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D O SIM ETRY O F VERY SM A LLPH O TO N FIELD S
b y
K am en A. Pas k alevD epartm ent of Med ical Ph ys ics
M cGill Univers ity, M ontrealM ay 2002
A th es is subm itted to th e Faculty ofGraduate Studies and Research in partial
fulfillm ent of th e req uirem ents for th edegree of M aster of Science
K am en A. Pask alev, 2002
ii
Abstract
Several dosimetric parameters were measured for three very small radiation fields
(1.5, 3, and 5 mm diameter at the machine isocenter) with a small ionization chamber and
a new type of radiochromic film. The experiments were carried out on a Clinac-18 linac
and the fields were shaped by specially manufactured collimators. When measuring dose
profiles, the ionization chamber measurements were first corrected for response variation
in off-axis direction, and then deconvolved to eliminate the blur due to the poor
resolution of the chamber. The measured data agreed with Monte Carlo simulations
within the established statistical uncertainties.
Dynamic stereotactic radiosurgery was carried out on the same accelerator using
the very small radiation beams. The dose distributions and their displacements from the
laser-defined isocenter of the linac were measured and then compared to 3-D Monte
Carlo calculations. The results proved that dynamic radiosurgery with very small beams
has potential for clinical use.
iii
Résumé
Plusieurs paramètres dosimétriques ont été mesurés pour trois très petits champs
de radiation (1.5, 3 et 5 mm de diamètre à l’isocentre de la machine de traitement) avec
l’aide d’une chambre à ionisation à petit volume et un nouveau type de film
radiochromic. Les mesures ont été effectuées avec un accélérateur linéaire Clinac-18 sur
lequel les champs de traitement sont définis par des collimateurs spécialement usinés.
Lors des mesures des profils de dose, les mesures initiales sont premièrement corrigées
pour la variation de la réponse en direction hors axe, et puis convoluées pour éliminer le
flou causé par la faible résolution de la chambre. Les données mesurées sont en accord
avec les simulations Monte-Carlo à l’intérieur des incertitudes statistiques établies.
Des irradiations de radio chirurgie stéréotaxique dynamique ont été effectuées sur
le même accélérateur en utilisant les très petits champs. Les distributions de dose et leurs
déplacements par rapport à l’isocentre, défini par les lasers de la machine de traitement,
ont été mesurés et puis comparés aux calculs 3-D de Monte-Carlo. Les résultats
démontrent que la radio chirurgie dynamique à l’aide de très petits champs est
potentiellement utilisable en clinique.
iv
Acknowledgments
I would like to express my gratitude to Dr. Ervin B. Podgorsak, firstly for being
my teacher in medical physics, and secondly for giving me the opportunity to work on
such a challenging and interesting project, as well as for being my supervisor. He has
allowed me to work independently and has encouraged me to explore any idea related to
the subject. At the same time Dr. Podgorsak has always been very helpful and open for
discussions, providing me with the real scientific point of view. He also secured all the
resources I needed to work quickly and efficiently, regardless of the expenses and the
time required to do so.
I would also like to thank Dr. Jan Seuntjens for providing me with all knowledge I
needed in the areas of precise dosimetry and Monte Carlo simulations, and for his
friendly and supportive attitude.
During my research I had very helpful discussions with Dr. Dimitre Hristov, Dr.
Pavel Stavrev, Dr. François DeBlois and my fellow students Wamied Abdel-Rahman,
Kristin Stewart, Robert Doucet, and Khalid Al-Yahya. I want to thank them and all the
staff and students at the Department of Medical Physics for being a friendly and helpful
environment
Finally, I would like to thank my family for their constant support, and all my
previous teachers for their dedication over the years.
Table of Contents
Chapter 1: Introduction............................................................................................... 1
1.1. Overview of external photon beam therapy................................................. 1
1.2. Stereotactic Radiosurgery ........................................................................... 3
1.3. Treatment planing ant the basic dosimetry functions................................... 5
1.4. Dosimetry of very small fields.................................................................... 15
1.5. Thesis objectives ........................................................................................ 21
1.6. Thesis organization..................................................................................... 22
Chapter 2: Materials and Methods – Equipment and Experimental Techniques........... 29
2.1. Radiation source......................................................................................... 29
2.2. Dosimeters ................................................................................................. 33
2.3. Experimental setups.................................................................................... 40
2.4. Dynamic stereotactic radiosurgery.............................................................. 43
Chapter 3: Materials and Methods – Monte Carlo Particle Transport Simulations....... 48
3.1. Theoretical basics....................................................................................... 48
3.2. Monte Carlo transport of electrons and photons.......................................... 51
3.3. Monte Carlo code systems for photon and electron transport ...................... 54
3.4. Monte Carlo simulation of the Clinac-18 linear accelerator......................... 60
3.5. Monte Carlo simulations in water phantoms............................................... 63
Table of Contents
vi
Chapter 4: Exradin A14P ionization chamber study.................................................... 69
4.1. Geometry of the measuring volume............................................................ 69
4.2. Deconvolution of dose profiles in water...................................................... 75
4.3. Correction factors for off-axis measurements.............................................. 83
Chapter 5: Experimental Results
5.1. Beam quality.............................................................................................. 89
5.2. Physics of dose deposition .......................................................................... 100
5.3. Off-axis ratios (dose profiles)..................................................................... 105
5.4. Central axis measurements......................................................................... 112
5.5. Dynamic stereotactic radiosurgery with the 1.5 mm and 3 mm beams......... 117
Chapter 6: Conclusions and Future Work................................................................... 123
6.1. Summary and conclusions ......................................................................... 123
6.2. Future work ................................................................................................ 126
List of Figures............................................................................................................ 128
List of Tables ............................................................................................................. 136
Bibliography .............................................................................................................. 137
Chapter 1:
Introduction
1.1. Overview of external photon beam therapy
Radiation was first used for cancer treatment soon after the discovery of x-rays by
Roentgen in 1895 and radioactivity by Becquerel in 1896. Since then the knowledge of
how ionizing radiation cures disease has grown tremendously as a result of large
improvements in technologies employed for this purpose and experience gained from
clinical work. There are several different types of treatment techniques in modern
radiation therapy, but the vast majority of cancer treatments are carried out using the
external photon beam irradiation techniques in which the radiation source is placed at
some distance (typically 100 cm) from the patient. For almost five decades since the
beginning of last century, the treatments of this kind were performed using x-ray tubes
and Van de Graaff generators. However, these devices were capable of producing x-ray
beams only in the 100 kV range, and thus were not very useful for treating tumors located
deep inside the human body1.
At the end of 1951, the first patient treatment with cobalt-60 gamma rays was
delivered. The cobalt teletherapy unit was developed by Harold Johns’ group in
Saskatoon, Saskatchewan, Canada1,2. The operation of the unit was based on a cobalt-60
radioactive isotope source, emitting gamma rays with energies of 1.17 MeV and 1.33
MeV, and having an average energy of 1.25 MeV. The cobalt unit had a great impact on
Chapter1: Introduction
2
radiotherapy at that time and was the most widely used equipment for external beam
treatments during the following twenty years.
In the beginning of the 1960s a new machine for external beam dose delivery was
introduced: a relatively small linear electron accelerator (linac), specifically designed for
cancer treatment in a clinical environment1,2. A photograph of a modern clinical linac is
shown in Fig. 1.1. The operating principle of a linac is based on a narrow high-energy
electron beam striking a target in order to produce bremsstrahlung photons. The linac has
many advantages compared to the cobalt unit, and only a few disadvantages. It is capable
of delivering photon and electron beams with energies much higher than the 1.25 MeV
gamma rays produced by a cobalt unit. Because of its considerable advantages over the
cobalt unit, the linac became the equipment of choice in radiotherapy during the past
twenty years.
Figure 1.1: Typical view of a linear accelerator used in cancer therapy.
Chapter1: Introduction
3
1.2. Stereotactic radiosurgery
AAPM Report No. 54 defines Stereotactic Radiosurgery (SRS) as a treatment
technique that combines the use of stereotactic apparatus and energetic radiation beams to
irradiate a lesion with a single treatment3. This treatment modality is mainly used to treat
intracranial lesions, such as primary brain tumors, functional disorders (epilepsy,
Parkinson’s disease, etc.), arteriovenous malformations (AVMs), and brain metastases.
Several clinical applications have been presented by Podgorsak et al.4,5, McKenzie et al.6,
Luxton et al.7, etc. The doses delivered in a single session can be as high as 50 Gy, and
the typical dimensions of the planning target volume are on the order of several
millimeters to several centimeters1.
A digital subtraction angiography (DSA) image of a small AVM is shown in Fig.
1.2 with the dimension of the malformation on the order of 5 mm. Since the targets are
even smaller when some functional disorders are treated with radiation8,9, the sizes of
radiation beams used for radiosurgery are thus typically much smaller than those used in
conventional radiotherapy.
During the 1960s and the 1970s, photon beam radiosurgery was carried out with a
special device called the Gamma knife or Gamma unit1,10-12, based on 201 cobalt-60
sources and dedicated solely to radiosurgery. The beams were collimated in such a way
that they crossed one another at the isocenter (focus) of the unit. In the 1980s, when
linear accelerators with well-defined and precise isocenters became commercially
available, several linac-based radiosurgery techniques were introduced into clinical
practice4,5,13.
Chapter1: Introduction
4
In the current clinical practice both the linac and the Gamma knife are used for
radiosurgery treatments. The diameter of the radiation beam is between 10 mm and 40
mm when the radiosurgery treatment is carried out with a linear accelerator, while the
Gamma unit uses four collimators defining beam diameters of 4, 8, 14 and 18 mm.
Because the fields are so small, there are three main issues that have a great
impact on the treatment accuracy: target localization, target positioning and dose
distribution calculations.
The uncertainty associated with target localization is an issue that the different
imaging modalities (MRI, CT, DSA) are dealing with. The modern equipment is capable
of determining the target position with uncertainties as low as ±1 mm.
The second issue is related to target positioning with respect to the isocenter of
the treatment machine. It introduces uncertainties firstly because of possible tissue
1 cm
Figure 1.2: DSA image of a small AVM.
Chapter1: Introduction
5
motion between the imaging and treatment processes and secondly because of problems
in defining the isocenter of the treatment machine. The isocenter of a Gamma unit is
defined within ±0.3 mm whereas that for a linac is defined within ±1 mm1.
The third issue is related to the accuracy of dose distribution calculations, and this
represents a serious problem, especially for fields smaller than a few millimeters in
diameter. The basic dosimetry parameters for such fields, as discussed bellow, are
difficult to measure.
The first and second issues will not be addressed in this thesis; the third one, on
the other hand, motivated this work. Very small radiation fields (defined with dimensions
bellow 5 mm) have a great potential for use in treatment of functional disorders;
however, defining their parameters, be it with measurement or calculation, represents a
considerable challenge, as discussed in this work.
1.3. Treatment planning and the basic dosimetry functions
The goal of every external photon beam treatment is to deliver a dose distribution
which conforms to the planning target volume (PTV) as precisely as possible, sparing the
surrounding healthy tissue. The term planning target volume, as well as some other terms
commonly used in radiation therapy, are defined by the International Commission on
Radiation Units and Measurements (ICRU), Report No. 50 (Ref. 14) and refined in the
ICRU, Report No. 62 (Ref. 15). The typical steps associated with an external beam
treatment are shown in the block diagram in Fig. 1.3.
Chapter1: Introduction
6
After a patient is diagnosed with cancer and a decision is made to treat the disease
with radiotherapy, a physician and a medical physicist determine the planning target
volume (PTV), taking into account margins for non-visible (microscopic) spread of the
decease and for all uncertainties in dose delivery. When the volume to be irradiated is
determined, a particular treatment technique must be chosen. The beam geometry is
selected either on a computer using 3D diagnostic data from a CT scanner (virtual
simulation) or on a low energy x-ray machine, which has the geometry that the high-
energy accelerator will have during the treatment, but incorporates a high quality imaging
system (conventional simulation). After all parameters of the treatment technique are
Figure 1.3: Typical steps in radiotherapy treatment process.
Virtual Simulation/Conventional Simulation
Treatment
Diagnosis Target localizationand PTV definition
Dose distributioncalculation Prescription
Chapter1: Introduction
7
determined, a special software commonly called the “treatment planing software” is
used, generally by a dosimetrist, to calculate the dose distribution inside the patient’s
body. If the dose distribution conforms well to the PTV and spares the organs at risk, a
physician will prescribe the actual dose to be delivered, and the treatment will begin. The
dose distribution of a typical four-field box treatment plan superimposed on a CT axis
abdominal image is shown in Fig. 1.4.
In order to understand the relationship between radiation dosimetry and radiation
therapy, one should be familiar with the basic principles on which treatment planing
algorithms are based. The radiation dose delivered to an arbitrary point (a point-of-
interest) in a phantom or a patient is calculated by multiplying the dose to a certain point,
called a reference point, with a coefficient, which relates the dose at the reference point to
Figure 1.4: Dose distribution for a typical four-field box technique.
Chapter1: Introduction
8
the dose at the point-of-interest. We need to know both the absolute dose delivered to the
reference point and the relationship between this dose and the dose to the point-of-
interest to perform this calculation.
The standard procedures developed for measuring absolute dose follow absolute
dose measurement calibration protocols. Examples of commonly used protocols are the
protocol that was developed by the Task Group 51 (Ref. 16) of the American Association
of Physicists in Medicine (AAPM) and the protocol developed by the International
Atomic Energy Agency (IAEA) TRS-398 (Ref. 17). Usually linacs are adjusted in such a
way that the maximum dose rate delivered over the central axis of the radiation beam for
field size of 10×10 cm2 and a source-surface distance (SSD) of 100 cm is 1 cGy/1
Monitor Unit (MU). One monitor unit corresponds to a given amount of electrical charge
collected by the monitor ionization chamber embedded in the linac treatment head. It is
an adjustable quantity, used for dose measurement instead of time, because it
compensates for the small output variations that are very typical for linacs.
The relationship between the dose to the very specific point mentioned above and
the dose to any other point within any beam geometry is derived using several tabulated
dosimetric functions, often called dosimetric parameters. These parameters are
determined by relative measurements and can be divided into two general categories: (i)
central axis functions and (ii) off-axis parameters.
For a given photon beam hν at a given source-surface distance (SSD), the dose at
point P (at depth maxd in phantom) depends on the field size A; the larger the field size,
the larger the dose. The relative dose factor RDF (often referred to as the total scatter
Chapter1: Introduction
9
factor Sc,p or sometimes the machine output factor) is defined as the ratio of the dose at P
in phantom for field A to the dose at P in phantom for a 10×10 cm2 field, i.e.:
( )( , )
(10)P
P
D ARDF A h
Dν = , (1.1)
The geometry for measurement of the RDF(A) is shown in Fig. 1.5; part (a) for
the measurement of ( )pD A and part (b) for the measurement of (10)pD . It is important to
note that maxd might be different for different field sizes. RDF increases with the field
size and has a value of one for the standard 10×10 cm2 field. As it follows from the
definition, RDF is useful for calculating absolute dose delivered to a point at maxd .
Central axis dose distributions inside the patient or phantom are usually
Figure 1.5: Geometry for the measurement of the relative dose factor RDF(A). Thedose at point P at dmax in phantom is measured with field A in part (a)and with field 10×10 cm2 in part (b).
Chapter1: Introduction
10
normalized to Dmax = 100% at the depth of dose maximum maxd and then referred to as
the percentage depth dose (PDD) distributions. The percentage depth dose is thus
defined as follows:
( , , , ) 100 Q
P
DPDD d A f h
Dν = × , (1.2)
with the geometry shown in Fig. 1.6. Point Q is an arbitrary point at depth d on the beam
central axis; point P represents the specific dose reference point at maxd d= on the beam
central axis. PDD depends on four parameters: depth in phantom d , field size A, source-
surface distance SSD = f , and photon beam energy hν. PDD ranges in value from 0 at
d → ∞ to 100 at maxd d= .
Figure 1.6: Geometry for percentage depth dose measurement and definition.Point Q is an arbitrary point on the beam central axis at depth d, pointP is the point at dmax on the beam central axis. The field size A isdefined on the surface of the phantom.
Chapter1: Introduction
11
A typical PDD curve for a 10 MV photon beam (SSD of 100 cm and field size of
10×10 cm2) is shown in Fig. 1.7. Tabulated curves for different photon beams are
published in the British Journal of Radiology, Supplement No. 25 (Ref. 18). In modern
radiotherapy, the treatments are mostly done using isocentric setups, which means that
the center of the PTV is placed at the linac isocenter. The main advantage of this setup is
that several beams might be used in patient treatment with no change in patient position
on the treatment machine when switching from one beam to the next. However, as a
result of the human body not being cylindrically symmetric, the SSD will change with the
gantry rotation. Hence, using PDD, which depends on SSD, is not a very convenient way
of determining the dose along the central beam axis. Therefore another approach is taken
in case of isocentric, often called source-axis-distance (SAD), setups. The function used
0
20
40
60
80
100
120
0 2 4 6 8 10 12 14 16
Depth (cm)
PD
D
Figure 1.7: PDD curve for a 10 MV photon beam, SSD = 100 cm, 10×10 cm2.
Chapter1: Introduction
12
for this purpose is the Tissue Maximum Ratio (TMR). The definition of TMR is as
follows:
max
( , , )
Q
DTMR d A h
Dν = ’ (1.3)
where DQ is the dose in phantom at arbitrary point Q on the beam central axis and maxQD
is the dose in phantom at depth maxd on the beam central axis. The geometry for the two
dose measurements is shown in Fig. 1.8. It has been established that TMR does not
depend on SSD over the SSD range used in clinical radiotherapy.
The most commonly used off-axis function is the Off-Axis Ratio (OAR). OAR
shows how the dose changes in lateral direction with respect to the dose delivered to the
point on the central axis at the same depth:
dmax
Figure 1.8: Geometry for the measurement of the tissue-maximum ratio, TMR(d,AQ,hν).
Chapter1: Introduction
13
( )( )(0)
D rOAR rD
= , (1.4)
where r is the off-axis distance. This function has to be tabulated for every particular
field, including fields in which additional accessories, such as wedges, are used.
A typical algorithm for calculating the dose to a certain point-of-interest using all
the data obtained by absolute and relative measurements is given in the block diagram in
Fig. 1.9. Obviously, one needs very precise data in order to calculate a dose distribution
with very low uncertainties. Therefore it is very important to improve continuously the
dosimetry equipment and techniques in order to develop new and more precise dose
delivery methods.
With the recent rapid development in the field of microelectronics and computer
systems, a new concept for dose delivery calculations is becoming more and more
common. The idea is to use computer simulations for all physical processes taking place
in a medium through which high-energy particles are moving. Several different
algorithms for this simulation have been developed19-21 under the common name of
“Monte Carlo particle transport simulations.” There is a very strong relationship
between the computer power involved and the calculation time on one hand, and the
precision of the Monte Carlo results on the other. For this reason, the Monte Carlo
algorithms are becoming more and more popular, as modern computers become ever
faster, cheaper and more affordable. However, even if very precise simulation results are
obtained, they must be verified by real experiments, using extremely accurate dosimetry
measurement techniques. On the one hand, Monte Carlo techniques are quite suitable for
simulations of the small diameter radiosurgical beams, minimizing calculation time in
comparison with relatively large standard radiotherapy beams. On the other hand,
Chapter1: Introduction
14
experimental verification of radiosurgical beams is considerably more difficult than that
of standard radiotherapy beams.
