain the PSF for high energy photon beams, indirect measurements
are used to estimate the primary and scattered dose components at d,,. Some of these
methods might require extrapolation of measured data which are some times guided by
results obtained fiom Monte Carlo simulations.
Nizin and Kase" developed a method to measure the primary dose for high
energy photon beams. The method was based on using small attenuators, as s h o w
schematically in figure 2-7. The dose DQ at a point Q on the central axis can be separated
into a prirnary component PQ and a scattered component SQ as follows:
DQ = PQ+SQ . (2- 15)
37
Chapter Two -
With the introduction of a small attenuator, the dose at the same point is given by:
D; = PL +SA , (2- 16)
where we have used a superscript i when the attenuator is used. Because of the small
cross sectional area of the attenuator, the attenuator affects the primary dose component,
yet it does not perturb significantly the scattered dose component. Therefore:
s; ;.se. (2- 1 7 )
4 I f
Small attenuator
Figure 2-7: Diagram ilIustrating the geometry used by Nizin and ~ a s e ' j for separating the primary component fiom the scatter component in high-energy photon beams.
The ratio of the primary dose components D& is constant at the same depth d,
and we can write:
4 - = constant = CD . DL
Cornbining Eqs. (2- 19 , (2- 16) and (2- 1 a), we obtain:
or in terms of the ionization I:
Chapter Two
where I' is the ionization at Q', Ip is the primary ionization at Q, and CI is :
I P -- - constant = CI . (2-2 1) 1;
The task then is to determine 4, which ultimately allows determining il,. Nizin
and &sel3 showed that Cl for a monoenergetic photon beam is given by:
where ph is the linear attenuation coefficient for the prirnary photon spectrum in an
attenuator of thickness h. This technique was applied to a Cod0 beam using aluminum
and graphite attenuators14 and the PSF values obtained were closer to values calculated
by Rice and chin'' using Monte Carlo simulations than to the values published in the
BIR supplement 17.
Kijewski, Bjiirngard and petti16 used the EGS (electron gamma shower) Monte
Car10 code to calculate the scattered dose for small field sizes in a Co-60 beam. They
obtained SPR data for the simulated Co-60 beam and compared the results to SPR values
denved fiom data in the BJR supplement 17 using Eq. (2-4). The SPR values derived
fiom the BJR supplement 17 were lower than the results fkom the simulation. The group
suggested that this mismatching of results is due to the TAR((I.0) data posted in the
supplement and they recommended decreasing TAR(<I, O) by 3%. In a series of papers,
~ j i i m ~ a r d " - ' ~ used tabulated Co-60 data in the B R supplement 17 and showed that plots
of TAR(~,A~)x@ against field size A for a constant ratio of Md were linear and
converged to 1 .O at zero field size. They concluded that TAR(d. O) should be given by e - -
Chapter Two
instead of Eq. (2-2). ~ c ~ e n ~ e ' ~ argued against this proposition and suggested thaf
instead of reducing TAR(d. O), the non-zero TARs should be increased.
Burns, Prichard and ICnigh?O agreed with McKenzie's suggestion of increasing
the TARs for Co-60. However, they argwd that, since the published TARs are calculated
frorn the PDD and the PSF, the discrepancy found by Bjiimgard might be caused by the
values of the PSF and they concluded that the PSF of Co-60 posted in the BJR
supplement 17 should be increased. They venfied their conclusions experimentally by
comparing the absorbed dose in phantom fiom a measurement in air and the application
of the TAR (or the PSF and the PDD) to the absorbed dose in phantom fiom a
measurement in phantom and the application of conversion factors fiom a dosimetry
protocol. The absorbed dose measured in the latter procedure was found to be 2.0% larger
than the absorbed dose obtained with the former. In addition, they perforrned a Monte
Carlo simulation of a Co-60 beam and the calculated PSFs were about 1.8% higher than
the values given in the BJR supplement 1 7 (reference 17).
2.5 The British Journal of Radiology, Supplement 25
The BJR supplement 25 (reference 4), published in 1996, is a revision of the BJR
supplement 17 and is the rnost recent supplement released by the British Institute of
Radiology containhg dosirnetric data for radiotherapy bearns.
Regarding the PSF and the TAR data, there were two major changes in the BIR
supplement 25 in cornparison with the BJR supplement 17. For Co-60 beams2', the PSF
and the TAR values were increased by almost 2% following suggestions by ~ c ~ e n z i e ' ~ .
40
Chapter Two --
Also, ~unis', inspired by the def i t ion of the SF i d e KRU report 23, proposed a new
definition of the TAR. He defined the TAR as the ratio of the total dose D at a point Q in
phantom at depth d and field size AQ to the primary dose PL at the point Q,, which is at
depth d,, for the same field size AQ defmed at d,, , as illustrated in figure 2-8. The
mathematical relation is:
This proposed definition of the TAR implies that at d = à'', the TAR becomes identical to
the PSF as defined by the ICRU report 23.
Figure 2-8: Schematic illustration o f the definition of the TAR proposed by the BJR supplement 25 (reference 5).
2.6 Conclusion
Problems and concem associated with the definitions and measuring methods for
the PSF and the TAR have existed since the hc t ions were first defined and introduced.
Physicists where divided into two camps with regards to the defuiition of the PSF. One
Chapter Two --
camp, motivated by the practicaiity of measuring the TAR, assumed that the PSF was a
special case of the TAR. The other camp, supporthg the defuition of the PSF using the
total dose and the primary dose component at d,, (ICRU report 23), was challenged to
provide techniques for separating the primary dose component fiom the scattered dose
component. This camp eventually developed several methods for SF determination and
suggested a new definition of the TAR in the recent BJR supplement 25 consistent with
the definition of the PSF provided by the ICRU report 23.
C hapter Two
References
ICRU 1962 "Clinical Dosirnetry", Report 1 Od, International Commission on
Radiation Units and Measurement (ICRU).
K R U 1973 "Measurement of absorbed dose in a phantom irradiated by a single
beam of X or gamma rays", Report 23, International Commission on Radiation
Units and Measurement (ICRU).
The British Journal of Radiology, Supplement 17. Br. J. Radiol-, Supplement
17 (1 983).
The British Journal of Radiology, Supplement 25. Br. J RadioL. Supplement
25 (1996).
Burns J. E. "Definition of tissue-air ratio", Br. J. Radiol-, Supplement 25 :
177-1 82 (1996).
Cohen M. "General in!roduction9', Br. J. Radiol., Supplement I l : viii-xvii
(1 972).
Cohen M. "Gamma rays: Cobalt 60 teletherapy units", Br. J. Radiol.,
Supplement 1 1 : 53-56 (1972).
Cunningham J. R. and Johns H. E. T h e caIculation of absorbed dose fiom the
exposure measurements: practical problems in dosimetry", fhys. Med Biol. 15 :
7 1-77 (1 970).
Henry W. H. "Tissue-air ratio, peak scatter factor and consistency",
Phys. Med. BioZ. 19 : 43-50 (1974).
Bradshaw A. L. "General introduction", Br. J. Radiol., Supplement 17 : v-viii
(1 983).
Godden T. J. "Gamma radiation fiom cobalt 60 teletherapy Units",
Br. J. Radiol, Supplement 17 : 45-49 (1983).
Day M. J. "The nonnalized peak scatter factor and nomalized scatter functions
for high energy photon beams", Br. J. Radiol.. Supplement 1 7 : 1 3 1 - 1 3 5 (1 983). Kase K. and Nizin P. "A method of measuring the primary dose component in
hi&-energy photon beams", Med. Phys. 15 : 683485 (1988).
Chapter Two
Kase K. and Nizin P. ''Determination of primary dose in 6 0 ~ o gamma barn
using a small attenator", Med Phys. 17 : 92-95 (1990).
Rice R. K. and Chin L. M. "Monte Carlo cdculations of scatter-to-primary
ratios for normalizaîion of primary and scatter dose", Phys. Med Bioi. 35 : 333-
338 (1990).
Bjiimgard B. E., Kijewski P. K., and Petti P. L. " Monte Carlo cdculations of
scatter dose for smdl field sizes in a 6 0 ~ o beam", Med Phys. 13 : 74-77 (1986).
Bjanigard B. E. and Petti P. L. " Description of the scatter component in
photon-beam data", Phys. Med- Bioi. 33 : 2 1-32 (1 988).
Bjhgard B. E., Rashid H., and Obcemea C. H. "Sepamtion of primas. and
scatter components of measured photon beam data", Phys. Med Biol. 33 : 1939-
1945 (1989).
McKemie A. L. "Should 6 0 ~ o tissue-air ratios be re-evaluatedr', Phys. Med
Biol. 37 : 1601-1610 (1992).
Burns J. E., Pritchard D. H., and Knight R. T. "Peak scatter factors for 6 0 ~ o
gamma- radiation", Phys. Med BiUL 37 : 2309-23 18 (1 992).
McKenzie A. L. "Cobalt-60 gamma-ray beams", Br. 1 Radio l... Supplement
25 : 46-5 1 (1996).
Chapter Three
MATERIALS AND EXPERIMENTAL TECHNIQUES ........................................... 51
32.1 A r n u ~ n o ~ ............................................................................................ 53
3.2.2 COLLIMATOR FACTOR (Co ...................................................................... -55
3 -2.3 TISSUE OUTPUT RATIO (TOR) .................................................................... 57
........... - . -
This chapter presents a derivation of the method fust developed by Bjiüngard for
obtaining the Scatter Factor SF for megavoltage photon beams. This chapter also
discusses the materials and the experimental techniques used in our measurements.
3.1 Theory
According to the KRU report 23 (reference l), the SF is defined as "the ratio of
the exposure (or the absorbed dose) at a oint in a phantom to the part of that exwsure (or
absorbed dose) which is due to primarv photons". The definition of the SFcould be
applied to any point in the phantom; however, in our work, we will detemine the SF only
for points along the central axis of square fields.
