Download Tomographic Imaging on a Cobalt Radiotherapy Machine Matthew Brendon Marsh

Tomographic Imaging on a Cobalt
Radiotherapy Machine
by
Matthew Brendon Marsh
A thesis submitted to the
Department of Physics, Engineering Physics & Astronomy
in conformity with the requirements for
the degree of Master of Applied Science
Queen’s University
Kingston, Ontario, Canada
January 2012
c Matthew Brendon Marsh, 2012
Copyright Abstract
Cancer is a global problem, and many people in low-income countries do not have access to the treatment options, such as radiation therapy, that are available in wealthy
countries. Where radiation therapy is available, it is often delivered using older Co-60
equipment that has not been updated to modern standards.
Previous research has indicated that an updated Co-60 radiation therapy machine
could deliver treatments that are equivalent to those performed with modern linear
accelerators. Among the key features of these modern treatments is a tightly conformal dose distribution– the radiation dose is shaped in three dimensions to closely
match the tumour, with minimal irradiation of surrounding normal tissues. Very
accurate alignment of the patient in the beam is therefore necessary to avoid missing
the tumour, so all modern radiotherapy machines include imaging systems to verify
the patient’s position before treatment.
Imaging with the treatment beam is relatively cost-effective, as it avoids the need
for a second radiation source and the associated control systems. The dose rate from
a Co-60 therapy source, though, is more than an order of magnitude too high to use
for computed tomography (CT) imaging of a patient. Digital tomosynthesis (DT), a
limited-arc imaging method that can be thought of as a hybrid of CT and conventional
radiography, allows some of the three-dimensional selectivity of CT but with shorter
i
imaging times and a five- to fifteen-fold reduction in dose.
In the present work, a prototype Co-60 DT imaging system was developed and
characterized. A class of clinically useful Co-60 DT protocols has been identified,
based on the filtered backprojection algorithm originally designed for CT, with images
acquired over a relatively small arc. Parts of the reconstruction algorithm must be
modified for the DT case, and a way to reduce the beam intensity will be necessary
to reduce the imaging dose to acceptable levels. Some additional study is required
to determine whether improvements made to the DT imaging protocol translate to
improvements in the accuracy of the image guidance process, but it is clear that Co-60
DT is feasible and will probably be practical for clinical use.
ii
Acknowledgments
This has been an enjoyable and memorable project, thanks in large part to the excellent team I have had the privilege of working with for the last two years.
Dr. L. John Schreiner’s technical insights, his understanding of the broader global
picture, and his ability to keep a project on track have been a great help to me. Dr.
Andrew Kerr’s meticulous editing and his assistance with experiment design and
analysis were invaluable in ensuring that my time was put to good use.
This project also depended on a large army of physicists (Dr. Johnson Darko,
Dr. Chandra Joshi and Dr. Greg Salomons), fellow graduate students (Nick Rawluk,
Tim Olding and Amy MacDonald), technicians and technical staff (Chris Peters, Kevan Welch, Mauro Natalini, Tom Feuerstake and Steve Kloster), and administrators
(Loanne Meldrum, Lynda Mowers and Carol Botting). Without them, any of a thousand minor issues could have brought the entire project to a standstill. Thanks to all
of you for keeping things running smoothly every step of the way.
I’d also like to give thanks to my wife, Katy Marsh, and to my parents, Kerry and
Marius Marsh. They have supported me, unconditionally, throughout my university
career. They are always there for me when I need ideas, help, or just a sounding
board. And, finally, to Bahá’u’lláh and Abdu’l-Bahá, whose inspiring words have
kept me going through whatever challenges life has presented.
iii
Table of Contents
Abstract
i
Acknowledgments
iii
Table of Contents
iv
List of Tables
vi
List of Figures
vii
1 Introduction
1.1 Motivation . . . . . . .
1.2 Background . . . . . .
1.3 Objectives . . . . . . .
1.4 Organization of Thesis
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Literature Review . . . . . . . . . . . . . . .
Tomography . . . . . . . . . . . . . . . . . . . . . . . .
Image Guidance in Radiation Therapy . . . . . . . . .
Cobalt Therapy Equipment . . . . . . . . . . . . . . .
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Chapter 2:
2.1
2.2
2.3
Chapter 3:
3.1
3.2
3.3
3.4
3.5
3.6
Theory . . . . . . . . . . . . . . . . . . . . . .
Photon Attenuation . . . . . . . . . . . . . . . . . . . .
Detector Physics . . . . . . . . . . . . . . . . . . . . .
Forward Projection and the Radon Transform . . . . .
Filtered Backprojection . . . . . . . . . . . . . . . . . .
Shift-and-Add Digital Tomosynthesis . . . . . . . . . .
Algebraic Reconstruction . . . . . . . . . . . . . . . . .
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Chapter 4:
4.1
4.2
4.3
4.4
Experimental Methods
Imaging Apparatus . . . . . . .
Image Reconstruction . . . . . .
Image Analysis . . . . . . . . .
Dose Estimates . . . . . . . . .
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Results . . . . . . . . . . . . . . . . . . . . .
Radiation Dose . . . . . . . . . . . . . . . . . . . . . .
Spatial Filtering . . . . . . . . . . . . . . . . . . . . . .
Resolution . . . . . . . . . . . . . . . . . . . . . . . . .
Contrast Sensitivity . . . . . . . . . . . . . . . . . . . .
Geometric Considerations in DT . . . . . . . . . . . . .
Appearance of Anthropomorphic Phantoms . . . . . .
Image Guidance Accuracy . . . . . . . . . . . . . . . .
Cone Beam CT . . . . . . . . . . . . . . . . . . . . . .
Other Applications . . . . . . . . . . . . . . . . . . . .
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Chapter 5:
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Chapter 6:
6.1
6.2
Summary and Conclusions . . . . . . . . . . . . . . . . . . 126
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Appendix A:
Glossary . . . . .