Relativemeasurements
Absolutemeasurements
Dose to a referencepoint in standard
field
Dose to a referencepoint in the field of
interest
Dose to the centralaxis at the depth of
interestDose to the point of
interest
RDF
PDD
OAR
Figure 1.9: Basic treatment planning algorithm.
Chapter1: Introduction
15
1.4. Dosimetry of very small fields
The photon fields used in the conventional radiation therapy are commonly
referred to as standard or large fields. Their sizes are larger than 5×5cm2. The fields with
diameters from 1 cm to 4 cm, used for radiosurgery, are known as small photon fields. In
this work we will refer to photon fields with diameters on the order of several millimeters
as very small fields. Dosimetry of very small photon fields is a very interesting subject,
because most of the standard dosimetry functions become extremely sensitive in the
range of small and very small radiation field sizes. For example, the depth of maximum
dose maxd decreases significantly with field size for fields smaller than 1 cm. The subject
is also challenging, because there are several specific requirements for the detectors,
which are very difficult to fulfill in very small radiation fields.
Many studies have been done using various detectors for different measurements
in small fields. The usefulness of small ionization chambers for central axis and for off-
axis measurements has been studied in detail22-27. The p-type silicon diodes have also
been considered because of their small measuring volume22,23,25. Several other
dosimeters such as radiochromic film26, plastic scintillator22,28, TLD26, MOSFET26, and
liquid-filled ionization chamber22 have been used as well. In addition, Monte Carlo
simulations have often been used for theoretical verification of experimental results29.
There are two important parameters concerning all detectors used for
measurements in very small photon fields: (i) resolution and (ii) water-equivalence of the
measuring material. Usually, the dose profiles (OAR) for fields smaller than 5 mm in
diameter change drastically over off-axis distance as small as 1 mm. Thus, the resolution
Chapter1: Introduction
16
of the detector used will have a great impact on both the central axis and off-axis dose
measurements. There are two different approaches to solving this problem: (i) we either
need a detector with a well-known geometry or (ii) we need a detector with a very small
size, at least 6 to 7 times smaller than the field size.
Evidently, it is difficult to manufacture a detector small enough and accurate at
the same time when, for example, the field size is as small as 2 mm in diameter.
However, if the exact geometry of the detector sensetive volume is known, it is possible
to perform a deconvolution procedure that is very suitable for off-axis measurements.
The real dose profile will be the result of deconvolving the measured one (Fig. 1.10).
Several extensive studies on dose profile deconvolution have been conducted30-33 and in
all of them 1-D deconvolution was performed using the Line Spread Function (LSF) of
the detector. However, in the case of very small fields the dose fall-off in all lateral
directions should be considered. Therefore, 2-D deconvolution based on the Point Spread
Function (PSF) of the detector must be performed.
The second detector-related issue is water-equivalence of the measuring material
in terms of radiation properties, since water is the most commonly used phantom
OAR1
2
Off-axis Distance
Figure 1.10: Narrow beam profiles: curve (1) represents a measured profile, curve(2) a deconvolved profile.
Chapter1: Introduction
17
material, similar to the human body tissue. Having a water-equivalent detector is
important, because the concept of the charged particle equilibrium (CPE) does not apply
to small photon fields in a lateral direction. In order to illustrate the importance of this
concept, let us take a closer look at how the radiation dose gets deposited in the phantom
when small photon beams are used.
When a high-energy photon enters a medium, photon-electron interactions will
occur with a certain probability. There are four main types of interactions: photoelectric
effect, coherent scatter, incoherent (Compton) scatter, and pair production. Usually, the
very rare triplet production interaction is taken into account in the pair production cross-
section. Due to these interactions, a significant part of the incident photon energy might
be transferred to an electron that thereafter will be set in motion. This electron will then
ionize the medium over its track by electron-electron Coulomb interactions. The radiation
dose deposited as a result of this two-step process is expressed as follows:
LD φ
ρ =
, (1.5)
where φ is the electron fluence at the point-of-interest and ( )/L ρ is the restricted mass
stopping power averaged over the electron energy spectrum. The restricted mass stopping
power is defined as:
1L Exρ ρ
=
VV , (1.6)
where ρ is the density of the medium and EV is the energy transferred to low-energy
electrons that deposit this energy locally, over a small distance xV .
Chapter1: Introduction
18
For large photon fields, the assumption is made that the number of electrons that
stop inside a small volume VV is equal to the number of electrons set in motion by
photons inside the same volume (Fig. 1.11). Thus, the electrons can be considered as
continuously moving through the medium, instead of stopping and being set in motion.
This assumption actually underlines the concept of CPE. The electron fluence is constant
when this concept applies.
Generally, the detectors and the phantoms are made of different materials.
According to Eq. (1.5), the relationship between the dose delivered to the detector, dD ,
and the dose delivered to the medium, medD , is:
( ) ,med
medmed d d
d
LD D φρ
=
(1.7)
where med
med
d
d
LL
Lρ
ρρ
=
and ( )med medd
d
φφφ
= .
The dose to the phantom (medium) is calculated by multiplying the dose to the
detector by two correction factors: restricted stopping power ratio ( )/med
dL ρ and electron
fluence perturbation factor ( )med
dφ for the two materials: medium and detector. The
restricted stopping power ratio accounts for the difference in the energy deposited by an
electron per unity track length in the two different materials. The electron fluence
perturbation factor corrects for the difference in the electron fluence. When the detector
size is much smaller than the electron range for a given photon energy, in which case the
Bragg-Gray or Spancer-Attix cavity theories apply34, the second correction factor is
Chapter1: Introduction
19
considered to be equal to one. Under condition of CPE, the two factors are constant for a
given photon energy, so that, even if they are not established, relative measurements may
be carried out without adversely effecting the reliability of measurements results.
For very small photon fields, the field size is usually smaller than the electron
range in the phantom material. In this situation a very important difference appears when
comparing an electron moving in a lateral direction in a very small field to an electron
moving in the same fashion in a large field (Fig. 1.12). When an electron moving
laterally in a large photon field approaches the point where it will stop, another electron
will be set in motion by a photon in the vicinity of this point. This will provide CPE in
the irradiated volume except for the penumbra region, which is very small in comparison
to the field size. In a very small field, many electrons will be able to reach points outside
the photon beam where no photon-electron interaction occurs, and the electron fluence
will change with the increase in the off-axis distance. Thus there will be no CPE in a
lateral direction, leading to the conclusion that the correction factors defined in Eq. (1.7)
Figure 1.11: Charged particle equilibrium: number of electrons stopped in a smallvolume is equal to the number of electrons set in motion by photonsin the same volume.
VV
Chapter1: Introduction
20
will vary causing difficulties not only for absolute measurements, but even for relative
dosimetric measurements. In order to overcome this obstacle and to obtain reliable results
one would therefore need either a phantom-equivalent detector with both correction
factors equal to one or else a detector whose correction factors are precisely known.
Obviously, the choice of a detector is not an easy one. For this reason, the
experimental results have to be compared to reliable reference data until a reliable
measurement technique is established. Monte Carlo simulations can provide such reliable
data, as they are always relevant, regardless of the field size and shape. Of course, the
size of the voxels, in which the radiation dose is calculated, has to be very small to
achieve a high resolution and this requires a lot of computer power. Another very useful
application of the Monte Carlo simulations is calculating the correction factors for
different detector positions. Establishing such correction factors for ionization chambers,
for example, has recently become a routine approach in absolute dosimetry35-38.
Large fieldVery small
field
Figure 1.12: Electrons moving in lateral direction in large and very small photon fields.
Chapter1: Introduction
21
1.5. Thesis objectives
The dosimetry of very small radiation fields is a challenging problem, largely
unexplored to date, but of great clinical importance for further developments in
radiotherapy. It could inspire many studies in the area of basic physics of dose delivery
and radiation dosimetry and result in new techniques in treatment of functional disorders
requiring very small radiation fields.
The first objective of this thesis is to explore the usefulness of two dosimeters for
very small field measurements: a small volume ionization chamber and radiochromic
film. The chamber is the smallest commercially available ionization chamber,
manufactured under the name Exradin A14P (Standard Imaging, Middleton, WI, USA).
This chamber is important because ionization chambers in general are very precise
measuring devices. An A14P dose response study should include not only the acquisition
of accurate measurements but also development of algorithms for both the profile
deconvolution and calculation of correction factors. The second dosimeter is a new type
of radiochromic film that recently appeared on the market under the commercial name
HS GafchromicTM (International Specialty Products, Wayne, NJ, USA). This film is a
very good reference dosimeter, however it has high uncertainties. It is meant to be water
equivalent over a very large energy range in contrast to the standard radiographic film.
The second objective of the present work is to examine the mechanism of dose
delivery by studying both photon and electron fluence and energy in a water phantom
using Monte Carlo simulations.
Chapter1: Introduction
22
The third objective of the thesis is obtaining reliable data for PDD, OAR and RDF
by A14P ionization chamber, HS film measurements and Monte Carlo calculations for
several very small field sizes that might prove useful for clinical radiosurgery.
The final objective of the thesis is to determine whether or not linac-based
radiosurgery may be useful for irradiating intracranial targets with typical sizes on the
order of few millimeters. This study involves calculation of 3-D dose distributions as well
as dose distribution measurements.
1.6. Thesis organization
The present thesis consists of six chapters. Chapter 1 started with a brief overview
of external photon beam radiation therapy, followed by the basic concepts of stereotactic
radiosurgery and an introduction to treatment planing algorithms. Physics of radiation
dose deposition in very small photon fields is discussed later in this chapter, and the main
problems of dosimetry of such fields are outlined. The objectives of the thesis are stated
at the end of the first chapter.
Both the equipment as well as the experimental techniques, used for the purposes
of this work, are described in Chapter 2. The dynamic stereotactic radiosurgery technique
is introduced briefly in this chapter as the technique that we used to perform stereotactic
radiosurgery with very small photon beams.
Chapter 3 is dedicated to Monte Carlo particle transport simulation. It starts with
theoretical introduction to the Monte Carlo method, followed by an overview of all
Monte Carlo code systems used in this work.
Chapter1: Introduction
23
An extensive study of the Exradin A14P ionization chamber is presented in
Chapter 4 starting by calculating the active measuring volume of the A14P chamber.
Based on this result, a simple deconvolution algorithm as well as method for studying the
dose response variation in a lateral direction are described.
All results are presented in Chapter 5. The results include measurements and
Monte Carlo calculations of several dosimetric parameters associated with static photon
beams, as well as 3-D dose distributions of dynamic radiosurgery procedures.
Chapter 6 contains a brief summary of the thesis, conclusions, and a discussion on
possible future studies and developments.
Chapter1: Introduction
24
References:
1 J. Van Dyk, The Modern "Technology of Radiation Oncology," Medical Physics
Publishing, Madison, Wisconsin, 1999.
2 H. Johns and J. Cunningham, "The Physics of Radiology," Charles C Thomas,
Springfield, Illinois, 1983.
3 M. Schell, F. Bova, D. Larson et al., "Stereotactic Radiosurgery: Report of Task
Group 42 radiation Therapy Committee," Americam Institute of Physics, 1995.
4 E. B. Podgorsak, A. Olivier, M. Pla et al., “Dynamic stereotactic radiosurgery,” Int. J.
Radiat. Oncol. Biol. Phys. 14, 115-126 (1988).
5 E. B. Podgorsak, A. Olivier, M. Pla et al., “Physical aspects of dynamic stereotactic
radiosurgery,” Appl. Neurophysiol. 50, 263-268 (1987).
6 M. R. McKenzie, L. Souhami, J. L. Caron et al., “Early and late complications
following dynamic stereotactic radiosurgery and fractionated stereotactic
radiotherapy,” Can. J. Neurol. Sci. 20, 279-285 (1993).
7 G. Luxton, Z. Petrovich, G. Jozsef et al., “Stereotactic radiosurgery: principles and
comparison of treatment methods,” Neurosurgery 32, 241-259 (1993).
8 D. Urgosik, J. Vymazal, V. Vladyka et al., “Treatment of postherpetic trigeminal
neuralgia with the gamma knife,” J. Neurosurg. (Suppl. 3) 93, 165-169 (2000).
9 A. Haas, G. Papaefthymiou, G. Langmann et al., “Gamma knife treatment of of
subfoveal, classic neovascularization in age-related macular degeneration: a pilot
study,” J. Neurosurg. (Suppl. 3) 93, 172-175 (2000).
Chapter1: Introduction
25
10 L. Leksell, “Cerebral radiosurgery I. Gamma thalamotomy in two cases of intractable
pain,” Acta Chir. Scand. 134, 585-595 (1968).
11 D. G. Leksell, “Stereotactic radiosurgery: current status and future trends,” Stereotact.
Funct. Neurosurg. 61 (Suppl. 1), 1-5 (1993).
12 M. R. McLaughlin, B. R. Subach, L. D. Lunsford et al., “The origin and evolution of
the University of Pittsburgh Department of Neurological Surgery,” Neurosurgery 42,
893-898 (1998).
13 W. Lutz, K. R. Winston, and N. Maleki, “A system for stereotactic radiosurgery with a
linear accelerator,” Int. J. Radiat. Oncol. Biol. Phys. 14, 373-381 (1988).
14 A. Wambersie, T.G. Landberg, J. Chavaudra et al., ICRU Report No. 50, 1993.
15 T. Landberg, J. Chavaudra, J. Dobbs et al., ICRU Report No. 62.
16 P. R. Almond, P. J. Biggs, B. M. Coursey et al., “AAPM's TG-51 protocol for clinical
reference dosimetry of high-energy photon and electron beams,” Med. Phys. 26, 1847-
1870 (1999).
17 P. Andreo, D.T. Burns, K. Hohlfeld et al., IAEA TRS Report No. 398, 2000.
18 E. Arid, J. Burns, M. Day et al., “Central axis depth dose data for use in radiotherapy:
1996,” British Journal of Radiology Supll. 25 (1996).
19 I. Kawrakow, “Accurate condensed history Monte Carlo simulation of electron
transport. I. EGSnrc, the new EGS4 version,” Med. Phys. 27, 485-498 (2000).
20 D. W. Rogers, B. A. Faddegon, G. X. Ding et al., “BEAM: a Monte Carlo code to
simulate radiotherapy treatment units,” Med. Phys. 22, 503-524 (1995).
Chapter1: Introduction
26
21 J. Sempau, S. J. Wilderman, and A. F. Bielajew, “DPM, a fast, accurate Monte Carlo
code optimized for photon and electron radiotherapy treatment planning dose
calculations,” Phys. Med. Biol. 45, 2263-2291 (2000).
22 M. Westermark, J. Arndt, B. Nilsson et al., “Comparative dosimetry in narrow high-
energy photon beams,” Phys. Med. Biol. 45, 685-702 (2000).
23 X. R. Zhu, J. J. Allen, J. Shi et al., “Total scatter factors and tissue maximum ratios for
small radiosurgery fields: comparison of diode detectors, a parallel-plate ion chamber,
and radiographic film,” Med. Phys. 27, 472-477 (2000).
24 B. E. Bjarngard, J. S. Tsai, and R. K. Rice, “Doses on the central axes of narrow 6-MV
x-ray beams,” Med Phys 17, 794-799 (1990).
25 C. McKerracher and D. I. Thwaites, “Assessment of new small-field detectors against
standard-field detectors for practical stereotactic beam data acquisition,” Phys. Med.
Biol. 44, 2143-2160 (1999).
26 P. Francescon, S. Cora, C. Cavedon et al., “Use of a new type of radiochromic film, a
new parallel-plate micro-chamber, MOSFETs, and TLD 800 microcubes in the
dosimetry of small beams,” Med. Phys. 25, 503-511 (1998).
27 Y. W. Vahc, W. K. Chung, K. R. Park et al., “The properties of the
ultramicrocylindrical ionization chamber for small field used in stereotactic
radiosurgery,” Med. Phys. 28, 303-309 (2001).
28 D. Letourneau, J. Pouliot, and R. Roy, “Miniature scintillating detector for small field
radiation therapy,” Med. Phys. 26, 2555-2561 (1999).
29 F. Verhaegen, I. J. Das, and H. Palmans, “Monte Carlo dosimetry study of a 6 MV
stereotactic radiosurgery unit,” Phys. Med. Biol. 43, 2755-2768 (1998).
Chapter1: Introduction
27
30 P. Charland, E. el-Khatib, and J. Wolters, “The use of deconvolution and total least
squares in recovering a radiation detector line spread function,” Med. Phys. 25, 152-
160 (1998).
31 F. Garcia-Vicente, J. M. Delgado, and C. Peraza, “Experimental determination of the
convolution kernel for the study of the spatial response of a detector,” Med. Phys. 25,
202-207 (1998).
32 P. D. Higgins, C. H. Sibata, L. Siskind et al., “Deconvolution of detector size effect
for small field measurement,” Med. Phys. 22, 1663-1666 (1995).
33 C. H. Sibata, H. C. Mota, A. S. Beddar et al., “Influence of detector size in photon
beam profile measurements,” Phys. Med. Biol. 36, 621-631 (1991).
34 L. V. Spencer and F. H. Attix, “A theory of cavity ionization,” Radiat. Res. 3, 239-254
(1955).
35 J. E. Bond, R. Nath, and R. J. Schulz, “Monte Carlo calculation of the wall correction
factors for ionization chambers and Aeq for 60Co gamma rays,” Med. Phys. 5, 422-
425 (1978).
36 J. Borg, I. Kawrakow, D. W. Rogers et al., “Monte Carlo study of correction factors
for Spencer-Attix cavity theory at photon energies at or above 100 keV,” Med. Phys.
27, 1804-1813 (2000).
37 C. M. Ma and A. E. Nahum, “Monte Carlo calculated stem effect correction for
NE2561 and NE2571 chambers in medium-energy x-ray beams,” Phys. Med. Biol. 40,
63-72 (1995).
Chapter1: Introduction
28
38 J. Mazurier, J. Gouriou, B. Chauvenet et al., “Calculation of perturbation correction
factors for some reference dosimeters in high-energy photon beams with the Monte
Carlo code PENELOPE,” Phys. Med. Biol. 46, 1707-1717 (2001).
Chapter 2:
Materials and Methods -Equipment and Experimental
Techniques
1.1. Radiation source
All experiments presented in this work were carried out using a Clinac-18 linear
accelerator (Varian Oncology Systems, Palo Alto, CA) as a radiation source. A
photograph of the linear accelerator (linac) is given in Fig. 2.1. The machine has been in
clinical service in the Radiation Oncology Department of the Montreal General Hospital
since 1977. Currently the machine is used for special procedures such as total skin
electron irradiation and stereotactic radiosurgery. The distance between the linac
isocenter and the source of radiation (source-axis distance SAD) is 100 cm and the
distance between the isocenter and the floor is 126 cm.
The Clinac-18 linac has two operating modes. It can be used as a source of high-
energy electron beams with five different energies between 6 MeV and 18 MeV, and as a
source of 10 MV photons represented by a bremsstrahlung spectrum with a maximum
energy of 10 MeV. The design of the linac treatment head in the two different modes is
shown in Fig. 2.2. In both cases a narrow beam of electrons, accelerated in a 1.4 m long
waveguide, is transported to the treatment head assembly by a 270o achromatic bending
Chapter2: Materials and Methods – Equipment and Experimental Techniques
30
magnet system. When the machine is used in the photon mode, the electrons are slowed
down and completely stopped in a target, and the resulting bremsstrahlung radiation is
flattened by a flattening filter (Fig 2.2(a)). The electron range in the target material is
smaller than the thickness of the target itself, so that no high-energy electron can pass
through it. Such a target is called a thick target. The intensity of a photon beam produced
in a thick target decreases with the increase in the off-axis distance. Therefore after the
photon beam is collimated by a primary collimator, it traverses a flattening filter. The
purpose of this filter is to provide a constant intensity of the beam in off-axis directions.