C hapter Three
The SF for a point Q in phantom along the beam central axis is given by:
where d is the depth of point Q along the central axis in the phantom, AQ is the field size
at Q, DQ is the total dose, and Pp is the primary dose. For d = d-, the SF is called the
PSF (reference 1) and, therefore, the PSF is given by:
Selecting a reference point dong the central axis in the phantom denoting
its depth as drefi the field size as AQmr , and using Eq. (3-l), the ratio of the SF at a point Q
on the central axis to the SF at Qrefi where both points are located at the sarne distance f
fiom the source, is given by the following relationship:
The ratio of the total doses, which appears on the nght hand side of Eq. (3-3), is
called the Tissue-Output-Ratio (TOR) (reference 2), and its definition is shown
schematically in figure 3- 1.
Equation (3-4) appears to be similar to the defuiition of the TPR as given by Eq. (1-12),
but this is not the case. The reason is that the field size at depth d for point Q and the field
size at reference depth dreJ for the reference point Qrefin the definition of the TPR are
equal, whereas the field size at depth d for point Q may by different fiom the field size at
Chapter Three
the reference depth ddfor the reference point Q4in the definition of the TOR. One might
interpret the TOR as a more general h c t i o n than the TP R (figure 1-7) and it wouid be
identical to the TPR if Ap = Ae,, .
Figure 3-1: Schematic diagrarn illustrating the definition of the TOR.
As illustrated in figure 3-2, let us denote the point at which the maximum dose
occurs as Qmm when the field size is AQ at the depth dm- and the point at whichthe
maximum dose occurs as Q" when the field size is AQmf at the depth dm=. The primary
dose at the point Q may be related to the primary dose at Q- using the following
relationship:
C hapter Three
and the primary dose at the reference point Qn/ may be related to the primary dose at
Qy using the following expression:
where ,u is the linear attenuation coefficient. The attenuation factors in Eqs. (3-5) and
(3-6) are expressed in an integral form to take into account the variation o f p for a
polyenergetic beam as the beam penetrates the phantom. Taking the ratio of Eqs. (3-6)
and (3-3, we obtain:
The ratio of the primary doses at d,, in Eq. (3-7) describes the relative change in
the primary dose component at d,, when the field size is changed fiom AQ to AQ,, .
Since this change depends on the collimator settings only, we can replace this ratio of the
primary doses by a CF, and Eq. (3-7) becomes:
where Arr(d) is an attenuation factor normalized to 1 at dM and CF(AQ) is normalized to
unity at AQ . Equation (3-8) could also be obtained using the following diagram: */
Chapter Three
- --
Figure 3-2: Diagram to illustrate the calculation of the ratio of the prirnary doses at Q and QmF
Inserting Eqs. (3-4) and (3-8) into Eq. (3-3), we get:
The right hand side of Eq. (3-9) consists of three functions that are rneasurable
with techniques discussed in the next section; however, on the left hand side, both
C hapter Three
SF(d,AQ) and SF(d& /QI) are unkwwn. To extract the SF using Eq. (3-9), it is necessary
to introduce one additional assumption. The assumptionz4 is that as both d - + 0 and
AQ + O, it follows that the SF + 1. Referring to Eq. (3-9), if TOR(dJQ)/[Att(d)xCF(AQ)]
Using Monte Car10 calculations for a circular 15 MV X-ray beam with radius r,
~ j i k n ~ a r d ~ has demonstrated that the SF is approximately a linear hct ion of r and d if
r/d is constant. Introducing a parameter Z = rd/(r+d), the approximation:
S F ( d , A p ) = l + a x Z , (3- 1 O)
where a is a coeficient that varies with rld, was shown to represent well the results of the
simulation. It is expected that this approximation will also be true for square fields AQ of
side s if the average radiusS r , = 0.56 1 -s is used. The parameter Z is then given by:
After inserting Eqs. (3- 10) and (3- 1 1 ) into Eq. (3-9), we obtain:
for a constant dd. In addition to the 1 5 MV X-ray beam data fiom which Eq. (3- 12) was
derived, sh i l a r success was seen for Co40 and higher energy photon bea~ns~-~"*'. By
extrapolating Eq. (3- 1 2) to Z = 0, the intercept value should equal to 1 /SF(drefi &). Then,
SF(d,AQ) can be calculated by inserting the value of SF(d4 &) into Eq.(3-9).
Chapter Three
3.2 Materials and experimental techniques
Dosimetry protocols recomrnend ushg water for meauring dosimehic data.
Nowadays, various solid phantoms, which are equivalent to water and tissue as far as
beam attenuation property are concemed, are commercially available. For a phantom to be
used for dosirnetric measurements, its mass density p, effective atomic number Zg, and
electron density p./ must be similar to those of water or tissue. In the photoeffect region,
Zgof a rnaterial can be calculated using the following relationsgg:
where ai is the fiaction by weight of the i-th element of atomic number 2,. The electron
density f i l is given by:
where NA is Avogadro's number (6.023~ 1 atoms/g-atom), p is the physical density, Z
is the atomic number, and A is the atomic weight . Water, solid water, and polystyrene
phantoms were used for data acquisition in our experiments and the physical parameters
for these rnater ia l~~*~ are listed in table 3-1. Slabs of solid water ranging fiom 2 cm to
5 cm in thickness and sheets of polystyrene ranging in thickness nom 0.6 mm to 3.2 mm
were available in the Radiation Oncology department of the Montreal General Hospital.
Three radiation units were used for external karn irradiations : a cobalt unit (Theratron
780; AECL, Ottawa, Ontario), an intermediate energy linear accelerator (Clinac- 1 8;
Varian Associates, Palo Alto, CA) producing a 10 M V X-ray beam, and a dual energy
Chapter Three - - - --
Iinear accelerator (Clk-2300 CID; Varian Associates, Pa10 Alto, CA) producing 6 MV
and 18 MV X-ray beams. For ionization measurements, most of the data was acquired
using a Famer cylindrical ionization chamber (model 257 1 ; Nuclear Enterprises,
Beenham, Reading, England) in conjunction with various build-up caps required for
establishing electronic equilibrium within the chamber for measurements in air. The
thickness and material of the build-up cap used for each beam depended on the d,, of the
particular beam. The Fanner ~hamber '~ has a volume of 0.6 cm3 and a 0.065 gkm2
graphite thimbie wall thickness. The inner diameter of the thunble is 0.63 cm and the
inner axial length is 2.25 cm. Additionally, a parallel plate ionization chamber
(model 30-329; Markus PTW, Freiburg, Gemany) was used for measurements at d,, in
the Co-60 beam. The parallel plate chamber has a graphite collector with a diarneter of
0.54 cm and a guard ring width of 0.07 cm. The spacing between the electrodes is 0.2 cm
and the sensitive air-volume is 0.055 cm3 (reference 1 1). Also, a water-sealed chamber
(model RK 83-05; RK-chamber, Kallerd, Sweden) was used for measurements in water.
Al1 ionization chambers were operated in the standard configuration and were connected
to an electrometer (model CDX-2000A; Standard Imaging Inc., Middleton, WI).
- -- - -
Table 3-1: Dosimebic parameters of polystyrene, tissue, water, and solid water.
Chapter Three
3.2.1 Attenuation
One of the hc t i ons requked by Eq. (3-9) describes the attenuation of the primary
dose in the phantom. For a monoenergetic beam, the attenuation is ca~culated'~ using the
linear attenuation coefficient p Eq. (1 -1)l; however, for a polyenergetic beam, in the k t
approximation, a parameter known as the hardening coefficient q, in addition to f i is used
for calculating the attenuation NIN, with the following relationship:
where t is the thickness of the attenuator.
The experimental procedure for deteminhg ,u and q requires setting the apparatus
in a "narrow beam geometry" 12, as shown schematically in figure 3-3. Simply stated, this
geometry requues measurement under a very small field and placing the detector at a
distance from the attenuating material much larger than the detector's size, in order to
minirnize the number of scattered photons which are produced by the attenuating materiai
and reach the detector. While maintainhg the distance fiom the source to detector and
varying the thickness of the attenuator, an attenuation curve is obtained and, by using least
square fitting to Eq. (3-1 5)' both p and can be determined fiom the measured data.
For these measurements, the Farmer ionization chamber with an appropriate
build-up cap was placed at a distance which assured a n m w beam geometry. The
radiation field was set to a size just large enough to cover the chamber and the build-up
cap. For the Co-60 beam, the minimum possible field size obtainable by the collimator
setting was 5x5 cm2 at 80 cm fiom the source, and with the aid of lead blocks placed on
the shielding tray a smaller field size was achieved. The collimators of the linear
Chapter Three
accelerators were capable of providing the necessary small field sizes for the
measurement.
obtaining data
An acrylic tank with the dimensions of 30x30~30 cm3 was used for
in water, while slabs and sheets of solid water and polystyrene provided the
data for the solid phantoms. The setup
experiment are listed in table 3-2.
parameters for the various used in ow
Figure 3-3: Schematic diagram of a narrow beam geometry sehip used for attenuation measurement where f is the source-detector distance and t is the attenuator thickness.
Beam Build-up cap
0.551 mm Lucentine
(mode1 258 1) 5.32 mm Al 9.2 mm Al
Source - Attenuator - detector detector
Table 3-2: Experimental setup parameters for attenuation measurements.
3.2.2 Collimator factor
13.14 For in air measurements, Day showed that the introduction of a build-up cap
increases the dose measured by the chamber because of scattering within the build-up cap.
This increase in the measured dose was described by a factor B that depends on the size
and shape of the cap but not on the field size. Because the CF is used to compare the
change in beam output relative to a reference field, the ratio of the measured doses in air
would equal the ratio of the primary doses at d,, and would represent CF. as shown in
the following relationship:
where DQ(A) and ( A p m f ) are the doses in air for fields AQ and a f a t a distance f
f?om the source, respectively. For fields smaller than ar, the CF is expected to be
smaller than 1 .O, while for fields greater than A,, it is larger than 1 .O.
