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TRANSCRIPT
VALIDATIO� OF CO�FORMAL RADIOTHERAPY TREATME�TS
I� 3D USI�G POLYMER GEL DOSIMETERS A�D OPTICAL
COMPUTED TOMOGRAPHY,
by
Oliver Edwin Holmes
A thesis submitted to the Department of Physics, Engineering Physics and Astronomy
In conformity with the requirements for
the degree of Master of Science
Queen’s University
Kingston, Ontario, Canada
(December, 2008)
Copyright ©Oliver Edwin Holmes, 2008
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Abstract
Polymer gel dosimeters are a three dimensional (3D) dosimetry system that may be
conveniently applied for verifying highly conformal radiation therapies where standard dosimetry
techniques are insufficient. Polymer gel dosimetry with optical computed tomography (OptCT)
can be used to measure spatial dose distributions with high resolution. While long experience
with MRI has yielded many studies reporting on experiments involving validation of clinical
deliveries using polymer gel dosimeters, there are very few studies of this type where OptCT is
used. OptCT is a relatively new technique and consequently has not yet been adopted into the
clinical environment. As a result, methods and software tools for integrating OptCT
measurements into clinical systems are not available. Previous studies from the Medical Physics
research group at the Cancer Centre of Southeastern Ontario (CCSEO) and Queen’s University
have therefore been limited to simple deliveries and two dimensional (2D) comparisons. In this
thesis various software tools and calibration techniques have been developed to allow
comparative analysis between OptCT measurements with dose distributions calculated by
treatment planning software. Further, a modification of the γ-evaluation (Low et al. 1998) is
presented whereby the vector components of γ are used to identify the sources of disagreement
between compared dose distributions. Test simulations of the new γ-tool revealed that individual
vector components of γ, as well as the resulting vector field can be used to identify certain types
of disagreements between dose distributions: especially spatial misalignments caused by
geometric misses. The polymer gel dosimetry tools and analysis software were applied to a
clinical validation mimicking a prostate conformal treatment with patient setup correction using
image guidance. In one experiment greater than 90 % agreement was found between dose
distributions in 4%T 50%C NIPAM/Bis dosimeters (Senden et al. 2006) measured with the Vista
OptCT unit and dose distributions calculated by Eclipse treatment planning software.
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Acknowledgements
Above all, I would like to express my gratitude towards my supervisor Dr. L. J. Schreiner as well
as Dr. A. Kerr for their guidance and humour throughout my research at Queen’s. My time at the
CCSEO was enlightening and enjoyable, I am grateful to have had the opportunity to work with
such inspiring and enthusiastic people.
I would also like to thank Chris Peters, Tim Olding, Sandeep Dhanesar, Dr. J. Darko, Chandra
Joshi, Dr. G. Salomons, Laura Drever and Dr. K. McAuley for their assistance with experimental
work and their direction over the course of my studies. Many thanks to the faculty and staff of
the Department of Physics who I have come to know so well since I came to Queen’s in 2001.
Finally, I am especially grateful to my family for their love and helping me to realize my
dreams. I am especially grateful to Kelly for her continuing support and companionship.
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Table of Contents
Abstract ............................................................................................................................................ ii
Acknowledgements ......................................................................................................................... iii
Table of Contents ............................................................................................................................ iv
List of Figures ................................................................................................................................. vi
List of Tables ................................................................................................................................... x
Chapter 1 Introduction ..................................................................................................................... 1
1.1 Motivation and Objectives ..................................................................................................... 1
Chapter 2 Literature Review ............................................................................................................ 4
2.1 Introduction ............................................................................................................................ 4
2.2 3D Dosimetry ......................................................................................................................... 4
2.2.1 Gel Dosimeters ................................................................................................................ 5
2.2.2 The NIPAM/Bis gel dosimeter ....................................................................................... 6
2.3 Optical Scanning .................................................................................................................... 8
2.3.1 Development of Scanning Techniques ........................................................................... 8
2.3.2 The Problem of Scatter in Cone Beam OptCT.............................................................. 12
2.4 Dose Comparison Techniques ............................................................................................. 13
2.4.1 Introduction ................................................................................................................... 13
2.4.2 Dose Difference ............................................................................................................ 14
2.4.3 Distance-to-Agreement ................................................................................................. 14
2.4.4 Composite Evaluation ................................................................................................... 16
2.4.5 The Gamma Comparison .............................................................................................. 17
2.4.6 Discretization Artefacts in γ Distributions .................................................................... 24
2.4.7 The Vector Nature of γ ................................................................................................. 27
2.5 Clinical Radiotherapy Validations in 3D ............................................................................. 29
2.6 Research Objectives ............................................................................................................. 30
Chapter 3 Theory ........................................................................................................................... 32
3.1 Radiation Dose ..................................................................................................................... 32
3.1.1 Photon Interactions ....................................................................................................... 33
3.1.2 Generation of Free Radicals .......................................................................................... 37
3.2 Chemical Dosimetry ............................................................................................................ 38
3.3 Polymer Gel Dosimetry ....................................................................................................... 44
3.3.1 Free Radical Polymerization ......................................................................................... 45
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Chapter 4 Materials and Methods .................................................................................................. 49
4.1 Materials and Equipment ..................................................................................................... 49
4.1.1 Preparation of Polymer Gel Dosimeters ....................................................................... 49
4.1.2 Dosimeter Irradiation .................................................................................................... 50
4.1.3 Optical Scanning ........................................................................................................... 54
4.1.4 X-ray Scanning ............................................................................................................. 56
4.2 The γ-Evaluation Algorithm ................................................................................................ 57
4.3 Dose Evaluation Experiments .............................................................................................. 63
4.3.1 Interpreting Dose Distribution Disagreements.............................................................. 63
4.3.2 Calibration..................................................................................................................... 66
4.3.3 Simple Delivery Validations in 3D ............................................................................... 69
4.3.4 Clinical Implementation of Delivery Validation ........................................................... 70
Chapter 5 Results and Discussion .................................................................................................. 76
5.1 The Response of the γ-Vector Field ..................................................................................... 76
5.1.1 Validation of the γ-Algorithm ....................................................................................... 76
5.1.2 γ-Vector Field Response under Dose Perturbation ....................................................... 80
5.1.3 γ-Vector Field Response to Gaussian Noise ................................................................. 83
5.1.4 γ-Vector Field Response under Misalignment .............................................................. 85
5.1.5 Towards Clinical Application ....................................................................................... 88
5.2 Gel Calibration ..................................................................................................................... 90
5.2.1 Intersecting Pencil Beam Method ................................................................................. 91
5.2.2 20 MeV Electron Beam Method ................................................................................... 91
5.2.3 Inter and Intra batch variability ..................................................................................... 93
5.3 Validating Radiation Deliveries in 3D ................................................................................. 96
5.3.1 Cobalt Tomotherapy ..................................................................................................... 96
5.3.2 Prostate Teletherapy / Interpreting Geometric Misses .................................................. 99
Chapter 6 Conclusions ................................................................................................................. 119
Bibliography ................................................................................................................................ 125
vi
List of Figures
Figure 2.1: A schematic diagram of a 1st generation optical computed tomography scanner used
for scanning polymer gel dosimeters. ...................................................................................... 9
Figure 2.2: Schematic diagrams of various OptCT scanners.. ....................................................... 11
Figure 2.3: Superimposed continuous 1D dose distributions showing dose difference and
distance-to-agreement evaluations. ........................................................................................ 15
Figure 2.4: Superimposed continuous 1D dose distributions showing and the corresponding γ
distribution ............................................................................................................................. 15
Figure 2.5: Geometric representations of the acceptance criteria used to evaluate distributions
with 1 and 2 spatial dimensions respectively. ........................................................................ 20
Figure 2.6: A colour wash image representing a γ-distribution from a 2D dose distribution
comparison ............................................................................................................................. 21
Figure 2.7: Cumulative volume histograms corresponding to a 3D comparison for a conformal
prostate delivery validation with polymer gel dosimetry. ...................................................... 22
Figure 2.8: A one dimensional example demonstrating the discretization artefact of γ ................ 27
Figure 2.9: A diagram showing the γ angle as it was described by Low et al. (1998) and Stock et
al. (2004). ............................................................................................................................... 28
Figure 3.1: A flow diagram showing a simplified version of the process leading to biological
damage from ionizing radiation (adapted from Johns and Cunningham 1983). .................... 34
Figure 3.2: Kinematics of a Compton event. ................................................................................. 36
Figure 3.3: A schematic of a proposed initiation reaction mechanism in free radical
polymerization. ...................................................................................................................... 46
Figure 3.4: Simplified polymer chain diagram. ............................................................................. 48
Figure 3.5: A proposed reaction mechanism for a propagation reaction of free radical
polymerization.. ..................................................................................................................... 48
Figure 3.6: A possible combination termination reaction stopping the growth of a polymer chain..
............................................................................................................................................... 48
Figure 4.1: Monte Carlo (MC) simulated spectra for 10x10 cm2 photon beams of Co-60 and
6 MV photons at the depth of 10 cm in water at the SAD’s. ................................................. 51
Figure 4.2: The Theratron 780C cobalt therapy unit and source. .................................................. 51
Figure 4.3: Benchtop tomotherapy apparatus for the Theratron 780C. ......................................... 53
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Figure 4.4: The Clinac 21iX and corresponding percent-depth-dose (PDD) curves for Co-60 and a
15MV treatment beam ........................................................................................................... 53
Figure 4.5: The Vista OptCT scanner with the protective cover removed .................................... 55
Figure 4.6: The PQ 5000 large bore at the CCSEO and the experimental setup. .......................... 57
Figure 4.7: Pictoral representation of the γ search algorithm. ....................................................... 61
Figure 4.8: Flow diagram showing the software process of our in-house gamma evaluations......62
Figure 4.9: The test distributions provided by the Department of Radiation Oncology,
Washington University School of Medicine .......................................................................... 64
Figure 4.10: Dose distribution that has been perturbed with a double Gaussian dose shift .......... 65
Figure 4.11: Dose distribution that has been perturbed with an inverted double Gaussian dose
shift. ....................................................................................................................................... 65
Figure 4.12: Test dose distribution characteristic of a head and neck cobalt tomotherapy
treatment. ............................................................................................................................... 66
Figure 4.13: Intersecting pencil beam calibration patterns. ........................................................... 67
Figure 4.14: Example calibration curve and OptCT measurement.. .............................................. 68
Figure 4.15: Photographs of the AQUA phantom used for simulating the human torso in
irradiations and CT scans. ...................................................................................................... 71
Figure 4.16: An X-ray CT scan of the AQUA phantom and gel dosimeter insert made using
Eclipse treatment planning software.. .................................................................................... 73
Figure 4.17: 7-field 15 MV conformal prostate treatment plan from Eclipse ............................... 74
Figure 4.18: A photograph of the experimental setup for the 7-field conformal prostate delivery
.............................................................................................................................................. .75
Figure 5.1: Gamma comparisons between test distributions used by Low and Dempsey (2003).
............................................................................................................................................... 77
Figure 5.2: The γ-vector evaluation for Low and Dempsey’s test distribution .............................. 78
Figure 5.3: Vector analysis of double Gaussian dose perturbation errors ..................................... 81
Figure 5.4: Negative divergence in γ-vector fields ........................................................................ 83
Figure 5.5: Plots showing the response of the mean γ-vector components to zero mean Gaussian
noise... .................................................................................................................................... 84
Figure 5.6: The mean component vector response to misalignments along each of 3 distribution
dimensions (dose is the third dimension).. ............................................................................. 87
Figure 5.7: Double Gaussian dose perturbation in Co-60 tomotherapy dose distributions ........... 89
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Figure 5.8: A one dimensional γ-comparison between a reference distribution and an evaluated
distribution showing a γ-vector artefact associated with discretization. ................................ 90
Figure 5.9: An attenuation to dose calibration for the Vista 4%T 50%C NIPAM/Bis dosimeter
system.. .................................................................................................................................. 92
Figure 5.10: 20 MeV electron beam percent-depth-dose (PDD) curves from OptCT and ion
chamber measurements. ......................................................................................................... 92
Figure 5.11: The combined calibration data for the entire series of experiments presented in this
research project.. .................................................................................................................... 94
Figure 5.12: A set of carefully controlled calibration experiments. .............................................. 95
Figure 5.13: A 3D treatment validation using polymer gel dosimetry with OptCT with complete
3D gamma analysis. ............................................................................................................... 97
Figure 5.14: The cumulative gamma volume histograms (GVH)’s for the cobalt tomotherapy
validation ............................................................................................................................... 98
Figure 5.15: A 4 Gy seven field 15 MV conformal prostate treatment plan created for the AQUA
phantom ............................................................................................................................... 101
Figure 5.16: A 3D OptCT measurement of a 4Gy dose distribution preserved in a NIPAM/Bis
polymer gel dosimeter.. ........................................................................................................ 102
Figure 5.17: Dose profiles comparing the polymer gel dose measurement with the planned dose
distribution calculated by Eclipse ........................................................................................ 103
Figure 5.18: 3D gamma comparison between the polymer gel dose measurement and the planned
dose distribution ................................................................................................................... 104
Figure 5.19: The component vector plot for a 2D γ-vector comparison between the sagittal planes
of the polymer gel measurement and Eclipse plan............................................................... 106
Figure 5.20: Dose profiles comparing the polymer gel dosimeter measurement of the dose
distribution with the modified eclipse plan. ......................................................................... 108
Figure 5.21: The retroactively modified Eclipse plan with an error accounted for ..................... 109
Figure 5.22: A 3D γ comparison between the modified Eclipse plan and the OptCT measurement
of the dose distribution ......................................................................................................... 110
Figure 5.23: Cumulative volume histograms comparing the OptCT measurement of the dose
distribution delivered to the polymer gel dosimeter and the modified planned distribution
from Eclipse. ........................................................................................................................ 111
Figure 5.24: The planned 3Gy treatment dose distribution calculated by Eclipse. ...................... 114
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Figure 5.25: A calibrated and registered OptCT measurement of a 3Gy dose distribution
preserved within a polymer gel dosimeter.. ......................................................................... 115
Figure 5.26: Dose profiles comparing the polymer gel dosimeter measurement of the dose
distribution with a 3Gy Eclipse plan. ................................................................................... 116
Figure 5.27: A 3D γ-comparison between the planned 3Gy dose distribution calculated by
Eclipse, and the OptCT measurement .................................................................................. 117
Figure 5.28: he component vector plots corresponding to the 2D γ-vector analysis between the
sagittal planes of the 3Gy planned dose distribution from Eclipse and the OptCT
measurement of the dose distribution.. ................................................................................ 118
x
List of Tables
Table 2.1: Definitions of symbols used to describe the γ-index (Low and Dempsey 2003) ......... 19
Table 3.1: Radiolysis of water (adapted from Swallow 1973; Spinks and Woods 1976). ............. 39
Table 3.2: Oxidation of the Fe2+ ion in the Fricke dosimeter ........................................................ 40
Table 3.3: Simplified free radical polymerization reactions of the NIPAM/Bis dosimeter ........... 47
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Chapter 1 Introduction
1.1 Motivation and Objectives
This year (2008) an estimated 166,400 new cases of cancer will be reported in Canada.
Roughly one half of people that will be treated for their disease will receive radiation therapy. An
estimated 73,800 will die from their disease (Canadian Cancer Society, 2008). Radiation therapy
involves the use of ionizing radiation (photon, proton, electron, neutron or ion beams) to destroy
diseased tissue by causing damage to its DNA. Ionizing radiation damages DNA either through
direct interactions with DNA molecules or, more commonly, indirectly through interactions with
other biological compounds (especially water) via highly reactive free radicals. The radiation
damage to DNA disrupts its structure and impairs its normal function. Sufficient irreparable
damage will kill or severely weaken the cell and its progeny. Although cancer cells are often
more susceptible to radiation damage because they typically divide much more rapidly than cells
comprising healthy tissue, an unfortunate reality is that ionizing radiation damages all tissue.
Therefore, the goal of radiation therapy is to deliver sufficient dose of ionizing radiation to the
tumour while minimizing dose to the surrounding healthy tissue thereby reducing complications.
With this goal in mind, dose delivery techniques are becoming increasingly sophisticated (in
parallel with advancements in computer technology) allowing radiation to be tightly conformed to
the target.
Careful calibration and quality assurance of the radiotherapy equipment before the
irradiation of patients is critical. These tasks constitute some of the major clinical responsibilities
of medical physicists. Recently, the Radiological Physics Center (RPC) (Molineu et al. 2005)
surveyed 104 institutions in their capacity to deliver head and neck Intensity-Modulated-
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Radiation-Therapy (IMRT) to a mailable anthropomorphic IMRT phantom distributed to the
institutions. Each institution irradiated the phantom according to their own IMRT treatment plans
and routine quality assurance (QA) checks. Surprisingly, 30 % of 136 irradiations failed to match
the treatment plans within tolerances in spite of wide margins of error (± 7 % dose, ± 4 mm)
beyond the standard 3% 4mm criteria recommended for photon beams (Van Dyk et al. 1993).
Furthermore, since there are no standardized three dimensional (3D) dosimetry techniques
available to medical physicists, the dose distributions were measured using point detectors and
planar films. It is unclear what failure rate would have been detected had a true 3D dosimeter
been available. The study illustrates the need to improve QA routines in parallel with
developments in conformal techniques. It has also been identified as a compelling argument for
the development of a clinically viable 3D dosimeter system (Oldham 2006).
Polymer gel dosimeters are a very promising group of 3D dosimetry systems that are
currently under investigation. A typical polymer gel dosimeter is a hydrogel with monomer and
crosslinker precursors in solution. Irradiation initiates free radical polymerization reactions that
cause polymer particles to precipitate out of solution in proportion to the radiation dose
(Maryanski et al. 1993; Fuxman et al. 2005; Senden et al. 2006). The gel network suspends the
polymer particles, preserving the dose distribution in the dosimeter. The presence of polymer
particles alters the physical properties of the gel, such as the optical attenuation coefficient,
permitting acquisition of a digital 3D image that provides a direct measure of delivered dose. For
over two years our group has been successfully obtaining 3D dose images of polymer gel
dosimeters through cone beam Optical Computed Tomography (OptCT). However, until now we
have not attempted to use OptCT dose distribution measurements for their ultimate purpose: 3D
dose validations.
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The primary objective of the research reported in this thesis was to develop techniques
for comparing 3D OptCT images of polymer gels to conformal dose plans, establishing necessary
protocols for 3D delivery validation using polymer gel dosimetry. Working towards true 3D
comparisons required careful construction of a number of software tools, including an efficient
3D gamma comparison tool. During the preparation of a new set of gamma tools, it was
recognized that the standard gamma value provides little information into the significance of dose
and spatial disagreements. For this reason, an investigation into the additional information that
the gamma vector field could provide was undertaken. Finally, the polymer gel dosimetry tools
and analysis software were applied to a specific clinical validation mimicking potential setup
correction using image guidance.
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Chapter 2 Literature Review
2.1 Introduction
This chapter serves as a brief historical background of the state of the art of three
dimensional (3D) dosimetry as it applies to radiation therapy. It includes a discussion of the
development and the obstacles associated with using optical computed tomography (OptCT) for
scanning 3D dosimeters. The techniques currently available to medical physicists for making
comparisons between dose distributions and efficiently evaluating large dose data sets are also
reviewed. The goal is to introduce the research on 3D dose verifications with polymer gel
dosimeters.
2.2 3D Dosimetry
The need for accurate, high resolution 3D dosimetry becomes more pressing as
conformal techniques (e.g., Intensity Modulated Radiation Therapy (IMRT) and tomotherapy)
make it possible to achieve more complicated dose patterns with steeper dose gradients.
Verifying the accuracy of the dose delivery calculation from the treatment planning software
(TPS) is an important aspect of regular clinical quality assurance. Achieving high resolution 3D
measurements with conventional dosimetry techniques such as ionization chambers,
thermoluminescent dosimeters (TLD)’s and radiosensitive films, is extremely laborious and may
be insufficient to achieve accurate dosimetry. This underscores the motivation behind the
development of new 3D dosimetry techniques that are capable of obtaining high resolution dose
measurements in three dimensions.
Adamczyk and Skorska (2007) used stacks of radiation sensitive film as a tomographic
3D dosimeter. While they showed that stacked-film 3D dosimetry is feasible with 6 MV photon
5
beams; development, digitization, registration, calibration and analysis of an entire stack of films
is not a practical solution under the time constraints typical of a clinical environment.
Alternatively electronic portal imaging devices (EPID)’s, which were designed to verify patient
setup, can be used to verify treatment plans (El-Mohri et al. 1999; McDermott et al. 2006). One
promising technique for performing 3D dosimetry with an EPID involves performing beam
transmission measurements behind a phantom and using these to reconstruct the dose distribution
(Louwe et al. 2003; McDermott et al. 2006; van Zijtveld et al. 2007). One major advantage of
this type of 3D dosimetry is that it is easily performed during delivery and may therefore be used
to verify individual patient treatments. However perturbation of exit field measurements due to
scatter, which is energy, field size, and anatomy dependent, makes accurate dosimetry difficult.
The technique is still under development. Another exciting 3D dosimetry technique involves the
use of chemical dosimeters suspended in a hydrogel. The basic concept is that irradiation initiates
a chemical reaction and the gel matrix provides spatial stability to the reaction product. The
distribution of reactants within the gel dosimeters provides a direct measurement of radiation
dose in a tissue equivalent material, constituting a true 3D dosimeter.
2.2.1 Gel Dosimeters
In their letter to Nature, Day and Stein (1950) were the first to report on radiosensitive
hydrogels for the purpose of 3D dosimetry. They were looking for a system that was “quasi-
solid, [that gave an easily observable chemical change] and [had] the same average atomic
number and electron density as body tissue (that is as water).” Having tested several
formulations, they recommended a Methylene blue dye and agar gel recipe which changed colour
upon irradiation, because of a hypothesized chemical reduction of dye molecules by ions and free
radicals produced by ionizing radiation. Day and Stein (1950) also noted that dissolved oxygen,
if present, competed with the dye for the reducing agents (ions and free radicals). They observed
6
a threshold dose in the Methylene blue system which had to be reached (to reduce all the oxygen)
before there was a dose response.