The flattened beam then passes through a monitor ionization chamber, which is used to
Figure 2.1: Clinac-18 linear accelerator.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
31
count monitor units (see Chapter 1). The secondary collimator, commonly referred to as
collimator upper and lower jaws, determines the actual field size defined at SAD. There is
a tray holder on the bottom side of the treatment head to which different accessories, such
as wedges, radiosurgical collimators and electron beam cones, are attached when special
treatment techniques are performed.
When the Clinac-18 linac is used in the electron mode, the target is removed and
the flattening filter is replaced with a scattering foil (Fig. 2.2(b)). The foil spreads out the
high-energy pencil electron beam, so that flat electron fields with relatively large field
sizes (up to 25×25 cm2 at machine isocenter) can be produced at an SSD of 100 cm.
The 10 MV photon beam was used as a radiation source in our experiments: the
gantry angle was 180o, the collimator angle was 90o, and the jaws were set to a 5×5 cm2
field at the isocenter. The very small photon fields were shaped using specially
manufactured collimators. Three circular fields with diameters of 1.5 mm, 3 mm, and 5
mm at the isocenter have been studied and the 5 mm collimator is shown in Fig. 2.3. The
Figure 2.2: Treatment head design in (a) photon and (b) electron mode.
?- ?-
Target
PrimaryCollimator
MonitorChamber
SecondaryCollimator
Tray
FlatteningFilter
ScatteringFoil
(a) (b)
Electron beamcone
Chapter2: Materials and Methods – Equipment and Experimental Techniques
32
collimators were designed in such a way that they could fit into a radiosurgery holder
developed at the McGill University Health Centre for the Clinac-18 linac (Fig. 2.4). The
radiosurgery holder is attached to the tray holder of the machine and allows for adjustable
and very precise collimator positioning.
The collimators are made of 10 cm thick blocks of lead or tungsten. The bottom
side of the collimators is at 70 cm from the source and at 30 cm from the isocenter when
a collimator is placed onto the holder. The 5 mm collimator consists of two hollow
cylinders made of lead, each of them 5 cm thick. The outer diameter of both cylinders is
6.8 cm. The inner diameter of the upper cylinder is 2.95 mm, whereas the diameter of the
lower one is 3.25 mm, as shown schematically in Fig. 2.5(a). The 1.5 mm collimator is
also made of lead, but the diameter of the hole is 1 mm all the way through the collimator
(Fig. 2.5(b)). The 3 mm is also a cylinder, but is made of tungsten and the diameter of the
collimator hole is 2 mm (Fig. 2.5(c)). The metal pieces themselves are placed in plastic
boxes, so that the collimators have outer geometry corresponding to the inner diameter of
the holder.
Figure 2.3: External view of a 5 mm collimator.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
33
2.2. Dosimeters
There are two main issues related to detectors that could be used for dose
measurements in small photon fields: resolution and water-equivalence. These issues and
the relevant radiation physics explanations have been discussed in Chapter 1 and an
Figure 2.4: Radiosurgery holder with a small field collimator on, attached to theClinac-18 treatment head.
2.95 mm 1 mm
3.25 mm
10 cm
Pb Pb W
(a) (b) (c)
2 mm
Figure 2.5: Design of the collimators: (a) 5 mm field, (b)1.5 mm field, and (c)3 mm field.Collimators in (a) and (b) are made of lead, in (c) of tungsten.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
34
overview of the use of different detectors in several studies has been presented in Chapter
1 as well. None of the detectors discussed, except for the radiochromic film, has the
resolution required for measurements in fields smaller than 5 mm. When film is used, the
aperture of the scanner/densitometer determines the resolution. As far as water
equivalency is concerned, the only detectors that could be referred to as water-equivalent
with no additional corrections are the radiochromic film and the liquid-filled ionization
chamber. This chamber would be the best dosimeter for measurements in non-
equilibrium conditions, but it is not commercially available.
Two types of dosimeters were used for the purposes of this work: a micro
parallel-plate ionization chamber (Exradin A14P: Standard Imaging, Middleton, WI,
USA) and radiochromic film (HS GafchromcTM: International Specialty Products, Wayne,
NJ, USA). The ionization chamber is very accurate, and if the correction factors are
properly calculated, the water-equivalency problem can be resolved easily. The
radiographic film is a less precise dosimeter than the ionization chamber, however, in
terms of radiological properties, it is very close to water. In addition, this film has a very
high resolution and is therefore a very good reference dosimeter.
2.2.1. Exradin A14P ionization chamber
The Exradin A14P ionization chamber is one of the smallest commercially
available ionization chambers (Fig. 2.6) and was specifically designed for measurements
in small photon fields. Pankuch et al.1 have presented a detailed study of this chamber
and Francescon et al.2 have used this chamber for central axis measurements for fields as
small as 4.4 mm in diameter.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
35
Figure 2.7 shows the schematic design of an A14P ionization chamber. The
chamber actually resembles a cylindrical chamber with two caveats: (i) the top is flat, and
(ii) the guard electrode encompasses the collecting electrode all the way from top to
bottom. Therefore, the A14P chamber is referred to as a parallel-plate ionization
chamber. It is made of Shonka air-equivalent plastic C552, with the diameter of the
collecting electrode 1.5 mm and the inner diameter of the cavity 2 mm. Both the wall and
the entrance window are 1 mm thick. The chamber is waterproof and the measuring
volume is connected to the outside air by two ventilation tubes.
Obviously, the measuring volume of the A14P chamber is very small and this
results in a very low signal. According to the manufacturer, the collecting volume is 2.3
mm3 and an exposure of 1430 R is needed for collecting a charge of 1 nC. As a result, the
radiation-induced current forms a large fraction of the total signal measured, and this
means that the polarity correction factor, as defined in the Task Group No. 51 report3, is
relatively large. We calculated a value of 1.21 based on measurements in a large field.
Leakage of the ionization chamber is another important issue because of the low signal
current. According to the specifications, the leakage current of the A14P chamber is
Figure 2.6: Exradin A14P ionization chamber.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
36
lower than 10-15 A, but this value also depends on the electrometer with which the
measurements are taken.
The electrometer used for our measurements was Keithley 6517A (Keithley
Instruments Inc., Cleveland, OH, USA) and is shown in Fig. 2.8. This electrometer
incorporates an adjustable voltage source that can supply voltages between –1000 V and
+1000 V to the chamber. The device was used in charge mode and it was connected to
the A14P chamber with a shielded triaxial cable. When the chamber is used along with
this electrometer, the leakage current is on the order of 0.02 pA at 300 V, provided that
Figure 2.7: Sketch of A14P ionization chamber.
Figure 2.8: Keithley electrometer.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
37
the A14P chamber is well warmed up prior to the measurement. Usually irradiation with
30 Gy to 40 Gy in an open field is enough to attain such a low leakage current. A detailed
study of the A14P ionization chamber is provided in a separate chapter in this thesis.
2.2.2. Radiochromic film
The radiochromic film HS GafchromicTM was recently released on the market. In
general, the radiochromic films are good practical dosimeters, since they are not sensitive
to visible light, and no development is needed after irradiation. Moreover, they are water-
equivalent and are useful in a large energy range, which makes them very appropriate
dosimeters for measurements under non-equilibrium conditions.
Various types of radiochromic films that were widely used before the advent of
the HS film (MD55, MD–55-2, HD) have been extensively studied and the results of
these studies are summarized by the Task Group 55 of the American Association of
Physicists in Medicine4.
The biggest advantage of the HS film over other radiochromic films is its
sensitivity; the HS film is twice as sensitive as the MD-55 film. This is very important,
because generally the radiochromic films require very high radiation doses in order to
attain optical densities at reasonable levels. The first studies with HS film have already
been done5,6, showing that the film is water-equivalent, and its response linear and
energy independent.
Figure 2.9 shows the structure of the HS GafchromicTM film. The sensitive layer
of the film is sandwiched between two sheets of clear, transparent polyester. The
sensitive layer is made of a special polymer material that changes its optical density when
Chapter2: Materials and Methods – Equipment and Experimental Techniques
38
irradiated. The total thickness of the film is about 240 µm and it is usually available in
packages that contain five 12×12 cm2 sheets. All specification and performance
parameters are available at the manufacturer’s web site7. The two most important
parameters are: (i) the spatial response uniformity and (ii) the dose response curve (H&D
curve). Deviation of the response is reported to be as low as 3.4% within two standard
deviations. However, this result was determined using 49 measurements over a 12×12
cm2 piece of film, and it may overestimate the variation of the response over a smaller
area. The maximum deviation that was registered during the measurements of single
profiles in the present study was as low as 2%. Hence, this value is accepted as a typical
uncertainty in the film response for all profile measurements in this work.
The dose response curve for the radiation source, our 10 MV photon beam, used
for the purposes of this thesis was determined. The optical density of exposed film
changes during the first 48 hours after irradiation, and then practically remains constant
after that time. The dose response curves measured at 36 hours and 25 days after
Clear Polyester - ~97 microns
Clear Polyester - ~97 microns
Active Layer - 40 microns
Figure 2.9: Structure of HS radiochromic film.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
39
irradiation are presented in Fig. 2.10. The dose response is linear within the combined
uncertainty of response variation and the optical density readout (0.005).
All optical density measurements were carried out with a Nuclear Associates
Radiochromic Densitiometer, Model 37-443, and a film transport system, capable of
positioning the film with an uncertainty as low as 0.1 mm (Fig. 2.11). The densitometer
uses a red light source with a wavelength between the two absorption maxima of the
polymer dye, which are at 615 nm and 675 nm.
For all relative dose measurements the aperture of the densitometer was closed to
about 0.3 mm in order to achieve a high resolution. Obviously, when the aperture
diameter is changed from the standard value, the readouts no longer correspond to the
optical density. Therefore, before each series of measurements, the linearity of the
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25 30 35
Dose (Gy)
Opt
ical
Den
sity
36 hrs
3 weeks
Figure 2.10: Dose response curve for HS radiochromic film.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
40
readouts was checked against the optical density, using pieces of films with known
optical density that were provided by the manufacturer. When the optical density of the
film is linear with the delivered dose, and the readouts are linear with optical density, we
can conclude that the readouts are linear with the delivered dose. All readouts were
reduced by the readout for a non-irradiated film before performing any further
calculations.
2.3. Experimental setups
All experiments with the A14P ionization chamber were carried out in a
30×30×30 cm3 water phantom. The chamber was pointing toward the radiation beam
and the source-surface distance was 100 cm (Fig. 2.12).
Figure 2.11: Densitiometer Model 37-443 and the film transport system.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
41
The chamber was attached to a transport system that allowed positioning of the
chamber with an uncertainty as low as 0.1 mm. This transport system is used clinically at
the Radiation Oncology Department of the Montreal General Hospital for calibration of
linear accelerators. Some modifications were done so that the same transport system
could be used for off-axis measurements, as well as for central axis measurements (Fig.
2.13).
Prior to the measurements, the chamber was warmed up with 40 Gy in an open
field. After this irradiation, the readouts became consistent and the leakage had a stable
value between 0.5 and 1.0 pC collected over a time interval of 1 min. The leakage current
was lower than 0.2 pA. The experiments were carried out using two polarities: +300 V
and -300 V. During the experiments the chamber was irradiated with 400 MU (1.5 mm
field) and 300 MU (3 mm and 5 mm fields). The radiation dose was delivered at a rate of
400 MU/min. The leakage was checked every 5 minutes.
Waterphantom
Photon beam
A14P
SSD = 100 cm
Cable andventilation tubes
Figure 2.12: A14P ionization chamber orientation in the water phantom.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
42
All experiments with the HS radiochromic film were carried out in a phantom
made of a special plastic material that was water-equivalent and known as Solid WaterTM
(Gammex RMI, Middleton, WI, USA). The sheets of HS film were cut into strips in the
direction designated by the manufacturer as the direction with the lowest response
variation. Afterwards, the strips were cut into small pieces that were used for the
experiments. This approach minimized the uncertainty due to the film response variation.
For dose profile measurements, where only a single piece of film was used, the profile
was scanned in the lowest response variation direction. The film was irradiated with 2000
MU to 6200 MU, depending on the field size.
Both dosimeters were used for: (i) central axis percentage depth dose (PDD)
measurements, (ii) off-axis ratios (OAR) measurements at a depth of 2.5 cm, and (iii)
relative dose factor (RDF) measurements. When HS film was used for PDD
measurements, 2-D profiles for different depths were scanned in order to obtain the
values over the central axis.
(a) (b)
Figure 2.13: A14P chamber positioning (a) for central axis and (b) off-axismeasurements.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
43
2.4. Dynamic stereotactic radiosurgery
Dynamic stereotactic radiosurgery, often referred to as the McGill technique, is a
radiosurgery technique that was introduced in 1987 (Ref 8,9). When this dynamic
technique is performed, both the table and the gantry of the accelerator are moving
continuously and simultaneously. The irradiation starts at 330o gantry angle and –75o
table angle and it stops at 30o gantry angle and 75o table angle (Fig. 2.14). The beam trace
on the patient scull for this technique is shown in Fig. 2.15.
The dose distributions for dynamic radiosurgery carried out with both the 1.5 mm
and the 3 mm collimators were measured in a X-Y plane containing the isocenter of the
linac with a very slow radiographic film (Kodak EDR-2). The purpose of these
measurements was to determine the 50% isodose surface, which usually is the
Isocenter
330o
75o-75o
30o
Figure 2.14: Simultaneous gantry and tablerotations during a dynamicradiosurgery treatment.
Figure 2.15: Beam trace on the patient’sscull for the dynamicradiosurgery technique.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
44
prescription isodose surface in a radiosurgery treatment with very small fields. The
measurements did not aim to a very high precision and therefore, the fact that the film
may slightly differ from water in terms of radiological properties was not an issue. On the
other hand, the Kodak EDR-2 film was a convenient dosimeter, because it required a
dose of only 4 Gy in order to obtain a reasonable optical density. The film was squeezed
between two hemispheres made of polystyrene (Fig. 2.16) and the phantom was
positioned into the machine isocenter using a stereotactic frame. The aperture of the
scanner used to read the film was smaller than 0.1 mm. The technique was carried out
with 1700 MU for the 1.5 mm field and with 1000 MU for the 3 mm field.
Another experiment was performed to determine the displacement between the
center of the measured dose distribution and the isocenter of the machine defined by the
room lasers. A dynamic radiosurgery procedure was carried out again, but this time the
dose distribution in the X-Y plane was imaged on a piece of radiochromic film, which is
Figure 2.16: Hemispheres made of polystyrene, used as a dynamicradiosurgery phantom.
Chapter2: Materials and Methods – Equipment and Experimental Techniques
45
not sensitive to visible light so that we were able to mark precisely the lasers by four
pinpricks.
The results are presented in Chapter 5, where they are compared with Monte
Carlo-calculated 3-D dose distributions (see Chapter 3).
Chapter2: Materials and Methods – Equipment and Experimental Techniques
46
References:
1 M. Pankuch, J. Chu, J. Spokas et al., “Characteristics of a new parallel plate
microchamber explicitly designed for high spatial resolution, Bragg-Gray cavity
measurements of small photon beams,” presented at the 2000 World Congress on
Medical Physics and Biomedical Engineering, Chicago, 2000 (unpublished).
2 P. Francescon, S. Cora, C. Cavedon et al., “Use of a new type of radiochromic film, a
new parallel-plate micro-chamber, MOSFETs, and TLD 800 microcubes in the
dosimetry of small beams,” Med. Phys. 25, 503-511 (1998).
3 P. R. Almond, P. J. Biggs, B. M. Coursey et al., “AAPM's TG-51 protocol for clinical
reference dosimetry of high-energy photon and electron beams,” Med. Phys. 26, 1847-
1870 (1999).
4 A. Niroomand-Rad, C. R. Blackwell, B. M. Coursey et al., “Radiochromic film
dosimetry: recommendations of AAPM Radiation Therapy Committee Task Group 55.
American Association of Physicists in Medicine,” Med. Phys. 25, 2093-2115 (1998).
5 I. Das and C. Cheng, “Dosimetric Characteristics of New Gafchromic-HS Film,” Med.
Phys. 28, 1244-1244 (2001).
6 J. Ashburn, A. Al-Otoom, K. Sowards et al., “Investigation of the New Highly
Sensitive Gafchromic HS and XR Films,” Med. Phys. 28, 1244-1244 (2001).
7 International Specialty Products, “GAFCHROMIC® HS Radiochromic Dosimetry
Films For High Energy Photons Configuration, Specifications and Performance
Data,” (http://www.ispcorp.com/products/dosimetry/products/).
Chapter2: Materials and Methods – Equipment and Experimental Techniques
47
8 E. B. Podgorsak, A. Olivier, M. Pla et al., “Physical aspects of dynamic stereotactic
radiosurgery,” Appl. Neurophysiol. 50, 263-268 (1987).
9 E. B. Podgorsak, A. Olivier, M. Pla et al., “Dynamic stereotactic radiosurgery,” Int. J.
Radiat. Oncol. Biol. Phys. 14, 115-126 (1988).
Chapter 3:
Materials and Methods -Monte Carlo Particle
Transport Simulations
3.1. Theoretical basics
The Monte Carlo method is a mathematical method that provides solutions to
various mathematical problems using random number generators to assign specific values
to statistical variables following a predetermined statistical distribution. This
mathematical routine is commonly referred to as sampling a given distribution. The
standard deviation of a given statistical quantity calculated with the Monte Carlo method
decreases as 1/N2, where N represents the number of samples. Monte Carlo became a
popular scientific method in 1950s following the development of first computers,
however, the method was already known and used in the 19th century with random
number generators simulated through throwing a needle onto a line grid.
When a particle is moving through a medium, various interactions might take
place, each of them with certain probability. These interactions will result in different
outcomes: for example, the initial particle might get scattered, or another particle might
be created or set in motion. These events, again, will occur with certain probabilities,
following a certain distribution. For instance, in Compton scatter we can determine the
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
49
scattering angle and the energy of the scattered photon by sampling a Klein-Nishina
distribution. Hence, a particle can be transported through a medium by simulating all
interactions that this particle undergoes in the medium.
In general, there are three main requirements for performing Monte Carlo particle
transport simulations: (i) the cross-sections and the probability distributions that describe
all possible interactions must be known, (ii) a reliable random number generator must be
used for sampling, and (iii) adequate computing power must be available. Fortunately
theoretical physics has provided enough information about the interactions of different
particles with one another. In addition, random number generators and sampling
techniques have been developed since the first computing machines were introduced.
Lack of adequate computing power has always been the most serious obstacle when it
comes to Monte Carlo particle transport simulations. Recently, however, microelectronics
and computer technologies have been improved to such an extent that there are now
extremely fast and at the same time affordable computers on the market. For this reason,
the Monte Carlo simulations have become a very popular tool for dosimetric calculations.