The common practice for measuring the CF is to position the chamber at the
isocenter and assuring that the chamber with the build-up cap is totally covered by al1
fields. However, in some cases, the chamber may be placed at greater distances when
measuring the CF for small fields for high energy bearns, in situations where the small
fields do not cover the build-up cap when the chamber is positioned at the isocenter.
Using an appropnate build-up cap, the chamber was placed and maintained at the
isocenter, and ionization readings were obtained for different square fields, ranging fiom
3 x 3 cm2 to 20x20 cm2 for the same exposure time setting in the cobalt unit and monitor
C hapter Three
unit MU setting in the Iinac. The 10x10 cm2 was chosen to be the reference field 4,.
Figure 3 4 is a schematic diagram showing the setup for CF measurement and the
experimental setup parameters are tabdated in table 3-3.
Figure 3-4: A schematic diagram illustrating the setup for the CF measurement.
1 Source- Build-up cap 1 detector
distance V) 0.551 mm Lucentine
Range of square fields measured ( side length of field
Table 3-3: Experimental setup parameters used for the CF measurernent.
Chapter Three
3.2.3 Tissue output ratio (TOR)
In contrast to the previous two sets of measurements which are carried out in air
and similarly to the TPR and the T ' . measure~nents~~~, the TOR requires measurement
conducted in a phantom, as shown schematicaily in figure 3-5. By varying the depth d and
the field size A while maintaining f constant, ionization readings using equal exposure
times or MU settings could be obtained for different d and A combinations (d,AQ). The
TOR i s caiculated by taking the ratio of the doses at (d,AQ) and at (d4 %,), and if the
same chamber is used at both points, the ratio of the doses reduces to the ratio of the
ionization readings.
Figure 3-5: A schematic diagram illustrating the setup for the TOR measurement.
Chapter Three
Solid water and polystyrene phantoms were used for TOR data acquisition. The
chamber was kept at the isocenter. Both materials had special slabs shown schematically
in figures 3-6 and 3-7, which where used for placing cylindrical and parailel plate
shambers inside the medium. The slabs for cylindrical chambers were used with beams
higher in energy than CodO; meanwhile, for measurement at d,, for the Co-60 beam, it
was necessary to use the parallet plate chamber because the thickness of the cylindncal
slabs was greater than 2.0 cm making it impossible to carry out measurements at depths of
0.5 mm. The surface area of the special slabs for polystyrene is adequate for covering
fields up to 20x20 cm2. For solid water, the slab for cylindrical chambers was large
enough to allow measurements for the same range of fields; however, the dimensions of
surface area of the parallel plate chambers slab were 12x12 cm2 which limited TOR
rneasurements to fields up to only lOx 10 cm2. For measurements of TOR in water, a
water-filled acrylic tank with dimensions of 63x60~61 cm3 was used in conjunction with
the water-sealed chamber. Tables 3 4 and 3-5 summarize the TOR experimental setup
parameters for the various phantoms and photon beams.
Figure 3-6: A schematic diagram showing a cross sectional view of the slab used for cylindrical chambers.
Chapter Three
Figure 3-7: A Schematic diagram showing a cross sectional view o f the slab used for parailel plate chambers.
Material
Water
Solid Water
Polystyrene
Table 3-4: TOR experimental setup parameters used for rneasurements in water, solid water, and polystyrene for the Co-60 beam.
Source - chamber distance (cm)
80
Range of square Source - chamber Depth in fields measured
distance (cm) phantom (cm) ( side length of field in cm)
100 1 to 20 4 to 20
Depth in phantom (cm)
0.5 to 20
Table 3-5: TOR experimental setup parameters used for measurements in solid water and polystyrene for 6, 10, and 18 MV X-ray beams.
Range of square fields measured ( side length of
field in cm) 5 to 20
Chapter Three
References
ICRU 1973 "Meastuement of absorbed dose in a phantom irradiated by a single
beam of X or gamma rays", Report 23, International Commission on Radiation
Units and Measurements, (ICRU).
Bjmgard B. E. "Scatter factors for a 25 MV X-ray beam", Med P hys. 20 0: 3 57-
361 (1993).
Bjiirngard B. E. and Petti P. L. " Description of the scatter component in photon-
beam data", Phys. Med Biol. 33 : 2 1-32 (1 988).
Bjihgard B. E., Rashid H., and Obcemea C. H. "Separation of primary and scatter
components of measured photon beam data", Phys. Med. Biol. 33 : 1939-1945
( 1989).
B j h g a r d B. E. and Siddon R. L. "A note on equivalent circles, squares and
rectangles", Med Phys. 9 : 258-260 ( 1 982).
Nizin P. S. "Geometrical aspects of scatter-to-primary ratio and primary dose",
Med. Phys. 18 : 153-160 (1991).
Bjmgard B. E., Kijewski P. K., and Petti P. L. " Monte Carlo calculations of
scatter dose for small field sizes in a 6 0 ~ o beam", Med. Phys. 13 : 74-77 (1 986).
Khan F.M.: The Physics of Radiation Therapy. 2nd edition. Williams & Wilkins,
Baltimore, Maryland, U.S.A. ( 1 994).
Johns H. E. and Cunningham J. R.: The Physics of Radiology. 4th edition. Charles
C. Thomas, Springfield, Illinois, U.S.A. (1 983).
Gastorf R., Humphries L., and Rozenfeld M. "Cylindrical charnber dimensions and
the corresponding values of Awdl and NgJ(Nx Aion)", Med Phys. 13 : 75 1-754
(1986).
Kubo H., Kent L. J., and Krithivas G. "Determinations of Ng, and PRpi factors
fiom commercially available parallel-plate chambers, AAPM Task Group 21
protocol", Med. Phys. 13 : 908-9 12 (1 986).
Chapter Three
1 2. Turner J. E. : Atoms, Radiation, and Radiation Protection. 2nd edition. John W iley
& Sons, New York, New York, U.S.A. (1 995).
13. Day M. J. T h e nonnalized peak scatter factor and nonnalized scatter fwictions for
high energy photon beams", Br. J , Radiol, Supplement 17 : 13 1-1 35 (1 983).
14. Day M. J. "The nonnalized peak scatter factor and normaiized scatter functions for
high energy photon beams", Br. J. Radiol., Supplement 25 : 168- 1 76 (1 996).
Chapter Four
CHAPTER 4
RESULTS AND DISCUSSION
ME ASUREMENT OF ATTENUATION ............................................................................ 63
MEASUREMENT OF COLLIMATOR FACI'ORS .............................................. .......... -72
MEASUREMENT OF TISSUE OUTPUT RATIOS ............................. ...., .... .............. 73
2 EXTRACTION OF SF(5,10x10 cm ). ............................................................ ................. 74
SF AND PSF RESULTS ...................................................................................................... 79
4.5.1 PSF RE~ULTS FOR CO-60 ................................................................................ -8 I
...................................................................... 4.5.2 PSF RESULTS FOR L~NAC BEAMS 82
4.6 PSF AND ENERCY ................................. ............................................................................ 85
In this chapter, the experimental results of attenuation, collimator factor , and
tissue output ratio measurements are reported. From these results, scatter factors are
calculated in various materials for Co-60, 6 MV, 10 MV, and 18 MV X-ray beams.
Furthennbre, peak scatter factors were detemined experimentally and the values for
Co-60 are compared to tabulated values of peak scatter factor in the BJR supplements 17
and 25. Calculated normalized peak scatter factors for 6, 10, and 18 M V X-ray beams are
compared to normalized peak scatter factors tabulated in the BJR supplement 25.
Chapter Four
4.1 Measurement of attenuation
Using the experimental method for attenuation measurements, described in
section 3.2.1, attenuation curves in water, solid water, and polystyrene were obtained for
the Co-60 barn and are shown in figure 4- 1. The attenuation curves are also shown in a
semilog graph in figure 4-2. Fitting the attenuation curves to Eq. (1 Dl), the values of p
determined by the fitting were 0.0654,0.0661, and 0.0670 cm" for solid water, water, and
polystyrene, respectively. The value of p in water for Co-60 beams posted in the BJR
supplement 25 (reference 1) is 0.0657 cm-', while the value posted by the National
Institute of Standards and ~ e c h n o l o ~ ~ ~ (NIST) for p in water for 1 -25 MeV photons is
0.0632 cm-'. This difference is explained by the difference between a 1.25 MeV
a monoenergetic photon bearn and a Co-60 clinical radiotherapy beam which has a photon
spectrum differing fiom the spectnim of photons emitted by a Co-60 nuclide.
Chapter Four
C o 4 0 Bcam
y = I . O O O Q ~ ~ ~ ~ ~ O Solid Water
R2 = 0.9998
0.000 - - -- --- O 5 I O 15 2 0 25 JO 35
Thickntu (cm)
Figure 4-1: Attenuation curves for Co-60 clinical beam in water, solid water, and polystyrene.
Co-60 Bcam
0 . 0 1 0 - -- -
O 5 10 I S 20 25 3 0 3 5
ïhicknas (an)
Figure 4-2: Attenuation curves for Co-60 clinical bearn in water, solid water, and poiystyrene plotted on a semilog scale.