A.1 Imaging & Reconstruction
A.2 Equipment . . . . . . . . .
A.3 Radiation Therapy . . . .
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List of Tables
5.1
Imaging dose and failure rates for aligning Co-60 images to planning
images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
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List of Figures
1.1
1.2
1.3
Co-60 gamma ray spectrum . . . . . . . . . . . . . . . . . . . . . . .
Modern linear accelerator (photograph) . . . . . . . . . . . . . . . . .
Multi-leaf collimator . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.1
2.2
2.3
Principle of conventional tomosynthesis . . . . . . . . . . . . . . . . .
CT scanner geometry generations . . . . . . . . . . . . . . . . . . . .
Cone beam imaging geometry for portal, DT and CBCT images . . .
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3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Dominant photon interactions over a range of energies .
Photon interactions in a digital flat-panel detector . . .
Fourier slice theorem . . . . . . . . . . . . . . . . . . .
Filling and filtering in frequency space . . . . . . . . .
Backprojection of filtered projection images . . . . . .
Fan- and cone-beam geometry . . . . . . . . . . . . . .
FDK reconstruction co-ordinate frames . . . . . . . . .
Geometry for SAA DT . . . . . . . . . . . . . . . . . .
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4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
Experimental Co-60 imaging system . . . . . . . . . . . .
Cobalt imaging system photos . . . . . . . . . . . . . . .
QC3 spatial resolution phantom . . . . . . . . . . . . . .
Lead edge phantom . . . . . . . . . . . . . . . . . . . . .
CatPhan and Gammex phantoms . . . . . . . . . . . . .
DT geometric distortion phantom (fabrication drawing) .
RANDO anthropomorphic phantom (photo) . . . . . . .
CIRS pelvic phantom (photo) . . . . . . . . . . . . . . .
Alignment of Co-60 CBCT image to planning CT image
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5.1
5.2
5.3
5.4
5.5
5.6
Radiation dose due to imaging . . . . . . . .
Spatial filters . . . . . . . . . . . . . . . . .
DT of sharp edge with various filters . . . .
FBP DT ESF . . . . . . . . . . . . . . . . .
Edge spread functions . . . . . . . . . . . .
Modulation transfer function - portal images
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5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
5.22
5.23
5.24
5.25
5.26
Ray trace of QC3 . . . . . . . . . . . . . . . . . . . . . . . . . . .
Square wave relative modulation transfer function of CoDT . . . .
Sine wave modulation transfer function of CoDT . . . . . . . . . .
DT images of QC3 line-pair phantom . . . . . . . . . . . . . . . .
DT linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DT low-contrast sensitivity . . . . . . . . . . . . . . . . . . . . . .
DT distortion phantom images . . . . . . . . . . . . . . . . . . . .
DT distortion by radius from beam axis . . . . . . . . . . . . . .
DT distortion in each direction . . . . . . . . . . . . . . . . . . .
DT slice thickness images . . . . . . . . . . . . . . . . . . . . . .
Effect of projection spacing on DT image appearance . . . . . . .
Effect of total arc on DT image appearance . . . . . . . . . . . .
RANDO head, pelvis and torso comparison of CBCT, DT and PI
Co-60 vs. planning: Alignment error in 3D . . . . . . . . . . . . .
Co-60 vs. planning: Alignment error in 2D beam’s-eye view . . .
Cone beam CT resolution (CatPhan) . . . . . . . . . . . . . . . .
Cone beam CT contrast detail images (CatPhan) . . . . . . . . .
Prostate phantom . . . . . . . . . . . . . . . . . . . . . . . . . . .
RANDO head phantom CoCBCT . . . . . . . . . . . . . . . . . .
NDT of motor and encoder . . . . . . . . . . . . . . . . . . . . . .
viii
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Chapter 1
Introduction
1.1
Motivation
Canadians, and the residents of other wealthy countries, generally have access to a
wide variety of cancer treatment options. This is not the case in many developing
nations. Radiation therapy, an essential component of cancer treatment for well over
half a century, is simply not available to a large segment of the global population.
The International Atomic Energy Agency reported in 2003 that the developing world
had, at the time, only about 2200 of the roughly 5000 radiation therapy machines
necessary to manage current cancer rates. With an estimated five million new patients
per year needing radiation therapy, the IAEA predicted an ongoing, long-term cancer
management crisis if the need for such services continues to dramatically outpace the
health care systems’ abilities to provide them [IAEA, 2003].
At the same time, the wealthiest countries are facing a health care crisis of a different sort. Health care spending in Ontario is predicted to rise by 3% to 6% per year for
the foreseeable future, as an aging population demands more sophisticated treatments
1
CHAPTER 1. INTRODUCTION
2
and places heavier demands on the health care system [Stewart and Thomson, 2011].
Hospitals in Canada and other wealthy countries are seeking ways to reduce costs
and to use increasingly scarce resources more efficiently.
The solution to these problems cannot be purely technical; a great deal of social
and financial change is also involved. Technology, though, can greatly assist the
process, and in this case, a promising candidate technology is one that had generally
been dismissed as outdated: the cobalt teletherapy machine, originally invented in
Canada in 1949-51. The cobalt machine is much simpler and cheaper than the linear
accelerators (linacs) that form the basis of most modern external beam radiotherapy
equipment. A cobalt machine can be powered from a portable generator; a linac
requires a stable, high-voltage, high-current grid connection and an elaborate cooling
system. Linacs have complex calibration and output checking procedures that must
be performed on a regular basis; a cobalt machine’s quality assurance procedures are
relatively simple. Cobalt, though, has not seen the technological development that
has been applied to linacs over the last quarter-century, and so modern treatment
techniques that are routinely used with linacs are generally not available on cobalt
units [Schreiner et al., 2009].