The basic idea of Monte Carlo particle transport is presented in Fig 3.1. Let us
consider a volume of interest and an initial particle entering this volume. All interactions
that the particle undergoes, in addition to the path-length between two consecutive
interactions, may by simulated by sampling distributions, as described above.
Furthermore, all secondary particles either created or set in motion by the interactions
also should be transported through the volume of interest. Each particle is accounted for
until either it leaves the volume of interest or its energy becomes lower than a certain
cutoff energy. All particles with energies below the cutoff energy are considered to
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
50
deposit their energy locally. The Monte Carlo simulation goes on until there is no particle
left in the volume of interest. The initial particle is called history, because it creates the
secondary particles to be transported through the medium.
The standard deviation of all stochastic quantities calculated in the volume of
interest during the history transport, such as energy deposited, particle fluence, etc.,
depends on the number of events taking place in the volume of interest. There are three
fundamental parameters that have impact on uncertainties: (i) the number of simulated
histories, (ii) the dimensions of the volume of interest, and (iii) the cutoff energy. The
statistical uncertainties are lower when more histories are transported and when the cutoff
energies are lower, but this approach automatically increases the amount of computing
power required. Another way for decreasing uncertainties is by increasing the volume of
interest. Provided that in Monte Carlo simulations the phantoms are considered as sets of
voxels, increasing the voxel size will result in decreasing the spatial resolution, and this
often is not acceptable.
Figure 3.1: The basic idea of Monte Carlo particle transport: a particle istransported until either it leaves the volume of interest or itsenergy becomes less then the cutoff energy.
E<Ecutoff
E<Ecutoff
Initialparticle
Volume ofinterest
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
51
Another approach to the accuracy versus computing power compromise is to use
the variance reduction techniques. The idea behind these techniques is to change the
physical reality during the simulation so that more interactions would take place. For
example, if we increase the interaction cross-section, we will get a higher number of
interactions for the same number of histories. Of course, when these techniques are
applied the final results are statistically precise, but incorrect, because of the changed
reality. Therefore the results should be corrected by factors that take in account the
deviation from reality during the simulation.
First computer algorithms for Monte Carlo particle transport were developed at
the end of 1950s1, although the idea had been worked on for a long time before that time.
Nowadays, a variety of Monte Carlo algorithms for transport of different particles
(electrons, photons, protons, neutrons, etc.) are available. Each of these algorithms
usually applies to certain type of particles, within a certain energy range.
3.2. Monte Carlo transport of electrons and photons
In conventional radiation therapy the dose is delivered by either photon or
electron sources. Electrons, being charged particles, ionize the medium that they are
traversing, and lose energy through Coulomb interactions with orbital electrons and
nuclei of the absorber. A portion of the energy lost by the electrons is deposited in the
absorbing medium and a portion is transformed into bremsstrahlung. When photons are
used, they create high-energy electrons that deposit the dose to the medium. Therefore,
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
52
the Monte Carlo transport of photons and electrons is very important for practical
medical physics applications.
The photon transport is relatively easy to simulate, because photons undergo only
a few interactions while passing through a medium and the cross-sections for the various
possible photon-electron interactions were extensively studied in the past and are
tabulated for materials with atomic numbers from 1 to 100 (Ref. 2). The distributions
describing the outcomes of the interactions are well known as well. Hence, all
information needed to simulate a single interaction is available and the transport might be
carried out on a single interaction basis with no need for large computing power.
Unlike photons, high-energy electrons undergo about 105 interactions before they
stop in the medium. Obviously, if this physical process is simulated on a single
interaction basis, the simulation will take much longer than the photon transport. This
obstacle has been overcome by “condensing” multiple scattering events into a single
electron step, known as the condensed history (CH) technique3. This technique is based
on the multiple scattering theories and relevant electron multiple scattering distributions
that are sampled in order to determine the change in both position and direction of a
scattered electron. The theory that inspired the development of electron transport
algorithms was the Molière’s multiple scattering theory4. The energy that an electron
loses per single step in general is calculated using tabulated stopping power values.
There are two types of CH techniques, known as the class I and class II
techniques. In the class I techniques the electrons are moving on a predetermined energy
loss grid, and the secondary particles are added sampling a statistical distribution. This
approach was believed to be very accurate, but it turned out that it did not provide a good
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
53
correspondence between energy loss and production of secondary particles. In class II
algorithms all secondary particles are created in a very natural way as part of the primary
particle transport algorithm, considering the catastrophic events3.
Due to multiple scattering events, electrons are not moving over straight lines
during the CH steps. Therefore, every CH technique considers path-length corrections
(PLC) that account for the difference between the length of the real electron trajectory
and the step size, because this length is crucial for energy loss. Another correction that
CH techniques consider is the so-called lateral correction (LC) that accounts for lateral
deflection from the original direction again due to multiple scattering.
Often electrons have to be transported through inhomogeneous phantoms.
However, the multiple scattering theories apply to homogeneous media, and electron
transport algorithms have to take care of each electron crossing a boundary between two
different media.
In summary, the main characteristics of a Monte Carlo electron transport
algorithm are: (i) the multiple scattering theory used, (ii) the class of the CH technique,
(iii) the path-length corrections, (iv) the lateral corrections, and (v) the boundary
crossing algorithm. Generally, the precision of electron transport depends on the electron
step, commonly defined as fraction of energy lost over the step. The smaller the step, the
more accurate the simulation and the more computing power required. On the other hand,
electron steps must not be very small so as not to violate the restriction of the multiple
scattering theories. This issue is very important, especially for the boundary crossing
algorithms, and it will be discussed bellow.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
54
3.3. Monte Carlo code systems for photon and electron transport
Many Monte Carlo codes for photon and electron transport were developed, but
just few of them have become popular and have been studied and tested in detail over the
years. Special attention will be paid to the codes that have been used for the purposes of
this work.
3.3.1. Electron Gamma Shower (EGS4/EGSnrc)
EGS4 code system was introduced in 1985 (Ref. 5) and was developed in order to
extend the low energy limits of the previous version, EGS3. The EGS4 code has become
the most popular and the most tested Monte Carlo code. The system is written in the
MORTRAN structured language. After preprocessing, the MORTRAN macros are
translated into a FORTRAN code, which is to be compiled and executed. Generally, the
system consists of both an electron and a photon transport routine, as well as a routine
that handles a huge database with detailed information about radiological properties of
various materials (PEGS data).
Initially the EGS4 electron transport algorithm had some weaknesses, such as not
performing lateral corrections. Therefore, two years after its introduction a new electron
transport algorithm was developed in the new EGS4 version referred to as
EGS4/PRESTA6. PRESTA (Parameter Reduced Electron-Step Transport Algorithm) is
an algorithm based on the Molière’s multiple scattering theory, using a class II CH
technique. It performs both path-length and lateral displacement corrections.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
55
The most interesting feature of the PRESTA algorithm is the variable electron
step introduced in order to handle the boundary crossing problem, without slowing down
the calculations. The idea is presented in Fig 3.2. Since the multiple scattering theory
works for semi-infinite homogeneous media, the step at which an electron crosses the
boundary between two media will introduce some error. Hence, the algorithm aims to
minimize this step. Let us consider an electron to be transported through a voxel of
interest. Prior to each step, the minimum distance between the current electron position
and the boundary is calculated, and this distance limits the step so that the electron could
not reach the boundary. This procedure is repeated until the distance between the electron
and the boundary becomes smaller than a given minimum step mint . At this point the
lateral displacement correction is switched off and the electron crosses the boundary. The
minimum step cannot be smaller than the limit established by the underlying multiple
scattering theory.
EGS4/PRESTA was the most popular Monte Carlo code in the beginning of
1990s and was used and tested for many different applications with a continuously
Boundary
Medium 1
tmin
Medium 2
Figure 3.2: Boundary crossing algorithm in PRESTA.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
56
increasing demand for more accurate results under complicated dosimetry conditions. In
order to facilitate these demanding applications, a new electron transport algorithm called
PRESTA II was developed by the National Research Council of Canada in Ottawa,
resulting in a new EGS4 version referred to as the EGSnrc7. Instead of Molière’s theory,
PRESTA II uses multiple scattering based on the screened Rutherford single cross section
that leads to a better estimate of the lateral displacement corrections. Another very
important advantage of PRESTA II is its boundary crossing algorithm. When the distance
between an electron and the boundary becomes smaller than mint (Fig. 3.2), PRESTA II
switches off the multiple scattering and the electron is transported through the boundary
by single elastic scattering events, providing better results than the original PRESTA
algorithm. Obviously in PRESTA II the value of the minimum step is not crucial, since it
is only related to calculation efficiency. Series of tests have proved that PRESTA II is a
better electron transport algorithm than the original RPESTA, especially at low energies.
The EGSnrs code is incorporated into various user codes that calculate
different quantities. Every user code is responsible for: (i) reading both the geometrical
information and the Monte Carlo simulation parameters from a user-defined input file;
(ii) initializing EGSnrc system by setting several parameters; and (iii) creating an output
from the scoring information returned by the EGSnrc code. The user codes that have been
used in this work are: (i) DOSXYZnrc performing dose calculations in phantoms with
rectangular geometry; (ii) DOSRZnrc performing dose calculations in phantoms with
circular geometry; and (iii) FLURZnrc performing energy and fluence calculations in
circular phantoms.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
57
3.3.2. BEAM/EGS4
Monte Carlo simulations were first introduced into radiation therapy as a 3-D
dose calculation tool. Initially, the radiation beams were described by their spectra and
these beam models were used as radiations sources for the simulations. However, a better
approach was developed consisting of simulation of the treatment unit as well as the
phantom in which the dose distribution was calculated. The only problem in this
approach was that the treatment machines had a complicated design that was difficult to
describe precisely in the user code input files. This problem was successfully resolved by
the Monte Carlo code based on the EGS4/PRESTA system called BEAM8. The concept
of BEAM is simple: it supports a set of geometrical elements called component modules
(CMs). Some CMs as SLABS (stack of slabs) and CONESTAK (stack of cones) are
more general. Other CMs, such as JAWS and MIRROR are developed specially to
facilitate treatment machine simulations. A treatment unit is described in the user input
file as a series of CMs. The dimensions and the material should be specified for each of
the CMs as well.
The diagram in Fig. 3.3 illustrates how the BEAM code works. First, the
treatment unit is built of different CMs and the model is compiled resulting in an
executable program. This program is run, given both the input data (CMs dimensions,
materials, and incident particles) and physical properties of the materials (PEGS data).
When all the input information is loaded, BEAM invokes EGS4/PRESTA routines to
transport incident particles through the model of the treatment machine. As a result
BEAM scores all particles coming out of the treatment head into a certain plane in a file.
The scoring plane is called a phase space and the generated files are phase space files.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
58
The more particles in the phase space, the better the phase space describes the simulated
treatment unit. Another very useful feature of the BEAM software is the LATCH option.
This option keeps on record the CM that each particle in the phase space originates from.
LATCH is very helpful for determining where the contamination electrons come from,
when studying linear accelerators, for example.
BEAM is software that works on Linux platforms. Recently a graphical interface
was added to the system, and since then it has become easy to use the software. Moreover
there are auxiliary programs, such as BEAMDP, that can analyze the phase space data
and determine different quantities (spectra, mean energies, etc.). Some results obtained
with BEAMDP are presented in Chapter 5. BEAM also generates a graphical output that
might be used to view the simulated treatment unit. With all these features BEAM/EGS4
has become the most popular tool for precise linear accelerator simulations.
User input:- Geometry- Radiation
source
Phase Space
Medium dataEGS4/PRESTA MonteCarlo simulations
Treatment unit, buildof CMs
Figure 3.3: The concept of the BEAM/EGS4 Monte Carlo code.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
59
3.3.3. Voxel Monte Carlo Code (VMC, XVMC)
The Monte Carlo particle transport algorithms have undergone continuous
improvement since their introduction and they have become a very accurate and reliable
dosimetric tool. Despite the fact that computing power is very cheep nowadays, the
precise Monte Carlo simulations are unfortunately still not fast enough to be employed
for real treatment planning. Therefore, researchers have been looking for simplified
Monte Carlo algorithms that would be much faster, keeping the uncertainties in
calculated results within acceptable limits.
A fast Monte Carlo code for electron beam dose calculations, referred to as Voxel
Monte Carlo (VMC) code9, was introduced in 1995. VMC is based on the fact that in
radiation therapy the dose is delivered to materials with low density and low atomic
number (Z) by electrons within certain energy range. Thus, VMC was developed in a way
that it would be accurate for low Z materials with densities between 0 and 3 g/cm3 and
for electron energies between 1 and 30 MeV.
The most important changes that make the VMC code faster in comparison to
other Monte Carlo codes are: (i) some simplifications; (ii) new material data source; and
(iii) multiple use of each simulated history. Simplifications are made in all distributions
derived from the electron multiple scattering theory resulting in faster sampling. The
distributions are changed in such a way that the introduced errors are negligible within
the energy and material limits listed above. Some simplifications are also made in the
boundary crossing algorithm.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
60
VMC takes CT patient data as a set of voxels that represent the phantom.
Unlike the other codes, instead of reading the material properties from a special database,
it just calculates all quantities required for electron transport (density, stopping power,
etc.) based on the CT numbers. The calculations are performed by very simple
relationships, valid only within the VMC material and energy limits.
The multiple history use is the technique that speeds up the VMC code the most.
Every time a history is calculated, it is applied to several different regions in the
phantom. These regions should be away from one another so that any event that occurs in
one of them could not influence the events taking place in the others.
VMC Monte Carlo code proved to be a very fast and accurate code for electron
beam treatment planning and because of that, shortly after its advent, Monte Carlo photon
transport was added to VMC. The new code was called the XVMC10 code. In addition to
all material data that VMC calculates using the CT numbers, XVMC also calculates the
effective atomic number and electron density for each voxel in order to perform photon
transport.
XVMC, like all EGSnrc user codes, can use a phase space, obtained with BEAM,
as a radiation source. It has been established that XVMC is about 20 times faster than the
EGS4/PRESTA algorithm using similar transport parameters.
3.4. Monte Carlo simulation of the Clinac-18 linear accelerator
Various dosimetric quantities were calculated in water phantoms for the purpose
of this work. Given that dosimetry of small photon beams is very complicated, the only
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
61
scientific approach was to use the phase spaces below the small collimators as radiation
sources for all calculations in phantoms.
First, the treatment head of the Clinac-18 linear accelerator was simulated
according to the technical documentation provided by the manufacturer without any
small field collimator in place, using the BEAM/EGS4 code. The jaws were set to a
10×10 cm2 field at the isocenter of the machine. The model is shown in Fig. 3.4. Then
1,700,000,000 electrons, all with energy of 10 MeV, were simulated to strike the target.
All particles crossing a horizontal plane at SSD = 100 cm were scored in a phase space
file. This simulation, as well as all other Monte Carlo simulations presented in this work,
was performed without using any variance reduction techniques and with very low cutoff
Figure 3.4: Treatment head of the Clinac-18 linear accelerator: BEAM/EGS4 model.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
62
energies (0.01 MeV for both photons and electrons) in order to keep the simulations as
close as possible to reality. In total 4,700,000 particles were scored in the phase space.
The calculation time was approximately 1.5 sec per 1000 histories on a Pentium III 450
MHz processor. All calculations described below had approximately the same speed.
The phase space at SSD = 100 cm for a 10×10 cm2 field was used to calculate the
central axis percentage depth dose curve and a dose profile (off-axis ratios OAR) at a
depth of 10 cm in a water phantom. The calculations were performed with the
DOSXYZnrc user code. Figure 3.5 shows that after 6,100,000,000, histories the Monte
Carlo simulated PDD curve perfectly agrees with the measured curve. The profile
simulation was not that precise, but Fig. 3.6 clearly shows that the 50% width of the
profile simulated at depth of 10 cm is very close to 11 cm, which corresponds to a width
of 10 cm at the surface of the phantom. These two results validated the model of the
0
20
40
60
80
100
120
0 5 10 15 20 25Depth (cm)
PD
D
Monte Carlo
Measured
Figure 3.5: Monte Carlo simulated and measured PDD curves for 10×10 cm2 field sizeand SSD = 100 cm.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
63
Clinac-18 linear accelerator. Since the model was validated, the jaws were then closed to
a field of 5×5 cm2 at the isocenter and a phase space was calculated for each of the three
small collimators. The collimators were simulated using the geometry described in
Chapter 2. The phase space files were scored at 70 cm from the source, just bellow the
collimators, within a circular area with radius of 3 cm. The phase space results are
presented in Chapter 5.
3.5. Monte Carlo simulations in water phantoms
For each of the three small fields four different types of Monte Carlo simulations
were carried out in this work: (i) percentage depth dose curve at SSD = 100 cm; (ii) dose
profile at the same SSD and a depth of 2.5 cm; (iii) fluence and energy calculations at the
same depth; and (iv) A14P chamber response in case of off-axis measurements. All
0.0
0.2
0.4
0.6
0.8
1.0
1.2
-10 -5 0 5 10
Off-axis distance (cm)
OA
R
Figure 3.6: Monte Carlo calculated dose profile (OAR) for 10×10 cm2 field size,SSD = 100 cm and depth of 10 cm.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
64
calculations were carried out with the DOSRZnrc user code. As it has been pointed out
above, no variance reduction techniques were used and the cutoff energy was set to 0.01
MeV for both electrons and photons. The phase spaces obtained with the BEAM/EGS4
were used as radiation sources.
The PDD calculations were performed in a phantom, shown schematically in Fig.
3.7. The phantom is shown in the R-Z geometry, following the convention for describing
phantoms in the DOSRZnrc input files. The phantom starts with a 30 cm thick air slab.
This slab is needed to transport the phase space particles from the bottom side of the
collimator that is at 70 cm from the source to the surface of the water phantom that is
at100 cm from the source. First fifteen water slabs have a thickness of 2 mm in order to
obtain good resolution in the first 3 cm of the PDD curve. Beyond the depth of 3 cm, the
Figure 3.7: A phantom used for PDD curve Monte Carlo calculations with DOSRZnrc.
Air
Water
2 mm
5 mm
Centralaxis
Radius
PDD scoringvoxels
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
65
slabs are 5 mm thick. The last slab is 20 cm thick and its purpose is to serve as a
backscatter material that is not taken into account in the PDD curve.
In radial directions all slabs are divided into two regions. The first region has a
very small radius and it defines the small voxels at the central axis where the radiation
dose is calculated. The radius of these voxels varies with the field size: 0.5 mm for the 5
mm field, 0.3 mm for the 3 mm field, and 0.15 mm for the 1.5 mm field. The second
region has a radius of 15 cm and it is used as side-scattering material.
Figure 3.8 illustrates the phantom used for dose profile calculations at a depth of
2.5 cm. The phantom again starts with a 30 cm air slab, followed by a water slab that has
a thickness of 2.25 cm. The radiation dose is calculated in the next slab with a thickness
Figure 3.8: A phantom used for dose profile (OAR) Monte Carlo calculations with DOSRZnrc.
Air
Water
5 mm
0.5 mm
Centralaxis
Radius
0.2 mm
OAR scoringvoxels
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
66
of only 5 mm. There is again a thick backscatter slab at the bottom. In radial directions
the phantom consists of twenty-five rings with thicknesses of 0.2 mm and six rings with
thicknesses of 0.5 mm, and a 14.2 cm thick side-scatter ring. Resolution of 0.2 mm within
the field, and 0.5 mm outside the field is considered to be adequate. The same phantom
was used to calculate the photon and electron fluence, as well as photon and electron
energy as functions of the off-axis distance. These calculations were performed with the
FLURZnrc user code.