Chapter Four
A Co-60 nuclide emits two photons with energies of 1.17 and 1 -33 MeV, both
with intensities of aimost 100% (teference 3), and, therefore, the spectnim emitted fiom
such a nuclide has a mean photon energy of 1.25 MeV. Meanwhile, the radioactive
material of a Co40 source used in radiotherapy uni& is produced in the f o m of pellets
which are contained in a stainless steel container4. This container is placed inside another
tungsten container and sealed by welding, producing an arrangement known as a source
capsule, which is positioned inside the cobalt unit's head. The unit's head with al1 its
components provides scattering matenal for the primary photons emitted by the capsule,
and the scattered photons contribute to the final photon spectnim emerging fiom the head
which is used in patient treatment. To illustrate the changes produced by the components
in the unit's head to the photon spectnun emitted by a pure Co-60 nuclide, we carried out
a Monte Car10 simulation of the Co-60 unit5 using the BEAM software package6. The
material and the geometry were carefully considered in the modeling of the components
in the head of the unit. These components are the Co-60 source capsule, the source
housing, and the collimator assembly. Figure 4-3 is a schematic illustration of the Co-60
unit showing the different head components and identiming their constituent matenals. In
the simulation, the adjustable collimators and the trimmer bar settings produced a
5x5 cm2 field size at 80 cm fiom the source.
For the Co-60 source consisting of only two energy peaks, one at 1.17 MeV and
the other at 1.33 MeV, 2 . 0 2 ~ 109 photons were emitted fiom the source in the simulation.
Particles reaching a plane just below the trimmer bars were collected and ana! yzed. For
the particular field setthg, there were a total of 4.173~ 1 o5 particles reaching the plane
below the trimmer bars, and fiom these particles 4.161 x 1 o5 were photons and the
Chapter Four
remaining 0.02 1 x 1 O' particles were electrons. The spectral distribution of the photon
particles is shown in figure 4-4, and the calculated mean energy of the photon spectrum
was 1.10 MeV. The spectrum shows that in addition to the main two energy peaks at 1.17
and 1.33 MeV, there is a continuous energy spectrum of lower energy photons emerging
fiom the head which were produced by scattering that took place in the components
inside the head. es sen' has estimated that 13% of the total number of photons emitted
fiom a Co-60 unit have energies below the two peaks at 1.17 and 1 -33 MeV. The spectral
distribution of the photon particles shown in figure 4-4 is plotted on an expanded scale in
figure 4-5, magnifjring the continuous speceum of the scattered photons emerging from
the Co-60 unit.
Chapter Four
Cobalt Source
Lead
Steel
Depleted Uranium
Adjustable collimators - at nght angles
0
f i Source Housing
Primary Collimator
Adj ustable Collimators
Trimmer Bars
Figure 4-3: A schematic representation o f the Co-60 unit head used in the Monte Car10 simulation.
Chapter Four
Figure 4-4: Spectral distribution for the Co-60 beam using BEAM software package collected below the ûimmer bars for a 5 x 5 cm2 field size at 80 cm.
Figure 4-5: Spectral distribution for the Co-60 beam using BEAM software package collected below the trimmer bars for a 5x5 cm2 field size at 80 cm, ( data fiom Fig. 4-4 on an expanded scale).
68
Chapter Four -- -
Attenuation curves in solid water and polystyrene were also obtained for the 6, 10,
and 1 8 MV X-ray beams. Figure 4-6 (plotted on a semilog scale in figure 4-7) and figure
4-8 (plotted on a semilog scaie in figure 4-9) show the measured attenuation curves in
solid water and polystyrene, respectively, and they also show the results of fitting the
curves to the attenuation law given by Eq. (1-1). Because linac produces a spectruxn of
photons ranging from O MeV to the nominal accelerating potential of the electmn beam,
the beam hardening coefficient q, in addition to f i was ussd to describe the attenuation of
the photon beam in various media. By ushg least square fitting to the measured
attenuation data in solid water and polystyrene for the different linac beams, both p and q
were determined, and the values obtained from the fitting are listed in table 4-1. The
values of q in table 4-1 are negative, indicating that the barn becomes harder as it
penetrates deeper inside the attenuating matenal. The hardening of the beam is a result of
the increased attenuation of lower energy photons in the beam spectnim.
Material
Table 44: Linear attenuation coefficient and barn hardening coeflïcient in polystyrene and solid water for 6, 10, and 18 MV X-ray beams.
69
Chapter Four
0.000 - O 5 10 15 20 25 30 35
niiekncss (cm)
Figure 4-6: Attenuation curves in solid water for 6, 1 O , and 18 MV X-ray beams.
0.100 - -- O 5 I O 15 20 25 30 35
niicbnss (cm)
Figure 4-7: Attenuation curves in solid water for 6, 10 , and 18 MV X-ray beams shown on a semilog scale.
Chapter Four
0.000 O 5 10 15 a) 2s
niduiss (cm)
Figure 4-8: Attenuation curves in polystyrene for 6, 10, and 18 MV X-ray beams.
0.100 - O 5 10 15 20 25 - (an)
Figure 4-9: Attenuation curves in polystyrene for 6, 10, and 18 MV X-ray beams shown on a semilog scale.
C hapter Four
4.2 Measurement of collimator factors
Using the method discussed in section 3.2.2 for the CF measurement, the CFs
were measured for various megavoltage beams for several square fields ranging fiom 4x4
cm2 to 20x20 cm2 with the exception of the Co-60 unit where the minimum achievable
field size using the collimator setting was 5 x 5 cm2. Ionization readings obtained for the
different square fields were normalized to the ionization reading of the l Ox l O cm' field.
Results for Co-60, 6 MV, 10 MV, and 18 MV beams are plotted in figure 4- 1 O. The
figure indicates that the CF strongly depends on the design of the various components in
the treatment unit's head.
18 M V
O 2 4 6 8 10 12 14 16 18 20 Side of square field (cm)
Figure 4-10: Collimatot factors for the Co-60,6 MV, 10 MV, and 18 MV photon beams nomaiized to unity at 1 Ox l O cm'.
Chapter Four -- - - - --
4.3 Measurement of tissue output ratios
Measurement of the TOR was carried out as outlined in section 3.2.3. Afier
obtaining ionization readings for the various beams for different depths d and field size
AQ combinations, the ionization readings at point (d,AQ) were normalized to the ionization
at (5, 1 Ox 10 cm2). The measured TOR curves for al1 beams and in various materials are
shown in Appendix-A. Meanwhile, figure 4-1 1 shows the 10x 1 O cm2 TOR curves in solid
water for the Co-60,6 MV, 10 MV, and 18 MV photon beams. Because the normalization
point was selected at 5 cm depth and for a 1 Ox l O cm2 field, these particular curves in
figure 4- 1 1 also represent the 1 Ox 1 O cm2 TPR curves, normalized to a depth of 5 cm .
Figure 4-1 1: TOR curves for a IOx IO cm2 field for Co-6O,6 MV, 10 MV, and 18 MV photon beams in solid water normalized to 5 cm depth and lOx IO cm' field size.
Chapter Four
4.4 Extraction of SF(5,lOxlO cm3
For square fields AQ of side s, the three measurable fùnctions, namely, Att(d),
CF(AQ), and TOR(d,Ap), are used in Eq. (3-12). For a constant sld where d is the depth in
the phantom dong the central axis, the ratio { TOR(dJQ)/[CF(AQ)wltt($)]} is plotted
against a parameter Z given by Eq. (3-1 1). Because the Att(d) in Eq. (3-12) is n o d i z e d
to unity at dM= 5 cm while p and q in table 4-1 were obtained by fitting the attenuation
data which was normalized to 1 at d = 0, the Att(d) is calculated using the following
relationship:
For the Co-60 bearn where the attenuation of the beam may be described using
only fi the Att(d) is calculated using:
The linear extrapolation of SF(d&) in Eq. (3-12) was denved assuming that
electronic equilibrium exists for the points used in the extrapolation8. For this reason and
as a precaution, only points with depths greater than 5 cm and for fields greater than
5x5 cm2 were used for the 10 MV X-ray beam and the 18 MV X-ray beam in the linear
extrapolation avoiding points close to dm and small field sizes where electronic
equilibrium may not be established.
Six lines with different sld ratios were constructed and extrapolated to Z = 0,
where the intercept equals 1 lSF(5, 10x 10 cm2), as shown in figures 4- 12 through 4-1 8.
Chapter Four - - -
The average values of SF(5, 1 Ox l O cm2) obtained are reported in table 4-2 for al1 beams
in the various phantom materials. The estimated emr was cdculated by dividing the
difference between the maximum and minimum SF(5, lOx 10 cm2) value by their sum.
Figure 412: Linear extrapolation curves used in detemination of SF(5,lOx 10 cm2) in solid water for Co-60 beam.
C hapter Four
Figure 4-13: Linear extrapolation curves used in detennination of SF(5, 1Ox 10 cm2) in water for Co-60
Figure 4-14: Linear extrapolation curves in determination of SF(5, 1 Ox 10 cm3 in polystyrene for Ce60 beam.
Chapter Four
Figure 4-15: Linear extrapolation curves in determination o f SF(5, 1Ox IO cm" in solid water for 6 MV X-ray beam.
Figure 4-16: Linear extrapolation curves in determination of SF(5, 10x 10 cm2) in solid water for 10 MV X-ray bearn.
Chapter Four
Figure 4-17: Linear extrapolation curves in determination of SF(5, l Ox IO cm') in solid water for 1 8 MV X-ray beam.
z (cm) Figure 4-t8: Linear extrapolation curves in determination o f SF(5, 10% IO cm2) in polystyrene for 18 MV
X-ray kam.
C hapter Four
Table 4-2 : Average SF(5, 10% IO cm2) and estimated error in various materials for Co-60.6 MV, 10 MV, and 18 MV photon beams.