Modern gel dosimetry started when Gore et al. (1984a) used gelatin to provide spatial
stability to the well known Fricke dosimeter (Fricke and Morse 1927) and probed the gels with
MRI (1984b). However, post irradiation, the diffusion of ferric ions caused gradual blurring and
eventual loss of the dose pattern (Olsson et al. 1992; Harris et al. 1996; Kron et al. 1997; Tseng et
al. 2002). Rae et al. (1996) used chelating agents to reduce blurring caused by ion diffusion.
Yet, temporal instability remains a current issue with gel dosimeters based on the Fricke
dosimeter. To avoid the problem altogether, Maryanski et al. (1993) introduced a new type of gel
dosimeter, where the dose pattern is preserved by the formation of polymer particles that
precipitate out of solution. In a polymer gel dosimeter, monomer and crosslinker precursors are
dissolved in the gel matrix such that irradiation of the gel induces a free radical polymerization
reaction. The resulting polymer particles are large and exhibit negligible diffusion through the
gel matrix. The gel formulation presented by Maryanski et al. (1993) contained
N,N’-methylene-bis-acrylamide (Bis) crosslinker, Acrylamide monomer, Nitrous Oxide, ANd
Agarose, and was labeled with the acronym BANANA. Since then various groups have explored
new recipes and improved upon polymer gel dosimeters by introducing anti-oxidants (Fong et al.
2001; De Deene et al. 2002), switching to different gel networks (Maryanski et al. 1994a),
exploring new monomers and crosslinkers (Maryanski et al. 1996; Senden et al. 2006) and using
co-solvents to increase the solubility of the crosslinker (Koeva et al. 2008).
2.2.2 The NIPAM/Bis gel dosimeter
Due to its high dose sensitivity and early establishment, acrylamide is a preferred
monomer in polymer gel dosimeter formulations. Like the methylene blue system, the oxidizing
7
power of oxygen is also problematic in gel dosimeters based on acrylamide (Maryanski et al.
1993; Maryanski et al. 1994a; Salomons et al. 2002). Oxygen is a free radical scavenger that
inhibits free radical polymerization (Maryanski et al. 1993; Maryanski et al. 1994ab; Hepworth et
al. 1999; De Deene et al. 2001). As a result, early polymer gel dosimeters had to be prepared in
an oxygen free environment. If acrylamide is the monomer, these are known as PAG dosimeters.
It became possible to prepare polymer gel dosimeters under normoxic (normal atmospheric)
conditions when anti-oxidants, especially tetrakis hydroxymethyl phosphonium chloride (THPC)
(De Deene et al. 2002), were introduced to the dosimeter formulations (Fong et al. 2001).
Acrylamide based gel dosimeters prepared under normoxic conditions are commonly described as
nPAG. However, a concerning practical problem with both PAG and nPAG dosimeters is that
acrylamide is a neurotoxin (Maryanski et al. 1994a; Fong et al. 2001; Murphy et al. 2000;
McAuley et al. 2004, cited by Karlsson et al. 2007). Senden et al. (2006) replaced acrylamide
with a much less toxic yet chemically similar monomer: N-isopropyl acrylamide (NIPAM). The
NIPAM/Bis gel dosimeter introduced by Senden et al. (2006) exhibits good dose sensitivity, and
because it is relatively easy to prepare shows excellent potential for future clinical applications.
Furthermore, THPC can be added to NIPAM based dosimeters so that they can also be prepared
at room temperature under normoxic conditions. Therefore, NIPAM based polymer gel
dosimeters were used in these investigations.
Novel dosimeter systems continue to be developed by various groups for specific
dosimetric purposes (Adamovics and Maryanski 2003; Babic et al. 2008; Jordan 2008). For
example, Adamovics and Maryanski (2003) introduced PRESAGETM, a new class of 3D
dosimeter which does not involve hydrogels. In PRESAGETM the soft gel network of
conventional gel dosimeters is replaced with solid optically clear plastic epoxy (polyurethane).
The solid epoxy matrix allows the dosimeter to be cast and machined into clinically relevant
8
shapes and obviates the need for a rigid container (a current requirement for gel dosimeters).
Nevertheless, radiation induced chemical changes that are spatially preserved in a polymer matrix
remains a common feature of 3D dosimeters. The resulting post irradiation changes in the
physical properties of the dosimeters permit interrogating them with a variety of imaging
modalities. The goal is to digitize the 3D dose information so that it can be analyzed and
presented to the physicist in a meaningful way.
2.3 Optical Scanning
2.3.1 Development of Scanning Techniques
Even though the first gel dosimeters exhibited optical changes upon irradiation (Day and
Stein 1950; Andrews et al. 1957; Hoecker and Watkins 1958), NMR has been the historical
method of choice for dose information readout from 3D dosimeters (Gore et al. 1984b;
Maryanski et al. 1993; Schreiner et al. 1994; Ibbott et al. 1997; De Deene et al. 1998; Oldham et
al. 1998; Low et al. 1999; Love et al. 2003; Vergote et al. 2004). There is some interest in using
X-ray CT to probe 3D dosimeters due to its robustness and clinical accessibility (Hilts et al. 2000;
Audet et al. 2002; Baxter and Jirasek 2007). X-ray CT is limited in this application for two
reasons: 1) each X-ray CT scan adds dose to the dosimeter. 2) the achievable dose contrast is low
and only permits dosimetry when the measured dose is relatively high, > 8 Gy (Audet et al.
2002). Currently X-ray CT scanners exhibit limited sensitivity to the density changes caused by
radiation induced polymerization. Mather et al. (2002) used ultrasonic measurements to correlate
absorbed dose in PAG dosimeters, finding a strong relationship between dose and speed of sound
propagation. While ultrasonic imaging devices are portable and relatively cheap, the attainable
image quality is inferior to MRI and optical measurements. Unfortunately, the problem with
using MRI to probe polymer gel dosimeters is access. An initial investment for an MRI device is
9
on the order of two million dollars. Although this modality may become more achievable as
cancer centres acquire MRI units for treatment planning in the future (Chen et al. 2004).
Additional operational and maintenance costs are significant, and as a result our health care
system supports a limited number of MRI scanners.
The cloudy white precipitate formed after irradiating a polymer gel dosimeter is easily
visible with the naked eye and provides the potential for optical analysis. Jordan (2001b)
provided an excellent survey of techniques that could be used to probe the optical properties of
gel dosimeters such as attenuation, fluorescence, and index of refraction. Along with the advent
of polymer gel dosimetry, Gore et al. (1996) developed an optical scanner capable of measuring
3D dose distributions with high spatial resolution (see Figure 2.1).
Figure 2.1: A schematic diagram of the 1st generation optical computed tomography scanner used for scanning polymer gel dosimeters. The mirrors simultaneously translate back and forth to obtain a complete 1D projection. A stepper motor rotates the gel between acquisition of projections (from Gore et al. 1996).
The first generation device used a He-Ne laser, translating mirrors, a rotating stepper motor, and a
photodiode detector to acquire transmission measurements through cylindrical container for the
gel dosimeter. The authors used a filtered backprojection algorithm to reconstruct 2D images
corresponding to the optical attenuation. The technique is completely analogous to X-ray
computed tomography except that optical photons probe the sample instead of high energy
10
X-rays. This type of method is now known as Optical Computed Tomography (OptCT).
Compared with MRI OptCT uses a compact imaging device requires less infrastructure and is
much cheaper. OptCT units are now commercially available for less than $30 000, e.g., the
VistaTM unit from Modus Medical (London, ON) and the OCTOPUSTM from MGS Inc.,
(Newhaven, CT). Furthermore, because of advances in CCD technology driven by the digital
camera industry, photodetectors with exquisite sensitivity and resolution are available at low cost.
One limitation of OptCT systems is that optical effects, such as refraction, lead to
artefacts in reconstructed images. Cylindrically shaped dosimeter containers and tanks filled with
liquid matching the index of refraction of the gel are employed to reduce refraction at the gel-jar
and tank medium-jar interfaces. These adaptations are not required for MRI based polymer gel
dosimetry. Consequently, MRI has some unique advantages over OptCT, for example the ability
to image irregular dosimeter shapes and/or gels containing opaque and irregular structures (e.g.,
bone).
A disadvantage of the first generation laser systems, like the one introduced by Gore et
al. (1996), is that data acquisition is limited to one dimension per projection and is relatively
slow. Even when the translational stage was replaced with rotating mirrors, the acquisition of 75
slices of data required ~25 minutes (Van Doorn et al. 2005; Conklin et al. 2006). Various groups
have developed and investigated OptCT scanners with parallel beam, fan beam, and cone beam
geometries (see Figure 2.2) allowing simultaneous acquisition of projection data in 1 and 2
dimensions (e.g., Bero et al. 1999; Wolodzko et al. 1999; Jordan et al. 2001; De Jean et al. 2006;
Olding et al. 2007; Rudko et al. 2008). Both cone beam and parallel beam OptCT systems allow
data acquisition in 2D, but cone beam computed tomography (CBCT) systems have the added
advantage of avoiding expensive optics, which also makes them more compact. Optical
computed tomography based on transmission measurements provides detailed information about
11
a.
b.
c.
Figure 2.2: Schematic diagrams of various OptCT scanners. (a) A parallel beam setup (from Krstajic and Doran 2006a). (b) A fan beam system (adapted from Rudko et al. 2008). (c) Cone beam geometry (reproduced with permission from Doran et al. 2006b and Wolodzko et al. 1999).
the spatial variation of the total optical attenuation, µ, which is the sum of the attenuation due to
scatter, µscat, and absorption, µabs. For a pathlength, x, the transmitted photon intensity, I, is given
by Beer’s law
xeII µ−= 0 [Eqn. 2.1]
where I0 is the incident photon intensity. Often the attenuation data is returned in Hounsfield
units (CT#) where the attenuation is normalized to water (see Section 3.2).
12
2.3.2 The Problem of Scatter in Cone Beam OptCT
Cone beam CT geometry is now also widely used in X-ray CT, particularly for image
guidance before radiation delivery. As in OptCT, the advantage of an X-ray CBCT system is that
projections are acquired in 2D and a complete 3D volume can be reconstructed from a single scan
over one rotation. However, because of the broad beam geometry, photons associated with
scatter are mixed with the primary beam that reaches the detector (Siewerdsen and Jaffray 2001).
The result is that the projection data usually show a higher photon count than would be the case if
the intensity of light at the detector depended only on Beer’s law. Both X-ray and optical CBCT
systems are known to suffer from artefacts associated with scatter such as cupping, a depression
in measured attenuation, and a reduction in contrast-to-noise (CNR) (Siewerdsen et al. 2006;
Ning et al. 2004).
Maryanski et al. (1996) investigated the optical properties of BANG polymer gel
dosimeters. Noting an absence of absorption bands in the visible absorption spectra of both
acrylamide monomer and polyacrylamide solutions, they postulated that scatter is the primary
mode of optical extinction in irradiated BANG polymer gel dosimeters. Having also measured
the size of the polymer particles, they concluded that the microparticle precipitate constituted an
array of scattering centres consistent with Mie scattering. This is assumed to be the case for other
polymer gel systems where the dose response corresponds to the formation of a precipitate.
Then, the problem of scattered light inherent to cone beam OptCT is compounded in the
application of polymer gel dosimetry (Oldham 2006; Gore et al. 1996). Therefore, managing and
reducing the effects of scatter remains an important challenge for polymer gel dosimetry with
cone beam OptCT.
In our current work, the total concentration of monomer and crosslinker precursors has
been reduced from 6% (Senden et al. 2006), to 4% by mass in order to reduce background
13
polymerization in the NIPAM/Bis dosimeter and to minimize scatter related artefacts (Olding et
al. 2007). This approach reduces the base scatter-to-primary ratio (SPR) of the dosimeter.
Unfortunately, it also reduces the inherent dose sensitivity of the dosimeter. Recently, several
groups have implemented scatter correction techniques that have already proven successful in
X-ray CBCT (Ning et al. 2004; Siewerdsen et al. 2006; Wagner et al. 1988; Molloi et al. 1998;
Rinkel et al. 2007) for cone beam OptCT (Holmes et al. 2008; Olding et al. 2008; Jordan and
Battista 2008). It has been further shown by Holmes et al. 2008, that optical techniques (such as
the use of polarizing filters) could be applied to reduce scatter. While, these techniques were not
applied to improve the quality of optical scans for the research presented in this thesis, they may
lead to improved dosimetry in similar investigations.
2.4 Dose Comparison Techniques
2.4.1 Introduction
The technological advance of treatment planning systems, radiotherapy equipment and
therapeutic techniques is thought to improve the standard of care and quality of life through
achieving tighter treatment margins between the target and high dose delivery, thus sparing more
tissue. Clinical implementation of these advances requires careful commissioning and regular
quality assurance checks from medical physicists and technicians. To these ends, comparing
calculated dose distributions to physical measurement is a task frequently faced by radiation
oncology physicists. A comprehensive comparison should involve analysis in both dose and
spatial domains (Harms et al. 1998). One popular and conceptually simple dose comparison
technique involves independently representing the dose information from two distributions with
contours (known as isodose distributions) and superimposing them. This type of analysis allows
a qualitative comparison between distributions considering both dose and spatial dimensions.
14
However, analysis of three dimensional data becomes cumbersome and a more quantitative
investigation is necessary (Harms et al. 1998).
2.4.2 Dose Difference
The numerical dose difference between distributions can be determined point by point
between measured and calculated distributions and used to highlight regions of disagreement
(Harms et al. 1998; Mah et al. 1989). Statistical data can be represented with histograms of the
dose difference while colour wash presentations direct the eye towards regions of disagreement
(Fraass 1996; Fraass and McShan 1995; and Fraass et al. 1994). The major shortcoming of the
dose difference technique is that it is inherently oversensitive in regions of high dose gradient
such as at the edge of a target in conformal deliveries. As shown in Figure 2.3, in regions of high
dose gradient a small spatial error results in a large numerical difference between measured and
planned dose distributions. Meaningful analysis of agreement in regions of high dose gradient
must therefore be performed using a separate method. In their evaluation of 2D and 3D electron
beam dose calculation algorithms, Mah et al. (1989) presented isodose curves to accompany their
dose-difference plots, obtaining only qualitative information in high dose regions.
2.4.3 Distance-to-Agreement
The distance-to-agreement (DTA) concept was developed to provide a quantitative
analysis of dose distributions in regions of high dose gradient (Hogstrom et al. 1984; Shiu et al.
1992; Harms et al. 1998; Dahlin et al. 1983; Low et al. 1998). “The DTA is the distance between
a measured dose point, and the nearest point in the calculated distribution with the same dose
value,” (Harms et al. 1998). In an early implementation, Hogstrom et al. (1984) determined each
DTA value manually. With 50-60 TLD measurements superimposed on top of the isodose plot
calculated by the electron beam dose calculation algorithm each DTA was determined by finding
15
Figure 2.3: Superimposed continuous 1D dose distributions showing dose difference and distance-to-agreement evaluations. The inherent sensitivities of the dose difference and DTA tool are shown for regions of high and low dose gradient respectively (reproduced with permission from Low et al. 1998).
Figure 2.4: Superimposed continuous 1D dose distributions showing, as shown above. The corresponding 1D γ distribution is also shown. There is no oversensitivity in regions of high or low dose gradient (reproduced with permission from Low et al. 1998).
16
the distance between each point measurement and the nearest corresponding isodose curve.
However, manual analysis is not practical when the volume and resolution of the measured data is
high, as is the case for films and 3D dosimeters. The DTA distribution provides an excellent
measure of the calculation quality in regions of high dose gradient, but the converse of the dose
difference comparisons is oversensitive in regions of low dose gradient. Figure 2.3 illustrates
how a small dose shift results in large DTA values in regions with low dose gradient.
2.4.4 Composite Evaluation
Harms et al. (1998) combined the complementary nature of the DTA and dose difference
distributions in a software tool called the composite evaluation. Included in their presentation of
the composite evaluation algorithm was the description of a software tool which measured the
DTA distributions automatically. In the composite evaluation, the dose difference and DTA
distributions are independently evaluated as either meeting or exceeding predefined tolerances.
Harms et al. used the 3 % criteria (i.e., 3 % of the maximum dose) for the dose difference
recommended by Van Dyk et al. (1993) but adopted a 3 mm DTA limit instead of the
recommended 4 mm guideline. The 3 mm criteria was subsequently adopted in many other
studies (Low et al. 1998; Depuydt et al. 2001; Low and Demspey 2003; Bakai et al. 2003; Stock
et al. 2005; Spezi and Lewis 2006; Wendling et al. 2007; Ju et al. 2008). In the composite
evaluation, the tolerance criteria are used to create two binary pass-or-fail distributions,
corresponding to the DTA and dose difference. These are multiplied point by point yielding a
single binary distribution. The combined binary distribution contains an array of 0’s or 1’s for
agreement or failure respectively within 3% and 3mm. The final output shows only regions that
fail to meet both dose difference and DTA tolerance criteria, and therefore it is not overly
17
sensitive in regions of low or high dose gradient. Because it is a binary distribution, the
composite distribution does not lend itself to a display that is easily interpreted (Harms et al.
1998; Low et al. 1998). Therefore, by convention, the dose difference is displayed in regions of
failure. This approach heightens the impression of disagreement in regions of high dose gradient.
Furthermore, it is not representative of the significance of agreement in these regions.
2.4.5 The Gamma Comparison
To overcome the limitations of the composite evaluation, Low et al. (1998) developed the
concept of the γ-index, unifying the dose difference and DTA criteria with a single evaluation.
Instead of considering the DTA and dose difference distributions independently, the γ-index
combines them as vectors. Like the composite evaluation, the γ evaluation avoids oversensitivity
to low and high dose gradients (see Figure 2.4). Before a detailed review of the γ concept is
given, an important change of notation, introduced by Low and Dempsey (2003), should be
recognized. Neither the γ tool nor the DTA are symmetric with respect to the two distributions
they evaluate, and either or both distributions could be measured or calculated. For example it
may be necessary to perform comparisons between Monte Carlo computations and calculations
made by planning software, or between film measurements (Dhanesar et al. 2008). To avoid
confusion, the terms reference and evaluated were adopted to correspondingly describe a trusted
dose distribution and a dose distribution under investigtion. In the original change of notation,
the terms evaluated and reference referred to measured and calculated distributions respectively.
These terms are not restrictive however, and other groups have used them to describe other
combinations of dose distributions. The same notation is used in later publications (Ju et al. 2008;
Wendling et al. 2007; Stock et al. 2004). The γ comparison is used to measure the extent to
which an evaluated distribution agrees with a reference distribution, which is treated as the true
distribution (though, strictly speaking, obtaining a true distribution may not be possible). In the
18
research presented in this thesis, polymer gel dosimeters are being commissioned as a clinical QA
tool for the process of radiotherapy. Data obtained by probing gel dosimeters therefore comprises
the evaluated distributions while distributions that have been calculated with treatment planning
software are the reference distributions. Thus, compared to the use during the development of the
DTA and dose difference tools (i.e., the evaluation of electron beam dose calculation software),
the scenario is reversed in this thesis.
A γ comparison is only possible when the dose data are coupled with corresponding
spatial information. In their original work, Low et al. (1998) compared continuous distributions
(i.e., described by mathematical functions) having only one spatial dimension. The theoretical
concept also applies to distributions with any higher number of spatial dimensions. The 1D
continuous reference and evaluated distributions used by Low et al. (1998), which represent the
beam edge of a 10x10 cm2 6MV photon beam, provide an excellent visual representation of the
γ-index (see Figure 2.3). Every position in the reference distribution, rrv
, has a corresponding
( )rrvv
γ value which is a measure of agreement with the evaluated distribution. Each rrv
can be
coupled with any point in the evaluated distribution rrv
. For all pairs there exists a value
( )re rrvvv
,Γ , defined by the difference between the dose and physical position. Each ( )re rrvvv
,Γ is
normalized to the dose difference and distance-to-agreement tolerance criteria, ∆DM and ∆dM
respectively. ( )rrvv
γ is defined as the smallest possible value of ( )re rrvvv
,Γ that can be found
considering the entire evaluated distribution. The mathematical formalisms are reviewed in Table
2.1 which has been adapted from Low and Dempsey (2003).
The magnitude of ( )rrvv
γ is a quantitative measure of the agreement between the
distributions at the point, rrv
. When ( ) 1≤rrvv
γ , there is a point in the evaluated distribution which
19
lies within the specified acceptance criteria. Conversely, when ( ) 1>rrvv
γ , no point in the
evaluated distribution can be found within dose difference and distance-to-agreement tolerances.
Table 2.1: Definitions of symbols used to describe the γ-index (Low and Dempsey 2003)
Symbol Defining Equation Description
( )rr rDvv
N/A Reference dose rDv
at position rrv
( )ee rDvv
N/A Evaluated dose eDv
at position erv
MD∆ N/A
Dose difference tolerance criterion (e.g., 3%). In the research presented in this thesis, percentages refer to the maximum dose in the reference distribution.
Md∆ N/A Distance-to-agreement tolerance criterion (e.g., 3mm).
Dr∆ ( ) ( )re rDrDD
vvvvv−=∆ Difference between evaluated dose
and reference dose.
d∆ re rrdvvv−=∆ Spatial distance between evaluated
and reference dose points
Xv∆ re XXX
vvv−=∆
Spatial distance, in the x-dimension, between evaluated and reference dose points
Yv∆ re YYY
vvv−=∆
Spatial distance, in the y-dimension, between evaluated and reference dose points
Zv∆ re ZZZ
vvv−=∆
Spatial distance, in the z-dimension, between evaluated and reference dose points
( )re rrvvv
,Γ ( )( ) ( )
2
2
2
2
,M
rree
M
re
reD
rDrD
d
rrrr
∆
−+
∆
−=Γ
vvvvvvvvv
Generalized Γ function, computed
for all evaluated positions erv
and
reference positions erv
.
( )rrvv
γ ( ) ( ){ } { }erer rrrrvvvvvv
∀Γ= ,minγ γ function, the minimum generalized Γ function in the set of evaluated points.