A modified version of the DOSRZnrc user code, that has the capability to displace
the phase space in lateral directions, was used to study the A14P chamber response as a
function of the off-axis distance. This study is presented in Chapter 4.
3.6. 3-D dose distribution calculation for dynamic stereotactic radiosurgery
One of the goals of this work is to explore the precision of dynamic radiosurgery
performed with very small photon beams by calculating the 3-D dose distribution and
carrying out the procedure with the Clinac-18 linear accelerator. The technique has been
described in Chapter 2. Unfortunately, the treatment planning software used at the McGill
University Health Centre could not handle calculations in phantoms with voxel size as
small as 0.5 mm. On the other hand, we really need very small voxels in order to
calculate a reliable dose distribution for radiation beams as small as few millimeters in
diameter. Therefore, the dose distributions for the dynamic radiosurgery carried out with
the 1.5 mm and the 3 mm collimator were calculated with the XVMC Monte Carlo code.
When this dynamic technique is performed, both the table and the gantry of the
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
67
accelerator are continuously moving. The irradiation starts at 330o gantry angle and –75o
table angle, and it stops at 30o gantry angle and 75o table angle (see Chapter 2). The
XVMC code facilitates gantry rotation over a user-defined arc during the irradiation, but
the table angle should be fixed. Therefore, we slightly modified the software, adding few
lines of code that dynamically change the table angle, as a function of the gantry angle.
The relation is then as follows:
90 0.5 oTable Angle Gantry Angle= − × (3.1)
The calculations were performed in a sphere made of water, centered at the
isocenter of the machine. The phase spaces for the 1.5 mm and the 3 mm collimator were
used as radiation sources. The voxel size for both beams was 0.5 mm. It seems that this
resolution is not high enough to perform calculations with the 1.5 mm collimator.
However, we are interested in the approximate size of the 50% isodose surface, which is
expected to be about 2.5 mm. Moreover, the auxiliary software that analyses the XVMC
calculated dose distribution performs interpolation between the voxel dose values in
order to obtain the isodose surfaces. This procedure improves the resolution of the
isodose distribution. The calculated results for the 1.5 mm and the 3 mm collimators are
presented in Chapter 5, where they are compared with measured distributions.
Chapter 3: Materials and Methods - Monte Carlo Particle Transport Simulations
68
References:
1 J.C. Butcher and H. Messel, “Electron number distribution in electron-photon
showers,” Phys. Rev. 112, 2096-2106 (1958).
2 J. H. Hubbell, J. M. Berger, and S. M. Seltzer, “X-ray nad Gamma-ray cross sections
and attenuation coefficients,” National Bureau of Standards Standard Reference
Database, 1985.
3 M.J. Berger, “Methods in computational physics, ” Academic Press, New York, 1963.
4 H. A. Bethe, “Molière's theory of multiple scattering,” Phys. Rev. 89, 1256-1266
(1953).
5 W. R. Nelson, H. Hirayama, and D. O. Rogers, Report No. SLAC-265, 1985.
6 A. F. Bielajew and D. W. O. Rogers, Report No. PIRS-0042, 1987.
7 I. Kawrakow, “Accurate condensed history Monte Carlo simulation of electron
transport. I. EGSnrc, the new EGS4 version,” Med. Phys. 27, 485-498 (2000).
8 D. W. Rogers, B. A. Faddegon, G. X. Ding et al., “BEAM: a Monte Carlo code to
simulate radiotherapy treatment units,” Med. Phys. 22, 503-524 (1995).
9 I. Kawrakow, M. Fippel, and K. Friedrich, “3D electron dose calculation using a
Voxel based Monte Carlo algorithm (VMC),” Med. Phys. 23, 445-457 (1996).
10 M. Fippel, “Fast Monte Carlo dose calculation for photon beams based on the VMC
electron algorithm,” Med. Phys. 26, 1466-1475 (1999).
Chapter 4:
Exradin A14P IonizationChamber Study
4.1. Geometry of the measuring volume
The two detector-related issues associated with dose measurements in small
photon fields, namely (i) resolution and (ii) water-equivalency, have been discussed in
Chapter 1. Obviously, the A14P parallel-plate ionization chamber is neither a high-
resolution detector nor a water-equivalent one. Its resolution is not sufficiently high
because the diameter of the collecting electrode is 1.5 mm (see Chapter 2). Therefore, the
diameter of the sensitive chamber volume which has at least this value, is large in
comparison to sizes of the fields studied in this work (1.5, 3, and 5 mm). The sensitive
measuring material for this chamber is air with a density of 1.293×10-3 g/cm3 at 0o C and
101.3 kPa.
In order to handle both the resolution and water-equivalency problems, we must
know the exact geometry of the measuring volume of the chamber. A good approach to
its determining is to determine the lines of the electric field inside the chamber cavity,
and this is equivalent to finding the lines of constant potential. The electric potential in
the cavity may be obtained by solving the Laplace equation, assuming that the charge
density in the chamber is zero:
Chapter4: Exradin A14P Ionization Chamber Study
70
∇ =2 0U , (4.1)
where U is the electric potential inside the cavity. If we want to solve this equation
numerically, particularly for the A14P chamber, we have to define the boundaries of the
cavity first and then set the boundary conditions over the boundaries. We can simplify the
geometry of the cavity slightly by neglecting the air gap between the collecting and the
guard electrodes (Fig 4.1(a)).
The Laplace equation written in cylindrical coordinates is given as follows:
∂ ∂ ∂ ∂+ + + =∂ ∂ ∂φ ∂
2 2 2
2 2 2 2
1 10
U U U Ur r r r z
, (4.2)
where the space variables r , z and φare defined in Fig 4.1(b). Because of the rotational
symmetry of the A14P ionization chamber, the potential does not depend on φ. Hence
2 2/ 0U∂ ∂φ = and the Laplace equation simplifies to the following:
1 mm
3 mm
4 mm
Z axis
CentralElectrode
Cap
(a) (b)
Z axis
r1
r2
(2)
(1) φ
z
r
s
Figure 4.1: Exradin A14P ionization chamber: (a) simplified geometry and (b) areawhere the equation is solved.
Chapter4: Exradin A14P Ionization Chamber Study
71
2 2
2 2
10
U U Ur r r z
∂ ∂ ∂+ + =∂ ∂ ∂
, (4.3)
which is equivalent to:
2 2
2 2 0U U U
rr z r
∂ ∂ ∂+ + = ∂ ∂ ∂ . (4.4)
Equation (4.4) represents a 2-D problem and the boundaries are much easier to
define. Figure 4.1(b) shows the contour that envelops the air cavity in the R-Z geometry
and the boundary conditions must be defined over this contour. The potentials of both the
cap and the central electrode are fixed during the measurements; hence, it is convenient
to use the Direchlet boundary conditions and this implies the use of the value of the
electric potential over the contour as a boundary condition.
Usually, the cap is grounded when voltage is applied to the chamber. Thus we can
assume that the potential of the cap is equal to zero and the potential of the electrode
maxU is equal to the applied voltage. The potential over the segment (1) in Fig. 4.1(b)
( 0r = ) is given as follows:
max 1z
U Us
= − , (4.5)
where z is the distance form the collecting electrode and s is the separation between the
two electrodes of the chamber. Essentially, Eq. (4.5) represents the potential between two
infinite surfaces and applies over the central axis in this particular case because of
symmetry considerations. The segment (2) (Fig 4.1(b)) is considered to be far enough
from the edge of the electrode and thus the potential over this segment is given by the
formula for the potential between two infinite coaxial cylinders:
Chapter4: Exradin A14P Ionization Chamber Study
72
1max
2
1
ln1
ln
rr
U Urr
= −
. (4.6)
The basic numerical methods for solving partial differential equations may be
found in many reference books1. If we consider the Taylor expansion of the function
( ),U r z at points ( , )r h z+ and ( ),r h z− located at a small distance h from the point
( ),r z we obtain:
( ) ( ) ( ) ( )2 2
2
, ,, , ...
2U r z U r z hU r h z U r z h
r r∂ ∂
+ = + + +∂ ∂ (4.7)
and
( ) ( ) ( ) ( )2 2
2
, ,, , ...
2U r z U r z h
U r h z U r z hr r
∂ ∂− = − + +
∂ ∂(4.8)
Neglecting all terms above the second order and adding Eq. (4.7) and Eq. (4.8), we find:
( ) ( ) ( ) ( )2
2 2
, , , 2 ,U r z U r h z U r h z U r zr h
∂ + + − −=
∂. (4.9)
The uncertainty associated with Eq. (4.9) depends on 4h . If we now subtract Eq. (4.8)
from Eq. (4.7) we obtain for the first derivative:
( ) ( ) ( ), , 2 ,2
U r z U r h z U r h zr h
∂ + − −=
∂, (4.10)
where the uncertainty goes with 3h . By analogy with Eq. (4.9) we can find the second
partial derivative with respect to z :
( ) ( ) ( ) ( )2
2 2
, , , 2 ,U r z U r z h U r z h U r zz h
∂ + + − −=
∂. (4.11)
Chapter4: Exradin A14P Ionization Chamber Study
73
Finally, if we substitute all derivatives into Eq. (4.4) with Eq. (4.9), (4.10) and
(4.11), we get:
( ) ( ) ( ) ( ) ( )
( ) ( )
1, , , , ,4
, , .8
U r z U r h z U r h z U r z h U r z h
h U r h z U r h zr
= + + − + + + − +
+ + + − (4.12)
Equation (4.12) gives a relationship between the value of the electric potential at a
given point inside the air cavity, and the values of four adjacent points at distance h in
both r and z directions from the given point.
For the purposes of this study a value of 0.02 mm was assigned to the step h , so
that there were 50 points per millimeter in each direction. After that, the value of the
electric potential at each point was calculated using Eq. (4.12), starting from the contour.
The calculations were performed using the MATLAB software package and they were
repeated iteratively until average relative difference between two consecutive runs
became as low as 0.01%. The data was divided into two matrices to speed up the
calculations. The matrix (A) contained all points in the separation region above the
collecting electrode (in Fig. 4.2: from segment (1) to the side wall of the cap). The other
matrix (B) contained all points in the side region between the side walls of the cap and
the electrode (in Fig 4.2: above the segment (2)). The guard electrode that engulfs the
collecting electrode will collect all charges created by radiation in the side region (matrix
(B)). Therefore only the electric field in the top region (matrix (A)) is important for
determining the measuring volume.
Figure 4.3 shows the lines of constant potential and a line of the electric field that
determines the measuring volume in the top region. The figure is drawn in the R-Z
geometry. The line of the electric field that determines the measuring volume is chosen
Chapter4: Exradin A14P Ionization Chamber Study
74
to start at the middle of the air gap. The measuring volume calculated according to Fig.
4.3 is 3.3 ±0.2 mm3. The uncertainty is mainly due to the fact that dimensions of the air
gap and the guard electrode are not very well defined. The measuring volume was
verified by measurements with a 10 MV photon beam at maxd (2.5 cm) in a water
phantom in a standard field (SSD = 100 cm, 10×10 cm2), immediately after a routine
check of the output of the machine, when the dose delivered to water was very well
known. Using values of 0.001197 g/cm3 for the density of air at 22 oC and 101.3 kPa, and
33.97 J/C for the ionization potential of air, we obtained 3.4 ±0.1 mm3 for the chamber
sensitive volume. The uncertainty in this result is due firstly to about 1% uncertainties in
measurements, and secondly to not accounting for any correction factor for the A14P
ionization chamber.
The geometry of the measuring volume is important for developing the algorithms
described below.
Z axis
(B)
(2)
(1)(A)
Figure 4.2: Calculation regions.
Chapter4: Exradin A14P Ionization Chamber Study
75
4.2. Deconvolution of dose profiles in water
The idea of using deconvolution to eliminate the blur of a low-resolution detector
is not a new one. Several studies have been done with the aim to increase the resolution
in the penumbra region for relatively large fields2-5. Figure 4.4(a) shows a detector placed
at the edge of a large square field from a beam’s eye of view. Obviously in this region the
radiation dose decreases in the X direction and stays constant in the Y direction.
Therefore the studies mentioned above have considered 1-D deconvolution using the
detector Line-Spread Function (LSF). For very small circular fields though, the radiation
dose changes in both directions (Fig 4.4(b)), making the measured dose profile a result of
a 2-D convolution between the dose field and the detector Point-Spread-Function (PSF)
and requiring that a 2-D deconvolution be performed.
Guardelectrode
Measuring Volume
Collectingelectrode
Cap
Z axis
Figure 4.3: Electric field in the air cavity.
Chapter4: Exradin A14P Ionization Chamber Study
76
The first problem to be solved is to determine the PSF of our detector.
Theoretically this could be done by taking measurements in a X-Y plane of a very narrow
beam, mathematically presented as a 2-D δfunction. In reality, however, even if such a
photon beam is collimated, the electrons set in motion in the phantom will spread out,
and the electron fluence will not follow the 2-D δfunction pattern any more.
Another, much more practical, approach is to model the PSF of the detector. If the
measuring material has the same properties everywhere in the measuring volume, the
response of the detector for a given point in the X-Y plane is equal to the thickness of the
measuring volume at that point. The shape of the detector PSF, resulting from the
measuring volume geometry that is obtained from the electric field lines, is shown in Fig.
4.5(a). However, it turns out that the deconvolution algorithm described below, also
works well even for a slightly simplified PSF, shown in Fig. 4.5(b).
The two functions are almost identical in terms of the resolution of the
deconvolved profile that this study aims for. The underlying assumption is that the
chamber has a constant response over a circle with a diameter of 2 mm and zero response
X
Y
(b)
X
Y
(a)
Figure 4.4: Detector in the penumbra region of (a) a large square field, and (b) asmall circular field.
Chapter4: Exradin A14P Ionization Chamber Study
77
elsewhere. When the PSF is determined and the measured profile is obtained, there are
two different ways of performing deconvolution. The first is to perform direct
deconvolution, often referred to as filtering. This is usually done in the Fourier space,
where this operation corresponds to a simple division: the Fourier transform of the
function to be filtered is divided by the Fourier transform of the PSF, known as the
system transfer function (STF). After this, the result of division undergoes an inverse
Fourier transformation that yields the deconvolved profile. The block diagram in Fig.
4.6(a) illustrates the whole deconvolution procedure. The measured profiles are
designated as 2-D functions, whereas they are usually one-dimensional. For circular
fields this is appropriate, because of their circular symmetry. It is clear that the measured
profiles do not represent the real dose values, since they incorporate some errors.
However, the PSF model introduced is not perfect and the final result of the filtering
could be very unrealistic, occasionally resulting even in negative doses.
The second algorithm for performing deconvolution is more practical and gives
more reliable results; however, it also requires more computing power. The block
diagram in Fig. 4.6(b) presents this algorithm. It starts from some arbitrary values for the
X
PSF(X,Y)
Y
(?)
X
PSF(X,Y)
Y
(b)
Figure 4.5: Point-Spread Function (PSF) of (a) A14P chamber and (b) a simplified PSF.
Chapter4: Exradin A14P Ionization Chamber Study
78
real dose profile (the deconvolved one) and performs convolution with the PSF for all
points at which measurements are taken. After that, the calculated results are compared
with the measured ones and a new real profile is generated. This routine is repeated until
the difference between the calculated and the measured profile becomes small enough
and a given condition is satisfied. This kind of algorithms are referred to as minimization
algorithms. The method by which the real profile is generated will be discussed below,
but it is important to note that, when the profile is generated, certain restrictions might
apply. These restrictions keep the dose profile within a set of acceptable solutions. The
second approach (Fig. 4.6(b)) was chosen for the purposes of this study and a simple
minimization algorithm, whose description follows, was developed.
Convolution2-D PSF
2-DDeconvolved
Profile ConvolvedProfile
Comparisonwith the
MeasuredProfile
2-D PSF
Measured2-D Profile
Filtering
Fourier Space
2-DDeconvolved
Profile
(a)
(b)
Figure 4.6: Direct deconvolution by (a) filtering and (b) a minimization algorithm.
Chapter4: Exradin A14P Ionization Chamber Study
79
Let us consider a geometrical model of a radiation field with a circular symmetry
(Fig 4.7). The field is divided into very small pixels, so that the dose delivered to a pixel
is constant throughout the pixel. The radiation dose jD is delivered to all pixels, which
are at distance jr from the central axis. Different detector positions are shown in the
figure as well. According to the model, for a given position i , the measured value iM is:
i ij jj
M c p D= ∑ , (4.13)
where: ijp is the number of pixels receiving the dose jD within the measuring volume
when the detector is at position i ; c is a constant that relates the dose measured in Gy on
the equation’s right hand side to the measurements in nC on the left hand side. This
constant incorporates the density of air, the ionization potential of air, the pixel size, and
Dj
rj
M1 Mn
Ion chamberpositions
Figure 4.7: Geometrical model of taking measurements in a small circular field.
Chapter4: Exradin A14P Ionization Chamber Study
80
the separation of the ionization chamber. However, the study aims to obtain a profile
normalized to the central axis value, so the constant can be neglected. Then Eq. (4.13)
becomes:
i ij jj
M p D= ∑ , (4.14)
actually representing a discreet convolution of the dose field with the detector PSF.
Mathematically, this calculation is one-dimensional because of the circular symmetry of
the radiation field.
The main input parameters for the minimization algorithm are: (i) all detector
positions, (ii) all measured values and (iii) the radius of the detector. The algoritm starts
by calculating all ijp . Then the first approximate dose profile is calculated using the
formula:
2
1meas
ij ii
jij
i
p MD
R p=
π
∑∑ , (4.15)
where R is the detector radius in number of pixels and measiM are the measured values.
Equation (4.15) represents a weighted sum of all measured values in which jD takes
place, divided by the number of pixels that fit within the detector. This is the initial
profile from which the minimization algorithm starts and is very important. This profile
could be an arbitrary one, but if it is close to the ideal solution, the minimization is much
faster and the final result is very reliable. Several different ways of calculating the initial
profile have been tested, and Eq. (4.15) shows the most successful approach.
When the initial profile is determined, the minimization starts as indicated in Fig.
4.6(b). The values iM are calculated according to the geometrical model (Eq. (4.14)) and
Chapter4: Exradin A14P Ionization Chamber Study
81
they are compared to the measured values measiM . The minimization criterion, referred to
as the objective function, is given as:
21 meas
i imeas
i i
M Mn M
−
∑ , (4.16)
representing the average relative error. In the beginning of every new run the dose profile
is modified. The new values are obtained by multiplying the values from the previous run
with coefficients jk defined as follows:
( )1 0,1jk = + σΝ , (4.17)
where σ is an input parameter usually close to 0.1 and ( )0,1Ν is a random function that
generates numbers following the normal distribution, with zero mean and unity variance.
After the values are generated, several restrictions are applied allowing the algorithm to
distinguish the meaningful solutions. Many different restrictions have been tested and a
final set of three of them that were found useful is as follows (Fig 4.8): (i) radiation dose
should decrease with off-axis distance; (ii) the second derivative of the profile should be
negative before a given point (inflexion point) and positive beyond this point; (iii) over a
small extent in the tail of the profile the dose is constant.