4.5 SF and PSF results
The value of TOR(dJp)/[CF(AQ) xAtt(d) J is multiplied by SF(5, 1 Ox 1 O cm2) to
yield the SF for a given depth d and field size AQ, as was shown in Eq. (3-9) where
= 5 cm and AQm, = 1 Ox 1 O cm2. The SF curves for the various beams and materials
10 MV
Solid Water
1.110
e . 0
6 M V
Solid Water
1.170
I l .5
Co-60
used in our measurements are shown in Appendix B. Using these curves, we can examine
the dependence of the SF on the depth d in the phantom, field size AQ defined at depth d,
and on the energy of the photon beam. The dependence of SF on depth d in the phantom
could be examined by observing the variation of the SF with depth for a fixed field size
and beam energy. As the curves in Appendix B indicate, SF increases with the depth in
the phantom and this increase is govemed by the exponential decrease of the primary
dose component and by the variation of the scattered dose cornponent which is difficult to
analyze because of its dependence on other parameters, such as beam energy and field
size.
Similarly, the dependence of SF on field size could be examined by observing the
variation of SF at a fixed depth and beam energy with the field size. Again by observing
79
18 MV
Polystyrene
1.229
&l .O
Water
1.222
I l .2
Solid Water
1 .O52
k1.4
Solid Water
1.233
Il .2
Polystyrene
1 .O50
+1 .O
C hapter Four
the SF c w e s in Appendix B, the SF increases with increasing field size as a result of the
increase in the nurnber of scattered photons produced in the phantom.
Finally, figure 4-1 9 is a plot of SF for a 1 Ox 10 cm2 field size in solid water for
various photon beams. For a given depth in phantom SF decreases with increasing beam
energy for photon beams with energies between Co-60 and 18 MV. The decrease in SF is
attributed to an increase in bbfonvard" scattering in the phantom as photon energies are
increased.
0.900
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0
Dcpth (cm)
Figure 4-19: Calculated SF curves for a lOx 10 cm' field in solid water for Co-60,6 MV, 10 MV, and 18 MV photon beams.
Cbapter Four
4.5.1 PSF results for Co40
A cornparison of PSFs values for Co-60 which were extracted fiom the SF curves
in solid water, water, and polystyrene with tabulated values of the PSF for Co-60 beams
in the BJR supplement 17 and BJR supplement 25 is given in table 4-3. Most of our
measured PSF values in various materials are close to the PSF values tabulated in the
BJR supplement 25 giving confidence to the procedure we have used in the PSF
detennination. Also, comparing PSF values obtained in the various materials and taking
into account the uncertainty in our measurements which was about f l.2%, we may
conclude that there is no difference in the PSF measured in water, solid water, and
polystyrene, and this result supports the common practice in radiotherapy clinics of using
the PSF of water even though the dosimetric measurement is conducted using solid
phantoms equivalent to water.
H Field size (cm4 7
Material 5x5 6x6 8x8 10x10 12x12 15x15 20x20
Water 1 .O40 1 .O4 1 1 .O43 1 .O47 1.054 1 .O57 1 .O62
Solid Water 1.044 1 .O5 1 1 .O52 1 .O60 N/A N/A N/A
Polystyrene 1 .O44 1.047 1 .O52 1 .O59 1 .O64 1 .O69 1 .O76
BJR-17 1.018 1 .O22 t .O29 1 .O35 1 .O41 1 .O49 1 .O59
BJR-25 1 .O36 1.040 1.048 1.054 1.060 1.068 1 .O78
Table 4-3: PSF results in water, solid water, and polystyrene and tabulated PSF values in the BJR supplement 17 (reference 9) and the BJR supplement 25 (reference 1 ) for Co40 bearns.
Chapter Four --- - -
4.5.2 PSF results for Zinac bearns
PSF in solid water for 6, 10, and 18 MV X-ray beams were extracted from the SF
curves and are shown in table 4-4. Because the SF are measured for field sizes defmed at
depth, the PSF in table 4-4 are for field sizes A,- defmed at dm.
Johns and cunningham4 calculated the TAR fiom PDD and PSF pq . (1-IO)]
using the PSF of a field size A defmed at the surface of the phantom. For Co-60 beams
and lower energy beams, the field size A at the surface of the phantom approximately
equals the field size A,- at dm. For high energy beams, however, the approximation
A = A,- may produce errors in dosimetric calculations using PSF. For this reason, to
calculate the TAR for high energy photon beams, one has to use the following
relationships:
T A R ( ~ , A,) = P D D ( d 9 A 9 n ~ ~ s ~ ( ~ ) X 1 O0 (r,
where
and
For small field sizes, the PSF for the 10 MV and 18 MV X-ray beams resulting
fiom measured data were less than 1, but according to the definition of the SF given in the
KRU report 23, the SF has to be greater than 1. As demonstrated by ~ i x e l ' ~ , d,, was
Chapter Four
shown to be field size dependent with the largest value occurring near the 5x5 cm2 field
(figure 1-4). Meanwhile, the PSF reported in table 4-4 are for field sizes defined
geometrîcally assurning a fixed d,, for al1 fields. For the small field sizes of the 10 MV
and 18 MV X-ray beams, the position of the true peak dose might be deeper than the
assumed "geometrical" dm. For the small fields where the tme peak dose is greater than
the "geometrical" d,, the PSF obtained is for a point where electronic equilibrium is
established which may have resulted in calculating PSF values less that 1.0 and it seems
that the calculated PSF is sensitive to the degree of electmnic equilibrium and to the tme
peak dose position.
Field sue (cm4
6MV 1 .O24 1 .O29 1 .O35 1 .O45 1 .O52 1 .O59 1 .O66 1 .O76
10 MV 0.970 1.014 1.024 1.035 1.040 1.046 1.055 1.063
Table 4-4: PSF in solid water for 6, 10, and 18 MV X-ray beams. (The field size is defined at d-).
Table 4-5 lists the PSF for the 18 MV X-ray beam measured in solid water and
poly sty rene. The uncertainties in the values obtained are about f 1 .5% and f 1 .O% for solid
water and polystyrene, respectively. The PSF values in table 4-5 show that, in general, the
PSF is not sensitive to the material of the water-equivalent phantom, similarly to the
conclusion observed for the Co-60 beam. Accordingly, we rnay conclude that the PSF
does not depend significantly on the material of the water-equivalent phantoms for beams
ranging from Co-60 to 18 M V X-ray beam.
Chapter Four
I Field sue (cm4 I
Tabk 4-5: PSF msults for 18 MV X-ray beam in solid water and poiystyrene.
Solid Water
Poiystyrene
Although ~urns" in the BJR supplement 25 offered a definition of the TAR
consistent with the definition of the PSF given in the ICRU report 23 which used the SF,
separation of the primary dose and scattered dose components is still a difficult task and
even the rneasured data for higher beams requires verification by obtaining more data
fiom different units producing similar bearns. For this reason, the BJR supplement 25 still
reports the NPSF and the TMR, in addition to the PDD but not the TAR and the PSF for
megavoltage beams. In table 4-6, our calculated NPSFs for the linac beams are compared
to the NPSFs posted in the BJR supplement 25. The posted NPSF seems to be
independent of the beam energy which agrees with our NPSF results in general.
4x4
0.944
0.967
5x5
0.978
0.993
6x6
0.992
1.003
8x8
1 .O04
1.013
10x10
1 .O12
1.016
12x12
1.01 8
1 .O20
15x15
1 .O22
1.021
20x20
1 .O3 1
1.024
Chapter Four
Field she (cm3
Table 4-6: Our measured NPSFs in solid water for 6 MV, 10 MV, 18 MV X-ray beams compared to the NPSF values tabulated in the BJR supplement 25 (reference 12).
Beam
6MV
10 MV
18 MV
NPSF
m - 2 5 )
4.6 PSF and energy
The variation of the PSF with energy is often published in many dosimetric
references as curves of the P SF versus HYL in copper for various fields. Figure 1-8 is an
example of this practice showing a plot of the PSF for 5x5, 1Ox 10, and 20x20 cm2 fields
versus the barn energy descnbed by its W L in copper.
To report the our measured PSFs with the mean energy of the beams used,
additional attenuation curves in aluminurn, copper, and lead were measured. The
attenuation curves in these media, in addition to the attenuation cwves in solid water and
polystyrene, are shown in figures 4-20 through 4-23 for Co-60, 6 MV, 10 MV, and
18 MV photon beams, respectively, and the calculated W L in the various media are
listed in table 4-7. The attenuation figures are also shown on a semilog scale in figures
4-24 through 4-27 for the same beam qualities.
4x4
0.973
0.933
5x5
0.978
0.975
6x6
0.984
0.984
0.933
0.979
0.980
0.987
0.966
0.983
8x8
0.993
0.995
0.992
0.994
10x10
1.000
1 .O00
1.000
1.000
12x12
1.006
1 .O06
1.006
1.006
15x15
1.013
1.014
20x20
1.023
1.021
1.010
1.013
1.019
1.023
Chapter Four
O Sol id W;m
O Fblystyrrrr
OAluminwn
a C'Wcr
XLcad
0.000 ---- 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00
T h i c k (cm)
Figure 4-20: Attenuation curves for a Ce60 beam in solid water, polystyrene, aluminum, copper, and lead.
0 Solid Wircr
O Polyrtytenc
O Aluminum
a CW-
X L d
0.000
0.00 5.W 10 00 15 .00 20 00 25.00 30 00 35.00
Thicknas (cm)
Figure 4-21: Attenuation curves for our 6 MV X-ray beam in solid water, polystyrene, aluminum, copper, and lead.
C hapter Four
Figure 4-22: Attenuation curves for our 10 MV X-ray bearn in solid water, polystyrene, aluminum, copper, and lead.
0.000 -- 0.00 3.00 10.00 15.00 20.00 25.00 30 00 35.00
Thicknas (cm)
Figure 4-23: Attenuation curves for our 18 MV X-ray bearn in solid water, polystyrene, aluminum, copper, and lead.
Chapter Four
0010 - p-
O M ) 5.00 1000 15 00 20 00 300 30 00 35 M)
ïhickncu (cm)
Figure 4-24: Attenuation curves for a Co-60 beam in solid water, polystyrene, aluminum, copper, and lead shown in a semilog scale.