If a cobalt unit could be fitted with additional hardware to image the patient,
shape and modulate the radiation beam, and verify the accuracy of the treatment,
it could offer a way to give modern radiation therapy to more people at a lower cost
per treatment [Van Dyk and Battista, 1996]. Such modifications are the subject of
an ongoing project at the Cancer Centre of Southeastern Ontario. The problem of
beam shaping and modulation is currently being addressed by others at the CCSEO
[Joshi et al., 2009] [Schreiner et al., 2003b]. In the present work, we will focus on the
CHAPTER 1. INTRODUCTION
3
problem of getting radiographic images of the patient during a treatment session, both
for positioning the patient accurately in the beam and for monitoring the progress of
the treatment.
1.2
Background
Radiation therapy can be broadly divided into two categories. In external beam
radiotherapy, or teletherapy, a beam of photons or charged particles is directed at
the tumour from a source located outside the patient. Internal radiation therapy, or
brachytherapy, uses a photon or particle source that is placed near to or inside the
tumour [IAEA, 2003]. In both cases, the goal of the treatment is to give a lethal dose
of radiation to the cancer, while minimizing the radiation dose to the surrounding
healthy tissues. This radiation is most commonly in the form of photons, with energies
from about 100 keV to about 20 MeV depending on the situation, or as electrons with
energies from about 4 MeV to 20 MeV. The Co-60 machine used for the present work
utilizes a photon beam in a teletherapy configuration.
The teletherapy machine used for the present work is a Theratron 780-C cobalt-60
machine. Its radioactive source consists of many small pellets of Co-60. The pellets
are produced by transmutation of Co-59 in the neutron flux of a nuclear reactor, and
are then packaged into sealed cylinders, 1.5 cm to 2 cm in diameter and up to 5 cm
high, for use in the Theratron machine. Cobalt-60 undergoes beta-minus decay to an
excited form of nickel-60 with a half-life of 5.27 years. As the excited Ni-60 relaxes
to a stable nuclear state, it gives off two gamma rays at 1.1732 and 1.3325 MeV.
These gamma rays are what we colloquially refer to as the “cobalt beam” and use for
radiation therapy and other purposes. The cobalt source is stored inside a shield of
CHAPTER 1. INTRODUCTION
4
tungsten or depleted uranium, and is exposed by moving the source into alignment
with an opening in the shield. Sources are typically replaced after approximately one
half-life.
Most modern teletherapy equipment does not use radioactive sources. Rather,
a particle accelerator– usually a linear accelerator (linac)– is used to create a high
energy electron beam. It is possible to treat directly with the electron beam, and this
is common practice when treating cancers that lie on or near the skin. Alternatively,
the electron beam can be fired at a target, typically made of tungsten or another
dense, high atomic number metal. As the electrons slow down in the target, they give
off brehmsstrahlung (braking) radiation, i.e. X-ray photons, which we can use as a
therapy beam.
A photon is uniquely characterized by its energy and its direction of travel; a
gamma ray is distinguished from an X-ray only by our knowledge of its means of
production (nuclear decay for a gamma, accelerating or decelerating charged particles
for an X-ray). The photon energy spectrum, though, looks quite different for a cobalt
source than for a linac beam. The pure Co-60 beam effectively contains only two
photon energies, which are so close as to behave almost like a monoenergetic 1.25
MeV beam. The linac beam, by the nature of the brehmsstrahlung process, contains
a broad spectrum of energies, ranging from the lowest energy photon that can escape
the target to the highest energy present in the charged particle beam used to create
the photons.
Our goal in radiation therapy is to deposit the energy of these radiation beams in
the tumour, doing biological damage and preventing the cancer cells from reproducing.
The biological damage mechanisms involved are mainly related to the breaking of
CHAPTER 1. INTRODUCTION
5
Figure 1.1: The gamma ray spectrum of Co-60 is dominated by the 1.1732 MeV and
1.3325 MeV photons released by the relaxation of the Ni-60 nucleus that is produced
by the beta decay of Co-60 [Traitor, 2007].
bonds in DNA; these bonds may be directly disrupted by the ionizing radiation, or
broken by free radicals (H+ or OH− ) created when the ionizing radiation interacts
with the water inside the cell [Hall, 2000]. With its DNA sufficiently damaged, a cell
can no longer divide, or the damage to the cell may be enough to induce apoptosis.
To minimize the radiation dose given to surrounding healthy tissues, common
practice is to treat a patient with multiple radiation beams from multiple angles,
with the beams overlapping in the tumour. A convenient and practical configuration
is therefore to mount the radiation source on a gantry or arm that can rotate around
the patient, as illustrated in Figure 1.2; most teletherapy machines use some variant
of this configuration.
The concept of dose will be brought up frequently in the following pages. As
ionizing radiation (high energy photons or charged particles) interacts with matter,
some of the energy in the radiation is transferred to the target matter. The dose is
CHAPTER 1. INTRODUCTION
6
Figure 1.2: An example of a modern radiation therapy linac: a 15 MV Varian Trilogy
at the Cancer Centre of Southeastern Ontario. The therapy beam, produced by the
MV accelerator, exits through the collimators, which are mounted in the circular ring
in the head of the gantry. Retractable arms support the source and detector panel
for the on-board kV imaging system, and a second detector panel can be extended
for imaging with the treatment beam.
CHAPTER 1. INTRODUCTION
7
the amount of energy absorbed per unit mass of the target; should a target with a
mass of 1 kg absorb 1 joule of energy from a radiation beam, the dose to that target
is 1 J/kg or 1 gray (Gy). Reference will also be made to dose distributions, in which
case we are considering the dose to each of a large number of very small volumes
within the target. An ideal dose distribution would give the dose prescribed by the
oncologist to all volumes containing cancer cells, and a near-zero dose to volumes
that contain only healthy cells. For a more thorough discussion of radiation dose, the
reader is referred to [Podgorsak, 2004].