The first restriction is natural, because there is no physical reason for an increase
in the dose with off-axis distance for the very small fields that we studied. The second
restriction takes care of the smoothness of the profile, because otherwise some strange
edges due to errors in the measured values might appear. The inflexion point, an input
parameter for the algorithm, is easy to determine. Usually, it is the point of the 50% value
that is the same for both the convolved and deconvolved profiles. Even if it is not very
precisely determined, this point is not crucial for the minimization algorithm. The third
Chapter4: Exradin A14P Ionization Chamber Study
82
restriction is not needed, however, it speeds up the calculations. This restriction is applied
to a small region in the tail where the differences between the measurements are smaller
than their uncertainties.
The minimization algorithm, as described above, was coded in the C
programming language. The C-routine that was used for the function ( )0,1Ν (Eq. (4.17))
was obtained from a book called “Numerical Recipes in C”6. The size of the pixel for all
calculations was 0.2 mm and the radius of the A14P measuring volume was 5 pixels. The
same resolution was used in all Monte Carlo simulations (see Chapter 3).
The software was tested using computer-generated profiles. Another software was
developed to generate fake measured profiles given the “ideal” ones, according to Eq.
(4.14). Then the minimization algorithm was used to retrieve the ideal profiles. The result
of one these tests is shown in Fig 4.9. The average relative error, as defined in Eq. (4.16),
in this particular case is 0.03%. The deconvolved profiles for the three different fields
studied in this thesis are presented in Chapter 5.
OAR
Off-axis distance (pixels)
Second derivative control:Inflexion point
Tail
Figure 4.8: Restrictions applied to the profiles.
Chapter4: Exradin A14P Ionization Chamber Study
83
4.3. Correction factors for off-axis measurements
The problem of the water-equivalence of a detector used for measurements in
very small photon fields has already been discussed in Chapter 1. The A14P ionization
chamber is not a water-equivalent detector because the measuring material in the
chamber sensitive volume is air. The standard relationship between the dose delivered to
water waterD and the dose delivered to air airD is given as follows:
( )water
waterwater air air
air
LD D =
φρ
, (4.18)
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20 25
Off-axis distance (pixel)
OA
RIdeal profile
Deconvolved profile
Figure 4.9: Test result for the minimization algorithm.
Chapter4: Exradin A14P Ionization Chamber Study
84
where the correction factors ( )/water
airL ρ and ( )water
airφ were defined and discussed in detail
in Chapter 1. The restricted mass stopping power correction factor is defined for the same
electron fluence in two different mediums. This correction factor is also relevant when
the electron fluence in the mediums is not the same, but the electron energy spectra are
identical. For this more complicated case the fluence perturbation correction factor is
introduced. However, when the fluence perturbation is very drastic, it is questionable if
the two correction factors are still independent, because the electron energy spectrum
might change as well. Therefore, in cases where the dosimetry and the underlying physics
are not well known, it is a better approach to combine the two correction factors into one,
so that Eq. (4.18) becomes:
( )waterwater air air
D D D= , (4.19)
where ( )water
airD is the total correction factor. In general, this total correction factor depends
on the beam geometry, the detector design, and the detector position. Therefore ( )water
airD
has to be calculated for each particular field and each particular detector position. The
best way to obtain ( )water
airD is by using Monte Carlo simulations because they are relevant
under any conditions. Moreover, when using simulations, there is no need of simplifying
the reality in order to apply some theoretical model. In other words, when the basic
physics of dose delivery is not well understood, it is difficult to say which theoretical
model is relevant and which one is not.
In this work ( )water
airD correction factors of the A14P chamber were calculated at
different off-axis distances for each of the studied very small photon fields. The
calculations were performed using the DOSRZnrc Monte Carlo code from the EGSnrc
Chapter4: Exradin A14P Ionization Chamber Study
85
package. This code has been discussed briefly in Chapter 3. It is used for Monte Carlo
particle transport in phantoms with cylindrical symmetry. The A14P chamber was
simulated as an air cavity that consists of two coaxial cylinders inside a water phantom.
Figure 4.10 shows the geometry of the cavity. Not only the measuring volume,
but the whole air cavity of the ionization chamber, was simulated because the size of the
cavity had an impact on the fluence perturbation. The measuring volume is modeled as a
cylinder with a radius of 1 mm. The geometry shown in Fig 4.10 is somewhat different
from the results obtained from the electric field (Fig 4.3). The real geometry could be
simulated using the DOSXYZnrc code, but the number of voxels in this case would
increase substantially. On the other hand, this simulation did not aim to very high
precision, therefore the DOSRZnrc code was chosen. The only problem that appeared
was that it was impossible to move the cavity into off-axis positions in a DOSRZnrc
phantom. Therefore another approach was taken: the code was slightly modified so that
instead of moving the air cavity the phase space was moved. The phase space contains all
2 mm1 mm
Z axis
1 mm
Figure 4.10: Geometry of the air cavity in the Monte Carlo simulations.
Chapter4: Exradin A14P Ionization Chamber Study
86
pertinent information about particles below the collimator (see Chapter 3). Therefore, if a
small displacement is added to the X coordinate of each particle, this will be equivalent to
moving the air cavity in the opposite direction, provided that the water phantom is
sufficiently large (Fig 4.11).
During the simulations, 20,000,000 to 100,000,000 particles were sent through the
phantom, depending on field size, and uncertainties as low as 1% were achieved at zero
off-axis distance. Uncertainties in the tail (off-axis distance of 7 to 8 mm) were about 6%.
Each simulation was performed twice: once for the air cavity and once for the cavity
filled with water.
DOSRZnrc code reports the radiation dose deposited in a voxel normalized to the
initial number of high-energy electrons striking the accelerator target. For a given
Figure 4.11: Monte Carlo simulated geometry for off-axis correction factors calculation. Thephase space is moved over the phantom, instead of moving the air cavity.
Air cavity
Water phantom
Z axis
Phase space
Chapter4: Exradin A14P Ionization Chamber Study
87
electron energy (10 MeV for our particular case) the number of electrons that have
striked the target corresponds to the practical dosimetric quantity Monitor Unit (MU)
used for dose delivery with linacs. Therefore, as a result of this normalization, the
reported doses are comparable even if a different number of particles is sent through the
phantom.
The ( )water
airD correction factors were established by dividing the dose calculated
in the measuring volume when filled with water to the dose to the measuring volume in
the air cavity for each different off-axis position. The results were used to correct the
A14P chamber measurements prior to applying the deconvolution algorithm, and are
presented in Chapter 5.
Chapter4: Exradin A14P Ionization Chamber Study
88
References:
1 W. Cheney and D. Kincaid, “Numerical Mathemetics and Computing,” Wadsworth,
Inc., Belmont, CA, USA, 1985.
2 P. Charland, E. El-Khatib, and J. Wolters, “The use of deconvolution and total least
squares in recovering a radiation detector line spread function,” Med. Phys. 25, 152-
160 (1998).
3 F. Garcia-Vicente, J. M. Delgado, and C. Peraza, “Experimental determination of the
convolution kernel for the study of the spatial response of a detector,” Med. Phys. 25,
202-207 (1998).
4 P. D. Higgins, C. H. Sibata, L. Siskind et al., “Deconvolution of detector size effect
for small field measurement,” Med. Phys. 22, 1663-1666 (1995).
5 C. H. Sibata, H. C. Mota, A. S. Beddar et al., “Influence of detector size in photon
beam profile measurements,” Phys. Med. Biol. 36, 621-631 (1991).
6 W. Press, S. Teukolski, W. Vetterling et al., “Numerical Recipes in C,” Cambridge
University Press, Cambridge, MA, USA, 1992.
Chapter 5:
Experimental Results
5.1. Beam quality
The quality of small radiation beams differs from the quality of standard clinical
photon beams with field sizes on the order of 10×10 cm2 even when both the small and
the standard beams are produced under the same linac operating conditions. The radiation
beam quality changes when the beam is collimated with the small field collimators
because of the photon interactions that take place inside the collimator. The beam quality
for three small photon fields (1.5, 3 and 5 mm) shaped with the collimators described in
Chapter 2 were studied with Monte Carlo simulations.
The particle transport through the Clinac-18 treatment head and the collimators
was simulated using the BEAM/EGS4 code, as described in Chapter 3. All particles
below the collimators were scored and their parameters, such as energy, charge, position
and direction were stored in three phase-space files; one file for each collimator. These
files contained all particles collected in a circular area with a radius of 3 cm at 70 cm
from the source, just bellow the collimators, and they were used for all Monte Carlo
simulations in various phantoms presented in this work.
Various beam quality parameters were analyzed using the BEAMDP code from
the BEAM/EGS4 package. The pictures presenting the X-Y scatter of the particles in the
phase-space files are shown in Fig. 5.1. The phase-space data for the 1.5 mm field
Chapter 5: Experimental Results
90
contains 50,284 (electrons and photons) particles and 49,735 or 98.9% of them are
photons (Fig. 5.1(a)). This particle fluence was produced by almost 3,900,000,000 initial
high-energy electrons, striking the target of the linac. Figure 5.1(b) shows 13,795
particles (electrons and photons) collected below the 3 mm collimator, with the photon
fraction of 99%. About 6,000,000,000 high-energy electrons hit the linac target in order
to produce this fluence. For the 5 mm collimator a simulation of 5,000,000,000 initial 10
MeV electrons produced 81,229 particles bellow the collimator. The X-Y particle scatter
is shown in Fig. 5.1(c). The photon fraction is again 99%.
In all experiments and simulations the collimator jaws of the accelerator were set
to project a 5 ×5 cm2 field at the isocenter of the machine, and this corresponded to a field
of 3.5×3.5 cm2 at 70 cm from the source, where the phase-space files were determined.
The transmission radiation with this field size is evident in Fig. 5.1(a) for the 1.5 mm
collimator and in Fig. 5.1(c) for the 5 mm collimator. For the 3 mm collimator the
transmission radiation cannot be distinguished in Fig 5.1(b), because this collimator is
made of tungsten, whereas the other two are made of lead. Since all collimators have a
thickness of 10 cm and the density of tungsten is about 1.8 times higher than that of lead,
we can expect a considerably lower photon transmission through the tungsten-made
collimator.
Collimator # of initial electronsstriking the target
# of particles inthe phase space
# of photons in thephase space
1.5 mm 3 900×106 50 285 49 735
3 mm 6 000×106 13 795 13 654
5 mm 5 000×106 81 229 80 484
Table 5.1: Phase space data for the three collimators used in our study.
Chapter 5: Experimental Results
91
The total numbers of particles listed in Table 5.1 above differ for the various
phase-space files, firstly because of the differences in field size, and secondly because of
the different transmissions through the collimators. However, the particle densities inside
Figure 5.1: Photon fluence for the (a) 1.5 mm, (b)3 mm, and (c) 5 mm fields. The calculationsare performed below the collimators at 70 cm from the radiation source.
(a) (b)
(c)
Chapter 5: Experimental Results
92
the radiation fields are similar, as shown from the following analysis. The number of
photons in a small circular region with a diameter of 1 mm is: 1460 particles for the 1.5
mm field, 2100 particles for the 3 mm field, and 2000 particles for the 5 mm field. This
particle fluence is considered sufficiently large to obtain good statistical results for any
further dose calculations in the phantom, although the total number of photons is not high
enough to obtain good results for the photon fluence analysis.
Figure 5.2 shows the photon fluence spectra for the three different fields, obtained
with the BEAMDP analyzing software. The spectra are not smooth because the total
numbers of photons analyzed are low, resulting in high statistical uncertainties. The
spectra are normalized to their maximum values beyond the energy of 0.511 MeV, where
there are sharp peaks in all spectra. These peaks result from electron-positron
annihilations that take place in the collimators. The positrons are produced by pair
production interactions; interactions with a relatively high probability for photons with an
energy on the order of several MeV in high-atomic number materials. The peak at 0.511
MeV is higher for the 1.5 mm (Fig. 5.2(a)) and 5 mm (Fig. 5.2(c)) collimators that are
made of lead in comparison with for the 3 mm collimator (Fig. 5.2(b)), made of tungsten.
This effect is mainly due to two reasons. Firstly, the atomic cross-section for a pair-
production interaction at a given photon energy depends on the square of the atomic
number of the attenuator. Since the atomic number of lead is 82 and the atomic number
of tungsten is 74, the probability for pair production interaction in lead is higher than that
for tungsten. Secondly, tungsten has a higher density and, since the collimators have the
same thickness, the 3 mm collimator attenuates more photons with the relatively low
energy of 0.511 MeV.
Chapter 5: Experimental Results
93
Figure 5.2: Normalized photon fluence density vs. energy for the (a) 1.5 mm, (b) 3 mm, and(c) 5 mm fields. The calculations are performed below the collimators at 70 cmfrom the radiation source.
(a)
(b)
(c)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 2 4 6 8 10
Energy (MeV)
Nor
mal
ized
flue
nce
dens
ity
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 2 4 6 8 10
Energy (MeV)
Nor
mal
ized
flue
nce
dens
ity
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 2 4 6 8 10
Energy (MeV)
Nor
mal
ized
flue
nce
dens
ity
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
94
The 0.511 MeV peak is slightly higher for the 1.5 mm collimator in comparisons
to the 5 mm collimator. This must be due to the fact that the 1.5 mm collimator covers a
larger area of the 5×5 cm2 radiation field and thus offers more lead for interaction
purposes.
Figure 5.3 shows the energy fluence spectra for the three radiation fields. The
0.511 MeV peaks are present again, but here they are lower compared to those in Fig.
5.2, because in this case the spectra are weighted by energy. Therefore, the low energy
part of the spectrum diminishes and the peaks are not as high. The uncertainty in the 3
mm energy fluence spectrum is very high because the phase-space file for this field
contains only 13,800 particles.
Figure 5.4 shows the change in photon fluence with the off-axis distance in the
scoring plane below the three collimators. The photon fluence is normalized to the central
axis value. When performing such an analysis, the BEAMDP software divides the area,
over which the phase space file has been collected into coaxial rings with equal surfaces.
Therefore the radial resolution is poor close to the central axis, and increases with the off-
axis distance. For all graphs, shown in Figure 5.4, the size of the first bin of the histogram
is 2.12 mm, which corresponds to a circular region with diameter of a 4.14 mm. This
region is larger than any of the fields at 70 cm from the source, where the analysis is
performed. Thus, there is not enough information about the photon fluence drop off at the
edge of the field. However, the transmission radiation is well presented.
Figure 5.4(b) shows a negligible transmission for the 3 mm collimator compared
to the 1.5 mm (Fig. 5.4(a)) and 5 mm (Fig. 5.4(c)) collimators. The transmission,
normalized to the central axis fluence, is much higher for the 1.5 mm collimator than for
Chapter 5: Experimental Results
95
Figure 5.3: Normalized photon energy fluence density vs. energy for the (a) 1.5 mm, (b) 3mm, and (c) 5 mm fields. The calculations are performed below the collimators at70 cm from the radiation source.
(a)
(b)
(c)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8 10
Energy (MeV)
Nor
mal
ized
ene
rgy
fluen
ce
dens
ity
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8 10
Energy (MeV)
Nor
mal
ized
ene
rgy
fluen
ce
dens
ity
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8 10
Energy (MeV)
Nor
mal
ized
ene
rgy
fluen
ce
dens
ity
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
96
Figure 5.4: Normalized photon fluence vs. off-axis distance for the (a) 1.5 mm, (b) 3 mm, and(c) 5 mm fields. The calculations are performed below the collimators at 70 cmfrom the radiation source.
(a)
(b)
(c)
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3
Off-axis distance (cm)
Nor
mal
ized
flue
nce
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3
Off-axis distance (cm)
Nor
mal
ized
flue
nce
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3
Off-axis distance (cm)
Nor
mal
ized
flue
nce
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
97
the 5 mm one, because the central axis fluence increases with the collimator opening,
whereas the transmission through a 10 cm thick lead block is the same. In addition, there
is an averaging effect over the first bin of the histogram, and this effect lowers the central
axis value for the 1.5 mm field much more than the central axis value for the 5 mm field.
For all fields the photon fluence starts decreasing at the edge of the field as determined by
the setting of the collimator jaws (3.5 cm at 70 cm from the source), although this effect
is not visible for the 3 mm field (Fig. 5.4(b)).
The energy fluence as a function of the off-axis distance, normalized to the central
axis value, is shown in Fig. 5.5. All considerations about the histogram resolution pointed
out for Fig. 5.4 also apply to Fig. 5.5. A very important observation is that energy fluence
for the different fields (Fig. 5.5) has a similar behavior to the corresponding photon
fluence (Fig. 5.4). Therefore, the average photon energy does not change significantly
with the off-axis distance for any of the fields.
Figure 5.6 shows the average photon energy as a function of the off-axis distance
for the three fields. For all fields the average energy has a value around 3 MeV on the
central axis. The averaging effect due to the low resolution of the histogram, as discussed
above, can be noticed in Fig. 5.6(a). Most probably, because of this effect, the central
axis value is lower than 3 MeV. The value of 3 MeV is in good agreement with the
average photon energy in an open field calculated according the rule of thumb as one
third of the maximum photon energy. For all collimators, the average energy drops to
about 2.5 to 2.7 MeV outside of the field. There are scattered photons, as well as
transmission photons in this region. After an off-axis distance of 1.75 cm, which
corresponds to the setting of the collimator jaws, the average energy starts diminishing,
Chapter 5: Experimental Results
98
Figure 5.5: Normalized photon energy fluence vs. off-axis distance for the (a) 1.5 mm, (b) 3mm, and (c) 5 mm fields. The calculations are performed below the collimators at70 cm from the radiation source.
(a)
(b)
(c)
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3
Off-axis distance (cm)
Nor
mal
ized
ene
rgy
fluen
ce
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3
Off-axis distance (cm)
Nor
mal
ized
ene
rgy
fluen
ce
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3
Off-axis distance (cm)
Nor
mal
ized
ene
rgy
fluen
ce
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
99
Figure 5.6: Average photon energy vs. off-axis distance for the (a) 1.5 mm, (b) 3 mm, and (c)5 mm fields. The calculations are performed below the collimators at 70 cm fromthe radiation source.
(a)
(b)
(c)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 1 2 3
Off-axis distance (cm)
Ave
rage
ene
ry (M
eV)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 1 2 3
Off-axis distance (cm)
Ave
rage
ene
ry (M
eV)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 1 2 3
Off-axis distance (cm)
Ave
rage
ene
rgy
(MeV
)
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
100
because, in general, there are only scattered photons in this area. The average energy for
the 3 mm field (Fig. 5.6(b)) has large statistical uncertainties, especially in the region
beyond 2 cm from the central axis. This is due to the low transmission of this collimator,
resulting in a very low number of photons available for analysis.
5.2. Physics of dose deposition
The basic physics of dose deposition in absorbing medium is essentially the same
for small and large photon fields: the photon fluence creates electron fluence and the
electron fluence deposits radiation dose to the medium. The dose deposition depends on
both the electron fluence and the electron energy. In large fields, under the condition of
charged particle equilibrium, there is a strong relationship between the photon fluence
and the electron fluence on one hand, and the photon energy and the electron energy on
the other. Thus, it is not very difficult to predict the dose deposition in a homogeneous
phantom, when the quality parameters of the photon beam are known. In small fields,
due to the lack of charged particle equilibrium in lateral direction, the relationships
between the photon and electron parameters are not well established. Moreover, these
relationships depend not only on the photon beam quality but also on the field size.
In this work the photon and the electron fluence, as well as the photon and the
electron average energy were studied using Monte Carlo simulations. The calculations
were performed at depth of 2.5 cm in a water phantom with the FLURZnrc code from the
EGSnrc package, as described in Chapter 3.