O. 100
0.00 5 .O0 10.00 15.00 20.00 25 W 30.W 35.00
Thickncu (cm)
Figure 4-25: Attenuation curves for our 6 MV X-ray beam in solid water, potystyrene, aluminum, copper, and lead shown in a semilog scale.
Chapter Four
Figure 4-26: Attenuation curves for our 10 MV X-ray bearn in solid water, polystyrene, aluminum, copper, and lead shown in a semilog scate.
O LOO
0.00 3.m 1000 ISQ) 2c.m zoo 30.00 35 00
Thidmm (an)
Figure 4-27: Attenuation curves for Our 18 MV beam in soiid water, polystyrene, aluminum, copper, and lead shown in a semilog scale.
Chapter Four
Beam
Medium
Solid Water Poiystyrene Muminum Copper Lead
10.36 10.3 3 4.49 1.37 1 .O2
14.61 14-55 6.12 1.78 1.24
18.64 18.47 7.52 2.10 1.39
24.06 23.85 8 -98 2.22 1.31
Table 4-7: Calculated HVL in cm for Co-60, 6 MV, 10 MV, and 18 MV photon beams in solid water, polystyrene, aluminum, copper, and lead.
Using the W L data in table 4-7, the mass attenuation coefficients ,dp were
calculated using the following relationship:
where p is the physical
(4-6)
density of the matenal. By using figure 1 - 1 which plots Np
versus photon energy fiom 1 keV to 100 MeV for the various attenuating media, the mean
energy of the beams in the various media was determined ( table 4-8). Data in table 4-8
demonstrate that the calculated mean energy of a polyenergetic megavoltage photon bearn
varies and depends on the attenuating medium. The variation is clear for the 10 MV and
the 18 MV X-ray beams. For the linac beams, the photon beam consists of a spectnun of
photons ranging in energy fiom O MeV to the nominal accelerating energy of the electron
90
Chapter Four ---- .
beam. According to figure 1- 1, photons are atte11uatd differently depending on their
energy and on the atomic number of the attenuating matenal. Therefore, the spectrum of
the photon beam d e r travershg a certain depth in the attenuating medium is different
fiom the spectnim of the photon kam at the surface of the attenuating medium. Hence,
reporting the PSF with W L in copper which is used by dosimetric data references,
proves to be a reliable way of reporting the PSF for different bearn energies. Figure 4-28
shows the PSF for fields of 5x5, 10x 10, and 20x20 cm2 versus photon beam energy. The
data for Co-60 and energies below Cod0 are fkom the BJR supplement 25, and the data
for 6, 10, and 18 MV X-ray beams are our measured data.
Table 4-8: Calculated mean energies in MeV for Co-60,6 MV, 10 MV, and 18 M V photon beams using the attenuation in solid water, polystyrene, aluminum, copper, and lead.
Chapter Four
10 M V O Cs-137 Co-60 6 MV 18 M V
HVL (mm ofCu)
Figure 4-28: The PSF versus HVL in copper for various square fields. Data for Co-60 and energies below Co-60 are fiom the BIR supplernent 25, and the data for 6, 10, and 18 MV X-ray beams are our measured data .
4.7 Summary
In this chapter, the results of the experimental procedure for obtajning the SF was
for Co-60, 6 MV, 10 MV, and 18 MV beams are reported. The PSF data obtained for the
Co-60 bearn favors the new PSF values posted in the BJR supplement 25. Also, the
calculated NPSF for the 6, 10, and 18 MV X-ray beams were similar to posted values of
NPSF in the sarne reference. In addition, the PSF for Co-60 and the 18 M V beams
obtained for a polystyrene phantom was similar to the PSF obtained in a solid water
phantom.
92
Chapter Four
1. McKenzie A. L. "Cobalt-60 gamma-ray beams", Br. J Radiol., Supplement
25 : 46-5 1 (1 996).
2. Hubbell J. H. and Seltzer S. M. "Tables of X-Ray Mass Attenuation
Coefficients and Mass Energy-Absorption Coefficients fiom 1 keV to 20 MeV
for Elements Z = 1 to 92 and 48 Additionai Substances of Dosimetric Interest",
NISTIR 5632, National Institute of Standards and Technology (NIST).
3. Turner J. E.: Atoms, Radiation, and Radiarion Protection. 2nd edition. John
Wiley & Sons, New York, New York, U.S.A. (1995).
4. Johns H. E. and Cunningham J. R.: The Physics ofRadiology. 4thedition.
Charles C. Thomas, Springfield, Illinois, U.S.A. (1983).
5 . Han K., Ballon D., Chui C., and Mohan R. "Monte Carlo simulation ofa
cobalt-60 beam", Med. Phys. 14 : 414-419 (1987).
6. Rogers D. W. O., Faddegon B. A., Ding G. X., Ma C-M., Wei J., and Mackie
T. R. "BEAM: A Monte Carlo code to simulate radiotherapy treatment units",
Med. Phys. 22 : 503-524 (1995).
7. Kijewski P. K., Bjhgard B. E., and Petti P. L. "Monte Carlo calculations of
scatter dose for srnail field sizes in a Co-60 beam", Med Phys. 13 : 74-77
(1 986).
8. Bjiimgard B. E. "Scatter factors for a 25-MV X-ray beam, Med. Phys. 20 :
357-36 1 (1 993).
9. Godden T. J. "Gamma radiation fiom cobalt 60 teletherapy Units",
Br. J. Rmiiol., Supplement 17 : 45-49 (1983).
10. Sixel K.E. and Podgorsak E.B. "Build-up region and depth of dose maximum
of megavoltage X-ray beams", Med Phys. 21 : 4 1 1-41 6 (1 994).
11. Bums J. E. "Definition of tissue-air ratio". Br. J. Radioi., Supplement 25 :
177- 182 (1 996).
12. Jordan T. J. "Megavoltage X-ray beams: 2-50 MV", Br. J. Radiol., Supplement
25 : 62-83 (1996).
Chapter Five
CHAPTER 5
CONCLUSIONS .......................................... 5.1 SUMMARY ............................................................... .................94
5.2 FUTURE WORK ............. ......................... ........................................................... .. ............... %
5.1 Summary
The main objective of this thesis was to obtain scatîer factors (SF) and peak
scatter factors (PSF) data for high energy photon beams in various water equivalent
materials. In chapter 1, a brief background covering several dosimetric concepts, such as
primary and scattered photons, exposure, dose, and kerma is given. Moreover, the chapter
includes definitions of some basic functions used in radiation therapy and demonstrates
some of the basic applications of the PSF in dosimetry, such as the calculation of the
tissue air ratios (TAR) fiom the percentage depth dose (PDD) and the calculation of the
relative dose factors (RDF) for irregular fields
Chapter 2 provides a historic development of the definition of the PSF. Basically,
in the early days of radiotherapy, the PSF was defined as a special case ofthe TAR
equaling the TAR at the surface. The definition of the PSF was changed by the KRU
reports 10 and 23 (reference 1) which introduced the SF and defmed PSF as SF at the
depth of dose maximum d-. Since then, medical physicists debated the consistency of
the PSF data quoted in dosimetric references, such as the BJR supplement 17, and the
argument led to development of several methods for measuring the SF in order to obtain
more accurate PSF values.
Chapter Five
The methods and materials used in the thesis for obtainuig the SF and the PSF for
high energy photon beams are described in Chapter 3. The me-, developed by
~ j i i r n ~ a r d ~ ~ , was based on results of Monte Car10 simulations of megavoltage photon
beams. Moreover, the chapter discusses the materials and experimental setup parameters
used in our work.
In Chapter 4, the results of the PSF in water, solid water, and polystyrene
phantoms are presented for various photon beams. First, the PSF in water, solid water,
and polystyrene materiais for Co-60 were extracted fiom the SF data and found in
agreement with the PSF values for Co-60 iisted in the BJR supplement 25. For a 1 Ox 1 O
cm2 field size, the PSF obtained in al1 three materials were within +1 .O% of the value
quoted in the BJR supplement 25.
In addition, the PSF for 6 MV, 1 0 MV, and 18 M V X-ray beams in solid water
and the PSF for 18 MV X-ray beam in polystyrene were obtained. The NPSF calculated
fiom the measured PSF for solid water data for the iinac beams were very similar to the
NPSF tabulated in the BIR supplement 25 for the respective beams. Also, the PSFs in
solid water for the 18 MV X-ray bearn were very similar to the PSFs in polystyrene for
the same photon beam. The results of the PSF for Co-60 and for the 18 MV X-ray beam
in solid water and polystyrene indicate that one set of PSF data is adequate for use in
dosimetry, justiming the cornmon practice in radiotherapy clinics of using PSF data for
water for al1 water equivalent phantoms.
The calculated PSF for small field sizes for 10 MV and 18 MV X-ray beams were
less than 1 .O which is inconsistent with the definition of the PSF. This inconsistency is
Chapter Five
suspected to be produced by using a fixed d- and not taking into account the variation of
the true peak dose with field size, which is considerable for high energy beams.
Finally, attenuation curves in various materials were measured in order to estimate
the mean energy of the photon beams used and to plot the PSF for various square fields
versus the mean energy of the photon beams. The calculated mean energies depend on the
material of the attenuator and the variation in the calculated mean energies for our 10 and
18 M V X-ray beams was greater compared to the 6 MV and Co-60 photon.
5.2 Future work
Presently, dosimetry protocols used for treatment planning make use of the
percentage depth dose, the tissue maximum ratios, and the tissue phantom ratios, in
addition to beam profiles, to calculate the dose distribution in the patient. Meanwhile,
scatter factors are rarely used in clinics and are hardly found in dosirnetric references.