N/A ( ) ( )
2
2
2
2
1M
rree
M
re
D
rDrD
d
rr
∆
−+
∆
−=
vvvvvv
Equation of the ellipse or ellipsoid whose surface represents the acceptance criteria
20
Alternatively, Low et al. (1998) used a unit surface ellipse or ellipsoid to graphically represent
and describe the simultaneous evaluation of the acceptance criteria (see Figure 2.5). If no
evaluated point can be found within the ellipse (or ellipsoid) surrounding rrv
, then ( )rrvv
γ is larger
than one. In the γ-evaluation it is assumed that the dose difference and DTA have equal
significance when determining the quality of agreement between distributions (Depuydt et al.
2002).
a.
b.
Figure 2.5: (a and b) Geometric representations of the acceptance criteria used to evaluate distributions with 1 and 2 spatial dimensions respectively (adapted from Low et al. 1998). In these illustrations the acceptance geometry is shown in green while the γ component vectors are shown in blue. The generalized Γ vector is shown in red.
In the original work only the theoretical basis for the γ comparison was reported. A tool
capable of performing γ analyses between clinical dose distributions such as those obtained from
planning systems or measurements was not presented. Having developed such a tool, Low et al.
(1999) used the γ analysis to compare MRI measurements of dose distributions in BANG®
polymer gels to calculation. Visually appealing color wash images, such as those shown in
Figure 2.6, were used to display 2D γ distributions that represented agreement at the axial x-y
plane. 2D analysis of 3D dosimetry measurements with a tool intended for high data content
seems limited; thus higher dimensional γ-comparison techniques soon became available (Spezi
21
and Lewis 2006; Wendling et al. 2007; Ju et al. 2008). Spezi and Lewis (2006) performed
complete γ comparisons between 3D IMRT head and neck dose plans using a γ-tool designed for
Figure 2.6: A colour wash image representing a γ-distribution from a 2D comparison between ion chamber measurements and calculation. The γ distribution was calculated using clinical software accompanying the “I’mRT MatriXX” product (Scanditronix Wellhöfer, Bartlett, TN). The colour bar corresponds to individual γ magnitudes between 0 and 1.28 shown on the plot (reproduced with permission from Mei et al. 2008).
2D comparisons only. This process is known as a 2.5D comparison (Wendling et al. 2008) and
involves performing 2D gamma comparisons between 3D distributions slice-by-slice until the
whole volume is analyzed. 2.5D comparisons will generally yield larger γ-values than a
comparison that considers the entire 3D volume.
22
Spezi and Lewis (2006) and Stock et al. (2005) used cumulative volume histograms that
were complementary to their colour wash images to summarize the volumetric γ data in one plot.
Dose volume histograms (DVH)’s (Shipley et al. 1979) are commonly used in planning and
evaluating radiation therapy to summarize volumetric dose information. Cumulative dose volume
histograms show the percentage of a volume of interest receiving up to a specific dose value (for
example see Figure 2.7). Gamma volume histograms (GVH)’s used by Stock et al. (2005) and
described by Spezi and Lewis (2006) are similar to dose volume histograms (DVH)’s, except that
the x-axis represents gamma magnitude instead of dose. In the research presented in this thesis,
where appropriate, cumulative DVH’s and GVH’s will be used to conveniently display statistical
data (of dose and γ respectively) pertaining to volumes of interest within the gel dosimeters.
0
25
50
75
100
0 2 4 6
Dose (Gy)
Fra
cti
on
of
Vo
lum
e (
%) Eclipse
Gel
0
25
50
75
100
0 2 4 6
Gamma Magnitude
Fra
cti
on
of
Vo
lum
e (
%)
Figure 2.7: Cumulative volume histograms corresponding to a 3D comparison for a conformal prostate delivery validation with polymer gel dosimetry. (Left) a dose-volume-histogram corresponding to the prostate volume. (Right) a cumulative gamma-volume-histogram corresponding to the prostate volume. These experimental results are described in greater detail in Chapter 5.
As noted previously, the clinical implementation of polymer gel dosimeters for validating
the process of radiotherapy, like that presented by Low et al. (1999), requires careful
manipulation of large data sets. Meeting the resolution criterion of < 1 mm3 specified for
23
(Oldham et al. 2001) means analysis of a 10x10x10 cm3 volume would require examining at least
106 individual data points. Computer assisted analysis is the only way to perform complete
quantitative dosimetric comparisons with this volume of information in a reasonable time frame.
The γ analysis has been developed specifically for this purpose and variations of the γ tool have
been used to compare dose distributions in numerous publications (Boyer et al. 2001; Caccia et
al. 2004; Cernica et al. 2005; Cilla et al. 2006; Kipouros et al. 2003; Dhanesar 2008; Monti and
Frigerio 2006; Petric et al. 2005; Renner 2007; Vedam et al. 2005; Wendling et al. 2006; Oliver
et al. 2008; Babic et al. 2008).
Since it was introduced, the γ-tool has been refined, modified and evaluated by several
authors (Depuydt et al. 2002; Low and Dempsey 2003; Bakai et al. 2003; Stock et al. 2005; Jiang
et al. 2006; Spezi and Lewis 2006; Wendling et al. 2007; Ju et al. 2008; Holmes et al. 2008). In
their clinical assessment of the γ evaluation, Depuydt et al. (2002) identified the importance of
considering the spatial resolution of the distributions under investigation. While Low et al.
(1998) presented a powerful theoretical concept for continuous functions real clinical
comparisons are typically made between discretized representations of dose distributions.
Depuydt et al. (2002) were concerned with overestimations of γ values caused by large grid
spacing in discrete dose distributions, particularly in regions of high dose gradient. To avoid
overestimating individual γ-values they reduced the γ index to a pass/fail metric and introduced a
filter cascade which tested for three geometric scenarios that would falsely lead to γ>1. In
addition, in order to reduce computation time, the search for ( )rrvv
γ only encompassed the
evaluated pixels lying within the spatial radius defined by the DTA criterion. For each reference
point, the search was terminated as soon as a value of ( ) 1<rrvv
γ was found. Effectually, they
reduced the continuous value of γ to a binary test equivalent to the composite evaluation (Ju et al.
2008). Recognizing the importance of the grid resolution and its effect on γ was an important
24
new idea. The authors observed that the individual γ values calculated from discrete distributions
will be larger than the true analytical minimum that would be found had the distributions been
presented as continuous functions. Several later studies were directed, in part, towards resolving
this issue (Bakai et al. 2003; Wendling et al. 2007; Ju et al. 2008)
2.4.6 Discretization Artefacts in γ Distributions
Low and Dempsey (2003) partially addressed the issue of sensitivity due to the discrete
nature of the data. They claimed that by re-sampling the distributions to 1x1 mm2 grids, the error
in γ associated with pixelization artefacts was reduced to less than 0.2, even in regions of high
dose gradient. However, the main focus of their investigation was to examine the behaviour of
the γ evaluation in the presence of noise. They used dose distributions that simulated a square 10
x 10 cm2 field from a 6 MV photon beam impingent on a water tank. The evaluated distribution
was obtained by modifying the reference distribution so that there were regions where
disagreement was caused by either an imposed dose difference or misalignment. Pseudorandom
noise was then added to either the reference or the evaluated distribution. Statistical analysis of
the resulting γ distributions revealed that adding noise to the reference distribution had little effect
on the mean value of γ. However, adding noise to the evaluated distribution caused an
underestimate of the mean value of γ compared to the noise free case. The authors stated that the
study was conducted with greater noise than typically found in standard deviations in clinical
measurements. Nevertheless, the noise level in the evaluated distribution must be considered
when interpreting the results of γ analyses. They suggested that some level of noise filtering may
be necessary, but did not indicate at what noise level filtering would be appropriate.
Bakai et al. (2003) proposed a modification to the γ tool where the acceptance
ellipse/ellipsoid is defined solely by the DTA criterion at each reference point. Multiplying the
25
dose at each point in the evaluated distribution by the ratio of the DTA and dose difference
criteria modified the dose axis such that it had units of distance (see Equation 2.2).
M
M
D
dDD∆
∆×=′ [Eqn. 2.2]
In the case of a comparison between 1D distributions the ellipses form a tube encompassing the
reference distribution. The thickness of the tube along the dose dimension is dependent on the
local dose gradient. The test of agreement is reduced to determining where the evaluated
distribution lies within the tube. The authors used the tube concept to define a factor, χ, which
quantifies the extent to which the evaluated distribution agrees at any given reference position.
Similar to the γ analysis, the comparison passes when χ≤1. The strengths of this comparison
technique are twofold: 1) it is not sensitive to grid resolution. 2) since there is no search for the
smallest Γ, the calculation time is greatly reduced. The authors reported the χ evaluation to be
~120 faster than the γ analysis. The main limitation with their technique is that the evaluated and
reference distributions must have the same grid spacing (Ju et al. 2008), because the comparison
is made solely in the dose dimension (to gain an advantage in computational time). In a similar
study, Jiang et al. (2005) converted the comparison in the spatial domain to a comparison in the
dose domain using a concept they called the maximum allowable dose difference (MADD). The
acceptance volume (e.g., an ellipsoid) and the dose gradient of the evaluated function are used to
determine MADD. If the dose difference is less than MADD at a particular reference point, the
distributions agree within spatial and dose tolerances. While the technique seems promising, the
authors did not specify whether calculating MADD has any computational advantage over γ.
Wendling et al. (2007) offered a solution to the discretization artefact through
interpolating additional data points in the evaluated grid. The computational speed of the
26
algorithm was enhanced by precalculating the interpolation factors, and further by restricting the
search around each reference point. Evaluated points that “do not have a chance” of yielding the
smallest value of Γ are not queried: i.e., as soon as ∆d/∆dM becomes larger than the smallest Γ
found so far, the search is terminated. They also imposed a maximum search distance of 1.0 cm
surrounding each reference point. The concept of limiting the search distance by the smallest Γ
found so far was first proposed by Stock et al. (2004) who used an expanding square search
algorithm to find γ. Wendling et al. (2007) achieved even greater computational speed by
carefully limiting the number of superfluous calculations. Furthermore, by interpolating more
points the γ values approach the analytical minimum of the corresponding continuous
distribution. In theory, interpolating to higher grid resolution would yield γ values approaching
the analytical values for a continuous distribution. However, with this method the computation
time grows cubically with increasing grid resolution (Ju et al. 2008).
Recognizing that the increase in computation time seen by Wendling et al. (2007) was
because the calculation required interpolation, Ju et al. (2008) proposed a geometric approach to
determining the smallest Γ. For 1D dose distributions the smallest Γ will either lie on an
evaluated point, or on the point on the line connecting neighbouring evaluated points where the
normal intersects the reference point (see Figure 2.8). In the case of 2 and 3 dimensional
comparisons, this approach is equivalent to determining the nearest distance to a dose surface or
hyper dose surface connecting adjacent evaluated pixels. Ju et al. (2008) used simplexes to
mathematically represent the dose surfaces and thereby calculate the minimum distance (a
simplex is an array of n+1 points describing a surface in n-dimensional space). Increased
computational speed was achieved by sorting the simplexes by their distance from each reference
point and sequentially calculating each Γ. The geometric approach is an excellent solution to the
discretization artefact. It is insensitive to dose grid resolution and dose gradient, and avoids long
27
computation time associated with interpolating large numbers of data points. However, the
method is analogous to linear interpolation as opposed to higher order spline interpolation. The
geometric method as presented by Ju et al. may therefore be sensitive in regions where the
change in gradient is large as linear interpolation leads to discontinuities in the second derivative
(Ju et al. 2008).
Figure 2.8: A one dimensional example demonstrating the discretization artefact of γ. (a) For point to point comparisons, the smallest value of Γ is typically larger than the analytical minimum, particularly in regions of high dose gradient. (b) The geometric method determines the smallest possible distance between the line segment connecting adjacent evaluated points. (reproduced with permission from Ju et al. 2008).
2.4.7 The Vector Nature of γ
Although the γ comparison provides a useful measure of agreement between distributions
when the index is less than one, the scalar gamma value provides little information into the
clinical significance or source of disagreements of failing gamma values (i.e., when γ>1). For
example, a comparison between a distribution calculated by treatment planning software, and an
Electronic Portal Imaging Device (EPID) measurement may show γ>1 over a critical structure
28
such as the spinal cord. Using the γ vector information that has been presented so far, it is
impossible to tell with the γ information whether the failure is insignificant or not (i.e., whether it
was caused by an underdose or overdose with respect to the measurement). However, it is
possible that the inherent vector properties of gamma may permit its application as a far more
comprehensive assessment tool than was originally intended.
Even though γ is a vector by definition, only Stock et al. (2004) have reported on the
information or utility of the vector properties of gamma. By convention, only the magnitude of γ
is presented in the γ distribution, the rest of the vector properties are ignored. Low et al. (1998)
called for a graphical analysis of the angle between the dose axis and the vector that defines
( )re rrvvv
,Γ . Stock et al. (2004) used colour wash images of the γ angle to guide the eye towards
regions where deviations were determined mainly by DTA or dose difference. They described
the range of the angle as being from 0 to π. An angle less than π/4 indicated that failure was
predominantly caused by dose difference, while an angle greater than π/4 implicated the DTA
(see Figure 2.9).
Figure 2.9: A diagram showing the γ angle as it was described by Low et al. (1998) and Stock et
al. (2004).
29
2.5 Clinical Radiotherapy Validations in 3D
While polymer gel dosimeters have not yet been clinically adopted, there have been a
number of studies for evaluating their application in clinical scenarios (Ibbott et al. 1997; De
Deene et al. 1998; Oldham et al. 1998; De Deene et al. 2000; Novotný et al. 2002; Love et al.
2003; Vergote et al. 2004; Wuu and Xu 2006; Gustavsson et al. 2003; Oldham et al. 2004;
Karlsson et al. 2007). Nearly all of the published works with clinical type deliveries involve
probing the polymer gel dosimeters with MRI. Of those listed above, only Oldham et al. (2004)
and Wuu and Xu (2006) used an optical system to obtain the dose distributions from polymer gel
dosimeters.
Oldham et al. (2004) copied a prostate treatment plan consisting of 5 18MV step-and-
shoot IMRT (Intensity Modulated Radiation Therapy) beams created using the Pinnacle treatment
planning system. They imposed the plan onto an X-ray CT scan of a phantom containing
polymer gel dosimeter and recalculated the dose distribution. After irradiation, the phantom was
scanned with a linear OptCT system. The attenuation maps were registered to the plan by
aligning three fiducial marks (visible both the optical and X-ray scan) on the bottom of the
phantom. The measurement was subsequently calibrated to dose. A single slice of the
measurement was compared to the treatment plan through gamma, DTA and dose difference
analysis and further by superimposing isodose lines. However, as this study was only intended to
demonstrate the potential for 3D validations, no quantitative analysis was provided. In a similar
study Oldham et al. (2006) used a PRESAGE dosimeter and the OCTOPUSTM linear OptCT
scanner to measure an 11 field 6MV IMRT treatment. Wuu and Xu (2006) used the
OCTOPUSTM scanner and a BANG®3 polymer gel dosimeter to verify the dose from a modified
head and neck IMRT plan made by the Helios IMRT treatment planning system. They used
30
superimposed isodose plots as well as dose difference and DTA analysis to compare the measured
distribution with the distribution calculated by the planning software.
2.6 Research Objectives
While long experience with MRI and polymer gel dosimetry has helped to establish
protocols for the future clinical application of this technique, cone beam OptCT devices are
relatively new. To date, there is an absence of studies involving clinical delivery verifications
with cone beam OptCT and polymer gel dosimetry. This study is intended to provide solutions
and establish protocols for performing 3D delivery validations with polymer gel dosimeters and
cone beam OptCT. To this end, various considerations and procedures forming a potential
approach for validating conformal prostate teletherapy deliveries are presented. These techniques
may be applied with modification for the verification of other radiation therapies.
The development of a clinically viable 3D dosimetry technique will constitute an efficient
and high resolution solution to measuring dose distributions in three dimensions. The ability to
quantitatively evaluate the large amount of data that becomes available with 3D dosimetry is at
least as important as the measurements themselves. The γ-evaluation has been developed as a
rapid analysis technique to serve this need. However, it is neither a perfect nor complete solution,
particularly when comparing noisy distributions. An efficient in-house 3D γ-tool was created in
order to compare dose distributions obtained by optically interrogating irradiated polymer gel
dosimeters. Further, in an effort to interpret the significance of failing γ magnitudes (i.e., when
γ≥1) a 2D γ-tool capable of returning the corresponding vector information was developed. The γ
angle as described by Low et al. (1998), and Stock et al. (2005) does not provide a complete
description of the γ-vector. For example, the γ angle does not even identify whether the dose
difference is positive or negative. Therefore, the classic definition of the γ-angle is by no means a
31
complete description of the vector nature of gamma. As a part of the research presented in this
thesis, an in-house version of the γ evaluation was written in MATLAB that returns the γ
magnitude information and the complete γ vector information in component form. A series of
investigations were then undertaken to explore the response of the γ vector field under various
scenarios. The goal is to observe trends in the vector field response that may aid other
investigators in interpreting the significance of γ>1. Further, the clinical utility of the γ-vector
algorithm is explored as it is applied for the validation of image guided radiation therapy of
prostate cancer.
32
Chapter 3 Theory
This brief chapter gives some theoretical background of the fundamental physical
interactions that lead to biological dose, and how dose can be measured with chemical
dosimeters. The discussion presented in Section 3.1 is based on Attix (1986), Khan (1994) and
Johns and Cunningham (1983). The discussion of chemical dosimetry in Section 3.2 has been
adapted from Attix (1986), and extended to include 3D chemical dosimetry by optical computed
tomography. Finally, a simplified discussion of free radical polymerization as it applies to
polymer gel dosimeters is presented in Section 3.3. Section 3.3 is only intended to provide a
conceptual understanding of polymerization reactions, it is based on theoretical models presented
by Fuxman et al. (2003) and reaction mechanisms from Solomons and Fryhle (2003), but it is not
a complete or rigorous discussion of free radical polymerization reactions in radiation dosimetry.
3.1 Radiation Dose
As a beam of particles (electrons, photons, neutrons, protons, pions, helium nuclei,
fission fragments etc.) with sufficient energy to ionize an atom, passes through biological tissue
some of the beam energy is transferred to the tissue, possibly causing biological damage.
Absorbed dose is defined as the amount of energy deposited per unit mass. In SI units, absorbed
dose is measured in Gray (Gy) which has units of Joules per Kilogram (J/Kg). In terms of
predicting biological outcomes, absorbed dose is a very useful quantity. However, the biological
effect for a given absorbed dose is also dependant on the type of tissue, and the type of radiation.
For example, bone marrow is more sensitive to radiation than skin, and alpha particles have more
biological effect than X-rays. To compare biological effect of radiation between tissues on a
33
common scale, the absorbed dose in Gy can be converted to effective dose in Sieverts (Sv)
through the application of radiation and tissue weighting factors. For the research presented in
this thesis, converting to effective dose is an unnecessary and potentially confusing step.
Therefore, absorbed radiation dose is reported in Gy.
The physical interactions and chemical processes leading to biological damage from a
beam of ionizing radiation are complicated and depend on the radiation type. While a complete
description of these processes is beyond the scope of this thesis, for high energy photons passing
through a medium the basic concept involves a chain of photon interactions with electrons in the
medium. Consider a high energy photon from a radiation beam (X-rays or γ-rays) the process
begins with an interaction, where some of the photon energy is transferred to an electron (see
Figure 3.1). The resulting high energy electron, a delta ray (δ-ray), creates a track where
Coulomb interactions occur causing losses in kinetic energy while travelling through the medium.
When tissue is the medium, biological damage may occur as the electron energy loss causes
ionizations, atomic excitations, and the breaking of chemical bonds. However, most of the
kinetic energy is lost as heat, with no biological effect. Both the scattered photon and the high
energy electron may interact to produce additional δ-rays. Further, Bremsstrahlung X-rays are
produced when high energy electrons decelerate in the field of a nucleus.
3.1.1 Photon Interactions
A high energy photon (X-ray or γ) may undergo five types of interactions as it passes through
matter: Compton (incoherent) scattering, the photoelectric effect, pair production, photonuclear
interactions, and Rayleigh (coherent) scattering. The probability of each interaction depends on
the individual reaction cross section. The cross section has units of area and is commonly
expressed in barns (10-24cm2). It is equivalent to the atomic attenuation coefficient
34
Figure 3.1: A flow diagram showing a simplified version of the process leading to biological damage from ionizing radiation (adapted from Johns and Cunningham 1983).
(measured in cm2/atom), which can be used to determine the number of photons left in a beam of
radiation as it passes through a medium. Consider a beam containing N photons incident on an
absorber with variable thickness. If all interactions, including scatter, result in photons being
removed from the beam then the number of photons, dN, reaching a detector behind the absorber
is proportional to the thickness of the absorber, dx:
�dxd� ∝ [Eqn. 3.1]
or
�dxd� µ= [Eqn. 3.2]
Ionizing radiation beam (i.e., photons) enters
tissue.
Scattered photon
Bremsstrahlung X-rays
Primary interaction, high energy photon ejects an electron
High speed electron loses energy as it moves through the tissue
Photon exits tissue
Heat, ionization, excitation, breaking molecular bonds
Chemical changes
Biological damage
(A)
(B)
More interactions like (A)
35
where the proportionality constant, µ, is the linear attenuation coefficient. Solving the differential
equation, leads to the following equation.
xe�� µ−= 0 [Eqn. 3.3]
where N0 is the number of incident photons, and N is the number of photons at a depth x.
Because the beam intensity is given by the photon flux, the number of photons is interchangeable
with the beam intensity, I, for example.
xeII µ−= 0 [Eqn. 3.4]
The linear attenuation coefficient, µ, has units of cm-1and depends on the energy of the photon
beam and the nature of the absorbing material. For example at the energy of interest, µ mainly
depends on the density of the medium. The mass attenuation coefficient is independent of
density, and can be obtained by dividing the linear attenuation coefficient by the density (i.e.,
µ/ρ). Therefore, the mass attenuation coefficient, µ/ρ, has units of cm2/g. The atomic mass, Aw,
and Avogadro’s number, NA, relate the mass attenuation coefficient to the atomic attenuation
coefficient, µa, or cross section.