Chapter 5: Experimental Results
101
The average photon and electron energies with respect to the off-axis distance for
the three fields are shown in Fig. 5.7. The average photon energies are calculated with
very high statistical uncertainties, because of the low number of photons in the phase-
space files. The average electron energies on the other hand, are calculated with
uncertainties as low as 0.1%. However, due to the photon energy uncertainties there are
additional inherent uncertainties in the electron energies, which are difficult to assess. In
general, the behavior of the average photon energy at a depth of 2.5 cm in water
resembles the graphs shown in Fig. 5.7, representing the average photon energy in air,
just below the collimators. For all fields the average photon energy has a value of about 3
MeV inside the field and it starts dropping at the geometrical edge of the field to level off
at about 2 MeV. After that due to the transmission photons, that have high energies, the
average energies of the 1.5 mm field (Fig 5.7(a)) and the 5 mm field (Fig5.7(c)) start to
increase. For the 3 mm field (Fig. 5.7(b)) the average photon energy keeps decreasing
because of the very low transmission through the tungsten collimator.
The average electron energies, presented in the same graphs, follow a similar
pattern, but their variations are smaller. They have values between 1.7 MeV and 1.8 MeV
inside the fields, and drop slightly at the field edges. The average electron energies of the
1.5 mm field (Fig 5.7(a)) and the 5 mm field (Fig5.7(c)) start to increase again, whereas
the energy of the 3 mm field (Fig. 5.7(b)) keeps decreasing beyond the field edge. An
important observation that is relevant to dose deposition in the medium is that, for all
fields, the average electron energy is always within a region where the electron stopping
power in water is almost constant.
Chapter 5: Experimental Results
102
Figure 5.7: Average electron and photon energies vs. off-axis distance for the (a) 1.5 mm, (b)3 mm, and (c) 5 mm fields. The calculations are performed at a depth of 2.5 cm ina water phantom.
(a)
(b)
(c)
0
1
2
3
4
0 2 4 6 8Off-axis distance (mm)
Ave
rage
ene
rgy
(MeV
)
Photons
Electrons
0
1
2
3
4
0 2 4 6 8Off-axis distance (mm)
Ave
rage
ene
rgy
(MeV
)
Photons
Electrons
0
1
2
3
4
0 2 4 6 8Off-axis distance (mm)
Ave
rage
ene
rgy
(MeV
)
Photons
Electrons
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
103
Figure 5.8 shows the photon and electron fluence against the off-axis distance for
the three fields. The fluence is normalized to the central axis value. Since the photon
fluence is determined with high uncertainties, due to reasons discussed above, the
normalization value is determined using an interpolation between the points close to the
central axis. The photon fluence in the three fields drops sharply at the geometrical edge
of the field and stays very low beyond the edge. This is in good agreement with the
average photon energy increase, shown in Fig. 5.7(a) and Fig. 5.7(c); since the photon
fluence is very low, the transmission photons represent a significant fraction of the total
fluence, and given that they have a relatively high energy, the average energy increases.
However, the electron fluence, shown in the same figure, does not follow the photon
fluence: the electron fluence profiles are significantly wider, because the electron range
in water is larger than the actual field sizes.
In the same figure, a Monte Carlo-calculated dose profile at a depth of 2.5 cm is
shown for each field. The dose profiles follow the electron fluence profiles almost
perfectly. This observation corresponds to the conclusion that electron energy stays
within a range where the stopping power is constant: the radiation dose delivered to the
medium is then simply equal to the electron fluence multiplied by the electron stopping
power (see Chapter 1). Therefore, the normalized electron fluence profiles are identical to
the normalized dose profiles for the three very small fields that we studied.
Chapter 5: Experimental Results
104
Figure 5.8: Normalized photon fluence, electron fluence and dose profiles vs. off-axis distancefor the (a) 1.5 mm, (b) 3 mm, and (c) 5 mm fields. The calculations are performedat a depth of 2.5 cm in a water phantom.
(a)
(b)
(c)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8Off-axis distance (mm)
Nor
mal
ized
flue
nce
Electrons
Photons
Dose profile
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8Off-axis distance (mm)
Nor
mal
ized
flue
nce
Electrons
Photons
Dose profile
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8Off-axis distance (mm)
Nor
mal
ized
flue
nce
Electrons
Photons
Dose profile
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
105
5.3. Off-axis ratios (dose profiles)
The dose profiles for the three small photon fields were measured with the A14P
ionization chamber and the HS GafchromicTM film at a depth of 2.5 cm in a water
phantom using the equipment and the setups described in Chapter 2. Profiles under the
same conditions were also calculated using EGSnrc Monte Carlo code (see Chapter 3).
The profiles measured with the A14P chamber were corrected by Monte Carlo-
calculated ( )/wat airD D correction factors in order to correct for the response variation
problem, because the chamber is not a water-equivalent dosimeter. The corrected profiles
underwent a 2-D deconvolution in order to eliminate the blur due to the low resolution
(large dimensions) of the chamber. These two procedures have been extensively
discussed in Chapter 4.
The Monte Carlo results for ( )/wat airD D correction factors as a function of the
off-axis distance in the three fields are shown in Figure 5.9. The statistical uncertainties
are as low as 2% on the central axis, because of the high particle density of the three
phase-space files close to the center of the field, and they increase with the off-axis
distance, due to the decrease in the number of analyzed particles. The ( )/wat airD D
correction factors for the 1 mm field (Fig. 5.9(a)) were obtained by simulating
100,000,000 histories for each chamber position. The value on the central axis is
1.58(1 ±0.015) and it drops with off-axis distance having a value close to unity outside of
the photon field. The central axis values decrease with field size: they are 1.52(1±0.012)
for the 3 mm field (Fig. 5.9(b)) and 1.3(1±0.02) for the 5 mm field (Fig. 5.9(c)). The
simulations for the last two fields were performed with 20,000,000 histories.
Chapter 5: Experimental Results
106
Figure 5.9: ( )/wat airD D correction factors vs. off-axis distance for the (a) 1.5 mm, (b) 3 mm,and (c) 5 mm fields. The calculations are performed at a depth of 2.5 cm in awater phantom.
(a)
(b)
(c)
0.0
0.4
0.8
1.2
1.6
0 1 2 3 4 5 6 7 8Off-axis distance (mm)
Dw
a
0
0.4
0.8
1.2
1.6
0 1 2 3 4 5 6 7 8Off-axis distance (mm)
Dw
a
0.0
0.4
0.8
1.2
1.6
0 1 2 3 4 5 6 7 8Off-axis distance (mm)
Dw
a
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
107
The central axis values of the ( )/wat airD D correction factors are much higher than
the stopping power ratio value that equals 1.12 in a 10 MV photon beam for a large field
size. When the air gap inside the chamber has dimensions close to the actual size of the
field, the fraction of the dose delivered by in-scattered electrons decreases. At the same
time the electrons passing through the cavity go over straight-line trajectories, and this
also decreases the dose delivered to the cavity. These two effects result in an electron
fluence perturbation in the cavity that has to be taken into account along with the
stopping power ratio value, and therefore, the total correction factor is larger than the
stopping power ratio value. Finally, the radiation dose delivered to the air cavity is
significantly smaller than the dose delivered to water on the central axis of the radiation
beam.
The correction factors for all fields are close to unity away from the central axis.
In this region the dose delivered to the air cavity is close to the dose delivered to water,
due to the higher electron fluence in the cavity that compensates for the lower stopping
power in air. For example, a stopping electron that would travel several micrometers in
water has enough energy to cross a 2 mm air cavity, resulting in increase of the electron
fluence in the cavity. This effect has a large impact on the ( )/wat airD D values, because
outside the photon field, the stopping electrons, coming from the field are a much higher
fraction of the total electron fluence than the electrons set in motion locally by either the
transmission or scattered photons. The conclusion based on graphs in Fig. 5.9 is that the
A14P chamber under-responds close to the center of the field and over-responds outside
the fields for photon fields smaller than 5 mm in diameter.
Chapter 5: Experimental Results
108
Figure 5.10 shows dose profiles of the three fields measured with the A14P
ionization chamber. The raw data represents measurements at two-polarities, corrected
for leakage current. The uncertainties due to the linac output variations and signal
variations are very low: less than 1%. The uncertainties due to ( )/wat airD D corrections
are less than 2% of the central axis value of the OAR curve. The uncertainties due to the
deconvolution procedure are about 1%. An assessment of the uncertainties is presented in
Table 5.2 below.
Figure 5.10 shows that the importance of both the deconvolution and the
( )/wat airD D correction increases with a decreasing field size: the difference between the
three profiles is significant for the 1.5 mm field, whereas for the 5 mm field the profiles
are very close to each other. Figure 5.9 has already illustrated that the smaller is the field
size, the large is the variation in the ( )/wat airD D correction. As far as the convolution is
concerned, it is clear that the smaller is the field size, the larger is the blur effect due to
the detector size. Based on the data presented in Fig. 5.10, we can make the conclusion
that both the ( )/wat airD D correction and the deconvolution are extremely important when
the A14P chamber or any other air-filled ionization chamber is used for off-axis
measurements in very small photon fields.
The profiles (corrected and deconvolved) measured with the A14P chamber are
compared with HS radiochromic film measurements and Monte Carlo simulations in Fig.
5.11. The Monte Carlo simulations were performed with the DOSRZnrc user code, as
described in Chapter 4. About 450,000,000 histories were sent through a water phantom
for each field in order to attain statistical uncertainties less than 1%. Table 5.2 shows the
uncertainties for the various profiles.
Chapter 5: Experimental Results
109
Figure 5.10: Dose profiles (OAR) measured with the A14P chamber at a depth of2.5 cm in awater phantom for the (a) 1.5 mm, (b) 3 mm, and (c) 5 mm fields. The measured,corrected and deconvolved profiles for each field are presented.
(a)
(b)
(c)
0
0.2
0.4
0.6
0.8
1
1.2
-10 -8 -6 -4 -2 0 2 4 6 8 10Off-axis distance (mm)
OA
R
Raw data
Corrected
Deconvoved
0
0.2
0.4
0.6
0.8
1
1.2
-10 -8 -6 -4 -2 0 2 4 6 8 10Off-axis distance (mm)
OA
R
Raw data
Corrected
Deconvolved
0
0.2
0.4
0.6
0.8
1
1.2
-10 -8 -6 -4 -2 0 2 4 6 8 10Off-axis distance (mm)
OA
R
Raw data
Corrected
Deconvolved
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
110
Figure 5.11: Dose profiles (OAR) for the (a) 1.5 mm, (b) 3 mm, and (c) 5 mm fields at a depthof 2.5 cm.
(a)
(b)
(c)
0
0.2
0.4
0.6
0.8
1
1.2
-10 -8 -6 -4 -2 0 2 4 6 8 10Off-axis distance (mm)
OA
R
HS film
A14P chamber
Monte Carlo
0
0.2
0.4
0.6
0.8
1
1.2
-10 -8 -6 -4 -2 0 2 4 6 8 10Off-axis distance (mm)
OA
R
HS film
A14P chamber
Monte Carlo
0.0
0.2
0.4
0.6
0.8
1.0
1.2
-10 -8 -6 -4 -2 0 2 4 6 8 10Off-axis distance (mm)
OA
R
HS film
A14P chamber
Monte Carlo
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
111
Profile 1.5 mm 3 mm 5 mm
A14P chamber
Measurements:
Correction*:
Deconvolution:
Total*:
HS film
Measurements*:
Non-linearity:
Spatial response variation:
Total*:
Monte Carlo Calculations:
0.5% - 1.0%
0.5% - 1.5%
1.7 %
1.0% - 4%
1.0%
1%
2%
0.8% - 4.0%
0.7%
0.5% - 1.0%
0.2% - 1.2%
0.4%
1.0 % - 2.5%
1.0%
1%
2%
0.6% -4.0%
0.4%
0.5% - 1.0%
0.6% - 2.1%
1.1%
2.5% – 4.2%
1.0%
1%
2%
0.7% -4.0%
0.2%
The total uncertainties are reported as a percentage of the profile value on the
central axis, which is unity as a result of normalization. They are less than 1% far away
from the central axis and 2.5% to 4% close to the central axis. Figure 5.11 shows an
agreement between the measurements and the Monte Carlo simulations within ±3% of
the value on the central axis, which is within the reported uncertainties. Partially these
discrepancies are due to imperfections in the setup, such as the collimator geometry and
positioning that is very difficult to account for.
In the steepest part of the profiles a mispositioning may introduce errors as high
as 5%. However, these uncertainties are usually systematic (type B) resulting in a profile
shift that is very easy to eliminate. In general, the determined profiles are adequate for
stereotactic radiosurgery dose calculations. Moreover, the agreement between
* Percentage of the OAR value on the central axis
Table 5.2: Assessment of the uncertainties associated with the variousmeasurements and calculations of the dose profiles.
Chapter 5: Experimental Results
112
measurements and Monte Carlo calculations validates the three phase spaces, obtained by
simulating treatment head of the linac along with the radiosurgical collimators.
5.4. Central axis measurements
Percentage depth doses (PDDs) and relative dose factors (RDFs) were determined
for the three different fields. The experimental techniques have been discussed in
Chapter 2. The Monte Carlo calculations for the same quantities were performed with
DOSRZnrc user code, as explained in Chapter 3.
The measured and calculated percentage depth doses are presented in Fig. 5.12.
We had some problems with measuring the PDD curves with the A14P ionization
chamber, because the positioning was not precise enough and it was difficult to keep the
chamber on the central axis as it was moving down in the water tank. As the profiles
show, even a lateral displacement as small as 0.2 mm might lower the PDD value at
certain depth by several percent, and obviously the smaller the field, the more serious the
problem becomes. For these reasons the agreement between the measurements and the
Monte Carlo calculations is best for the 5 mm field and worst for the 1.5 mm field. For
all fields the uncertainties of the film measurements are about 5%, taking into account the
spatial response variation, densitometer error, and uncertainty in the film dose-response
curve.
The uncertainties in the ionization chamber measurements are manly due to the
positioning problem, as mentioned above: considering the profiles, we can estimate
uncertainties of about 1% for the 5 mm field, 3% for the 3 mm field, and 5% for the 1.5
Chapter 5: Experimental Results
113
mm field. Initially, the complete PDD curves were measured with two polarities,
verifying that within the stated uncertainties there was no difference between the two
polarities beyond the depth of the maximum dose maxd . As a result, we have presented
only the positive polarity data beyond maxd for the 1.5 mm and the 3 mm field in Fig 5.12
in order to minimize the mispositioning errors.
Monte Carlo simulations were performed using between 450,000,000 and
500,000,000 histories resulting in uncertainties in PDD values of less than 0.5%. The
various calculated and measured PDD curves agree within the stated uncertainties, and
this again validates the three phase spaces used as particle sources for the Monte Carlo
simulations.
The most interesting effect, considering PDD measurements for small and very
small photon fields, is the well-known maxd shift toward the surface. We determined the
following maxd values: 1.0 cm for the 1.5 mm field, 1.2 cm for the 3 mm field, and 1.4 cm
for the 5 mm field. These values are much lower than the maxd values for large clinical
photon fields that are on the order of to 2.5 cm for 10 MV x-ray beams, but match the
radiosurgical data by Sixel and Podgorsak, who measured maxd values in the range of
field diameters from 10 mm to 30 mm (Ref. 1).
The surface doses for the three fields were measured with the HS radiochromic
film. The following values were determined: 15% for the 1.5 mm field, 11% for the 3
mm field, and 9% for the 5 mm field. However, it is difficult to make any conclusion,
based on these values, because the surface dose depends on the collimator design, and in
our study we have used collimators made of two different materials (the 1.5 mm and the
5 mm collimators are made of lead, and the 3 mm collimator is made of tungsten).
Chapter 5: Experimental Results
114
Figure 5.12: Percentage depth dose curves for the (a) 1.5 mm, (b) 3 mm, and (c) 5 mm fields.
(a)
(b)
(c)
0
20
40
60
80
100
120
0 2 4 6 8 10 12Depth (cm)
PD
D
A14P chamber
Monte Carlo
HS film
0
20
40
60
80
100
120
0 2 4 6 8 10 12Depth (cm)
PD
D
A14P chamber
Monte Carlo
HS film
0
20
40
60
80
100
120
0 2 4 6 8 10 12Depth (cm)
PD
D
A14P chamber
Monte Carlo
HS film
5 mm
3 mm
1.5 mm
Chapter 5: Experimental Results
115
The presented PDD curves prove that the A14P chamber may be useful for
central axis dose measurements in very small circular photon fields, provided that a very
precise setup is employed. In order to verify this statement, we conducted a Monte Carlo
based study to evaluate the importance of the detector size in relative central axis
measurements in very small fields. Using the phase-space of the 1.5 mm collimator, we
calculated several PDD curves in a water phantom with different diameter of the scoring
region. The results are shown in Fig 5.13. Three curves, calculated with scoring regions
of diameters of 0.3 mm, 0.6 mm, and 1.5 mm, agree perfectly within the statistical
uncertainty of the simulations. This result proves that PDDs of small circular photon
fields may be measured successfully with a circularly symmetrical detector with a
diameter close to that of the field because the small fields have a negligible divergence.
Of course, another issue, that of the water equivalence of the detector must also be
considered. Since the radiation quality changes with depth in phantom, it is very likely
0
20
40
60
80
100
120
0 2 4 6 8 10 12Depth (cm)
PD
D
1.5 mm
0.6 mm
0.3 mm
Figure 5.13: Monte Carlo-calculated percentage depth dose curves for the1.5 mm field with various diameters of the scoring region.
Chapter 5: Experimental Results
116
that the response of a non-water equivalent detector will also change, and this will have
an impact on the PDD measurements. However, effects like this are minor and a very
precise setup is required to study them.
The results for the relative dose factor (RDF) (see Chapter 1) measurements and
calculations for the three collimators are presented in Fig 2.14. The ionization chamber
measurements are corrected for ( )/wat airD D , using the correction factors on the central
axis for the three small fields presented above and a ( )/wat airD D correction of 1.12 for
the 10×10 cm2 field. The value of 1.12 is equal to the ratio of the electron stopping
powers of water and air for a 10 MV photon beam, and its considered to be very close
(within 2%) to the total ( )/wat airD D correction factor for chambers as small as the
Exradin A14P chamber. The RDF increases with field size as expected and the RDF
values are presented in Table 5.3.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 1 2 3 4 5 6Diameter of the field (mm)
RD
F
Monte CarloA14P chamberHS Film
Figure 5.14: Relative dose factor (RDF) vs. the diameter of the field.
Chapter 5: Experimental Results
117
The Monte Carlo calculated RDFs are very close to the film measurements.
However, the A14P chamber measurements are consistently lower than the other two
values, and the discrepancy increases with the decrease in field size. This effect is due to
the relatively large diameter of the A14P chamber collecting volume (about 2 mm: see
Chapter 4). Our measured and calculated RDFs are consistent with some results that
have been already published2-5.
5.5. Dynamic stereotactic radiosurgery with the 1.5 mm and 3 mm photon beams
Radiosurgery represents the main practical application for the very small photon
beams that were studied here. Since we measured the basic dosimetric parameters of
three very small photon beams, we were able to explore two issues of great practical
importance for the potential use of these beams in radiosurgery: (i) the dose distribution
of a radiosurgical technique carried out with the very small beams, and (ii) the capability
of a linear accelerator to carry out the radiosurgery with the very small beams.