The amount of healthy tissue that is damaged by the radiation can be reduced
if the beam is shaped to conform to the outline of the tumour as viewed from that
beam angle. In the past, this beam shaping was done with carved blocks of lead or
cerrobend (lead alloy), an effective but labour intensive process. Modern methods
use a multileaf collimator (MLC) to define the edges of the beam. An MLC (Figure
1.3) is an array of tungsten leaves that can be moved individually, under computer
control, to block parts of the radiation beam. By using many such leaves, a custom
shaped beam aperture can be created. The common case in which beams are aimed
at the tumour from several angles, each one shaped by an MLC to match the shape
of the tumour from that angle, is called conformal radiation therapy.
If we move the leaves of the MLC while the beam is on, we can block some parts of
the beam for longer than others, effectively changing the intensity of the beam within
the limits of the beam aperture. Intensity modulated radiation therapy (IMRT)
makes use of this capability to produce dose distributions that conform more tightly
to the tumour, offering additional ways to spare adjacent healthy tissues from receiving a high radiation dose. The calculations necessary to plan the treatment, though,
CHAPTER 1. INTRODUCTION
8
Figure 1.3: A multi-leaf collimator (MLC). Tungsten leaves (gray), motorized and
under computer control, are moved in and out of the radiation beam (orange) to
define the edge of the beam.
become too complex to optimize manually, so IMRT also includes software that uses
“inverse planning” algorithms. This type of planning system uses computerized optimization routines to calculate appropriate MLC movements and beam parameters
based on the shape of the tumour and surrounding organs and the desired dose constraints for each organ. This is a notable difference from the conventional case, in
which the beam parameters are defined first, and the resulting dose distribution is
then calculated [Webb, 2001].
Cancer cells and normal cells do not respond to radiation in exactly the same
way. In general, at some low dose, the cancer cells will be less successful at repairing
the radiation damage than the healthy tissues are; whereas at some higher dose, the
opposite is often true. Thus, a common strategy is to find a dose that kills more
cancerous cells than healthy ones, and repeat that dose on a regular (often daily)
CHAPTER 1. INTRODUCTION
9
basis until the desired total dose has been delivered to the tumour. The treatment
details are specific to each type of cancer, and are chosen based on a compromise
between cure rate and minimizing the risk of complications. Treatment plans often
consist of 16 to 38 treatments over three to six weeks, for a total dose of 20 to 80 Gy;
lymphomas tend to be given lower doses, while solid tumours generally receive higher
doses. This “fractionated” approach maximizes the therapeutic ratio, i.e. the ratio of
cancer damaged to normal tissue damaged as a result of the treatment [Hall, 2000].
The combination of tightly conformal, possibly intensity-modulated treatments
and multiple treatment sessions over a long period poses challenges for patient setup
and monitoring. If the tumour is not properly aligned in the treatment beam, some
tumour will be missed and some healthy tissue may receive a high dose. Furthermore, if the tumour shrinks or changes shape in response to the first few radiation
treatments, subsequent treatment sessions might miss the tumour if the change is not
caught and the treatment plan is not updated accordingly. Both of these problems
call for some form of image guidance in the treatment room, and this is the problem
that forms the basis of the present work.
1.3
Objectives
The overall objective of the cobalt modernization project is to improve the survival
rates and the quality of life of cancer patients by making radiation therapy more
readily available worldwide. A wide range of advanced radiation therapy technologies
and techniques are available in the developed world, but they rely on expensive,
complicated equipment that is difficult to finance and maintain in remote or lessdeveloped areas.
CHAPTER 1. INTRODUCTION
10
Decision makers in new or expanding cancer clinics are understandably reluctant
to invest scarce funds in cobalt units that are perceived by established institutions as
outdated or second-rate. At the same time, those established institutions are being
asked to treat more patients and to survive on tight budgets. A cobalt teletherapy
machine updated to modern standards could be an affordable way to perform many
conformal and IMRT treatments in busy, established first-world clinics, if the treatments are of comparable quality to those delivered by existing state-of-the-art linacs
[Van Dyk and Battista, 1996]. The essential core of the treatment machine could
then be marketed in the developing countries as a reliable, modern system that can
be purchased for a fraction of the cost of a linac, and can later be upgraded. An
incremental upgrade path would start with an inexpensive, basic cobalt unit, which
would be a major step forward in regions that currently have no radiotherapy equipment at all. When a clinic’s finances and requirements call for it, such a machine
could be upgraded with a multi-leaf collimator and the ability to do conventional
conformal delivery. Additional add-on hardware, plus software updates, could add
on-board imaging and eventually IMRT capabilities.
When performing conformal or IMRT radiation deliveries with a modern therapy
linac, some way to monitor the position of the patient is necessary to ensure that
the tightly conformal beam is in fact targeted on the tumour. Periodic X-ray imaging of the patient also provides the oncologist with a way to track the progress of
the treatment, and to adjust the treatment regimen if the tumour shrinks or changes
shape. It has now been established that fan-beam IMRT and 3D conformal and IMRT
deliveries are feasible with a suitably upgraded Co-60 unit [Schreiner et al., 2009]
[Joshi et al., 2009]. Such a cobalt unit, like its linac counterpart, would require some
CHAPTER 1. INTRODUCTION
11
form of image guidance. The present work focuses on the problem of patient positioning and image guidance in the context of modernizing Co-60 radiation therapy
technology.
Given sufficient funds, a cobalt unit could be fitted with an onboard kilovoltage
X-ray imaging system identical to those used on modern therapy linacs. Such systems
have been commercially available for many years, and their clinical application is well
understood. The objective of the present work is not to simply recommend buying
additional hardware, but rather to determine if a more cost-effective imaging system
can be implemented with existing hardware and with relatively little modification of
the treatment machine. The focus is on the specific case in which a digital gamma-ray
imaging panel is added to the treatment gantry, and used to acquire two-dimensional
radiographic projection images of the patient using the full strength therapy beam.