A
w
a�
A⋅=ρµ
µ [Eqn. 3.5]
For a given material, the total mass attenuation coefficient, µ/ρ, for a photon beam of a specific
energy is the sum of the individual mass attenuation coefficients for each of the five possible
interactions. Neglecting photonuclear interactions the mass attenuation coefficient is,
prodpairCompton
c
ricphotoelectcoherent
coh
_
+
+
+
=
ρκ
ρσ
ρτ
ρσ
ρµ
[Eqn. 3.6]
36
where, σcoh, τ, σc, and κ, are the linear attenuation coefficients for Rayleigh scattering,
photoelectric effect, Compton interactions and pair production respectively. Of these interactions
only Compton scattering, the photoelectric effect and pair production, involve the transfer of
energy to electrons. Rayleigh scattering can be ignored because it is elastic the photon scatters
through a small angle with no energy loss.
The polymer gel dosimeters used in this research are 90 % water by mass. For photons
energies between 1 and 8 MeV Compton scattering constitutes 99.9 % to 83.1 % of the total
attenuation coefficient in water. In other words, the vast majority of photon interactions in this
energy regime are Compton events. Pair production becomes more important in water with
increasing photon energy, surpassing Compton scattering for photon energies between 20 and 30
MeV. Compton scattering, involves an elastic collision between a photon and an unbound
electron (see Figure 3.2). Some of the photon energy is transferred to the electron, causing a
change in momentum for both the photon and the electron which scatter away from each other at
different angles.
Figure 3.2: Kinematics of a Compton event. A photon with energy Eγ strikes an unbound electron. The electron and photon depart at angles of θ and φ from the horizontal (adapted from Attix 1986).
37
The relationships between the photon energies hv and hv’, the electron kinetic energy, T, and the
scattering angles, φ and θ, can be derived assuming a totally elastic collision and applying the
relativistic energy-momentum equation.
( )( )ϕνν
νcos1/1 2 −+
=′cmh
hh
e
[Eqn. 3.7]
νν ′−= hhT [Eqn. 3.8]
The electron energy therefore depends on the scattering angle as well as the initial photon energy.
The main point of understanding is, that for the range of photon energies used in this thesis
(<15MeV), secondary electrons are primarily produced by Compton scattering and that these
electrons are responsible for most of the absorbed dose.
3.1.2 Generation of Free Radicals
Free radicals are highly reactive uncharged molecules with unpaired electrons. Unlike
ions, which can be produced by heterolytic bond breakage (unequal sharing of electrons), free
radicals result from homolytic cleavage of covalent bonds (equal sharing of electrons). In tissue
biological damage occurs as free radicals interact with biological molecules, especially DNA.
Free radicals are produced by radiation induced radiolysis. The mechanisms of water radiolysis
caused by ionizing radiation are well understood (Swallow 1973; Spinks and Woods 1976) and
proceeds in three stages. The first stage is often called the physical stage and involves the
excitation or ionization of water (e.g., via Compton scattering). During the second stage, called
the physicochemical stage, high energy electrons become thermalized and hydrated. Ionized and
excited water molecules also split into hydronium ions (H30+) and free hydroxide and hydrogen
radicals (OH• and H• respectively) during this stage. The third stage is the chemical stage, where
hydrated electrons ( −.aqe ) free radicals and ions interact with each other and with water molecules
38
to produce new ions and radicals, water and hydrogen peroxide (H2O2). These reactions are
summarized in Table 3.1. In general, the products of the radiolysis decomposition of pure water
are: OH-, OH•, H•, −.aqe , H2O2 and H3O
+.
3.2 Chemical Dosimetry
Chemical dosimetry involves measuring radiation induced chemical changes in a
dosimeter and relating them to absorbed dose. While chemical dosimeters can be based on any
medium (gas solid or liquid), those based on liquid water are advantageous because their
radiological properties closely approximate biological tissue, which is mostly water (with the
exception of adipose tissue and bone). The Fricke dosimeter (Fricke and Morse 1927) is a
popular aqueous dosimeter based on dilute sulfuric acid (H2SO4) and ferrous sulfate (FeSO4) or
ferrous ammonium sulfate hexahydrate (Fe(NH4)2(SO4)2•H2O). The Fricke dosimeter has
applications in gel dosimetry (see Section 2.2.1 and Section 2.2.2) but the standard composition
does not involve a gel matrix. The relatively simple underlying chemical mechanisms of the
Fricke dosimeter provide a basis for understanding chemical dosimetry with more complex
systems, such as polymer gel dosimeters. The Fricke chemistry involves the oxidation of ferrous
ions (Fe2+) to form ferric (Fe3+) ions through interactions with free radicals. In general, Fricke
solutions are bubbled with oxygen (aerated) to achieve a higher radiation chemical yield of Fe3+
ions. The Fricke reactions are summarized in Table 3.2.
39
Table 3.1: Radiolysis of water (adapted from Swallow 1973; Spinks and Woods 1976).
1. Physical stage (10-15 seconds or less)
+− +→ OHeOH 22γ
(1)
*22 OHOH →γ (2)
2. Physicochemical stage (10-11 seconds or less)
−− →+ .2 aqeOnHe (3)
•++ +→+ OHOHOHOH 322 (4)
•• +→ HOHOH *2 (5)
3. Chemical stage (10-8 seconds)
−•− +→+ OHHOHeaq 2. (6)
OHHOHeaq 23. +→+ •+− (7)
−− +→+ OHHOHeaq 222 22. (8)
−•− →+ OHOHeaq. (9)
−•− +→++ OHHOHHeaq 22. (10)
OHOHH 2→+ •• (11)
222 OHOH →• (12)
Net reaction
2232 ,,,,, OHHeOHOHOHOH aq
•−•−+→γ (13)
40
Table 3.2: Oxidation of the Fe2+ ion in the Fricke dosimeter
1. Reactions with oxygen present in solution
•• →+ 22 HOOH (1)
−++• +→+ OHFeFeOH 32 (2)
−++• +→+ 2
322 HOFeFeHO (3)
222 OHHHO →+ +− (4)
2. Reactions with no oxygen in solution
232 HFeHFeH +→++ +++• (5)
The standard Fricke solution is conventionally used to measure the average dose, D ,
over an entire solution volume. Absolute dosimetry is achieved by relating the change in ferric
ion concentration before and after irradiation, ∆M, to the radiation chemical yield G(Fe3+) of
ferric ions per unit of radiation energy by
( )+∆
=3FeG
MD
ρ [Eqn. 3.9]
where ρ is the density of the solution. The radiation chemical yield G(Fe3+) describes the number
of of Fe3+ ions produced per unit energy of absorbed radiation dose, and has units of mol/J.
∆M can be probed by absorption spectroscopy, because the concentration of ferric ions
affects the optical density of the Fricke solution at specific wavelengths (e.g., 304 nm). Small
samples of the irradiated Fricke solution can be poured into spectrophotometer cells for optical
analysis. The change in optical density, ∆(OD), is related to the ratio of transmitted light
intensity between an irradiated and a non-irradiated sample (i.e., as measured with a
spectrophotometer).
41
( )OD
I
I ∆−= 100
[Eqn. 3.10]
For a given optical wavelength, the optical density and transmitted intensity are dependent on the
path length, l, through the sample and the molar extinction coefficient, ε, for Fe3+ ions.
( ) MlOD ∆=∆ ε [Eqn. 3.11]
When the radiation chemical yield is known, the absolute absorbed dose can therefore be
obtained through optical measurements, combining Equations 3.9 and 3.11.
( )( )+
∆=
3FeGl
ODD
ρε [Eqn. 3.12]
The radiation chemical yield for the reaction can be determined experimentally, but it is
dependent on a variety of factors, including impurity concentration, reaction temperature and
photon energy. Experimental reproducibility of dose measurements requires careful control of
these factors. Nevertheless, under certain conditions (e.g., dose rate and temperature) the
chemical yield is well known, allowing absolute dosimetry with the Fricke system.
If spatial information related to the dose measurements is required, a gel matrix (e.g.,
agarose or gelatin) can be added to the Fricke solution. After irradiation, the gel temporarily
preserves the physical location of Fe3+ ions allowing measurement of not only the volumetric
average dose, but also the dose pattern. 3D gel dosimetry began when Gore et al. (1984a) used
nuclear magnetic resonance imaging (MRI) to obtain 3D images from irradiated Fricke solutions
in gelatin (see also Section 2.2.1). Spectrophotometric analysis of optical cells containing gel
dosimeter solution is insufficient to readout the high-resolution spatial information from a
complex dose pattern. However, in 1996 Gore et al. showed that high spatial resolution optical
attenuation measurements can obtained using optical computed tomography (OptCT) (see also
42
Section 2.3). In gel dosimetry, the technique involves using a reconstruction algorithm (e.g.,
filtered backprojection) and a set of optical transmission measurements through the dosimeter
volume to calculate a map of the corresponding local optical attenuation coefficients. The optical
attenuation coefficient, µoptical, is the optical wavelength analogue to the linear attenuation
coefficient derived in Eqn.’s 3.2 – 3.4 for X-ray interactions.
xopticaleII
µ−= 0 [Eqn. 3.13]
The change in concentration of Fe3+ ions, ∆M, similarly manifests as a change in optical
attenuation coefficient, ∆µoptical. Like ∆(OD), ∆µoptical is related to the molar extinction
coefficient, ε, but it is independent of sample thickness.
Moptical ∆=∆ εµ [Eqn. 3.14]
The change in optical attenuation coefficient is given by,
opticalopticaloptical µµµ −′=∆ [Eqn. 3.15]
where opticalµ and opticalµ ′ correspond to the optical attenuation coefficients before and after
irradiation, respectively. Using Eqn. 3.15 and 3.13, ∆µoptical is related to the incident and
transmitted optical intensity before and after irradiation by
′′
′−
=∆
00
ln1
ln1
I
I
xI
I
xopticalµ [Eqn. 3.16]
Where I0 and I correspond to the incident and transmitted intensity before irradiation and I0’ and
I’ correspond to the incident and transmitted intensity after irradiation. Assuming that the
pathlength and the incident optical intensity are the same between the two measurements,
00 II ′= [Eqn. 3.17]
43
xx ′= [Eqn. 3.18]
the change in optical intensity becomes
′
=∆I
I
xoptical ln
1µ [Eqn. 3.19]
By combining Equations 3.9 and 3.14, the average absorbed dose can be related to ∆µoptical by
( )+∆
=3FeG
Doptical
ερ
µ [Eqn. 3.20]
or more generally, for 3D chemical dosimetry systems,
( )XG
Doptical
ερ
µ∆= [Eqn. 3.21]
However, the quantity, D , is no longer representative of the average dose over the entire
dosimeter volume, but only over the region (i.e., voxel) associated with ∆µoptical. The commercial
reconstruction software for the Vista OptCT unit returns attenuation data in Hounsfield units
(CT#). For a given photon wavelength, the CT# in a medium is related to the linear attenuation
coefficient in the medium, µx, and the linear photon attenuation in air and water, µair and µwater
respectively by,
1000# ×−
−=
airwater
waterxCTµµµµ
[Eqn. 3.22]
The Vista scanner uses red or amber light with optical wavelengths of 633 nm or 590 nm
respectively. The change in CT# after irradiation, ∆CT# is related to the change in linear
attenuation coefficient, ∆µx, by,
1000# ×−
∆=∆
airwater
xCTµµ
µ [Eqn. 3.23]
44
where ∆µx is equivalent to ∆µoptical. Therefore, absorbed radiation dose can also be related to a
change in CT#.
( )( ) 1000
1#×
−∆=
XG
CTD airwater
ερµµ
[Eqn. 3.24]
3.3 Polymer Gel Dosimetry
A confounding problem with the Fricke gelatin dosimeter is that after irradiation the
Fe3+ ions slowly diffuse through gel matrix causing gradual blurring of the dose distribution (see
also Section 2.2.1). Maryanski et al. (1993) introduced a new type of gel dosimeter where the
free radicals from water hydrolysis initiate a polymerization reaction, causing the formation of
tiny polymer particles. The resulting polymer particles do not diffuse through the gel matrix.
While MRI scanners can be used to digitize the dose information in polymer gel dosimeters,
optical scanning techniques may become the preferred method for readout due to reduced cost
(see also Section 2.3). In polymer gel dosimetry, the dose response is due to the formation of
light scattering polymer particles suspended within the gel after irradiation. Scatter is the primary
mode of optical attenuation in polymer gel dosimetry. The amount of scatter depends on the size,
density, and index of refraction of the polymer particles. Therefore, irradiation temperature,
thermal history and the concentration of dissolved impurities affect the measured attenuation.
While in Fricke dosimetry, the dose response is the change in concentration of the Fe3+ ion, in
polymer gel dosimetry there is a vast number of possible chemical configurations of the polymer
reaction products. Consequently constructing theoretical models to predict the chemical yield is
more difficult. Nevertheless, Zhang et al. (2001), Fuxman et al. (2003) and Senden (2006)
developed models to describe the reaction kinetics of the radiation induced free radical
polymerization reactions in polymer gel dosimeters.
45
3.3.1 Free Radical Polymerization
Free radicals from the radiolysis of water initiate the free radical polymerization that constitutes
the dose response of polymer gel dosimeters. The actual chemical process of free radical
polymerization is quite complicated (Fuxman et al. 2003) but a simplified version of the possible
reactions is summarized in Table 3.3. There are three basic types of interactions: 1) initiation
reactions which involve the activation of a monomer unit by a free radical. 2) propogation
reactions which cause lengthening of the polymer chain by addition of a monomer or crosslinker
molecule. 3) termination reactions which cause the deactivation of a polymer chain, and can
occur through the formation of covalent bonds, or transfer of an unpaired electron to another
molecule. The reactions shown in
Table 3.3 are only representative chemical equations and some of the molecules shown (i.e., the
polymer chains) are simplified versions of a much more complex structure. In the reaction
diagrams, unpaired electrons are represented by ‘•’.
The free radical addition mechanisms for several typical reactions are illustrated in Figure
3.3 through 3.6. In initiation reactions, a hydroxide or hydrogen radical attacks one of the two
carbons in the sp2 state (the carbons with shared double bonds) homolytically breaking one of the
two bonds and bonding to the carbon. The unpaired electron is transferred to the other sp2 carbon
creating either a primary or secondary carbon radical, depending on which sp2 carbon the primary
radical interacted with. Of the two sp2 carbons, the primary radical preferentially interacts with
the one with the larger number of attached hydrogen atoms (i.e., Markovnicov addition), this is in
part because the resulting secondary carbon radical is more stable than a primary radical (which
would result if the addition occurred on the other carbon). The secondary carbon radical (2˚
radical) is further stabilized by a resonance structure where the unpaired electron is transferred to
46
the amide oxygen. The initiation process and resonance stabilization are illustrated for primary
hydroxide radicals in Figure 3.3 (see also Figure 3.4). Propagation interactions proceed by the
same basic mechanism as the initiation reactions, free radical addition to sp2 carbons (shown in
Figure 3.5). The activated polymer chains react with monomer and cross-linker molecules and
other polymer chains causing lengthening and cross-linking of the backbone polymer chain. The
possibility of interaction with monomer and crosslinker molecules, as well as with other polymer
chains results in an enormous range of size and configuration of final the polymer products. But,
the amount of polymer formed is clearly related to the amount of dose deposited (Babic and
Schreiner 2006). Termination reactions result in the deactivation or transfer of the unpaired
electron that allows free radical polymerization (see Figure 3.6). This may occur by interaction
with another unpaired electron forming a covalent bond, and deactivating both free radicals (e.g.,
disproportionation). Sometimes the unpaired electron is transferred to another molecule, such as
gelatin, where it becomes so stable that further interactions effectively stop.
Figure 3.3: A schematic of a proposed initiation reaction mechanism. Paired electrons are shown as blue dots, while unpaired electrons are red dots. In this illustration, a hydroxide radical is the primary radical, but the primary radical may also be a hydrogen atom with an unpaired electron. Further, in this diagram the primary radical attaches to the carbon with the least number of bound hydrogen atoms (because it is the more dominant interaction) though it is also possible for the primary radical to attack the other sp2 carbon.
47
Table 3.3: Simplified free radical polymerization reactions of the NIPAM/Bis dosimeter
1. Initiation
(1)
2. Propagation
a. Propagation
(2)
or
(3)
b. Crosslinking
(4)
c. Cyclization
(5)
3. Termination Reactions
a. Bimolecular termination (Disproportionation)
(6)
b. Transfer to monomer
(8)
c. Transfer to Gelatin
(9)
48
=
Figure 3.4: For simplicity the body of the polymer chain can be replaced with the symbol P.
Figure 3.5: A proposed reaction mechanism for a propagation interaction involving the addition of a NIPAM monomer molecule. Unpaired electrons are shown as red dots, while paired electrons are represented by blue dots. In this illustration the free radical attacks a sp2 carbon on a NIPAM monomer molecule, however it may also interact with an sp2 carbon from a cross-linker molecule or another polymer chain.
Figure 3.6: A possible combination termination reaction stopping the growth of a polymer chain. In this reaction, the two unpaired electrons interact to form a covalent bond combining a hydrogen radical and the polymer chain. In another set of chain termination reactions, known as disproportionations (or bimolecular termination), the two reactants interact to change their electronic structure forming two new molecules.
49
Chapter 4 Materials and Methods
This chapter describes the experiments performed during this work. The materials and
equipment used in these experiments are presented in Section 4.1. The γ algorithm is described in
detail in Section 4.2, while the various dose validation experiments are laid out in section 4.3.
4.1 Materials and Equipment
The equipment used to prepare, irradiate, and probe polymer gel dosimeters is now
described as it pertains to the research presented in this thesis. Detailed explanations of the
operational principals of the equipment are not provided.
4.1.1 Preparation of Polymer Gel Dosimeters
NIPAM/Bis polymer gel dosimeters were prepared by a method similar to that described
by Senden et al. 2006. However, the original formulation was modified in order to reduce
background polymerization and improve optical scanning (Olding et al. 2007). The following
procedure outlines the preparation of 2 L of NIPAM/Bis gel. This provides sufficient active
material to make two 1 L gel dosimeters, one for calibration and the other for measurement.
Two solutions, A and B, were simultaneously prepared in a fume hood. 40 g of NIPAM
and 380 g of de-ionized water were mixed together in a 500 mL Erlenmeyer flask (solution A).
The Erlenmeyer flask was covered with parafilm and set in a dark location to allow the NIPAM
to dissolve. In a separate flask, 100 g of 300 bloom gelatin powder was allowed to swell in 1400
g of de-ionized water for 10 minutes (solution B). Solution B was then heated to 50 ºC under
continuous stirring by a magnetic puck. 40 g of N, N’-methylene-bisacrylamide (Bis) was then
added to Flask B. Usually, some of the Bis adheres to the mouth of the flask as it is poured in. A
50
small amount of de-ionized water, 36.7 g, was set aside to wash down any dry chemicals stuck to
the mouth of the flask. After the crosslinker had dissolved completely, solution B was cooled to
34 ºC. 3.3 g of THPC was added to solution A. Solution A and B were then combined and
stirred for 1 minute. Finally, the combined solution was evenly divided between two 1 L
polyethylene terephthalate (PET) jars and refrigerated 12 hours prior to irradiation.
4.1.2 Dosimeter Irradiation
The polymer gel dosimeters and phantoms described above were used to measure a
variety of teletherapy (external beam) radiation deliveries. Two therapy units were used for this
purpose; a Theratronics (Kanata ON), Theratron 780C (T780C) cobalt therapy unit and a Clinac
21iX (Varian Medical Systems, Palo Alto, CA) linear accelerator.
The radiation source of the T780C is based on the decay of the radioactive isotope of
cobalt Co-60. Co-60 undergoes beta decay to Ni-60 through the emission of a β- particle (an
electron) and an anti-electron neutrino. The Co-60 beta decay transition energy is approximately
318 keV and has a half life of 5.27 years. The resulting Ni-60 nucleus is in a highly excited state
that rapidly decays to a more stable state through the emission of γ-photons that constitute the
useful part of the treatment beam. The dominant photon energies are 1.17 MeV and 1.33 MeV.
Conventionally, the average photon energy 1.25 MeV is specified in reference to cobalt therapy
devices and the beam is described as monoenergetic. The actual spectrum of a treatment beam,
shown in Figure 4.1, contains a range of photon energies resulting from photon interactions
within the treatment unit (Joshi et al. 2008). The T780C source shown in Figure 4.2 is a 20 mm
diameter cylindrical capsule of many Co-60 pellets (Joshi et al. 2007), its activity in July 2005
was approximately 426.1 TBq. The T780C has movable components, the gantry, treatment
51
bench, and treatment head, which may be translated and rotated in order to effectively target the
treatment volume with the beam.
Figure 4.1: Monte Carlo (MC) simulated spectra for 10x10 cm2 photon beams of Co-60 and X-ray photons from a linac operating at 6 MV at the depth of 10 cm in water at the SAD’s (Joshi 2008).
Figure 4.2: (Left) A photograph of a Cobalt 60 source capsule and pellets (Best Theratronics Ltd. Ottawa ON). The source is 28 mm long and 20 mm in diameter. The pellets are also cylindrical, they are 1 mm long and 1 mm diameter. (Right) A photograph of the T780C Cobalt therapy machine at the CCSEO.
The unit has been modified (Schreiner et al. 2003), in order to perform more modern
conformal deliveries. The couch is shifted out of position, and is replaced with an in-house
benchtop tomotherapy unit. The benchtop apparatus is similar to the prototype device originally
52
tested by T.R. Mackie’s group: It consists of a single translational stage, and a rotational stage
upon which the gel phantom sits (Mackie et al. 1993). The entire apparatus sits atop a bench
which allows vertical translation. In-house software written in LabView (National Instruments
Corporation, Austin, TX) controls the vertical, rotational and translation motion of the system.