The dose distributions for dynamic stereotactic radiosurgery with the 1.5 mm
and the 3 mm collimators were calculated using the XVMC Monte Carlo code, as
Collimator Monte Carlo A14 chamber HS film
1.5 mm 0.26±0.005 0.15±0.01 0.28±0.02
3 mm 0.42±0.005 0.38±0.02 0.42±0.02
5 mm 0.56±0.01 0.53±0.02 0.57±0.03
Table 5.3: RDF of the three different collimators.
Chapter 5: Experimental Results
118
described in Chapter 3. The calculations were performed in a spherical water phantom,
using the validated phase spaces of the two beams. The dose distributions were also
measured in an X-Y plane containing the isocenter of the linac with a very slow
radiographic film (Kodak EDR-2) (see Chapter 2).
Dose distributions for the two collimators obtained by both Monte Carlo
simulations and measurements are shown in Fig 5.15. The 10%, 50% and 90% isodose
surfaces, normalized to 100% at the isocenter, are presented. The 50% isodose surface is
the most important one in case of small targets, as it would most likely serve as the
prescription isodose surface. The Monte Carlo-calculated 50% isodose surface of the 1.5
mm collimator has a diameter of 2.3 mm, as shown in Fig. 5.15(a). Compared to this
result the maximum deviation of the measured 50% isodose surface is -0.3 mm (Fig
5.15(b)). This discrepancy is due to imperfections in both the collimator and the setup, as
well as the uncertainty in the linac isocenter. The discrepancy between the calculated and
measured 10% isodose lines is larger mainly due to film positioning but does not exceed
1 mm.
The Monte Carlo-calculated 50% isodose surface of the 3 mm collimator has a
diameter of 3.8 mm (Fig. 5.15(c)), and the maximum discrepancy between the calculated
and the measured 50% isodose surface is again -0.3 mm. The 10% line for of the 3 mm
collimator is closer to the isocenter compared to the 10% line of the 1.5 mm collimator,
likely as a result of the 3 mm collimator being made of tungsten, that has a very low
transmission.
Chapter 5: Experimental Results
119
The last question to be answered was whether or not the measured dose
distributions were shifted with the respect to the isocenter, as defined by the lasers in the
1 cm
1.5 mm field: Kodak EDR-2 film1.5 mm field: Modified XVMC Monte Carlo code
5090
1050
9010
3 mm field: Kodak EDR-2 film
5090
10
3 mm field: Modified XVMC Monte Carlo code
5090
10
Figure 5.15: Isodose distributions obtained with (a) and (b) the 1.5 mmcollimator, and (c) and (d) the 3 mm collimator.
(a)
(d)(c)
(b)
Chapter 5: Experimental Results
120
treatment room. This issue actually determines the feasibility of radiosurgery with very
small beams, because in practice one must be interested not only in the dose distributions
but also in the target positioning. A dynamic radiosurgery procedure was carried out with
the 1.5 mm collimator in order to determine the position of the laser-defined isocenter
with respect to the delivered dose distribution. A small piece of HS radiochromic film
with four marks, coinciding with the treatment room lasers, was irradiated. The film was
positioned in the same way as the films used for dose distribution measurements. The
result is shown in Fig 5.16. Four pinpricks were used to designate the lasers on the film.
The 50% isodose surfaces for both 1.5 mm and 3 mm collimators, as established earlier,
are also presented in this figure. The distance between the center of the dose distribution
(point of maximum dose) and the isocenter defined by the lasers are: 0.3 to 0.4 mm in X
1 cm
Figure 5.16: Position of the dose distribution obtained with the 1.5 mmcollimator with respect to the lasers.
Chapter 5: Experimental Results
121
direction and 0.6 to 0.7 mm in Y direction. These results are in good agreement with the
results of a quality assurance study, carried out previously with the same linear
accelerator at the McGill University Health Centre6.
Both the isodose distributions and the isocenter check shown above prove that the
dynamic linac-based radiosurgery technique carried out with very small photon beams
may be used clinically with confidence that the dose will be delivered with an accuracy
of better than 1 mm, assuming of course the linac is in an excellent mechanical condition.
Chapter 5: Experimental Results
122
References:
1 K. E. Sixel and E. B. Podgorsak, “Buildup region of high-energy x-ray beams in
radiosurgery,” Med. Phys. 20, 761-764 (1993).
2 B. E. Bjarngard, J. S. Tsai, and R. K. Rice, “Doses on the central axes of narrow 6-MV
x-ray beams,” Med. Phys. 17, 794-799 (1990).
3 P. Francescon, S. Cora, C. Cavedon et al., “Use of a new type of radiochromic film, a
new parallel-plate micro-chamber, MOSFETs, and TLD 800 microcubes in the
dosimetry of small beams,” Med. Phys. 25, 503-511 (1998).
4 F. Verhaegen, I. J. Das, and H. Palmans, “Monte Carlo dosimetry study of a 6 MV
stereotactic radiosurgery unit,” Phys. Med. Biol. 43, 2755-2768 (1998).
5 X. R. Zhu, J. J. Allen, J. Shi et al., “Total scatter factors and tissue maximum ratios for
small radiosurgery fields: comparison of diode detectors, a parallel-plate ion chamber,
and radiographic film,” Med. Phys. 27, 472-477 (2000).
6 T. Falco, M. Lachaine, B. Poffenbarger et al., “Setup verification in linac-based
radiosurgery,” Med. Phys. 26, 1972-1978 (1999).
Chapter 6:
Conclusions and Future Work
6.1. Summary and conclusions
Detailed studies on dosimetry of very small photon fields produced by a linear
accelerator as well as physical aspects of dynamic radiosurgery with these fields have
been presented in this thesis. The studies concerning dosimetry of static beams may be
divided into two main groups: (i) beam quality and basic physics of dose deposition and
(ii) dosimetric parameters of very small fields. The properties of three very small
radiation beams (1.5 mm, 3 mm, and 5 mm in diameter) were studied experimentally and
with Monte Carlo simulations. The beams were produced with special collimators
attached to a 10 MV linac. The results showed that the radiation spectra are similar to the
spectra of large fields. The only noticeable difference was a strong spectral line at the
energy of 0.511 MeV resulting from pair production interactions in the collimators. The
average photon energy slightly decreases at the beam edges and it drops significantly at
the field edge defined by the collimator jaw setting.
The basic physics of dose deposition was studied by Monte Carlo calculations in a
water phantom. We saw that the photon fluence drops at the geometrical edge of a very
small photon field, whereas the electron fluence profile is much wider, because the sizes
of our very small fields were smaller than the electron range in water for 10 MV photon
beams. Moreover, the dose profiles almost perfectly matched the electron fluence
Chapter 6: Conclusions and Future Work
124
profiles, because the average electron energies do not change significantly off-axis and
the electron stopping power is almost constant in this energy range. The dose profiles,
percentage depth dose (PDD) curves, and relative dose factors (RDFs) were measured
with two dosimeters: a micro parallel-plate ionization chamber (Exradin A14P: Standard
Imaging, Middleton, WI, USA) and radiochromic film (HS GafchromicTM: International
Specialty Products, Wayne, NJ, USA).
The profiles measured with the ionization chamber were first corrected with
Monte Carlo-calculated (Dwat/Dair) correction factors, and then deconvolved to eliminate
the blur due to the poor resolution of the chamber. Based on the results, we conclude that
the A14P (and any other) ionization chamber is not a reliable detector for off-axis
measurements in very small fields, unless the response variation (Dwat/Dair correction
factors) is taken into account. This issue is relevant not only to measurements in very
small fields, but also in any field that is under non-equilibrium conditions (for instance
dynamic IMRT fields). Moreover, convolution of the real dose profile with the point
spread function (PSF) of the detector results in blur effects that cannot be neglected in
case of very small photon beams.
On the other hand, the A14P chamber is a good dosimeter for relative central axis
measurements beyond maxd in fields as small as 5 mm in diameter. The chamber is not
suitable for RDF measurements in fields smaller than 5 mm in diameter, even if
(Dwat/Dair) correction factors are considered, because of its poor resolution.
The HS GafchromicTM is a reliable dosimeter for any kind of measurements in
very small photon fields. It is not very precise, but may be used under non-equilibrium
Chapter 6: Conclusions and Future Work
125
conditions. In terms of radiological properties, moreover, its sensitivity to radiation is
about twice as high as that of other radiochromic films.
Since the basic dosimetric quantities were measured with adequate precision for
the three very small fields we decided to explore the usefulness of those fields for
dynamic stereotactic radiosurgery. We investigated two main aspects of the very small
fields for radiosurgery: (i) the 3-D dose distributions for dynamic radiosurgery and (ii)
the displacement of the dose distributions with respect to the laser-defined isocenter of
the linear accelerator.
The Monte-Carlo calculated 3-D dose distributions were in a good agreement
with measurements, proving that a 50% isodose surface as small as 3 mm may be attained
using a linac-based radiosurgery technique. Moreover, the displacements between the
center of the dose distributions and the isocenter of the linac, as defined by the room
lasers, were on the order of 0.6 mm or less. These results were very encouraging, because
they show that the dynamic radiosurgery might be useful for irradiating intracranial
targets on the order of 2 mm providing an option for radiosurgical treatments of
functional disorders that generally require very small radiation fields. Until now these
fields could only be provided by a Gamma knife, a specially designed radiosurgical unit
that is based on 201 stationary cobalt-60 sources. However, the Gamma knives are very
expensive and dedicated only to radiosurgery.
Chapter 6: Conclusions and Future Work
126
6.2. Future Work
The results presented in this thesis and the tools (software, Monte Carlo models,
experimental setups, etc.) developed during the research may be a good starting point for
a series of other studies.
Testing the usefulness of various detectors for measurements in very small fields,
or more generally, under non-equilibrium conditions, will be a study of a great practical
importance. For example, various types of radiographic silver-halide films are widely
used for dose delivery verification in dynamic IMRT fields. These fields are known as a
typical example of non-equilibrium radiation fields and therefore it is important to study
the response variation of silver-halide films in such fields. The best approach for these
studies is by Monte Carlo simulations.
Developing a more sophisticated profile deconvolution algorithm would be
another interesting project. The algorithm presented in this thesis applies only in the case
of very small photon fields with circular symmetry. However, very small irregular photon
beams, shaped by micro multi-leaf collimators are often used in modern radiosurgery.
Thus it is important to have a tool for deconvolving 2-D profiles, when the detector does
not have an adequate resolution. Such an algorithm will allow us to carry out quality
assurance procedures not only with film, but also with other, more precise dosimeters that
do not have the required resolution, such as diodes and liquid-filed ionization chambers.
As far as linac-based dynamic radiosurgery is concerned, the research can also be
extended. We have already calculated 3-D dose distributions using Monte Carlo
simulations and have validated these results by measurements. The next step would be to
Chapter 6: Conclusions and Future Work
127
develop an in-house Monte Carlo treatment planing system (TPS) for dynamic
radiosurgery. Software of this kind will calculate the 3-D dose distributions, using the 3-
D CT data as a phantom, and therefore the exact geometry of the phantom as well as its
non-homogeneity will be automatically taken into account with no further
simplifications. The biggest problem that Monte Carlo-based treatment planing systems
face in conventional radiotherapy is modeling the treatment units with their great variety
of settings used for defining the various radiation fields. In our radiosurgery TPS this
would not be a problem, since we have a predetermined set of clinically used collimators.
Therefore, we would have to do only one simulation of the treatment unit along with each
of the collimators and store the appropriate phase spaces. These phase spaces could be
used as radiation sources in the actual treatment planning.
The three future projects outlined above are feasible, however they would require
some research resources. The significant amount of work that has been done recently at
McGill University Health Centre in the areas of Monte Carlo treatment planning,
response calculation for different detectors, and verification of IMRT fields, would serve
as excellent base for new studies.
List of Figures
Figure 1.1: Typical view of a linear accelerator used in cancer therapy.
Figure 1.2: DSA image of a small AVM.
Figure 1.3: Typical steps in radiotherapy treatment process.
Figure 1.4: Dose distribution for a typical four-field box technique.
Figure 1.5: Geometry for the measurement of the relative dose factor RDF(A). The
dose at point P at dmax in phantom is measured with field A in part (a) and
with field 10×10 cm2 in part (b).
Figure 1.6: Geometry for percentage depth dose measurement and definition. Point Q
is an arbitrary point on the beam central axis at depth d, point P is the
point at dmax on the beam central axis. The field size A is defined on the
surface of the phantom.
Figure 1.7: PDD curve for a 10 MV photon beam, SSD = 100 cm, 10×10 cm2.
List of Figures
129
Figure 1.8: Geometry for the measurement of the tissue-maximum ratio,
TMR(d,AQ,hν).
Figure 1.9: Basic treatment planning algorithm.
Figure 1.10: Narrow beam profiles: curve (1) represents a measured profile, curve (2) a
deconvolved profile.
Figure 1.11: Charged particle equilibrium: number of electrons stopped in a small
volume is equal to the number of electrons set in motion by photons in the
same volume.
Figure 1.12: Electrons moving in lateral direction in large and very small photon fields.
Figure 2.1: Clinac-18 linear accelerator.
Figure 2.2: Treatment head design in (a) photon and (b) electron mode.
Figure 2.3: External view of a 5 mm collimator.
Figure 2.4: Radiosurgery holder with a small field collimator on, attached to the
Clinac-18 treatment head
List of Figures
130
Figure 2.5: Design of the collimators: (a) 5 mm field, (b)1.5 mm field, and (c)3 mm
field. Collimators in (a) and (b) are made of lead, in (c) of tungsten.
Figure 2.6: Exradin A14P ionization chamber.
Figure 2.7: Sketch of A14P ionization chamber.
Figure 2.8: Keithley electrometer.
Figure 2.9: Structure of HS radiochromic film.
Figure 2.10: Dose response curve for HS radiochromic film.
Figure 2.11: Densitiometer Model 37-443 and the film transport system.
Figure 2.12: A14P ionization chamber orientation in the water phantom.
Figure 2.13: A14P chamber positioning (a) for central axis and (b) off-axis
measurements.
Figure 2.14: Simultaneous gantry and table rotations during a dynamic radiosurgery
treatment.
List of Figures
131
Figure 2.15: Beam trace on the patient’s scull for the dynamic radiosurgery technique.
Figure 2.16: Hemispheres made of polystyrene, used as a dynamic radiosurgery
phantom.
Figure 3.1: The basic idea of Monte Carlo particle transport: a particle is transported
until either it leaves the volume of interest or its energy becomes less then
the cutoff energy.
Figure 3.2: Boundary crossing algorithm in PRESTA.
Figure 3.3: The concept of the BEAM/EGS4 Monte Carlo code.
Figure 3.4: Treatment head of the Clinac-18 linear accelerator: BEAM/EGS4 model.
Figure 3.5: Monte Carlo simulated and measured PDD curves for 10×10 cm2 field
size and SSD = 100 cm.
Figure 3.6: Monte Carlo calculated dose profile (OAR) for 10×10 cm2 field size, SSD
= 100 cm and depth of 10 cm.
Figure 3.7: A phantom used for PDD curve Monte Carlo calculations with
DOSRZnrc.
List of Figures
132
Figure 3.8: A phantom used for dose profile (OAR) Monte Carlo calculations with
DOSRZnrc.
Figure 4.1: Exradin A14P ionization chamber: (a) simplified geometry and (b) area
where the equation is solved.
Figure 4.2: Calculation regions.
Figure 4.3: Electric field in the air cavity.
Figure 4.4: Detector in the penumbra region of (a) a large square field, and (b) a small
circular field.
Figure 4.5: Point-Spread Function (PSF) of (a) A14P chamber and (b) a simplified
PSF.
Figure 4.6: Direct deconvolution by (a) filtering and (b) a minimization algorithm.
Figure 4.7: Geometrical model of taking measurements in a small circular field.
Figure 4.8: Restrictions applied to the profiles.
Figure 4.9: Test result for the minimization algorithm.
List of Figures
133
Figure 4.10: Geometry of the air cavity in the Monte Carlo simulations.
Figure 4.11: Monte Carlo simulated geometry for off-axis correction factors
calculation. The phase space is moved over the phantom, instead of
moving the air cavity.
Figure 5.1: Photon fluence for the (a) 1.5 mm, (b)3 mm, and (c) 5 mm fields. The
calculations are performed below the collimators at 70 cm from the
radiation source.
Figure 5.2: Normalized photon fluence density vs. energy for the (a) 1.5 mm, (b) 3
mm, and (c) 5 mm fields. The calculations are performed below the
collimators at 70 cm from the radiation source.
Figure 5.3: Normalized photon energy fluence density vs. energy for the (a) 1.5 mm,
(b) 3 mm, and (c) 5 mm fields. The calculations are performed below the
collimators at 70 cm from the radiation source.
Figure 5.4: Normalized photon fluence vs. off-axis distance for the (a) 1.5 mm, (b) 3
mm, and (c) 5 mm fields. The calculations are performed below the
collimators at 70 cm from the radiation source.
List of Figures
134
Figure 5.5: Normalized photon energy fluence vs. off-axis distance for the (a) 1.5 mm,
(b) 3 mm, and (c) 5 mm fields. The calculations are performed below the
collimators at 70 cm from the radiation source.
Figure 5.6: Average photon energy vs. off-axis distance for the (a) 1.5 mm, (b) 3 mm,
and (c) 5 mm fields. The calculations are performed below the collimators
at 70 cm from the radiation source.
Figure 5.7: Average electron and photon energies vs. off-axis distance for the (a) 1.5
mm, (b) 3 mm, and (c) 5 mm fields. The calculations are performed at a
depth of 2.5 cm in a water phantom.
Figure 5.8: Normalized photon fluence, electron fluence and dose profiles vs. off-axis
distance for the (a) 1.5 mm, (b) 3 mm, and (c) 5 mm fields. The
calculations are performed at a depth of 2.5 cm in a water phantom.
Figure 5.9: ( )/wat airD D correction factors vs. off-axis distance for the (a) 1.5 mm, (b)
3 mm, and (c) 5 mm fields. The calculations are performed at a depth of
2.5 cm in a water phantom.
Figure 5.10: Dose profiles (OAR) measured with the A14P chamber at a depth of2.5
cm in a water phantom for the (a) 1.5 mm, (b) 3 mm, and (c) 5 mm fields.
List of Figures
135
The measured, corrected and deconvolved profiles for each field are
presented.
Figure 5.11: Dose profiles (OAR) for the (a) 1.5 mm, (b) 3 mm, and (c) 5 mm fields at
a depth of 2.5 cm.
Figure 5.12: Percentage depth dose curves for the (a) 1.5 mm, (b) 3 mm, and (c) 5 mm
fields.
Figure 5.13: Monte Carlo-calculated percentage depth dose curves for the 1.5 mm field
with various diameters of the scoring region.
Figure 5.14: Relative dose factor (RDF) vs. the diameter of the field.
Figure 5.15: Isodose distributions obtained with (a) and (b) the 1.5 mm collimator, and
(c) and (d) the 3 mm collimator.
Figure 5.16: Position of the dose distribution obtained with the 1.5 mm collimator with
respect to the lasers.
List of Tables
Table 5.1: Phase space data for the three collimators used in our study.
Table 5.2: Assessment of the uncertainties associated with the various measurements
and calculations of the dose profiles.
Table 5.3: RDF of the three different collimators.
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