These projection images were studied on their own, and were also used to reconstruct
three-dimensional images. The techniques used for the present work can be separated into two classes. The first class is digital tomosynthesis (DT), in which several
projection images are taken over a small arc. These images are then combined into
quasi-3D images in which a single set of planes through the patient can be viewed,
with the overlying anatomy blurred out. The second class is computed tomography (CT), a true 3D method in which any arbitrary plane through the patient can
be viewed, without interference from overlying anatomy. The reconstruction methods are described in Sections 3.4 through 3.6. Some standard quantitative metrics
of imaging system performance were measured and compared, and new test objects
(phantoms) were designed and built to evaluate the various methods. Comparisons
of the various methods on a number of anthropomorphic (human-like) phatoms were
CHAPTER 1. INTRODUCTION
12
also performed, and strategies for reducing the radiation dose during imaging were
explored.
1.4
Organization of Thesis
We will begin Chapter 2 with an overview of radiographic imaging and, in particular,
tomographic reconstruction. Following a brief discussion of the historical background
in this field, a review of conventional film tomography and the more familiar computed tomography (CT) will provide the necessary context and technical basis for
the present work. The class of techniques known collectively as digital tomosynthesis
(DT) will be discussed in detail, as several of these methods are used extensively
in the present work. This technical background is followed by an overview of the
rationale for, and current solutions to, the problem of on-board image guidance in radiation therapy. Chapter 2 concludes with a review of recent developments concerning
improvements to the cobalt teletherapy machine.
The physical and mathematical basis for radiographic imaging and tomographic
reconstruction is presented in Chapter 3. This chapter begins with a brief discussion
of imaging physics, in which the interaction of photons with matter will be discussed
and the operation of the digital detector explained. The mathematical representation
of the radiographic imaging process will then be presented. Sections 3.4 through 3.6
explain several methods of tomographic reconstruction.
Chapter 4 will discuss the experimental apparatus and methods used for the
present work; this is followed in Chapter 5 by a summary of the results of these
experiments. The implications of these results will be discussed, with conclusions
and recommendations for future work, in Chapter 6.
Chapter 2
Literature Review
2.1
2.1.1
Tomography
Historical Background
Radiography is widely considered to have originated in 1895, in the laboratory of
Wilhelm Röntgen. Within two weeks of identifying what he termed X-rays, Röntgen
had determined that their attenuation in matter depended mainly on density, and
had produced the first projection radiograph: an image on photographic emulsion of
the bones of his wife’s hand [Röntgen, 1896]. He also established several important
properties of X-rays: notably, that they are not susceptible to the usual rules of reflection and refraction, but can be scattered: “...bodies behave to the X-rays as turbid
media to light”, and that they are not deflected by magnetic fields [Röntgen, 1896].
Röntgen’s technique is still in widespread use today, albeit with more sophisticated
equipment to produce and detect the X-rays. While their geometries differ, most
radiographic imaging systems work on the same principles as Röntgen’s original. A
13
CHAPTER 2. LITERATURE REVIEW
14
photon source, either an X-ray tube or a gamma-emitting radioactive isotope, creates
a radiation beam that is directed at the object to be imaged. These photons are
absorbed or scattered as they pass through the object; denser features (such as bone)
absorb more photons. Some form of detector, such as photographic film or an array
of silicon sensors, measures the photons that leave the far side of the object, and we
interpret the resulting patterns on the film or detector– in which dense bone casts a
deeper shadow than, say, muscle– as a radiographic projection image of the object.
The mathematical foundation of projection radiography and the various threedimensional reconstruction techniques lies in the Beer-Lambert law of attenuation
(section 3.1), and in the Radon transform (section 3.3). Derived in 1917 by Johann
Radon, this transform and its inverse provide the theoretical framework for radiographic imaging and tomography. Mathematically speaking, the Radon transform
allows one to convert between an arbitrary compact, continuous function in a plane
(for example, a tomographic slice through a patient) and a set of projections of that
function (i.e. projection radiographs of the patient) [Radon, 1917].
2.1.2
Conventional Tomography
A major limitation of projection radiography is that it produces two-dimensional
images, while a person has a complex three-dimensional structure. Organs, bones
and muscles are intertwined in three dimensions within a person. In a projection
radiograph, all these features are flattened and superimposed on a flat plane, making
it difficult to distinguish individual organs. Tomographic methods, to be discussed
shortly, use multiple projection radiographs acquired at different positions to obtain
three-dimensional views. All of these methods are based on the same physics as
CHAPTER 2. LITERATURE REVIEW
15
Figure 2.1: Principle of conventional tomosynthesis. When the films are overlaid and
the sum of all the shifted images is viewed, features in one plane are enhanced while
others are suppressed. This principle is also used in shift-and-add digital tomosynthesis (section 3.5).
projection radography; they differ in the geometry used to acquire the projection
images and in the way those images are combined.
In 1932, Ziedses des Plantes proposed a way around the two-dimensional limitations of projection radiography: multiple projections on film, from different beam
angles, which would then be shifted and superimposed so that features in a particular plane would be emphasized while those in other planes would be suppressed
[Ziedses des Plantes, 1932]. This shift-and-add method is the basis of conventional
tomosynthesis, also referred to as conventional film tomography.