The T780C gantry is rotated to 90º, such that the target is irradiated laterally. A 1x1 cm2 pencil
beam field at 80 cm source-to-surface distance (SSD) is generated by mounting a cerrobend (lead
alloy) pencil-beam collimator block in the accessory holder and closing the collimator jaws to
their minimum setting. These modifications allow computerized control of pencil beam
placement within a phantom, in a manner analogous to serial tomotherapy, while the beam and
gantry remain stationary. Unlike standard serial tomotherapy units, the system does not use a
multileaf collimator to modulate the Co-60 beam intensity; instead modulation is achieved by
shifting the phantom through the beam and pausing for predetermined dwell times. In this
fashion a closed shutter is achieved by rapid adjustment of the phantom position between pauses,
or by translating the phantom out of the beam. In order to reduce the dose delivered during these
transition periods a lead beam blocker can be included. To achieve the same dose with the beam
blocker is in place, the predetermined dwell times must be increased.
The Clinac 21iX is a linear accelerator which uses high energy electrons (with velocities
that approach the speed of light) to produce a high energy X-ray beam for teletherapy. With the
Clinac 21iX, the electrons themselves can provide radiation beams with a range of treatment
energies. However electrons have a relatively shallow penetration depth, and are appropriate for
treatment of superficial disease. To treat deep seated tumours, the electrons are directed into a
target within the treatment head in order to produce high energy Bremsstrahlung X-rays. The
Clinac 21iX at the CCSEO can provide either 6 MV or 15 MV photon beams. The
53
Figure 4.3: (Left)Photograph of the Co-60 tomotherapy setup. The primary components of the setup include: A T780C radiotherapy unit, a cerrobend pencil beam collimator (right) used to define a narrow beam, a gel dosimeter phantom, and a bench-top tomotherapy apparatus to adjust the position of the phantom.
0
25
50
75
100
0 5 10 15 20Depth (cm)
Rela
tive D
ose (
%) 15MV Photons
20MeV Electrons
Figure 4.4: (Left) A photograph of the Clinac 21iX (Varian Medical Systems, Palo Alto, CA). (Right) A comparison of the Clinac 21iX percent-depth-dose (PDD) curves for 6x6 cm2 teletherapy beams at 100 cm source to surface distance (SSD). A 15 MV photon beam profile is shown in blue, while the 20 MeV electron beam is shown in red. Both curves were obtained through ion chamber measurements in a water tank.
54
Bremsstrahlung X-ray spectrum produced by 15 MeV electrons from an accelerator is called a 15
MV beam. While the beam contains X-ray photons with energies up to 15 MeV, the average
energy of the spectrum is closer to 6 MeV.
The gantry and couch have a wide range of motion allowing radiation delivery from any
angle. The radiation dose to healthy tissue can often be reduced without compromising the
effective treatment by irradiating the target area from several angles. The treatment head of the
Clinac 21iX contains a series of collimators which are used to control the size and shape of the
beam. The final collimation stage consists of an array of individual motor driven tungsten leaves
called a multileaf collimator (MLC). The MLC is used to carefully shape the beam at each angle,
conforming the radiation delivery to the target structure and shielding sensitive organs and
tissues. This is known as conformal radiotherapy. In addition, inverse planning software can be
used to optimize the radiation delivery through the MLC motion such that sensitive structures and
treatment volumes receive dose within predefined tolerances. This is known as Intensity
Modulated Radiation Therapy (IMRT).
4.1.3 Optical Scanning
Optical scans of gels were performed using a commercial cone beam optical computed
tomography unit, the Vista scanner (Modus Medical, London, ON). The basic components of the
scanner are a light box, a camera, an aquarium, a sample holder, and a stepper motor (see Figure
4.5). The light box contains two arrays of LEDs and provides amber or red illumination with
light wavelengths of 590 nm and 630 nm respectively. A sheet of plastic and a collimator film
diffuses and collimates the light. The sample holder has been specially designed to fit the PET
jars described in Section 4.1.1 coupling them to the stepper motor and firmly supporting them in
the aquarium. The aquarium is filled with liquid, in this case 12 wt.% aqueous propylene glycol
55
solution, that matches the index of refraction the NIPAM/Bis gel. Index matching is intended to
reduce refraction which causes artefacts in the reconstructed images. The aquarium glass panels
have a special anti-reflective coating to minimize scattered light. Finally, a 16 bit 1024x768 pixel
monochrome digital camera is firmly secured to a rail opposite the light box.
Figure 4.5: Photographs of the Vista scanner showing the outside features, and with the covers removed. The aquarium has been removed in the bottom image.
Light filters may be attached to the same rail on a wheel ahead of the camera. The scanner
operates as follows: Light originating from the light box (red or amber) is attenuated by
absorption and scatter as it passes through the aquarium and sample. The camera samples the
transmitted light by taking snapshot projection images of the jar. The stepper motor rotates the
sample in 410 increments allowing acquisition of transmission data over 360º. These projection
56
images are used to reconstruct the 3D data through the Feldkamp cone beam backprojection
algorithm (Feldkamp et al. 1984).
In order to correct for intensity variations in the light source, and to reduce reflection and
refraction artefacts, two scans are required for each 3D reconstruction. The first scan, the
reference, is performed on the unirradiated gel dosimeter while the second scan is performed after
irradiation. Each scan constitutes a set of matching 2D projection images evenly distributed over
360º. 2D transmission data is generated by comparing each reference projection to the
corresponding data image pixel by pixel according to the relationship shown below (from Beer’s
law).
−
−−=
00
lnD
D
II
IIT [Eqn. 4.1]
Where I and I0 are the respective data and reference projection pixel intensity and T is the relative
transmitted intensity used to reconstruct the image. ID and ID0 correspond to dark field snapshots
acquired with the light source off to account for variations in base level pixel response. In this
work, each scan is comprised of 410 projection images (~1.14/º) under red illumination and one
dark field snapshot. The Vista unit is computer controlled by commercial software through a
serial port.
4.1.4 X-ray Scanning
One series of experiments in this thesis involved simulating a prostate cancer treatment
using the gel dosimeter, for this work, two X-ray CT scanners were used. The first was a Picker
PQ 5000 large bore, fan beam CT scanner (see Figure 4.6). This special purpose “CT simulator”
is used clinically at the CCSEO to create X-ray attenuation maps of patients for treatment
planning purposes. The PQ 5000 was designed specifically for this role in treatment planning.
57
The second X-ray CT scanner is an integral component of the Clinical 21iX treatment unit known
as an on-board-imaging (OBI) system. The Clinac OBI is a cone-beam-computed-tomography
(CBCT) device. The clinical role of the OBI is to scan patients to ensure that their
posture/position matches that was used to create the plan. The experimental units are shown in
Figure 4.6, the experimental role of these devices is further discussed in Section 4.3.3.
Figure 4.6: (Left) The PQ 5000 large bore at the CCSEO, including the experimental setup. (Right) A photograph of the Clinac 21iX showing the OBI (a cone beam X-ray device).
4.2 The γ-Evaluation Algorithm
The 3D data sets under investigation contain between 1283 and 2563 voxels of dose
information. Manipulating these large data sets within a reasonable timescale requires computer
processing. Whenever possible, large data sets were handled using existing clinical software such
as the treatment planning software Eclipse, and the clinical/research data visualization system,
CERR (the description of these systems is left to the description of the prostate experiment in
Section 4.3.3). Nevertheless, developing software to work with the large amount of data stored in
the 3D images was a key facet of this project. The γ-evaluation permits rapid analysis of
agreement between distributions considering both dose and spatial tolerances. Because the
γ-evaluation is ideally suited for comparing large data sets, it was chosen to compare OptCT
measurements of dose distributions in gel dosimeters with distributions calculated by planning
58
software. Since a detailed definition of the γ-evaluation is included in Section 2.2, only the
algorithm used to calculate γ distributions is described here.
The in-house gamma algorithm was written in MATLAB (The Mathworks, Inc., Natick,
MA). The algorithm uses an expanding cube search technique that is similar to the algorithm
presented by Stock et al. (2005). Some of the modifications made by Wendling et al. (2007) are
also included. The present algorithm is similar to that reported by Stock et al. (2005), as γ values
are calculated as a voxel by voxel comparison between the reference and evaluated distributions.
The result is a matrix of γ-values that is dimensionally equivalent to the reference distribution.
Therefore, as discussed in Section 2.4.6, this implementation is sensitive to discretization
artefacts (Depuydt et al. 2002, Low and Dempsey 2003, Jiang et al. 2006). To reduce this failing,
the resolution of the evaluated distribution was set at 0.5 mm/pixel which is twice the grid
resolution recommended by Low and Dempsey (2003), and 6 times finer than the acceptance
criteria. As outlined in Section 2.4.6, the evaluated grid resolution sensitivity of gamma could
have been eliminated using software solutions based on interpolation methods (Wendling et al
2007) or geometric techniques (Ju et al. 2008). At the time of this writing, these techniques have
not been adopted by our group.
The in-house algorithm for a fast evaluation of γ in 3D begins in the same way as that
presented by Stock et al. 2005. First the dose difference between the point, rrv
, and the point with
the same coordinates in the evaluated distribution is calculated. If the dose difference is zero, the
search for the smallest possible value of ( )re rrvvv
,Γ is terminated; ( )rrvvγ is set to zero and the
evaluation proceeds with the next point in the reference image. If a non-zero dose difference is
found, the value ∆D2/∆D2M is saved as the variable 2
minΓ , since so far it corresponds to the
smallest value of ( )re rrvvv
,Γ that has been found.
59
The evaluated distribution is then iteratively searched for a smaller value of 2minΓ . The use
of 2minΓ instead of minΓ was adopted by Wendling et al. (2007) because it enhances the
efficiency of the algorithm. Searching for 2minΓ removes multiple computationally costly
evaluations of square roots as they are evaluated only once per reference position at the end of
each search. The speed of the γr
-evaluation is further enhanced by precalculating the distances
between the search origin and the neighbouring grid positions (within the maximum range) and
storing them in memory (Wendling et al. 2007). For each search, the coordinates of the
reference grid position, rrv
, define the search origin. After finding a non-zero dose difference, Г2
is calculated for each bordering voxel forming a hollow cube centred at the search origin with a
side length of 3 voxels, where
( ) ( ) ( ) ( ) ( )( )
∆
−+
∆
−+−+−=Γ
2
2
2
2222
M
rree
M
rerere
D
rDrD
d
ZZYYXX [Eqn. 4.2]
as shown in Table 2.1. If any new value of Г2 is found in the cube that is less than 2minΓ , then this
Г2 value replaces 2minΓ . The cube side length is then expanded by 2 voxels and the process of
calculating each Г2 is repeated, replacing 2minΓ as appropriate. To save computational time Г2 is
not determined for every grid position in the evaluated distribution, rather only for voxels in the
neighbourhood surrounding the search origin are checked. Once the neighbourhood has been
searched, the square root of the current value of 2minΓ is returned for ( )rr
vvγ and the process is
repeated for the next reference grid position until the entire γ-distribution is created. This method
is significantly more efficient than the original implementation, where for each reference point
every possible evaluated position is queried for Γ.
60
This implementation of γ uses two neighbourhoods. The dynamic neighbourhood is a sphere
with a shrinking radius, rd, that is defined by
22min
2Md dr ∆×Γ≡ . [Eqn. 4.3]
Both Stock et al. (2005) and Wendling et al. (2007) showed that it is impossible to find a smaller
value of ( )re rrvvv
,Γ beyond this radius no matter what the dose difference is. When the entire
dynamic neighbourhood is checked, the smallest ( )re rrvvv
,Γ value is always found. This is why it
is not necessary to check every voxel in the evaluated distribution in the search for the smallest
( )re rrvvv
,Γ . Since the size of the dynamic neighbourhood for each iteration is defined by 2minΓ , the
number of operations (i.e., the processing time) depends on how well the distributions are in
accordance (Wendling et al. 2007). If the agreement is particularly bad, there may be little value
in performing an exhaustive search for the smallest possible 2minΓ (Wendling et al. 2007). To
avoid exhaustive searches in very poorly agreeing dose distributions a fixed maximum search
radius is set prior to calculation. This second neighbourhood has a fixed size. Employing a
maximum search distance is not a new idea (Harms et al. 1997; Depuydt et al. 2002; Wendling et
al. 2007). The search is terminated when all the evaluated grid positions in one of the
neighbourhoods -whichever is first- have been queried. For the research presented in this thesis,
a maximum neighbourhood (radius) of 9 mm was employed for comparing 3D distributions.
For comparisons between 2D dose distributions, the search neighbourhoods are defined by
circles instead of spheres. Similarly, the search pattern can be described as an expanding square
rather than a cube. A pictorial representation of the search algorithm for γ in 2D is shown in
Figure 4.7. A flow diagram for the gamma evaluation (which does not include a maximum
search limit) is shown in Figure 4.8. As an enhancement of the γ-tool presented by Stock et al.
61
(2005), all of the vector components of γ are returned in this implementation of the algorithm
along with the magnitude information. Comparisons between dose distributions with 2 spatial
and one dose dimensions (2+1)D yield a 3D vector field comprised of two distance and one dose
components. Therefore, γ-vectors for (2+1)D comparisons have three components: ∆X, ∆Y and
∆D. Similarly, γ-vectors for comparisons between dose distributions with 3 spatial and 1 dose
dimensions (3+1)D have four components: ∆X, ∆Y, ∆Z and ∆D. In both cases the algorithm
returns components that are normalized to the tolerance criteria (e.g., 3%3mm).
Figure 4.7: The 2D search pattern for the smallest Г in the neighbourhood surrounding the search origin is demonstrated above. When a non-zero dose difference is measured at the search origin, the expanding square search is initialized. New pixels to be queried are shown in dark gray, while previously sampled pixels are shown in light gray.
62
Figure 4.8: Flow diagram showing the software process of our in-house gamma evaluations.
Start at new reference grid
Position: rr
Calculate dose difference at search origin: ( ) ( )20
M
rree
D
rDrD
∆
−=Γ
?00 =Γ
0=rγ
( )202min Γ=Γ
Initialize Search Cube Sidelength, 1=b
2+= bb
( ) 2min
2
2 Γ≤b ? ( )2minΓ=rγ
On cube surface, start at new evaluated grid
Position: re
Find grid distance from search origin,
2
2
∆
−=
M
re
d
rrd
2min
2 Γ≤d ?
Calculate sample gamma:
( ) ( ) ( ) 22
2,
∆
−+
∆
−=Γ
M
re
M
re
reD
rDrD
d
rrrr All cube surface
voxels checked?
Find smallest sample gamma, 2nΓ
2min
2 Γ≤Γn?
All reference
voxels
checked?
E�D
Yes
No
No
Yes
Yes
No
No
No
No
Yes Yes
Yes
22min nΓ=Γ
63
4.3 Dose Evaluation Experiments
In this section, the simulations and irradiations used to test the utility of the vector algorithm
are outlined. The procedures for performing and validating three independent radiotherapy
deliveries with gel dosimetry are described. The deliveries simulate cobalt tomotherapy, and two
conformal prostate deliveries Further, more techniques used to calibrate OptCT attenuation
measurements of irradiated gel dosimeters to dose are explained as are experiments to investigate
the calibration reliability.
4.3.1 Interpreting Dose Distribution Disagreements
A series of computer simulations were performed to determine if the vector information
could be used to help identify the sources of clinical dose distribution disagreements. The 2D
γ-vector evaluation tool was assayed on test images under a variety of manipulations. Each test
involved modifying the original distribution and comparing it back to the unmodified image using
the γ-vector algorithm. The modified and unmodified distributions corresponded to the evaluated
and reference images respectively.
First the vector algorithm was tested for consistency with the original implementation
described by Low et al. 1998. The vector algorithm was applied to a pair of test distributions,
shown in Figure 4.9, that were used to evaluate the original gamma comparison (Low and
Demspey, 2003). The two distributions were generously provided by Daniel Low, of the
Department of Radiation Oncology, Washington University School of Medicine and are identical
to the data sets in their published work (Low and Dempsey 2003, Ju et al. 2008). The reference
distribution simulates a projection through a 10x10 cm2 field from a 6 MV beam incident on a
water phantom. Low and Dempsey (2003) obtained the evaluated distribution by modifying the
quadrants of the reference image in the following way: Quadrant 1 is unmodified. A spatially
64
dependant multiplicative dose shift is applied to quadrant 2 that is governed by the off-axis
distance, x, according to
xDose 012.0=∆ .
Quadrant 3 is space shifted by a function that is similarly governed by the off-axis distance such
that
xy 12.0=∆ .
Both of these modifications are applied to quadrant 4. Since the grid resolution is 1 mm2/pixel, 3
% dose disagreement and 3 mm distance to agreement occurs at x = ±2.5 mm in quadrants 2 and
3 respectively.
Low and Dempsey’s (2003) square field was also used to explore the effect of dose
perturbation on the resulting vector field. Simulated double Gaussian dose distributions were
created in MATLAB and added or subtracted from the region of uniform dose in the centre of the
square field (see Figure 4.10). In other words, a region of disagreement was imposed onto the
otherwise identical evaluated distribution. The double Gaussians had an amplitude of 15 % of the
Figure 4.9: The test distributions provided by the Department of Radiation Oncology, Washington University School of Medicine: (Left) the reference distribution. (Right) the evaluated distribution (Adapted from Low and Dempsey 2003; Ju et al. 2008).
65
maximum reference distribution dose (i.e., 0.15 Gy), and standard deviations of 15 and 30 pixels
in the y and x dimensions respectively. In a complementary pair of tests, the reference image was
uniformly shifted by 15 cGy (with additive and subtractive doses in separate tests). A double
Gaussian was the added to the region shifting the dose back towards the original value (see Figure
4.11). In other words, a region tending towards agreement was imposed onto an otherwise dose
shifted evaluated distribution. These double Gaussians also had amplitudes that were 15 % of the
maximum reference dose, but with standard deviations of 5 pixels in the x and y directions.
Figure 4.10: The reference distribution (left) is modified by adding/subtracting a double Gaussian dose distribution (middle) creating an evaluated distribution (right) with a central region of disagreement.
Figure 4.11: The reference distribution (left ) is modified by uniformly shifting the dose by 15cGy and then adding/subtracting a double Gaussian distribution (middle) to bring the central region of the evaluated distribution back towards agreement.
Another set of tests was performed to investigate the vector field response under
disagreements more similar to those that would appear in a clinical scenario. Simulated dose
66
errors, in the form of double Gaussians with amplitudes of 45 cGy (15 % of the reference
maximum) were imposed onto a simulated head and neck distribution at separate locations
corresponding to the surrounding tissue, target, avoidance structure, node, and the target
boundary area (see Figure 4.12). The last set of tests involved uniformly translating the head and
neck distribution along each of the three image dimensions one at a time (dose is the third
dimension), and comparing it back to the unmodified reference distribution. Forty misalignments
between -20 and 20 pixels were imposed along each spatial axis. An additional forty
misalignments were imposed along the dose axis between -30 and 30 % of the reference
maximum. For all cases, over a total of 120 trials, the entire γ-distribution was used to calculate a
mean value for each γ-vector component.
Figure 4.12: The head and neck test distribution (Dhanesar 2008). (Left), a geometrical representation of the treatment geometry. The target volume is shown in yellow, the node in green and the avoidance structure in red. (Middle) The planned treatment distribution is used as the reference distribution. (Right) The head and neck distribution (simulated using in-house planning software) has five regions corresponding to the positioning of the double Gaussians.
4.3.2 Calibration
Calibrating Optical CT attenuation maps of gels to dose is an important step in
implementing gel dosimetry as a validation technique. The primary calibration method utilized in
this work is an adaptation to that presented by DeJean et al. (2006b). Three dimensional OptCT
attenuation maps of gels were calibrated to dose using software written in MATLAB for the
purpose of this project. For each polymer gel dosimeter used for treatment validation, a second
67
identical dosimeter -a calibration gel- was prepared using the same batch of gel solution. The
calibration gel was irradiated using the Co-60 tomotherapy apparatus described in Section 4.1.1.
A simple calibration pattern of three intersecting pencil beams (see Figure 4.13) was delivered at
the top middle and bottom of a calibration gel. OptCT measurements of these three identical
distributions were compared to 2D treatment plans calculated by in-house treatment planning
software (Gallant 2006). In-house software -written for the purpose of this research- was then
used to select a slice through the central plane of each measured pattern yielding a two
dimensional map of attenuation data corresponding to the planned delivery. Slices were
registered to the 2D dose plan using computer selected point based registration (a tool written in
MATLAB for the purpose of this research). Calibration curves containing approximately 3000
points were obtained by matching data along the 4mm beam centres of the planned and measured
distributions.
Figure 4.13: (Left) a top view of the three beam calibration pattern plan. (Right) a maximum intensity projection (MIP) image of the planned three pattern delivery.
68
R2 = 0.9926
0
200
400
600
0 25 50 75 100 125
Optical CT Number
Do
se
(c
Gy
)
σ = 12.3664
Figure 4.14: (Left) a top view of the OptCT measurement of the calibration delivery. The beam centres and low dose regions are shown with red borders. (Right) the regions shown on the left are compared pixel by pixel with the plan to build a calibration curve. A 2nd order polynomial fit to the data is shown in red, along with the corresponding R2 value and the standard error.
Additional data were added to the calibration curve through matching areas within the low dose
regions of the two distributions. A fifth order polynomial fit was generated for each calibration
curve and used to calibrate OptCT numbers to dose. Because each gel dosimeter was prepared by
hand, there was some degree of variation in composition between batches. It follows that there
must also be variation in dose response between individual formulations of the same nominal
composition. Other factors, including thermal history irradiation temperature and time to
irradiation have been shown to affect the dose response of similar polymer gel dosimeters (De
Deene et al. 2007). The reproducibility of the 4%T 50%C formulation was investigated through
21 calibrations in 9 dosimeters. Of the nine dosimeters, two were prepared from the same batch
of gel solution in order to examine the intra batch variations in dosimeter response. In one trial, a
different calibration technique was attempted whereby the dosimeter was irradiated from the top
with a 6x6 cm2 field of 20 MeV electrons. The electron percent-depth-dose (PDD) measurement
was then compared with the OptCT data in order to correspond optical attenuation to dose.