Although data for the conventional dosimetric functions have k e n well established in
dosimetric references, the advantage of relying on scatter factors data is to provide
physicists with an alternative tool to be used in conjunction with the conventional
dosimetric functions in treatment planning and for dose calculation providing more
confidence on the treatment plan before treating the patient. In addition, scatter factors
data could be used to obtain dosimetric data which are difficult to measure directly, such
as the primary and scattered doses. Therefore, obtaining scatter factors data and
establishing sets of scatter factors reference data will enrich current dosimetric
procedures. Moremer, developing additional methods for measuring scatter factors may
provide a better understanding of the bebavior of the scatter factors at the buildup region
and near the depth of dose maximum.
Chapter Five
References
1. K R U 1973 "Measurement of absorbed dose in a phantom irradiated by a single
beam of X or gamma rays", Report 23, international Commission on Radiation
Units and Measwement (KRU).
2. Bjiüngard B. E. "Scatter factors for a 25 MV X-ray beam, Med Phys. 20 : 3 57-
361 (1993).
3. Bjiüngard B. E. and Petti P. L. " Description of the scatter component in photon-
beam data", Phys. Med Biol. 33 : 21-32 (1988).
4. Bjiirngard B. E., Rashid H., and Obcemea C. H. "Separation of primary and scatter
components of measured photon beam data", Phys. Med Biol. 33 : 1939-1945
( 1 989).
Tissue output ratio data in various materials
Field size (cm4 --
Depth (cm) 5x5 6x6 8x8 10x10 12x12 0.6 1 .O96 1.1 13 1.133 1.155 1.169 1.6 1 .O63 1 .O8 1 1.106 1.127 1.146 4.6 0.935 0.962 0.994 1 .O22 1 .O42 7.6 0.796 0.824 0.863 0.897 0.923 11.0 0.639 0.669 0.716 0.752 0.783 15.0 0.499 0.526 0.568 0.603 0.634
Table A-1: Tissue output ratio data for various square fields measured in solid water for a Co-60 beam.
0.400
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0
Depth (cm)
Figure A-1: Tissue output ratio curves for various square fields in solid water for a Co-60 beam.
Depth (cm)
0.5 1.0 3.0 5.0 7.0 9.0
1 Field size (cm3
Table A-2: Tissue output ratio data for various square fields measured in water for a Co-60 beam.
Figure A-2: Tissue output ratio cuwes for various square fields in water for a Cm60 beam.
Table A-3: Tissue output ratio data for various square fields measured in polystyrene for a Co-60 bearn.
Figure A-3: Tissue output ratio curves for various square fields in polystyrene for a Co-60 bearn.
Field size (cm3
1.5 0.986 1.002 1.019 1 .O46 1 .O66 1 .O83 1.102 1.124 2 0.994 1 .O07 1 .O24 1 .O50 1.070 1 .O87 1.104 1.125 4 0.93 1 0.953 0.971 1 .O01 1.024 1.041 1.062 1.084 6 0.859 0.885 0.906 0.940 0.965 0.985 1.008 1.034 8 0.787 0.809 0.834 0.870 0.898 0.920 0.945 0.975 10 0.722 0.747 0.769 0.808 0.838 0.862 0.889 0.922
Table Ad: Tissue output ratio data for various square fields measured in solid water for our 6 MV X-ray beam.
Figure A-4: Tissue output ratio curves for various square fields in solid water for our 6 MV X-ray beam.
Table A-5: Tissue output ratio data for various square fields measured in solid water for our 10 MV X-ray beam.
Depth (cm)
2 2.5 3 4 6 8 10 12 14 16 18 20
Figure A-5: Tissue output ratio curves for various square fields in solid water for Our 10 MV X-ray beam.
- -
Field s é e (cm3
20x20 1.088 1.093 1 .O92 1 .O73 1 .O3 2 0.986 0.941 0.897 0.850 0.807 0.763 0.722
1 2 x 1 2 1.040 1.050 1.053 1.035 0.989 0.941 0.891 0.843 0.795 0.749 0.702 0.662
10x10 1.023 1.036 1.038 1.022 0.975 0.923 0.873 0.824 0.772 0.727 0.679 0.639
15x15 1.062 1.070 1 .O7 1 1.052 1.010 0.961 0.914 0.868 0.819 0.776 0.729 0.689
m m
8x8 1 .O0 1 1.017 1.019 1.002 0.952 0.900 0.846 0.798 0.748 0.701 0.653 0.614
6x6 0.972 0.992 0.994 0.977 0.925 0.868 0.813 0.763 0.713 0.666 0.622 0.582
4x4 0.903 0.922 0.925 0.902 0.852 0.796 0.735 0.687 0.647 0.598 0.556 0.516
5x5 0.953 0.972 0.972 0.955 0.897 0.845 0.785 0.739 0.688 0.642 0.596 0.560
Field size (cmz)
Depth (cm) 4x4 5x5 6x6 8x8 10x10 12x12 15x15 20x20 3 0.860 0.903 0.928 0.963 0.994 1.016 1 .O40 1 .O67
3.5 0.877 0.919 0.944 0.978 1 .O04 1 .O24 1 .O45 1 .O68 4 0.881 0.923 0,950 0.983 1 .O07 1 .O24 1 .O42 1 .O63 6 0.857 0.906 0.932 0.962 0.984 0.999 1 .O14 1 .O32 8 0.814 0.863 0.890 0.922 0.943 0.958 0.974 0.993 10 0.773 0.818 0.845 0.878 0.901 0.916 0.933 0.954 12 0.729 0.775 0.803 0.836 0.860 0.877 0.895 0.917 14 0.693 0.734 0.760 0.795 0.818 0.836 0.855 0.878 16 0.651 0.693 0.72 1 0.754 0.779 0.796 0.816 0.840 18 0.615 0.658 0.682 0.715 0.739 0.758 0.778 0.802 20 0.583 0.622 0.647 0.679 0.702 0.721 0.742 0.767
Table Ad: Tissue output ratio data for various square fields measured in solid water for Our 18 MV X-ray beam.
Figure A-6: Tissue output ratio curves for various square fields in solid water for Our 18 MV X-ray bearn.
Depth (cm)
Field size (cm')
Table A-7: Tissue output ratio data for various square fields measured in polystyrene for our 18 MV X-ray beam,
Figure A-7: Tissue output ratio curves for various square fields in polystyrene for our 18 MV X-ray beam.
- -
Appendix-B
Scatter Factors
20x20 cm2
,' ,A-
/' /' 15x1s cm'
12x12 cm*
10x10 cm'
1.000 -- ----- - - - - - - - A-
0.0 2.0 4.0 6.0 8 0 10 O 12.0 14 O 16 0
Dcpib ( c i )
Figure 5 1 : Scatter factors in water for a Co-60 beam for various square fields.
r.000 - -- --
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0
Deptb (cm)
Figure Ef: Scatter factors in polystyrene for a Co-60 beam for various square fields.
12x12 cm' / /' 10x10 cm'
Figure B-3: Scatter factors in solid water for a Co-60 beam for various square fields.
,/-------y 4x4 cm'
1 .O00 ---- 0.0 5.0 10.0 15.0 20.0
Deptb (cm )
Figure 54: Scatter factors in solid water for our 6 MV X-ray beam for various square fields.
20x20 cm'
15x15 cm'
IOxIO cm'
8x8 cm'
6x6 cm'
5x5 cm'
4x4 cm'
0 .900 - 0.0 5 .O 10.0 15.0 20.0
Drpib ( c i )
Figure ES: Scatter factors in solid water for our 10 MV X-ray beam for various square fields.
0.900 - 0.0 5.0 10.0 15.0 20.0
Dcptb (cm)
Figure 56: Scatter factors in solid water for our 18 MV X-ray beam for various square fields.
_ _y-__ 6x6 cm' __--
-/--y- 5x5 cm'
/---
---!
- 4x4 cmL
--/ --y
/-- --
Figure &7: Scatter factors in polystyrene for our 18 MV X-ray beam for various square fields.