The method of Ziedses des Plantes allows a particular plane through the patient
to be emphasized, but with limitations; only planes normal to a particular axis (set
by the imaging geometry) can be viewed. Tomography using multiple films was
CHAPTER 2. LITERATURE REVIEW
16
extended to allow for arbitrary viewing planes with the system devised in 1972 by
David G. Grant as a generalization of circular tomography. Grant’s system acquired
twenty discrete X-ray projection images on films, which were then placed around
a three-dimensional projector in the same positions at which they were originally
exposed. The film images would be optically projected into the three-dimensional
volume within the projector device, where an arbitrary tomographic slice could be
viewed on a movable screen or recorded on film [Grant, 1972]. Such systems required
the operator to expose and handle many pieces of film, though, and did not see
widespread clinical use, possibly as a result of this complexity.
2.1.3
Computed Tomography
As the processing power of computers increased during the 1960s, numerous researchers began investigating their possible application to medical problems. Allan MacLeod Cormack investigated computational methods for inverting the Radon
transform in the early 1960s, and published these results in 1963-64 [Raju, 1999].
Further development by Godfrey Hounsfield led to a functional benchtop prototype
based on a pencil beam of Am-95 gamma rays. This first-generation (Fig. 2.2a) system would rotate and translate the object being scanned, until enough rays had been
sampled to reconstruct a slice through the object. With a nine-day scanning time,
though, even non-living organic samples were difficult to image on this early machine.
In 1971, Hounsfield’s improved computerized axial tomography (CAT) machine saw
its first clinical use, producing an algebraically reconstructed image of a frontal lobe
brain tumour [Beckmann, 2006]. Within a few years, the introduction of minicomputers and the switch to a new class of reconstruction algorithms known as “filtered
CHAPTER 2. LITERATURE REVIEW
17
backprojection” (see section 3.4) made it possible to view the images within a few
minutes after the scan, and second-generation geometry using multiple detectors per
slice reduced the scan times considerably. The fundamental principles of the CAT,
or CT, scanner have not changed since Hounsfield’s original system, although advancements in scanning hardware and reconstruction mathematics allow current CT
systems to produce sharper images, with less noise and better contrast, in less time.
The modern CT scanner is now the first step in radiotherapy planning; it provides
the oncologist and dosimetrist with detailed information about the size and shape
of the tumour as well as its location relative to surrounding tissues [Van Dyk, 1999]
[Verellen et al., 2008]. Radiotherapy planning CT systems now use one of three main
geometries, all based on a ring gantry. Third-generation fan beam machines (Figure
2.2c) have a rotating gantry that carries the rotating X-ray source along with enough
detector elements to span the width of the patient. Fourth-generation machines (Figure 2.2d) have a single 360◦ ring of fixed detectors and a rotating X-ray source. At
the time of writing, the state-of-the-art in planning CT systems is the multi-slice ring
gantry scanner. These systems share the rotating source, rotating detector geometry
of the third-generation fan beam machine, but use several rows of detectors instead of
just one row. This allows for faster scan times as well as the ability to image thinner
and higher-resolution slices. Many scanners also offer a spiral or helical mode; in this
mode, the detector geometry is not changed, but the patient is moved through the
scanner in a continuous smooth motion instead of slice-by-slice in steps. The projection data from the resulting spiral-like source trajectory is then mathematically
transformed to give a slice-by-slice reconstruction [Kalendar, 2006].
The advent of large area, two-dimensional digital flat-panel X-ray detectors in
CHAPTER 2. LITERATURE REVIEW
18
Figure 2.2: CT scanner geometry generations. Sources are shown in red, detectors in
turquoise. First-generation scanners use a thin pencil beam, and combine translation
and rotation of the source and detector to sample all ray paths. Second-gen scanners
share a similar translate-and-rotate motion, but use a narrow fan beam that exposes
several detectors simultaneously. Third-generation scanners use a wide fan beam and
a detector array wide enough to span the entire patient; the source and detector both
rotate around the patient. Fourth-generation scanners use a 360◦ ring of detectors
that are held stationary while the source, producing a wide fan beam, rotates around
the patient. Multi-slice and cone beam CT systems share the 3rd generation geometry
(rotating source, rotating detector) but use a wider, or flat panel, detector that scans
many slices at once.
CHAPTER 2. LITERATURE REVIEW
19
the early 1980s opened another possibility: the reconstruction of complete CT volumes, rather than slice-by-slice reconstructions, from sets of projection radiographs
taken at several angles around the patient. This approach is called “cone beam CT”
to distinguish it from the narrow fan beams used in many common CT systems.
Mathematical algorithms for this type of reconstruction date back to the mid 1980s
[Feldkamp et al., 1984] and will be discussed in further detail in chapter 3. The sliceby-slice reconstruction of a conventional CT scanner can be implemented in a manner
suitable for a computer with limited memory and processing power, by keeping most
of the data on disk or tape and only working on one slice at a time. But working on
a complete 3D data set is computationally far more taxing; full 3D image reconstruction on the computers of the time would have been too slow to use while a patient
was lying in the scanner.
In the 1990s, therapy linacs began to be fitted with on-board kilovoltage X-ray
imaging systems, and with digital imaging panels known as electronic portal imaging
devices (EPIDs, or portal imagers) that used the main treatment beam for imaging.
Early techniques used a pair of projection images, taken at 90◦ to each other, which
were compared to planning images to verify the patient’s position. By the turn
of the century, computing power was no longer a major stumbling block, and true
three-dimensional cone beam CT (CBCT) was demonstrated with a therapy linac’s
kilovoltage imager in 2000 [Jaffray and Siewerdsen, 2000]. The treatment planning
process was also becoming dependent on CT images, usually taken on a dedicated
planning CT scanner, to identify the extents of tumours.
By comparing CBCT images taken on the treatment machine to the planning CT
images in a patient’s file, radiation therapists can identify if the patient is misalignned,
CHAPTER 2. LITERATURE REVIEW
20
and correct the error before treating. CBCT has a distinct advantage over simple
radiographs in that it can show the patient’s rotation in all three axes as well as linear
translations. Furthermore, oncologists can review the CBCT images to determine if
the tumour itself has changed and if future treatment plans need to be modified.