69
4.3.3 Simple Delivery Validations in 3D
Polymer gel dosimeters were used to preserve 3D radiation dose distributions created
with the Clinac 21iX and the Theratron 780C. Afterwards, optical attenuation maps of the
irradiated dosimeters were obtained through measurement with the Vista scanner and calibrated
to dose as described above. The process of using the radiation dose response and optical
properties of polymer gel dosimeters for verifying dose distributions calculated by treatment
planning software is described in this section.
The cobalt tomotherapy apparatus described in Section 4.1.1 was used to irradiate the
dosimeters with simple dose patterns, such as the intersecting pencil beam calibration pattern
(Figure 4.13). The beam placement (time, angle and translation) required to produce these
patterns has been used before (Gallant 2006). Forward planning software, using models based on
ion chamber measurements of the pencil-beam profile and depth dose, were used to calculate the
expected dose distribution based on the shape and density of the polymer gel dosimeter as well as
the dwell time, and stepper motor positions (Gallant 2006). So far, ion chamber measurements
and Monte Carlo simulations of the beam profiles have only been completed in 2D. The forward
planning software assumes that the pencil-beam is symmetrical, yet the actual 3D shape is
unknown. Therefore, the forward planning software is known to calculate full 3D cobalt
tomotherapy dose distributions somewhat inaccurately.
Reference scans of each dosimeter were obtained with the Vista scanner prior to
irradiation. Afterwards, 6 fiducial marks were imprinted onto the gel dosimeters with a permanent
red marker. The tomotherapy software and the cross-hairs in the treatment field were used to
record the positions of the fiducial marks so they could later be identified in the 3D treatment
plan. Once the placement and dwell times of the pencil beams were uploaded into the
tomotherapy computer the dosimeters were irradiated using the experimental setup shown in
70
Figure 4.3 in Section 4.1.2. 24 hours after irradiation the second optical scan of the gel dosimeter
was obtained with the Vista OptCT system. The two sets of optical scans were used to
reconstruct a 3D optical attenuation image of the dose distribution. Attenuation images were
imported into MATLAB for calibration and comparison with calculated distributions. In-house
registration software written in MATLAB for the purpose of this research was used to align the
measured distribution with the cobalt tomotherapy plans by aligning the measured locations of
the fiducial marks with their recorded positions. After registration and calibration the measured
dose distributions were compared with calculated distributions using dose difference and gamma
comparisons to test the agreement within tolerance criteria (3% 3mm). For these comparisons the
maximum neighbourhood limit was 15 mm.
4.3.4 Clinical Implementation of Delivery Validation
To more closely mimic a clinical treatment of an actual patient with planning, image
guidance and irradiation was performed on gel dosimeters incorporated into the AQUA phantom
(Modus Medical, London, ON) the gel dosimeters. The AQUA phantom was used for two
purposes: 1) to simulate the geometry of a human torso. 2) to facilitate X-ray CT scanning in
order to use clinical planning software. The AQUA phantom, shown in Figure 4.15, is a water
tank consisting of PMMA (Polymethyl methacrylate). The radiological properties of tissue (at
therapeutic photon energies) are simulated throughout the tank volume by filling it with water. A
steel arm (outside of the radiation beam) clamps onto the PET dosimeter jar and allows
positioning anywhere within the tank. Horizontal and vertical scores on the PMMA surface allow
alignment with intersecting room lasers such that the setup geometry can be replicated with a
tolerance of 1-2mm. X-ray CT scans and LINAC deliveries are performed in different rooms. To
achieve a treatment matching the plan it is critical to set up the experiment in the exact same
position as in the X-ray CT suite.
71
Figure 4.15: Photographs of the AQUA phantom used for simulating the human torso in irradiations and CT scans (Modus Medical, London ON). The tank is filled with water to achieve approximate tissue equivalence, while a steel arm holds the gel dosimeter in place for 3D dose measurements.
In two experiments the phantom was treated as a patient undergoing conformal prostate
therapy with image guidance. Procedurally the phantom underwent the same stages as a cancer
patient receiving radiation therapy. X-ray CT scans were used to develop a treatment plan in
Eclipse (Varian Medical Systems, Palo Alto, CA) and the plan was delivered using the Clinac
21iX. Eclipse is the modern treatment planning system used clinically at the Cancer Centre of
Southeastern Ontario for all patient radiotherapy planning. The conformal prostate experiments
represent an actual 3D treatment validation as 7-field conformal prostate therapy with image
guidance is not yet available at the CCSEO.
To obtain the dose information from the gel dosimeter in these experiments the
procedure was slightly different than described previously for the Co-60 tomotherapy simulation.
Before the polymer gel dosimeters were prepared, the empty jars were filled with distilled water
and imprinted with 6 fiducial marks. Metal beads were fixed over the red fiducial marks with
masking tape. The jars were then placed in the AQUA phantom and scanned with the CT
simulator as shown in Figure 4.6. Intersecting room lasers in the CT simulator suite were
72
carefully aligned to the cross shaped score marks on the surface of the AQUA phantom. After
X-ray CT scanning, the water in the jar was replaced with 4%T 50%C NIPAM/Bis polymer gel
dosimeter solution, and the metal beads were removed. Reference scans were performed after the
gelatine matrix set (after ~24 hours in the laboratory refrigerator). The beads were replaced after
scanning.
With the X-ray CT data set it was possible to clinically plan and deliver conformal
radiation deliveries to the AQUA phantom setup. Eclipse was used to calculate dose distributions
based on the X-ray attenuation data collected by the CT ssimulator. Because the phantom lacks
any real anatomy, anatomical information from an anonymous patient was copied onto the X-ray
CT scan of the AQUA phantom to more closely simulate clinical geometry. An oncologist had
already contoured the prostate, rectum, and bladder based on the patients X-ray CT scan,
allowing these structures to be copied into the experimental delivery plan (see Figure 4.16).
These structures were considered as targets and organs at risk in planning two seven field 15 MV
prostate treatments with the clinical treatment planning software known as Eclipse (see Figure
4.17). In the first plan, the prescribed dose to the prostate is 4 Gy, while in the second it is 3 Gy.
This dose was chosen to establish the best conditions for the gel dosimeter readout. Otherwise
the two plans are identical. Each field is 10x10 cm2 with MLC leaves conforming to the
planning-target-volume (PTV) surrounding the prostate contour (see Section 5.3.2). The PTV has
the same general shape as the prostate, and was derived by defining a surface 1.5 cm distal to the
prostate surface.
After creating the plan, and preparing the gel dosimeter solution, the AQUA phantom and
the dosimeter were setup for irradiation in the Clinac 21iX radiotherapy suite (see Figure 4.18).
Intersecting room lasers were used to setup the phantom as in the X-ray CT suite. However, to
further ensure that the geometry of both setups matched, an X-ray cone beam CT scan was
73
Figure 4.16: An X-ray CT image of the AQUA phantom and gel dosimeter insert from Eclipse. (Left) the large image is a transverse view showing the prostate rectum and control volume contours in pink blue brown and blue respectively. (Right top) coronal view of the X-ray CT 3D data. (Right middle) sagittal view of the X-ray CT 3D data. (Right bottom) 3D image showing anatomical structures.
performed with the OBI. The intent of this image guidance step clinically is also to attempt to
correct for potential displacement of the internal target (prostate with margins) relative to the
external landmarks. Superposition of the OBI scan and the original CT scan allowed detection of
inconsistencies between the two setups. Translating the treatment couch and moving the AQUA
phantom into position accordingly eliminated any setup errors unaccounted for by laser
alignment. After carefully setting up the AQUA phantom, the seven field treatment was
delivered according to the plan. The fiducial beads were removed and the dosimeter was left to
develop in a dark place for 24 hours prior to optical scanning.
74
Figure 4.17: 7-field 15 MV conformal prostate treatment plan from Eclipse. (Top left) transverse view. (Bottom left and right) coronal view and sagittal view. (Top right) 3D image showing the field and anatomical structures. The prostate is pink, the rectum brown and the bladder light blue.
The reconstructed 3D dose image from the OptCT readout was imported into MATLAB
and calibrated as in the cobalt tomotherapy validation. However, an important difference from
the Co-60 tomotherapy procedure was that the position of the fiducial marks was only known in
the X-ray and OptCT scans. The measured OptCT distribution was therefore registered to the
OBI image, not to known coordinates in the treatment plan. Though it was possible to register the
OptCT measurement to the original CT scan, the OBI image has greater resolution than the Picker
5000 and therefore measures the metal fiducial positions more precisely. The clinical CT
scanners save the scan data in DICOM format. Before the X-ray scans can be used to correlate
fiducial positions in the OptCT image, the DICOM data must be imported into MATLAB. This
was done using the Computational Environment for Radiotherapy Research (CERR) toolkit
(University of Washington, School of Medicine, St. Louis). CERR is a software toolkit written in
75
MATLAB that hs been specifically developed for research in radiotherapy. As such it has a
variety of tools that facilitate visualization of radiation dose and anatomical scans. The CERR
toolkit was also used to import the anatomical structures and treatment plans from Eclipse to
MATLAB. In-house software tools were then used to register and calibrate the OptCT
attenuation maps of polymer gel dosimeters to dose. The registered and dose calibrated OptCT
data was then imported into CERR using in-house software tools written in MATLAB. Once in
CERR format, the measured dose data was normalized at isocentre to the planned distribution.
The CERR toolbox also includes a dose-volume-histogram (DVH) tool which permits convenient
non-spatial volume analysis of relatively complex anatomical structures, such as the prostate
bladder and rectum. After performing 3D γ-analysis and uploading the γ-distribution to CERR
with in-house software, the DVH tool was used to create cumulative dose volume histograms and
gamma volume histograms (GVH)’s for every structure.
Figure 4.18: A photograph of the experimental setup for the 7-field conformal prostate delivery. The AQUA phantom, with a polymer gel dosimeter insert, are shown on the Clinac 21iX treatment bench. The OBI apparatus is engaged and in position to perform cone beam X-ray CT scans.
76
Chapter 5 Results and Discussion
In this chapter, the results from the experiments described in Chapter 4 are presented
while their implications and importance are discussed. In the first section (Section 5.1), the
results from the performance testing of the in-house γ-vector algorithm developed by the author
for the evaluation of delivered dose distributions are presented. In Section 5.2 the results and
accompanying discussion from the calibration experiments for polymer gel dosimeters are
reported. These dosimeters were used to make high-resolution 3D dose measurements of
clinically relevant dose deliveries, which were compared with distributions calculated by
treatment planning software ( Eclipse). Section 5.3 reports on polymer gel experiments which
were designed to illustrate the clinical utility of the γ-vector algorithm are presented.
5.1 The Response of the γ-Vector Field
5.1.1 Validation of the γ-Algorithm
To compare two dose distributions, the new γ algorithm returns a map of γ magnitude
information that is also accompanied by the corresponding vector data (see also Section 2.4.7;
Section 2.6; Section 4.2). As outlined in Section 4.3.1 the test distributions used by Low and
Dempsey (2003) to evaluate the original γ-tool were compared using the new γ algorithm. A
qualitative comparison of the calculations made by the new in-house γ algorithm and the original
γ-tool is shown for Low and Dempsey’s test distributions in Figure 5.1. The corresponding
vector plot for the new comparison tool is shown in Figure 5.2. The γ-distribution from the
original implementation exhibits a characteristic pattern in each of the four quadrants.
77
Reference Evaluated
a.
b.
c.
d.
Figure 5.1: Gamma comparisons between test distributions used by Low and Dempsey (2003). (a) the reference distribution. (b) the evaluated distribution. (c) gamma magnitude distribution calculated with the original γ-tool (reproduced with permission from Ju et al., 2008). (d) gamma magnitude distribution calculated with the new in-house γ-tool.
Although the colour map is slightly different the colour wash plot of the γ-magnitude information
obtained from the new γ-tool shows the same characteristic pattern. A quantitative comparison
between each implementation of γ was not possible because the actual original γ-tool was not
available. However, the qualitative results indicate that the new algorithm returns γ magnitude
information that is comparable to the original γ-tool. The main advantage of the new algorithm is
that it also returns the complete γ-vector information, which, as will be shown later in this
chapter, is useful for identifying the cause of dose disagreements. Because our group at the
CCSEO has been the only group to explore the utility of component vectors of γ, there is no
standard format for presenting γ-vector information. The format of the vector plot shown in
78
Figure 5.2 was adopted as a convenient display of the γ-vector information for the purposes of
this research. It is not the only method to display the vector information and future investigators
are encouraged to explore new techniques for visualizing the vector field.
Figure 5.2: The γ-vector evaluation yields the same magnitude plot (Left), as well as the corresponding γ-vector information in component form (Right). The vector information shown on the right corresponds to the rectangular ROI on the top left corner of magnitude plot. The voids in the vector plot occur when the spatial components of γ are zero in magnitude.
The γ-vector plot shown in Figure 5.2 has some characteristics that should be explained so
that subsequent γ-vector plots presented as a part of this research can be properly understood.
First, to avoid confusion, the plot represents only a portion of the total vector field. The γ-vector
information is only shown for the green highlighted region-of-interest (ROI) in Figure 5.2. The
γ-vector information is presented in component form in the plot. The Dr∆ component is
represented by the contours while the arrows show the spatial γ components, Xr∆ and Y
r∆ .
Recall from Section 2.4.5, that Dr∆ represents the difference in dose between the evaluated grid
79
position and the reference grid position, e.g., from Table 2.1, ( ) ( )re rDrDDrrrrr
−=∆ . Since err
and
rrr
are not necessarily equal, Dr∆ is not equivalent to the dose difference as defined in Section
2.4.2. It is a common misconception to confuse the distance-to-agreement and dose different
components of γ with the actual dose difference or DTA values for a given point. The γ-
evaluation simultaneously uses both concepts to find the point in the evaluated distribution that is
most in agreement. To avoid confusion between these two seemingly similar definitions Dr∆ is
labelled as ∆D(re,rr) on the plot; it has units of percentage of the reference maximum. For
example, the γ-vectors in the region between the ∆D(re,rr) = 3% and ∆D(re,rr) = 4.5% contour
lines have Dr∆ values between 3.5 and 4 % of the maximum dose in the reference image. Also
recall from Section 2.4.5 that Xr∆ and Y
r∆ give the spatial separations along the X and Y
dimensions between the reference grid position, and the evaluated grid position that minimizes
the search for the smallest Γ. The vector arrows originate from each reference grid search origin
(see Section 4.2) and are indicative of the Xr∆ and Y
r∆ vector components. The arrows point
towards the evaluated grid position that minimizes the Γ search. The length of the arrows is
proportional to the magnitude of the vector sum of Xr∆ and Y
r∆ (i.e, the d
r∆ component, see
Table 2.1), though the actual scale is not given. When no arrows are given for a particular
location in the vector plot, the relative contribution of the spatial γ-vector components is nil.
As outlined in Section 4.2 (see also Section 2.4.6), aside from choosing a fine evaluated grid
resolution, neither the original implementation of the γ-tool nor the new γ-vector algorithm
employs any method to avoid discretization artefacts. Therefore, neither comparison tool yields
γ-values equivalent to the true analytical values. Low and Dempsey (2003) stated that
interpolating the evaluated distribution to a 1x1 mm2 grid (as in the test images shown in Figure
5.1) reduced the error in γ to less than 0.2 even in regions of high dose gradient (see also Section
80
2.5.6). Therefore, in clinical γ-comparisons, discretization errors may not present serious
problems particularly if the evaluated distribution grid resolution is high. Even though
interpolating to higher grid resolution yields γ-values with smaller associated error and may not
result in failure (i.e., a false γ>1), the effect of the discretization artefact is still evident. Using the
same test images shown in Figure 5.1, Ju et al., (2008) showed the reduction of ripples associated
with the discretization artefact (also apparent in Figure 5.1 and Figure 5.2) through the
application of their geometric technique and through interpolation techniques (Wendling et al.,
2007). Since only the magnitude information is considered in the standard γ-comparison
discretization artefacts, such as rippling, may not be significant unless they cause false
disagreement. On the other hand, the effects of discretization artefacts on the individual γ-vector
components are unknown, and as shown in Section 5.1.5, should be considered when using the
vector information to interpret dose disagreement these effects.
5.1.2 γ-Vector Field Response under Dose Perturbation
The square field test distribution (shown in Figure 5.1) was used for two additional pairs
of tests. As described in Section 4.3 double Gaussian dose distributions were added and then
subtracted from the centre of the test distribution creating two separate evaluation distributions.
Both of these distributions were compared with the original unchanged reference distribution
using the new γ-vector algorithm. The resulting γ-vector plots from these comparisons are shown
in Figure 5.3. The dose difference component of γ, ∆D, shows an increasing positive trend when
dose has been added (see Figure 5.3b) and a negative trend (see Figure 5.3c) when dose has been
subtracted. In these cases, ∆D, clearly indicates of both overdoses and underdoses. Further, the
magnitude of ∆D is related to the magnitude of the dose difference, as is shown by the contour
levels. In both the additive and subtractive tests the spatial components of the vector field show
positive divergence (i.e., the spatial vector components point away from the centre of the double
81
Figure 5.3: Vector analysis of double Gaussian dose errors in a region of uniform dose. The double Gaussian has a magnitude that is 15 % of the maximum value of the test distribution. (a) the test distribution showing a green ROI corresponding vector plots in b and c. (b) the γ-vector plot corresponding to the test where the double Gaussian dose error has been added to the test distribution. (c) the γ-vector plot corresponding to the test where the double Gaussian dose error has been subtracted from the test distribution (note all contours are negative percent difference in c).
Gaussian). The positive divergence occurs because the fringes of the region where the double
Gaussian dose distribution (positive or negative) has been added to the evaluated distribution are
more similar to the underlying reference distribution. For each point in the reference distribution
Γ is minimized through correspondence with evaluated points that are further from the centre of
the Gaussian peak or trough, because they have a smaller dose disparity with the reference image.
The spatial components of each γ vector are therefore directed towards regions in the evaluated
distribution that are in agreement with the corresponding reference position.
82
Considering the cause of positive divergence in the γ-vector field, it is not unreasonable
to expect negative divergence (i.e., the spatial vector components point inwards) when the
evaluated distribution disagrees with the reference distribution with the exception of a localized
region of agreement. In such a scenario the searches for the smallest Γ in the surrounding region
become minimized by correspondence with the same positions in the evaluated distribution.
Clinically, negative divergence in the γ-vector field may be useful for identifying false agreement
between distributions. For example, Low and Dempsey (2003) observed that noise in the
evaluated distribution caused underreporting of the average γ-value compared to the noise free
case. When an evaluated distribution that does not otherwise agree within tolerances with the
reference distribution has noise added to it, some locations in the evaluated distribution will be
brought into closer agreement with the reference distribution. Coupling the anomalous agreeing
evaluated position with neighbouring points in the reference distribution will minimize the search
for the smallest Γ. Therefore, regions of negative divergence in a γ-vector field may be
associated with a noisy evaluated image, possibly causing γ-values to be underreported.
The validity of the hypothesized cause of negative divergence in γ-vector field was tested
by creating a region of agreement at the centre of an evaluated test distribution which was
uniformly dose shifted with respect to the reference distribution axis by adding or subtracting
0.15 Gy, as explained in Section 4.3. A small central region of the square field was shifted back
into agreement by either adding or subtracting a double Gaussian with 0.15 Gy maximum.
Negative divergence in the γ-vector field in γ-comparisons can be seen when the dose in the
evaluated distribution for both positive and negative uniform dose shifts and a localized region of
agreement with respect to the reference (shown in Figure 5.4). Therefore, when interpreting γ-
vector plots positive divergence should be associated with a region of disagreement with respect
83
to the surrounding area, while negative divergence should be associated with a region of
agreement with respect to the surrounding area.
Figure 5.4: Negative divergence in γ-vector fields. (a) the evaluated distribution is created by uniformly shifting the dose in the reference distribution by 15%. (b) The γ-vector plot for the green ROI under a negative uniform the dose shift, with a central region of agreement. (c) The γ-vector plot for the green ROI under a positive uniform dose shift, with a central region of agreement.
5.1.3 γ-Vector Field Response to Gaussian Noise
Image noise, such as speckle, has the potential to cause localized regions of positive or
negative divergence, depending on the agreement of the underlying dose distributions. The
response of the vector field to zero mean Gaussian noise was tested by adding noise at levels of
variance between 0 and 100 % to test dose distributions. The plots in Figure 5.5 correspond to
noise testing of the cobalt tomotherapy test distribution shown in Figure 4.13. The mean
response of each γ-component vector to Gaussian noise is plotted as a function of noise variance.
84
-6
-3
0
3
6
0 25 50 75 100
Gaussian Noise Variance (%)
Mea
n G
am
ma
Vec
tor
Co
mp
on
en
t ∆r
∆D
-1
-0.5
0
0.5
1
0 25 50 75 100
Gaussian Noise Variance (%)
Me
an
Ga
mm
a V
ec
tor
Co
mp
on
en
t
∆X
∆Y
Figure 5.5: Plots showing the response of the mean γ-vector components to zero mean Gaussian noise. (Left) the mean values of the traditional γ-vector components ∆r and ∆D, are plotted as a function of the noise variance. (Right) the mean value of the spatial γ-vector components, ∆X and ∆Y are plotted as a function of the noise variance.
The individual mean spatial component vectors X∆ and Y∆ show no obvious trends with
increasing noise. The mean value of the net spatial separation r∆ increases much more rapidly
with increased noise variance than the net dose separation D∆ . This finding may be related to
the noise sensitivity of the γ-evaluation observed by Low and Dempsey (2003). Low and
Dempsey (2003) found that noise in the evaluated image caused an underestimation of γ. They
asserted that the addition of noise caused better apparent agreement than would be found in the
absence of noise. When noise is present in the evaluated distribution, anomalous points with
large disagreement (i.e., outliers associated with noise) are avoided in the search for the smallest
Г and do not significantly perturb the γ-distribution. However, when the underlying distributions
do not match, some outliers in the evaluated distribution associated with noise become better
points of agreement than would be found if the distribution were noise free. In this case, the point
of agreement in the evaluated distribution would also minimize Г for many neighbouring
reference positions. Both scenarios, especially the second, cause Γ to be minimized through
coupling with evaluated points that are further than usual from the search origin, leading to a
85
larger ∆r γ-vector component. In other words, noise in the evaluated distribution allows ∆D to be
minimized at the cost of ∆r, and as shown by Low and Dempsey (2003) also causes a net
underestimation of γ.