List of Figures
Figure 1-1
Figure 1-2
Figure 1-3
Figure 1-4
Figure 1-5
Figure 1-6
Figure 1-7
Figure 1-43
Figure 1-9
Figure 2-1
Figure 2-2
Figure 2-3
Figure 2-4
Figure 2-5
Figure 2-6
Figure 2-7
Mass attenuation coefficient for various materials published by the National Institute of Standards and Technology ............... .. ................................... 4
.................................. Schematic representation of the definition of the PDD 8
Several PDD curves in water for different photon beams for a field size of 10x 10 cm2 and source-surface distance (SSD) as indicated ........................... 9
The variation of d,, with square fields for 6. 10. and 18 MV X-ray beamsll
Beam profile sets of 10x 10 and 30x30 cm2 fields for a 10 M V beam ......... 13
................................... Schematic illustration of the definition of the RDF .14
............................................. Schematic illustration of the definition of the TAR 16
Schematic illustration of the definition of the TP R .................... ... .......... 18
......... ........ Variation of PSF with HVL in copper for several square fields .. 19
A schematic diagram illustrating the definition of PSF in the early days of radiotherap y ................................................................................................. -23
A schematic diagram illustrating the definition of TAR as introduced by Johns and colleagues. .................................................................................. -24
A schematic diagram illustrating the definition of the TAR as introduced by the K R U report 10 ....................................................................................... 25
A schematic diagram of primary and scattered photons contributing to the ........ ......................... exposure or absorbed dose at point Q in a phantom .. 30
Detennination of the absorbed dose to a point in air within a small mass of tissue material ............................................................................................... 31
Estimation of the PSF by extrapolating of the NPSF to zero field size to obtain NPSF(0) ............................................................................................ -36
Diagram illustrating the geometry used by Nizïn and Kase for separating the primary component from the scatter component in high-energy photon
............................................................................................................ beams 38
Figure 2-8
Figure 3-1
Figure 3-2
Figure 3-3
Figure 3 4
Figure 3-5
Figure 3-6
Figure 3-7
Figure 4-1
Figure 4-2
Figure 4-3
Figure 4 4
Figure 4-5
Figure 4 6
Figure 4-7
Figure 4-8
A schematic diagram illustrating the definition of the TAR proposed by the B JR supplement 25 ....................................................................................... 41
.................................. Schematic diagram illustrating the definition of TOR 47
Diagrarn to illustrate the calculation of the ratio of the primary doses at Q and Qm. ......................................................................................................... 49
Schematic diagram of a narrow beam geometry setup used for attenuation measurement where f is the source-detector distance and t is the attenuator thickness ...................................................................................................... -54
A schematic diagram illustrating the setup for the CF measurement ........... 56
........ A schematic diagram illustrating the setup for the TOR measurement 57
A schematic diagram showing a cross sectional view of the slab used for .................................................................................... cy lincirical chambers -58
A schematic diagram showing a cross sectional view of the slab used for parallel plate chambers ................................................................................ -59
Attenuation curves for Co-60 clinical beam in water. solid water. and poly styrene .................................................................................................... 64
Attenuation curves for Co-60 clinical beam in water. solid water. and polystyrene plotted on a semilog scale ......................................... .. ........... 64
A schematic representation of the Co-60 unit head used in the Monte Carlo simulation .................................................................................................... -67
Spectral distribution for the Co-60 bearn using BEAM software package collected below the trimmer bars for a 5x5 cm2 field size at 80 cm ............. 68
Spectral distribution for the Co-60 hem using BEAM software package collected below the trimmer bars for a 5x5 cm2 field size at 80 cm. ( data
. ........................................................*... from Fig 4-4 on an expanded scale) 68
Attenuation curves in solid water for 6. IO . and 1 8 MV X-ray beams ....... 70
Attenuation curves in solid water for 6. IO . and 18 MV X-ray bearns shown on a semilog scale ....................................................................................... -70
Attenuation cuntes in polystyrene for 6. 10. and 1 8 MV X-ray beams ........ 71
Figure 4-9 Attenuation c w e s in polystyrene for 6, 10, and 18 MV X-ray beams shown ....................................................................................... on a semilog scale 71
Figure 4-10 Collimator factors for the CodO, 6 MV, 10 MV, and 18 M V photon beams 2 ................................................................. normalized to unity at 1 Ox 1 O cm 72
Figure 4-1 1 TOR curves for a lOx 1 O cm2 field for cobalt, 6 MV, 10 MV, and 18 MV X-ray bearns in solid water norrnalized to 5 cm depth and 1 Ox 10 cm2 field
.............................................................................................................. size -.73
Figure 4-12 Linear extrapolation cuves used in detemination of SF(5,lOx 10 cm2) in solid water for Co-60 beam .......................................................................... 75
Figure 4-13 Linear extrapolation curves used in determination of SF(5,l Ox 10 cm2) in water for Co-60 beam ................................................................................... 76
Figure 4-14 Linear extrapolation curves used in determination of SF(5,l Ox 10 cm2) in ...................................................................... polystyrene for Co-60 beam 76
Figure 4-15 Linear extrapolation curves used in determination of SF(5,lOxlO cm2) in solid water for 6 MV X-ray beam ................................................................. 77
Figure 4-16 Linear extrapolation curves used in determination of SF(5,l Ox 1 O cm2) in solid water for 1 O MV X-ray beam ............................................................ 77
Figure 4-1 7 Linear extrapolation curves used in determination of SF(5,lOx 10 cmZ) in solid water for 18 M V X-ray beam ............................................................... 78
Figure 4-18 Linear extrapolation curves used in determination of SF(5,IOx 10 cm2) in polystyrene for 18 MV X-ray beam. ............................................................. 78
Fipre 4-19 Calculated SF curves for a 10x 10 cm2 field in solid water for Co-60,6 MV, ............................................................... 10 MV, and 1 8 MV photon bearns 80
Fipre 4-20 Attenuation curves for a CodO beam in solid water, polystyrene, aluminum, ........................................................................................... copper, and lead .86
Figure 4-21 Attenuation curves for our 6 MV X-ray beam in solid water, polystyrene, .......................................................................... aluminum, copper, and lead 86
Figure 4-22 Attenuation curves for our 10 MV X-ray beam in solid water, polystyrene, .......................................................................... aluminum, copper, and lead 87
Figure 4-23 Attenuation curves for our 18 MV X-ray beam in solid water, polystyrene, ....................................................................... aluminum, copper, and lead - 3 7
Figure 4-24 Attenuation c w e s for a Cod0 beam in solid water, polystyrene, aluminum, copper, and lead shown in a semilog scaie ................................................. -.ûû
Figure 4-25 Attenuation c w e s for our 6 M V X-ray beam UA solid water, polystyrene, aluminum, copper, and lead shown in a semilog scale ............................... 88
Figure 4-26 Attenuation c w e s for our 10 MV X-ray beam in solid water, polystyrene, aluminum, copper, and lead shown in a semilog scale ................................. 89
Figure 4-27 Attenuation curves for our 18 MV X-ray beam in solid water, polystyrene, aluminum, copper, and lead shown in a semilog sale ................................. 89
Figure 4-28 The PSF versus HYL in copper for various square fields. Data for Co-60 and energies below Co-60 are fiom the BJR supplement 25, and the data for 6, 10, and 18 MV X-ray beams are our measured data .................................... 92
Figure A-1 Tissue output ratio curves for various square fields in solid water for a Co-60 beam ......................... .. . ...................................... . . . ........ . ..................... 98
Figure A-2 Tissue output ratio curves for various square fields in water for a Co-60 beam .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - - . . .-!El
Figure A-3 Tissue output ratio curves for various square fields in polystyrene for a Co-60 beam ...... .. .. ..... . .. . .... .. .. . .... ...... . .. .....-. .. .... .... ...-. . . . . . . . .-.. .... .........-.... ... 100
Figure A 4 Tissue output ratio curves for various square fields in solid water for our 6 MV X-ray beam ........................ ....... . ........... . ........................................ ... 101
Figure A-5 Tissue output ratio curves for various square fields in solid water for our 1 0 MV X-ray beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -102
Figure A 4 Tissue output ratio curves for various square fields in solid water for our 18 MV X-ray beam ..................................................................................... 103
Figure A-7 Tissue output ratio curves for various square fields in polystyrene for our 18 M V X-ray beam ..................................................................................... 104
Figure B-1 Scatter factors in water for a Co-60 beam for various square fields .......... 105
Figure &2 Scatter factors in polystyrene for a Co-60 beam for various square fields.106
Figure B-3 Scatter factors in solid water for a Cod0 beam for various square fields.106
Figure B 4 Scatter factors in solid water for our 6 MV X-ray beam for various square fields ........................................................................................................... 107
Figure 5 5 Scatter factors in solid water for our 10 MV X-ray beam for various square fields ........................................................................................................... 107
Figure 8-6 Scatter factors in solid water for our 18 MV X-ray beam for various square fields ................................. .. ..................................................................... 108
Figure B-7 Scatter factors in polystyrene for our 18 MV X-ray beam for various square fields ........................................................................................................... 108
List of Tables
Table 1-1 Typical values of d' listed in the British Journal of Radiology supplement 25 for various photon beams ............ .. .......................................... 12
Tabk 3-1 Dosimettic parameters of poly styrene. tissue. water. and solid water ........... 52
Table 3-2 Experimental setup parameters for attenuation measurements ...................... 54
Tabk 3-3 Experimental setup parameters used for the CF measurement ...................... 56
Table 3-4 TOR experimental setup parameters used for measurements in water. solid .................................................... water. and polystyrene for the Cod0 beam 59
Table 3-5 TOR experimentai setup parameters used for measurements in water. solid ............................ water. and polystyrene for 6. 10. and 1 8 MV X-ray bearns 59
Table 4-1 Linear attenuation coefficient and beam hardening coefficient in polystyrene ............... ..........**. and solid water for 6. 10. and 1 8 MV X-ray beams ...... 69
Table 4-2 Average SF(5. 1Ox 10 cm2) and estimated error in various materials for Co-60. 6 MV. 10 MV. and 18 MV photon beams ...................................................... 79
Table 4-3 PSF results in water. solid water. and polystyrene and tabulated PSF values in .......................................... the BJR-supplements 17 and 25 for Co-60 beams 81
Table 4-4 PSF in solid water for 6. 10. and 18 MV X -ray bearns . (The field size is defined at &a) ............................................................................................................................................. 83
............... Table 4-5 PSF results for 18 MV X-ray beam in solid water and potystyrene 84
Table 4 4 Our measured NPSFs in solid water for 6. 10. and 18 MV X-ray beams .............. compared to the NPSF values tabulated in the BJR supplement 25 85
Table 4-7 Calculated HVL in cm for Co.60. 6 MV. 10 MV. and 18 MV X-ray beams in solid water. polystyrene. aluminum. copper. and lead .................................... 90
Table 4-8 Calculated mean energies in MeV for Co.60. 6 MV. 10 MV. and 18 MV photon beams using the attenuation in solid water. polystyrene. aluminum. copper. and lead ............................................................................................. -91
Table A-1 Tissue output ratio data for various square fields measured in solid water for a Co-60 beam ............................................................................................... -98
Table A-2 Tissue output ratio data for various square fields measured in water for a ................................................................................................... Co-60 beam 99
Table A-3
Table A 4
Table A-5
Table A 4
Table A-7
Tissue output ratio data for various square fields measured in polystyrene for a Co-60 beam .............................................................................................. lûû
Tissue output ratio data for various square fields measured in solid water for our 6 M V X-ray beam.. .............................................................................. -101
Tissue output ratio data for various square fields measured in solid water for out 1 O MV X-ray beam .............................................................................. 102
Tissue cutput ratio data for various square fields measured in solid water for ........................................... our 1 8 MV X-ray beam.. ....................... ... -103
Tissue output ratio data for various square fields measured in polystyrene for our 1 8 MV X-ray beam.. .......................................................................... -104
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