It is also possible to perform CBCT using a linac’s portal imager and megavoltage
treatment beam, running the accelerator in short, low-current pulses to minimize the
radiation dose [Morin et al., 2009]. The main advantage of this MV CBCT method
is its relative simplicity; only one imaging device (the portal imager) is needed and
the use of the existing linac-based X-ray source saves the expense and complexity
of an extra imaging source. However, megavoltage beams inherently produce images
with higher noise and reduced subject contrast than their kilovoltage counterparts,
which can limit their clinical practicality [Groh et al., 2002]. The decision of whether
to use kV or MV imaging, and whether to use single projections or CBCT, depends
largely on whether the substantial added cost and complexity can be justified by the
improvements in image quality. Most modern linacs are equipped with both kV and
MV imaging systems.
2.1.4
Digital Tomosynthesis
Conventional tomosynthesis, while effective, has notable limitations. If multiple projections are made on a single piece of film, only one slice through the patient is
emphasized- image data relating to slices above or below the target is intentionally
degraded in order to isolate the desired slice. Film-based techniques that overcome
this problem are tedious, requiring the radiologist to handle and develop many pieces
of film and to precisely align them for viewing. Three-dimensional conventional film
CHAPTER 2. LITERATURE REVIEW
21
Figure 2.3: Cone beam imaging geometry. The basic case is a simple radiograph using
a cone beam and a flat-panel detector; this geometry is used for diagnostic X-rays and
for “portal imaging” in a therapy machine’s treatment beam. Digital tomosynthesis
(DT) makes use of several projection images over a small arc. Cone beam CT uses
many projection images over an arc of at least 180◦ plus the width of the beam.
tomography had not yet become widely adopted when the development of the CT
scanner, with its true 3D images and relative ease of use, rendered conventional tomography largely obsolete. In digital form, though, tomosynthesis remains an appealing
tool for cases where it is unnecessary, undesirable or impossible to achieve the 360◦
source and detector motion necessary for CT.
One of the simplest DT methods is simply to digitize discrete projection images,
then shift and superimpose them digitally in a similar manner to the optical superposition of conventional tomosynthesis (figure 2.1, also section 3.5). This method, now
known as shift-and-add (SAA), is still in use, and has been applied to the problem
of imaging on the cobalt radiotherapy unit [McDonald, 2010]. Although digital SAA
does eliminate the tedious manipulation of films, it is subject to many of the same geometric constraints and field-of-view limitations as the conventional film techniques
CHAPTER 2. LITERATURE REVIEW
22
it duplicates. A large total imaging arc, for example, makes accurate SAA reconstruction difficult or impossible. SAA remains common, though, and is particularly
promising for mammography. In this case, simple translational or limited-arc geometry is suitable, and the breast is held fixed between compression plates during the
scan- thus eliminating motion artefacts [Niklason et al., 1997] [Dobbins, 2009].
An early attempt at digital tomosynthesis, known as ectomography, combined the
SAA approach with two-dimensional filtering of the projection images in the Fourier
domain. Ectomography was demonstrated in computer simulations as early as 1980,
which revealed that this approach gave better slice selectivity than conventional tomosynthesis [Petersson et al., 1980]. At the time, though, the digital flat-panel detectors necessary for clinically practical DT were not commercially available, and
digitally scanned films would have had the same workflow drawbacks as for conventional film tomography. Spatial filtering is an important part of many current CT
and DT reconstruction techniques, and is discussed in more detail in chapter 3.
The addition of frequency domain filtering brings us to the backprojection approach commonly used in fan and cone beam computed tomography. One can think
of DT as being a form of cone beam CT in which only a small subset of projection images is used, therefore not enough data is available for a full reconstruction.
In the idealized case, the CT reconstruction is simply an inverse Radon transform.
The Radon transform, however, does not account for noise, or for the large regions
of missing data that occur when, in DT, the detector and source do not rotate all
the way around the patient. Furthermore, DT generally uses two-dimensional area
detectors, similar to cone beam CT in third-generation geometry. This case is handled well by the Feldkamp-Davis-Kress filtered backprojection algorithm (FDK or
CHAPTER 2. LITERATURE REVIEW
23
FBP) provided that the cone angle is not excessively large [Feldkamp et al., 1984]
[Kak and Slaney, 1988]. A variant of this algorithm was used for the majority of the
present work, and is discussed in more detail in section 3.4.
Yet another class of algorithms is the algebraic / iterative group. Here, the threedimensional volume is broken into discrete voxels, each of which corresponds to one
column of a matrix. Each ray from the source to a pixel of one of the projection
images is treated as a row of that matrix, with individual coefficients representing
the fraction of each voxel that is intersected by that ray. The reconstruction, then,
comes down to solving a large sparse matrix, a well-understood but non-trivial task;
reconstructing a volume from 180 projections on a 512 x 512 detector would call for
a solution matrix with (5123 )=134 million columns and (512 × 512 × 180)=47 million
rows. The mathematical basis of this class of methods was well established by 1976
[Colsher, 1976], and the most popular of the current algebraic methods- the simultaneous algebraic reconstruction technique, or SART- was derived by Andersen and Kak
in 1984 [Andersen and Kak, 1984]. Due in large part to the extreme demands they
place on the reconstruction computer, algebraic methods have generally taken a back
seat to filtered backprojection techniques in the CT arena. For DT, though, the noise
reduction seen with some algebraic methods may be appealing [Sarkar et al., 2009].
Computer hardware is now powerful enough to negate the problems with computational time; it is now easy to fit a desktop computer with far more memory than
most reconstruction algorithms can use, and the gaming sector has spurred the development of inexpensive, massively parallel floating-point processors (GPUs) that
are well suited to the types of calculations involved in tomographic reconstruction
[Després et al., 2007] [Schiwietz et al., 2010].