5.1.4 γ-Vector Field Response under Misalignment
Clinically, misalignments between physical measurement and calculated distributions
may arise due to improper registration between dose distributions or may be the result of a
geometric miss during the radiation delivery. The later situation is more serious; “missing” the
target volume potentially means that not only has the tumour not received proper therapeutic
dose, but that the surrounding healthy tissue and sensitive organs were irradiated. The
consequences for the patient may be clinically insignificant or grave, depending on the magnitude
and location of the geometric miss. 3D gel dosimetry coupled with γ-vector analysis may permit
the identification of dose misalignments caused by systematic errors.
A series of misalignment tests, described in greater detail in Section 4.3.1, were
performed in order to determine whether the γ-vector field could be used to predict dose
distribution misalignments. Specifically, the test distribution shown in Figure 4.13 was uniformly
translated along each of three dimensions (dose is the third dimension) in over 120 separate trials.
The results from the uniform translation trials for the test distribution are shown in Figure 5.6.
For spatial misalignments along both the X and Y axis the mean ∆r component of the γ-vector
dominates the mean ∆D component. Furthermore, the mean value of the individual vector
components corresponds to the direction of misalignment. For example, when the evaluated
distribution is uniformly translated along the Y-axis, the mean ∆Y vector over the entire γ-vector
field dominated over the mean ∆X vector. Similarly, when the evaluated distribution is translated
along the X-axis, the mean ∆X vector dominated over the mean ∆Y component. The mean
86
spatial vector components also indicated the direction of misalignment. Finally, when the
evaluated distribution is obtained by shifting along the dose axis, the mean ∆D component
dominated the ∆r component and it was also indicative of the direction of dose misalignment.
When dose was uniformly added to form the test evaluated distribution D∆ is positive and when
dose is uniformly subtracted to form the test evaluated distribution, D∆ is negative. The
correspondence between spatial component vectors and dose distribution misalignment direction
and magnitude indicates that γ-vector information can therefore be used for detecting spatial
misalignments between reference and evaluated distributions.
87
-2
0
2
4
-20 -10 0 10 20Y-Axis Misalignment (pixels)
Co
mp
on
en
t M
ag
nit
ud
e
∆r
∆D
-3
-2
-1
0
1
2
3
-20 -10 0 10 20
Y-Axis Misalignment (pixels)
Co
mp
on
en
t M
ag
nit
ud
e
∆Y
∆X
-2
-1
0
1
2
3
-20 -10 0 10 20
X-Axis Misalignment (pixels)
Co
mp
on
en
t M
ag
nit
ud
e
∆r
∆D
-2
-1
0
1
2
-20 -10 0 10 20
X-Axis Misalignment (pixels)
Co
mp
on
en
t M
ag
nit
ud
e∆Y
∆X
-4
0
4
8
-30 -15 0 15 30
Dose Shift (% of Maximum)
Co
mp
on
en
t M
ag
nit
ud
e
∆r
∆D
-0.4
-0.2
0
0.2
0.4
0.6
-30 -15 0 15 30
Dose Shift (% of Maximum)
Co
mp
on
en
t M
ag
nit
ud
e
∆Y
∆X
Figure 5.6: The mean component vector response to misalignments along each of 3 distribution dimensions (dose is the third dimension). Plots showing the response of the traditional γ-vector components ∆D and ∆r are shown in the left column, while the response of the additional spatial vector components is plotted in the right column.
88
5.1.5 Towards Clinical Application
Misalignment testing was also performed on other test distributions. While the results are
not presented in this research, the individual vector components show the same trends as can be
seen in Figure 5.6. Not surprisingly, the actual misalignment response (e.g., the magnitude of
each mean component vector) varies somewhat between dose distributions. This is because the
response of the γ-vector field also depends on the particular properties, such as the dose gradient,
of the underlying dose distributions. To begin to understand how the underlying distribution
might affect the γ-vector field, another dose perturbation experiment was performed (see Section
4.3.1). The same test distribution used in Section 5.1.4, which is a cobalt tomotherapy dose
distribution typical for a head and neck treatment, was manipulated by adding double Gaussian
dose distributions (see Figure 5.7 and Figure 4.13). The γ-vector plots shown in Figure 5.7
correspond to two separate comparisons. In the first case a double Gaussian overdose has been
added to a region (1) associated with surrounding healthy tissue, in the second case the dose has
been added to a region associated with the target volume (2). The γ-vector comparison plot for
(1) (Figure 5.7b) does not show obvious positive divergence, even though positive divergence is
apparent when the same manipulation was applied to the square field test distribution (see Figure
5.3b). Considering the spatial component vectors separately, the ∆X component of each γ-vector
is directed away from the Gaussian peak and is consistent with positive divergence. However,
the ∆Y components of the γ-vector field are oriented in the positive y-direction towards
decreasing dose in the underlying distribution. It is possible that the underlying dose gradient
produced an overwhelming response in the ∆Y component vector concealing what would have
otherwise resulted in positive divergence. The γ-vector field from the second comparison (i.e., at
the target volume) shows positive divergence as expected. However, there are two regions where
89
∆D(re,rr) is negative. These two negative regions were unexpected because the disagreement was
caused by additive dose.
Figure 5.7: The reference dose distribution representing the clinical head and neck treatment is shown on the left along with two regions of interest. The evaluated dose distribution, not shown, was created by adding double Gaussian dose disagreements to the regions. The γ-vector fields corresponding to the green regions are shown on the top and bottom right for regions 1 and 2 respectively. The red labels point to regions where ∆D(re,rr) is unexpectedly negative.
The two negative regions can be understood considering the discrete nature of the
evaluated distribution (see Figure 5.8). Because the evaluated distribution is not continuous, γ is
not representative of the true analytic minimum Г (see Section 2.4.6). While no mathematical
proof is given here, when comparing continuous distributions where the evaluated distribution is
overdosed with respect to the reference distribution, it is not possible to minimize Г by finding a
point in the evaluated distribution with less dose than the reference point. Similarly, when the
evaluated distribution has been underdosed with respect to the reference, it is not possible to
90
minimize Г by finding a point in the evaluated distribution with more dose than the reference
point. This new aspect of the discretization artefact of γ is an important consideration when using
the vector components of γ to diagnose the cause of γ>1. Without geometric or interpolation
solutions to the discretization problem, ∆D may not be representative of the actual dose
difference component. The effect of the discretization artefact on the spatial γ-vector components
is unknown, but it is likely that they are perturbed by discretization effects too.
Figure 5.8: A one dimensional γ-comparison between a reference distribution and an evaluated distribution. Both plot axes are normalized to the tolerance criteria, DM and dM, (e.g., 3 % and 3 mm respectively). The evaluated distribution has a uniform additive dose shift with respect to the reference distribution. At each reference point, Г is only determined by coupling the point with evaluated grid points. The smallest Г that is found this way must be larger than or equal to the true analytical minimum, which is shown as a red arrow in this diagram. Further, in the case of comparisons between discrete distributions, even under a purely additive dose shift it is possible to minimize Г by correspondence with a reference point that has less dose than the reference position.
5.2 Gel Calibration
The advantage of the γ-evaluation is that it allows rapid comparative analysis of large
data sets such as those made available with 3D dosimetry (see Section 2.4.5). In this research,
polymer gel dosimeters and optical computed tomography (OptCT) are used to measure absorbed
91
radiation dose in 3D with high spatial resolution. In this work 3D dose distributions obtained
from cone beam OptCT reconstructions can contain up to 2563 individual measurements. The γ
evaluation is a convenient analysis tool for such large data sets. However, the OptCT attenuation
data must be calibrated before any dose comparison techniques can be applied. In this section,
the results from a series of optical calibrations of the dose response of the 4%T 50%C
NIPAM/Bis polymer gel dosimeter are presented. The goal is to correlate the optical attenuation
measurements made by the optical CT scanner to the physical dose deposited in the dosimeter. In
Section 5.3, the new γ-vector algorithm and an in-house γ-tool capable of performing 3D analysis
are used to compare gel measurements to calculation.
5.2.1 Intersecting Pencil Beam Method
A typical calibration dose distribution delivered using the T780C and the tomotherapy
apparatus (see Section 4.1.2) is shown in Figure 5.9 (DeJean et al. 2006b). As described in
Section 4.3.2, to produce a plot of dose versus attenuation, a 4 mm thick profile along the centre
of each intersecting pencil beam in the OptCT measurement was correlated to the same positions
in the calculated distribution. Depending on the quality of the OptCT image, 5th order polynomial
fits mapping the OptCT data to dose were found to have a standard error of 1.3 - 2.9 % or 7 - 15
cGy when the maximum dose was ~520 cGy. The error is associated with noise in the
measurement of the dose pattern as well as with image artefacts such as ringing.
5.2.2 20 MeV Electron Beam Method
The reference dose information for the intersecting pencil beams was calculated using
in-house forward planning software (Gallant 2006). Although the forward planning software was
verified with ion chamber measurements and Monte Carlo simulations (Dhanesar 2008), the
calibrations were verified against an alternative technique. The technique is discussed briefly in
92
Figure 5.9: An attenuation to dose calibration for the Vista 4%T 50%C NIPAM/Bis dosimeter system. (Left) the 4mm beam centres and zero dose regions are highlighted in red on the OptCT measurement. (Right) a plot of dose versus attenuation including a 5th order polynomial fit to the data. The R2 value and standard error are displayed to show the quality of the fit.
0
25
50
75
100
0 5 10 15
Depth (cm)
No
rmali
zed
Do
se (
%)
Att
en
uati
on
20 MeV Electron PDD
(600cGy maximum)
Attenuation Profile
(50CT# maximum)
Figure 5.10: 20 MeV electron beam percent-depth-dose (PDD) curves. (Top left) a side view of the sagittal plane of the irradiated calibration dosimeter. (Bottom left) top view of the irradiated dosimeter showing the 6x6 cm2 square electron field. (Right) two sets of measurements of the 6x6 cm2 20 MeV electron beam PDD through the centre of the field. The red curve represents raw optical attenuation data, while the black curve represents absorbed dose. Both curves are normalized to 100.
93
Section 4.3.2. It involves irradiating a polymer gel dosimeter from the top with a 6x6 cm2 20
MeV electron beam. From the top to the bottom of the dosimeter, the dose along the centre of
electron beam is known as the depth dose which has been characterized with ion chamber
measurements through a water tank. The characteristic 20 MeV percent-depth dose (PDD) curve
obtained from ion chamber measurements has been plotted along the same set of axes as a line
profile through the centre of an OptCT measurement of an irradiated NIPAM/Bis dosimeter (see
Figure 5.10). The normalized optical attenuation for the 600 cGy (maximum dose) electron beam
delivery matches the ion chamber measurement of the PDD very well. Deviations occur in the
high and low dose regions near the top and bottom of the dosimeter respectively. In the high dose
region, the CT measurement appears to underreport the dose. This effect could be a scatter
related artefact (see Section 2.3.2), and might be corrected by employing scatter correction
techniques (Holmes et al. 2008; Olding et al. 2008; Jordan and Battista 2008). Image artefacts
due to reflections from the tank walls could also contribute to noise near the edges of the
dosimeter volume. A calibration curve was obtained from the two PDD’s by correlating optical
attenuation to measured dose at a given depth along the profile. The calibration is shown in red
in Figure 5.11.
5.2.3 Inter and Intra batch variability
Calibration data were collected over many experiments, for a total of nine independent
dosimeter calibrations of seven different NIPAM/Bis polymer gel batches. The fifth order
polynomial fits for all the calibrations are shown in Figure 5.11. The calibrations exhibit a wide
variation in dose response, up to 200 cGy for the same measured attenuation value. These
variations are attributed to minor preparation differences between batches. For example,
eventually chemical reactants need to be resupplied. In one set of experiments, there was a
notable reduction of N,M’-methylene-bisacrylamide solubility which lead to reduced dose
94
sensitivity and increased turbidity of the dosimeters. Differences in the quality of the chemical
reactants could be the cause for the apparent split in the dose response apparent in Figure 5.11.
Alternatively, the split may have been caused by differences in irradiation temperature,
specifically some dosimeters were irradiated soon after being removed from the laboratory
refrigerator while others were not. The thermal history, especially the cooling rate, of polymer
gel dosimeters has also been shown to be an important factor in their dose response (De Deene et
al., 2007). Position in the laboratory refrigerator, and fluctuations in the cooling and defrost
cycle may have lead to differences in the cooling history of each dosimeter. In any case,
producing polymer gel dosimeters with equivalent dose response between batches is not a trivial
task. Therefore, in order to achieve accuracy in 3D dosimetry each batch of NIPAM/Bis polymer
gel dosimeter should be calibrated independently.
0
200
400
600
0 10 20 30 40
Normalized Attenuation
Dose (G
y)
Cobalt
20 MeV Electrons
011408-03
Figure 5.11: The combined calibration data for the entire series of experiments presented in this research project. Calibrations made using the intersecting pencil beam technique are shown in black, while the 20MeV electron beam calibration is shown in red. For clarity in presentation, the data is presented as a series of 21 5th order polynomial trendlines.
95
Inter and intra batch variability tests revealed that the dose response of the NIPAM/Bis
dosimeter reproducible provided that the dosimeters are prepared under identical conditions.
Closely agreeing fifth order polynomial fits to calibrations made using the intersecting pencil
beam technique are shown in Figure 5.12. When the same batch of solution was poured into two
different dosimeter jars and independently calibrated using the intersecting pencil beam
technique, the dose response matched over the entire irradiated range to within 3.65 %. The
average difference between the polynomial fits was 1.67 ± 0.03 %, well within the combined
standard error of the fits ~4 %. When two separate dosimeter batches were prepared and
independently calibrated the polynomial fits to the dose response differed by as much as 11.3 %,
however the average difference of 4.38 ± 0.06 % was within the allowable ~4.6 % tolerance from
the combined standard error in the fits. Thus a suitable way of calibrating the polymer gel
dosimeters to dose is to prepare a second dosimeter jar containing the same gel batch. The
second jar can then be used to batch-calibrate the polymer gel dosimeter solution.
0
100
200
300
400
500
0 10 20 30 40
Normalized Attenuation
Do
se (
cG
y)
Top
Middle
Bottom
Top
Middle
Bottom
0
100
200
300
400
500
0 10 20 30 40
Normalized Attenuation
Do
se (
cG
y)
Top
Middle
Top
Middle
Figure 5.12: A set of carefully controlled calibration experiments. (Left) intra-batch variability in dose response for two jars containing the same batch of 4%T, 50%C NIPAM/Bis polymer gel dosimeter. Fifth order polynomial fits are shown for each calibration pattern in both jars. (Right) inter-batch variability in dose response for two jars containing different batches of 4%T, 50%C NIPAM/Bis polymer gel dosimeter. Fifth order polynomial fits are shown for each calibration pattern in both jars.
96
5.3 Validating Radiation Deliveries in 3D
In spite of the potential for measuring dose information in 3D, there are relatively few
studies reporting on the use of polymer gel dosimetry and optical computed tomography in their
intended clinical application (see also Section 2.5 and 2.6). To this end and for the objectives
outlined in Chapter 1, results of three radiation delivery validations using polymer gel dosimeters
and cone beam OptCT are presented here. The first delivery represents a proof of concept, and
was irradiated using the T780C and the cobalt tomotherapy apparatus as outlined in Section 4.3.3.
The next two deliveries simulate 7-field conformal prostate deliveries that have not yet been
clinically adopted at the Cancer Centre of Southeastern Ontario (CCSEO); where this research
was undertaken. The seven field prostate treatments were also used to test the new γ-vector
algorithm under a clinical comparison between an actual measured distribution and treatment
plan. Most of the quantitative and qualitative analyses of these deliveries were performed using
in-house software written in MATLAB by the author for the purpose of this research. However,
the Computational Environment for Radiotherapy Research (CERR) Dicom RT toolbox
(Washington University in St. Louis, School of Medicine) was used to create volume histograms
as well as convenient displays in which dose distributions and γ-comparison maps are
superimposed on top of X-ray CT data (see also Section 4.3.3). A significant amount of effort
was involved in preparing the OptCT data and corresponding 3D gamma distributions so that they
could be imported into CERR appropriately.
5.3.1 Cobalt Tomotherapy
Three simple dose distribution patterns representing the letters ‘A’ ‘K’ and ‘A’ were
delivered to a NIPAM/Bis dosimeter using the T780C and the benchtop tomotherapy apparatus as
described in Section 4.3.3. The registered and calibrated OptCT data was compared to the 3D
treatment plan created using in-house treatment planning software (Gallant 2006). The
97
calibration was made using the intersecting pencil beam technique. A complete 3D γ-comparison
between the two distributions is shown in Figure 5.13. In this comparison the distribution
calculated by in-house software is the reference distribution while the OptCT measurement is the
evaluated distribution.
a.
b.
c.
d.
e.
Figure 5.13: A 3D treatment validation using polymer gel dosimetry with OptCT. (Top row) 3D dose distribution MIP images for the reference and evaluated distributions, a and b respectively. (Bottom row) MIP images of 3D γ-distributions with tolerance criteria of 3% 3mm, 5% 3mm, and 5% 5mm c, d, and e respectively. The colour-bars indicate γ-magnitudes for each image.
98
Figure 5.14: The cumulative gamma volume histograms (GVH)’s for the cobalt tomotherapy validation is shown above. The x-axis represents the magnitude of the γ-value, while the y-axis represents the fraction of dosimeter volume with at least the corresponding gamma magnitude.
The OptCT measurement was analyzed for agreement with the reference distribution under three
separate tolerance criteria: 3% 3mm, 5% 3mm and 5% 5mm. In the volume histogram (see
Section 2.4.5 for clarification on volume histograms) shown in Figure 5.13, only the volume
corresponding to 90 % of the cylindrical diameter is included. The cumulative gamma-volume-
histogram (GVH) shows excellent agreement with the plan under all three sets of tolerance
criteria (see Figure 5.14). However, these results should be interpreted with caution. Most of the
dosimeter volume has not been irradiated, and the vast majority of the data corresponds to zero
dose. Further, from the maximum intensity profile (MIP) γ-images shown in Figure 5.13, the
99
majority of failing γ-values occur in locations where dose has been deposited. Cumulative
volume analysis over the irradiated region would likely yield a much less positive result. The
extent to which individual γ-values are depressed due to noise in the evaluated image is unknown.
Finally, the 3D version of the inverse planning software that was used to calculate the reference
distribution has not yet been fully commissioned and is known to be inaccurate. A certain
amount of disagreement between the measured and the calculated distributions was expected.
However flawed, this 3D validation represents a proof of method for verification of cobalt
tomotherapy through polymer gel dosimetry with cone beam OptCT.
5.3.2 Prostate Teletherapy / Interpreting Geometric Misses
This last section reports on experiments which were designed, in part, to illustrate the
clinical utility of the γ-vector algorithm. The experiments were also intended to demonstrate a
process for using polymer gel dosimeters and cone beam OptCT as a clinical dose validation tool.
In these studies, two seven field 15 MV conformal prostate treatments planned using Eclipse
were delivered to two polymer gel dosimeters in separate trials. The rectum, bladder, and
prostate contours for the target and organs at risk were established using an actual treatment plan
created for an anonymous patient at the CCSEO (see also Section 4.3.3). As per clinical practice,
two additional contours surrounding the prostate correspond to volumes with surfaces 0.7 and 1.5
cm away from the prostate surface. These correspond to the clinical tumour volume (CTV) and
the planning tumour volume (PTV) respectively while the actual prostate contour is the gross
tumour volume (GTV). In both conformal deliveries, the treatment plans were developed using
the PTV. The calculated dose distribution for the first plan has been visualized as a set of three
colourwash images using CERR (see Figure 5.15). This image, and all subsequent images
obtained from CERR are rotated by 90° for convenient display. The three views correspond to
the sagittal, coronal and transverse planes through the phantom and dosimeter volume. The
100
planned dose distribution is superimposed on top of the X-ray CT scan that was used to calculate
the delivery. Contours showing the GTV, CTV, PTV and the organs at risk are present in all
three images. Subsequent displays of dose information created using the CERR toolkit are
presented in the same fashion; in this image only the anterior/posterior and superior/inferior axes
are shown as a dashed line and labelled ‘a’ and ‘b’ respectively.
After irradiating the AQUA phantom containing the polymer gel dosimeter, the dose
distribution was probed with the Vista scanner, registered, calibrated and normalized. The
measured dose data were then imported into CERR as described in Section 4.3.3. The resulting
measured dose distribution is shown in Figure 5.16. The extremities of the dosimeter volume
spatially limit the extent of the dose information displayed in this image; that is, there is no dose
information beyond the boundaries of the jar. A disparity between the measured distribution and
the planned distribution is apparent in Figure 5.15. There appears to be a misalignment in both
the anterior/posterior and lateral directions, which is also indicated by the dose profiles along the
axes (see Figure 5.17). The inconsistency between the two distributions is a geometric miss. A
3D γ-comparison (shown in Figure 5.18) between the two distributions revealed that 51 % of the
distribution within the jar volume did not agree within 3% 3mm tolerances. This situation
represents a serious clinical scenario. The prostate would not have received proper therapeutic
dose, and the surrounding tissue would have been damaged.
101
CALCULATED DISTRIBUTIO� # 1
Fig
ure
5.1
5:
A 4
Gy
seve
n fi
eld
15 M
V c
onfo
rmal
pro
stat
e tr
eatm
ent
plan
cre
ated
for
the
AQ
UA
pha
ntom
. F
or
conv
enie
nt d
ispl
ay t
he i
mag
e ha
s be
en r
otat
ed b
y 90
°.
The
pla
nned
dos
e di
stri
buti
on a
nd X
-ray
CT
sca
n ha
ve
been
sup
erim
pose
d us
ing
CE
RR
. T
he c
olou
rbar
and
col
ourw
ash
imag
es i
ndic
ate
radi
atio
n do
ses
betw
een
0 an
d 4.
12 G
y.
The
lar
ge i
mag
e re
pres
ents
the
dos
e di
stri
buti
on i
n th
e sa
gitt
al p
lan.
T
he t
wo
smal
ler
imag
es r
epre
sent
th
e tr
ansv
erse
pla
ne (
abov
e) a
nd th
e co
rona
l pla
ne (
belo
w).
All
7 f
ield
s ar
e cl
earl
y vi
sibl
e in
the
tran
sver
se p
lane
. E
ach
stru
ctur
e is
rep
rese
nted
by
a co
ntou
r, t
he P
TV
has
bee
n hi
ghli
ghte
d w
ith
a br
ight
red
con
tour
. T
he d
ashe
d li
nes
‘a’
and
‘b’
corr
espo
nd to
the
ante
rior
/pos
teri
or a
nd s
uper
ior/
infe
rior
axe
s re
spec
tive
ly.
102
MEASURED DISTRIBUTIO� # 1
Fig
ure
5.1
6:
A 3
D O
ptC
T m
easu
rem
ent
of t
he d
ose
dist
ribu
tion
pre
serv
ed i
n a
NIP
AM
/Bis
pol
ymer
ge
l do
sim
eter
. T
he s
hape
of
the
dose
dis
trib
utio
n m
atch
es t
he P
TV
(sh
own
in r
ed)
but
it i
s sh
ifte
d to
war
ds th
e an
teri
or, a
nd to
the
righ
t. T
he c
olou
rbar
cor
resp
onds
to d
oses
bet
wee
n 0
and
4.01
Gy.
103
a.
0
2
4
0 5 10Position (cm) [Ant/Post]
Do
se (
Gy)
Eclipse
Gel
b.
0
2
4
0 5 10Position (cm) [Sup/Inf]
Do
se (
Gy)
Eclipse
Gel
Figure 5.17: Dose profiles comparing the polymer gel dose measurement with the planned distribution calculated by Eclipse. The anterior/posterior profile (a) shows a misalignment towards the superior direction. As a result, the superior inferior profile (b) of the gel appears below that of the Eclipse plan.
104
3D GAMMA MAG�ITUDE DISTRIBUTIO� # 1
Fig
ure
5
.18
: T
he 3
D g
amm
a co
mpa
riso
n be
twee
n th
e tw
o im
ages
. O
nly
the
10x1
0x10
cm
3 vol
ume
surr
ound
ing
the
plan
iso
cent
re h
as b
een
incl
uded
in
this
com
pari
son.
W
ithi
n th
e cy
lind
rica
l vo
lum
e th
at
excl
udes
the
out
er 1
0% o
f th
e ja
r ra
dius
, ap
prox
imat
ely
51%
of
the
pixe
ls d
o no
t co
rres
pond
to
the
Ecl
ipse
pl
an w
ithi
n 3%
3m
m c
rite
ria.
The
col
ourb
ar in
dica
tes
gam
ma
mag
nitu
des
betw
een
0 an
d 5.
The
sag
itta
l vie
w
show
s a
regi
on o
f ag
reem
ent t
hrou
gh th
e ce
ntre
of
the
PT
V c
orre
spon
ding
to o
verl
ap b
etw
een
the
plan
ned
and
mea
sure
d di
stri
buti
ons.
105
A 2D γ-vector comparison between the sagittal planes of the measured and planned
distributions was also performed. The corresponding γ-vector plot for this comparison is shown
in Figure 5.19. Near the boundary of the control volume, the spatial component of the γ-vector
strongly indicates the direction of misalignment between the measurement and the plan. Nearly
every γ has a spatial vector component in the negative x-direction; the same direction associated
with the geometric miss. Although this experiment represents a failed treatment delivery, it
shows the potential for using polymer gel dosimetry for validating radiotherapy treatments, in this
case revealing a serious error. Further, 3D γ-analysis rapidly identifies regions in the
measurement outside of 3% 3mm agreement with the treatment plan. Finally, around the PTV
boundaries the spatial components of the γ-vector indicate a misalignment corresponding to the
direction of the geometric miss.
There were two causes identified for the spatial misalignment. The first error was
introduced during the process of copying the anatomical structures from the anonymous patient to
the X-ray CT scan of the AQUA phantom (see Section 4.3.3 for this procedure). The patient
origin was inadvertently copied over the origin of AQUA phantom. The patient’s origin was
most likely adjusted to correspond to fiducial marks on the body. These were not present on the
anthropomorphic phantom. The second error was introduced when a spatial shift, planned for the
patient delivery was not implemented before treatment of the anthropomorphic phantom.
The plan was retroactively modified and recalculated by replacing the patient origin with
the true scan origin (Figure 5.21) and correcting for the alignment error. After adjusting the plan
the position of the dose distribution came into accordance with the gel measurement as is shown
by comparing the dose profiles (see Figure 5.20). A 3D gamma analysis was performed to
quantitatively check the agreement between the new plan and the dosimeter measurement within
106
Figure 5.19: The component vector plot for a 2D γ-vector comparison between the sagittal planes of the polymer gel measurement and Eclipse plan. (Top) a complete component vector plot for the 2D γ-vector comparison with a square ROI. (Bottom) an expanded view of the ROI.
107
3% 3mm tolerances. Cumulative DVH’s and GVH’s were calculated for the entire dosimeter
volume (excluding the outer 10 % of the cylindrical radius) and for each structure (the bladder,
GTV, PTV and rectum). For every structure, and the jar volume, the DVH’s for the Eclipse plan
and the polymer gel measurement are in excellent agreement (see Figure 5.23). Furthermore, the
(GVH)’s show that the polymer gel dosimeter measurement agrees with the Eclipse plan to within
3% 3mm tolerances in over 90 % of the volume of every structure. This level of accordance
between the distribution calculated by the planning software and the measurement indicates the
reliability of polymer gel dosimetry for validating and/or verifying conformal radiation therapy.
108
a.
Do
se (
Gy)
0
2
4
0 5 10 Position (cm) [Ant/Post]
Eclipse Gel
b.
0
2
4
0 5 10
Position (cm) [Sup/Inf]
Do
se (
Gy)
Eclipse
Gel
Figure 5.20: Dose profiles comparing the polymer gel dosimeter measurement of the dose distribution with the modified eclipse plan. (a) the dose profile along the anterior/posterior axis. (b) the dose profile along the superior/inferior axis.
109
MODIFIED CALCULATED DISTRIBUTIO� # 1
Fig
ure
5
.21
: T
he E
clip
se p
lan
has
been
ret
roac
tive
ly m
odif
ied
to a
ccou
nt f
or t
he i
ncor
rect
ori
gin
loca
tion
and
re
calc
ulat
ed.
The
mod
ifie
d pl
an d
istr
ibut
ion
clos
ely
mat
ches
the
mea
sure
d di
stri
buti
on.
110
IMPROVED 3D GAMMA MAG�ITUDE DISTRIBUTIO� # 1
Fig
ure
5.2
2:
A 3
D γ
com
pari
son
betw
een
the
mod
ifie
d E
clip
se p
lan
dose
dis
trib
utio
n an
d th
e O
ptC
T m
easu
rem
ent
of
the
dose
dis
trib
utio
n pr
eser
ved
in t
he p
olym
er g
el d
osim
eter
. T
he c
olou
rbar
cor
resp
onds
to
γ m
agni
tude
s be
twee
n 0
and
2.
111
Jar Volume
0
25
50
75
100
0 2 4 6
Dose (Gy)
Fra
cti
on
of
Vo
lum
e (
%)
Eclipse
Gel
Bladder
0
25
50
75
100
0 2 4 6
Dose (Gy)
Fra
cti
on
of
Vo
lum
e (
%)
Rectum
0
25
50
75
100
0 2 4 6
Dose (Gy)
Fra
cti
on
of
Vo
lum
e (
%)
GTV
0
25
50
75
100
0 2 4 6
Dose (Gy)
Fra
cti
on
of
Vo
lum
e (
%)
PTV
0
25
50
75
100
0 2 4 6
Dose (Gy)
Fra
cti
on
of
Vo
lum
e (
%)
Cumulative GVH
Figure 5.23: Cumulative volume histograms comparing the OptCT measurement of the dose distribution delivered to the polymer gel dosimeter and the planned distribution from Eclipse. For each DVH, the solid black line represents the cumulative DVH for the Eclipse plan, while the broken red line corresponds to the measured distribution. Cumulative GVH’s are shown for each structure. The relative percentages of each volume that matches the planned distribution within 3% 3mm criteria are shown on the same plot as the GVH’s.
112
For the second 7 field 15 MV conformal prostate treatment trial, a new X-ray CT scan on
a new gel inserted into the anthropomorphic phantom was acquired for treatment planning with
Eclipse. The anatomical structures were once again copied from the anonymous patient. Once
the plan was recreated, the polymer gel dosimeter was irradiated, and later probed with the Vista
scanner. The resulting digital distribution was calibrated, registered, normalized and uploaded to
CERR as before. The measured distribution is shown superimposed on the X-ray CT scan in
Figure 5.25. The planned distribution (see Figure 5.24) is similar to the one shown in Figure 5.15
except that the prescribed radiation dose has been reduced from 4 Gy to 3 Gy. The prostate
contour corresponding to the surface of the prostate plus 0.7 cm has been excluded from the
remaining images. The dose distributions are otherwise presented in the same manner as
previously.
Once again there is a misalignment between the planned and measured dose distributions,
corresponding to a geometric miss. This time the measured distribution is shifted only along the
superior axis with respect to the plan. The misalignment is easily seen in Figure 5.25 as the dose
distribution does not match the PTV contour. The misalignment is also apparent in plot of the
dose profiles along the axes (see Figure 5.26). Again the cause of the geometric miss was a
difference between origins in the CT scans of the patient and the anthropomorphic phantom.
However, in this case the patient shift was applied before delivery. A 3D γ-comparison (see
Figure 5.27) was performed to analyze the extent to which the measured distribution agrees
within 3%3mm tolerances with the planned distribution. A 2D γ-vector comparison was
performed for the two distributions along the sagittal plane. Again, the spatial component of the
γ-vector at the boundary of the dose distribution (i.e., where γ>1) corresponds to the
misalignment direction. Nearly every γ has a spatial vector component in the positive y-
direction; the same direction associated with the geometric miss.
113
While these results will be summarized in greater detail in Chapter 6, this limited set of
experiments indicates the integrity of the NIPAM/bis dosimeter system. They also demonstrate
that optical computed tomography can be used in conjunction with gel dosimeters for clinical
validations. Finally, the γ-vector information is useful in detecting spatial misalignments between
dose distributions. In particular, the component vectors indicate the direction of misalignment
from the reference distribution to the evaluated distribution.
114
CALCULATED DISTRIBUTIO� # 2
Fig
ure
5.2
4:
The
pla
nned
tre
atm
ent
dose
dis
trib
utio
n ca
lcul
ated
by
Ecl
ipse
usi
ng t
he s
ame
view
s as
exp
lain
ed i
n F
igur
e 5.
15.
The
col
ourb
ar c
orre
spon
ds to
rad
iati
on d
oses
bet
wee
n 0
and
3Gy.
115
MEASURED DISTRIBUTIO� # 2
Fig
ure
5.2
5:
A c
alib
rate
d an
d re
gist
ered
Opt
CT
mea
sure
men
t of
the
dos
e di
stri
buti
on p
rese
rved
wit
hin
a po
lym
er g
el d
osim
eter
. T
he c
olou
rbar
cor
resp
onds
to r
adia
tion
dos
es b
etw
een
0 an
d 3G
y.
116
a.
0
1
2
3
0 5 10
Position (cm) [Ant/Post]
Do
se (
Gy)
b.
0
1
2
3
0 5 10
Position (cm) [Sup/Inf]
Do
se (
Gy)
Eclipse
Gel
Figure 5.26: Dose profiles comparing the polymer gel dosimeter measurement of the dose distribution with new Eclipse plan. (a) the dose profile along the anterior/posterior axis. (b) the dose profile along the superior/inferior axis.
117
3D GAMMA MAG�ITUDE DISTRIBUTIO� # 2
Fig
ure
5.2
7:
A 3
D γ
-com
pari
son
betw
een
the
plan
ned
dose
dis
trib
utio
n ca
lcul
ated
by
Ecl
ipse
, an
d th
e O
ptC
T
mea
sure
men
t of
the
dos
e di
stri
buti
on p
rese
rved
in
the
irra
diat
ed p
olym
er g
el d
osim
eter
. T
he i
mag
e sh
ows
sign
ific
ant
fail
ure
part
icul
arly
alo
ng t
he b
orde
rs o
f th
e co
ntro
l vo
lum
e (t
he v
olum
e to
whi
ch t
he M
LC
lea
ves
conf
orm
ed).
The
col
ourb
ar c
orre
spon
ds to
a r
ange
of
γ m
agni
tude
s be
twee
n 0
and
5.
118
Figure 5.28: The component vector plots corresponding to the 2D γ-vector analysis between the sagittal planes of the planned dose distribution from Eclipse and the OptCT measurement of the dose distribution preserved in the polymer gel dosimeter. (a) the full component vector plot for the 2D γ-vector comparison with a square ROI. (b) an expanded view of ROI 1. (b) an expanded view of ROI 2.
119
Chapter 6 Conclusions
Technological advancements in radiotherapy have improved therapeutic outcomes for cancer
patients worldwide. For example, the development of the Cobalt-60 beam therapy unit in the
1950’s revolutionized cancer treatment. The so called “cobalt bomb” was a relatively simple and
cheap device capable of providing an intense and penetrating photon beam for the treatment of
tumours lying deep within a patient’s tissue. More recently, developments in computer
technology have made it possible to optimize the shape and placement of external beams so that
the delivery of radiation dose is tightly conformed to the tumour while adjacent tissues are spared.
Complications associated with damaging healthy tissue are avoided, allowing more effective
treatment and higher quality of life.
The process of delivering radiation therapy is complicated. An integral stage typically
involves acquiring an anatomical scan with an X-ray CT simulator. A physician uses the scan to
identify malignant structures and sensitive organs, outlining the targets and avoidance structures
for planning purposes. Treatment planning software also uses the scan to calculate and/or refine
the distribution of radiation dose in three dimensions (3D). Afterwards, the patient must maintain
the same position in the treatment suite for which the scan was acquired. On-board-imaging
(OBI) devices can be used to verify the setup geometry. Each step of this process has the
potential to introduce systematic error that may result in improper delivery of therapeutic
treatment. Therefore, careful quality assurance of each step of the process is necessary to avoid
serious incidents.
Making measurements to ensure that the physical dose distribution corresponds to the
calculated plan is a key aspect of radiotherapy quality assurance. However, standard dosimeters
120
such as ion chambers, GafChromic film and thermoluminescent devices (TLD)’s cannot provide
the 3D spatial resolution that is needed to validate plans with the steep dose gradients typical of
highly conformal radiation treatments. Because they can potentially be used to acquire vast
amounts of dose data in 3D with a single measurement, clinical implementation of polymer gel
dosimeters will provide a powerful tool for validating new conformal radiotherapy techniques
such as tomotherapy and intensity modulated radiation therapy (IMRT). As individual clinics
expand and improve their treatment capabilities, polymer gel dosimeters will help to streamline
arduous commissioning processes. Further, optical scanning devices will make accurate dose
readout of polymer gel dosimeters more accessible.
The Medical Physics research group at the Cancer Centre of Southeastern Ontario (CCSEO)
and Queen’s University is well established in the field of gel dosimetry. Recent advances through
collaboration with the department of chemical engineering include the development of less toxic
polymer gel formulations (Senden et al. 2006) and dosimeters with increased cross linker content
(Koeva et al. 2008). In 2005, the group acquired a commercial cone beam optical computed
tomography (OptCT) unit known as the Vista scanner (Modus Medical, London ON). Since then,
the group has been characterizing the performance of the Vista scanner (De Jean et al. 2006a;
Olding et al. 2007; Holmes et al. 2008b) and using it to analyze irradiated dosimeters (De Jean et
al. 2006b). The initial goal of this thesis was to develop the necessary methods and tools for
using polymer gel dosimetry with OptCT to compare 3D measurements of clinical radiotherapy
dose distributions to their corresponding plans. This involved developing software tools for
calibrating and comparing the large 3D data sets. As outlined in Chapter 2, the gamma evaluation
(Low et al. 1998) is a comparison tool that allows rapid analysis of agreement between dose
distributions that accounts for both dose and spatial tolerances. During the development of an
efficient in-house version of the γ-tool, it was recognized that the standard γ-comparison provides
121
little information into the significance of failing γ-values (i.e., when γ > 1). A new γ-tool capable
of returning the complete γ-vector information was developed (a description of the algorithm is
given in Chapter 4). A series of investigations examining the response of the 2D γ-vector field
under various scenarios became a major focus of the research presented in this Master’s thesis.
The accuracy of the magnitude information returned by the new γ-algorithm was first tested
by comparing standard dose distributions that were provided by Dr. Daniel Low, Department of
Radiation Oncology, Washington University School of Medicine. As shown in Chapter 5,
qualitatively, the new algorithm returns the same γ magnitude distribution as presented by Low
and Dempsey (2003) and Ju et al. (2008) (as calculated by the original γ-tool). In order to
conveniently display the vector information, a technique for plotting the vector field was adopted
where the spatial components are represented by arrows and the dose components are collectively
represented by contours. Simulated dose perturbation tests were subsequently performed in order
to determine the source of positive and negative divergence apparent in the vector plots. The
results indicate that positive divergence in the γ-vector field is caused when the evaluated image
contains a region where the dose disagreement with the reference is larger than the surrounding
area. Similarly, negative divergence is caused when the evaluated image contains a region where
the dose disagreement with the reference is smaller than the surrounding area. In a clinical
comparison, positive and/or negative divergence may therefore be an indicator of noise in the
evaluated image. Future investigations may involve searching for localized regions of positive or
negative divergence in the γ-vector field when noise has been added to the evaluated distribution.
The net effect of noise on each vector component was examined by adding Gaussian noise to
the evaluated distribution in simulated dose comparisons. In these simulations, the noise variance
was adjusted from 0 to 100 %. As shown in Chapter 5, while the individual spatial components,
Xv∆ and Y
v∆ , showed no obvious trends, the dose component, D
v∆ , and net spatial component
122
rv∆ increased in magnitude as noise is added to the evaluated distribution. Further, r
v∆ showed a
more pronounced increase with added noise than Dv∆ . This may be related to Low and
Dempsey’s (2003) observation that noise in the evaluated distribution causes a depression in the
mean value of γ. Simulated misalignment testing (described in Chapter 4) revealed that the mean
value of the individual vector components indicates the direction of spatial misalignments and
uniform dose shifts between test distributions. In addition, the size of the vector components is
related to the magnitude of the misalignment or dose shift. Future simulations may include an
investigation of rotational misalignments or other spatial transformations in the evaluated
distributions.
Overall, the simulations showed that the information contained in the γ-vector field has great
promise for identifying disagreements caused by spatial misalignments and various perturbations
along the dose dimension. However, the simulated clinical example shown in Chapter 5 revealed
that under some circumstances a discretized evaluated distribution can cause erratic behaviour of
the vector components such that they do not indicate the true cause of disagreement. Therefore, a
logical extension of this work would be to apply a geometric (Ju et al. 2008) or interpolation
method (Wendling et al. 2007) with the γ-vector algorithm to eliminate the discretization artefact
and produce more reliable results.
As for the original goals of this thesis, two irradiations imitating 7-field 15 MV conformal
prostate treatments were delivered to NIPAM/Bis polymer gel dosimeters (see Chapter 4 and
Chapter 5). A water phantom containing a jar of NIPAM/Bis gel simulated the human abdomen.
An X-ray CT simulation of this phantom along with anatomical information from an actual
patient was used to create a planned conformal irradiation. The phantom was set up using
intersecting room lasers, verified with image guidance and irradiated according to plan with a
Varian Clinac 21iX linear accelerator. OptCT images of the irradiated dosimeters were calibrated
123
and then normalized to dose as per the method described in Chapter 4. Six metallic fiducial beads
and red marks on the surface of the dosimeter jar were used to register the measured dose data set
to the cone-beam X-ray CT scan acquired before delivery. After registration and calibration the
measured dose distributions were imported into CERR (see Chapter 4) where it became apparent
that in both cases the delivered radiation distribution missed the target (see Chapter 5). The
geometric misses were also indicated by 2D γ-vector analyses along the central sagittal plane of
both dosimeters. In both cases, the spatial vector arrows in the γ-vector plot strongly indicated
the direction of misalignment, particularly near the boundaries of the planning-tumour-volume
(PTV). In one of the radiation deliveries the cause of the geometric miss was identified. The
calculated distribution was recalculated with corrected spatial information in order to determine
the quality of the dosimetry. Subsequent comparison of cumulative volume histograms and 3D
gamma analysis showed excellent agreement between the polymer gel measurement and
calculated distribution.
In conclusion, the original goal of validating 3D radiation deliveries using polymer gel
dosimetry with OptCT was accomplished. During the research a variety of software tools and
methods were developed so that the process of using polmer gel dosimeters for verifying other
types of radiation deliveries will be greatly simplified. In particular, the efficient 3D γ-algorithm
will allow rapid comparison between dose distributions, indeed our software has been shared with
colleagues at other centres and acknowledged in published works (Babic et al. 2008; Oliver et al.
2008a; Oliver et al. 2008b). Also, the ability to quickly calibrate and register the OptCT data and
import them to CERR for visualization will facilitate and enhance future investigations. The γ-
vector tool introduced as a part of this research shows great potential for identifying the cause of
failing γ values, especially those caused by geometric misses. The vector plots used to convey
124
the γ-vector information in this thesis could be improved. The author would like to encourage
future investigators to explore other visualization techniques.
Interpreting vector plots is likely to be cumbersome for physicists and dosimetrists. The
strength of the γ-vector information may, therefore, be in allowing treatment planning computers
to detect geometric misses, and to discriminate their severity based on user defined tolerance
criteria (e.g., 3% 3mm). In this scenario it may not be necessary to present the γ-vector
information to the physicist, obviating the need for vector plots. Future work not already
discussed should go into upgrading the γ-vector code to permit 3D γ-vector analysis. Finally,
more studies are required to gain experience in using polymer gel dosimetry with OptCT as a
method for validating the process of various other radiation therapies.
125
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