CHAPTER 2. LITERATURE REVIEW
24
Each slice of a reconstructed DT volume contains some information about the
planes above and below it; features that exist in one plane also show up (albeit
blurred) in nearby planes. This fact begs the question of whether there is some
way to use known information about nearby slices to improve the selectivity of the
desired plane. Godfrey and Dobbins tackled this problem in the late 1990s, and discovered that the blurring function for each plane could be calculated, given sufficient
knowledge of the imaging geometry. Their technique, known as matrix inversion tomosynthesis (MITS), can be thought of as an extension of shift-and-add DT. It uses
a set of coupled algebraic equations to solve for the blurring function, thus allowing
the removal of out-of-plane blur artefacts [Godfrey et al., 2001]. Considerable effort
has been invested by other researchers in this particular method, which has proven to
be quite well suited for thoracic imaging, even showing individual bronchioles within
a lung [Godfrey et al., 2003] [Godfrey et al., 2006a]. The use of the MITS technique
for Co-60 imaging may be interesting, but was not included in the scope of the present
work.
Algebraic reconstruction is a large and diverse field, and this class of reconstruction
algorithms was deemed to be outside the scope of the present work.
2.2
Image Guidance in Radiation Therapy
Radiation therapy works, simply stated, by delivering a lethal dose of ionizing radiation to a cancerous tumour or other undesirable growth. Delivering a lethal dose
is a simple task; the challenge lies in sparing as much of the surrounding healthy
tissue as possible from the biological effects of the radiation. In order to minimize
the damage to healthy tissue, external radiotherapy beams are typically delivered
CHAPTER 2. LITERATURE REVIEW
25
from multiple angles, each beam being collimated to closely match the size and shape
of the tumour. Further advancements in collimator technology and treatment planning algorithms have led to the development of intensity-modulated radiation therapy
(IMRT), in which both the shape and the intensity of the treatment beams are optimized by “inverse planning” algorithms to come as close as possible to the oncologist’s
specifications for that particular treatment [Webb, 2001].
These improvements in the conformity of the treatment beam should, in theory,
allow a reduction in the amount of healthy tissue that is irradiated, without changing
the dose to the tumour. However, people are not rigid, organs move as the patient
breathes, and the patient may not lie in exactly the same position and orientation each
day. The position of a soft tissue tumour is not necessarily correlated to externally
visible features, such as skin tattoos. With a more tightly conformal beam, the risk of
missing part of the tumour increases. A feature common to all modern conformal and
IMRT systems, therefore, is some method to image the patient’s internal anatomy to
improve the positioning accuracy while they lie on the treatment couch.
Portal imaging, using the treatment beam as the imaging source to produce a
single projection radiograph, is one approach. When on-board kilovoltage imaging
devices were first added to linacs, they too were often used to create single projection
images. For many decades, until the rise of the planning CT in the 1990s, the standard
way of verifying patient position was to compare two orthogonal projection images
taken on the treatment machine with films shot earlier, in identical geometry, with
a kilovoltage X-ray tube. Should the films fail to match, an estimate of the error in
alignment would be made and further treatments adjusted accordingly. In some areas,
film was replaced by computed radiography (CR) phosphor panels. CR was itself
CHAPTER 2. LITERATURE REVIEW
26
supplanted by flat-panel X-ray detectors known as electronic portal imaging devices
(EPIDs). Portal images remain a valuable tool today, and an EPID is standard
equipment on most modern therapy linacs. Projection data from an EPID can be
used in CBCT or DT reconstruction algorithms, and EPIDs have also been used to
verify the dose delivered during a treatment [Nelms et al., 2010].
On-board kV CBCT imaging provides the most comprehensive image set of the
methods discussed here. It also offers the distinct advantage that images from the
treatment unit have similar contrast and noise characteristics to images from the
planning CT, having been made at similar beam energies. This quality makes it
relatively easy for therapists or image analysis software to match up anatomical features between the two 3D images. CBCT does involve a considerable radiation dose,
though, which can add significantly to the patient’s total dose over many treatments;
furthermore, CBCT scanning requires the gantry to rotate through at least 180◦ plus
the divergence angle of the beam, adding several minutes to each treatment and constraining the patient positioning options that can be used [Baydush et al., 2005]. The
radiation dose used for on-board kV CBCT imaging is on the order of 1.6 to 3.5 cGy,
or about 1% of the therapy dose, which is typically on the order of 200 cGy per session [Islam et al., 2006]. Bony anatomy can be used as a surrogate for localizing some
tumours. However, others, such as prostate cancers, move too much relative to the
bone and implanted fiducial markers may be used instead. The kV CBCT images can
also be useful to the oncologist, who may monitor them for signs of tumour shrinkage
between treatment sessions.
For patient positioning, it is not always necessary to have a full three-dimensional
data set; in many cases, two orthogonal views will suffice. Digital tomosynthesis offers
CHAPTER 2. LITERATURE REVIEW
27
some of the anatomical selectivity of CT in combination with the speed and low dose
of portal imaging, and may be an appealing option for cases where bony anatomy or
fiducial markers are adequate surrogates for positioning. Using an on-board imaging
system on a treatment machine, Pang et al demonstrated sufficient DT image quality
for localization with tomographic arcs as small as 22◦ [Pang, 2005]. A quantitative
comparison of DT and CT followed, in which it was found that– at least for planes
normal to the central projection, in which the DT method is valid– the in-plane
spatial resolution of the DT system was superior to that of CT [Pang et al., 2006].
Phantom and patient studies followed, confirming that, for the same dose, MV-CBDT
offered the same signal-to-noise ratio as MV-CBCT, and furthermore, that the images
produced were clinically useful, offering better spatial resolution than MV-CBCT in
the planes of DT reconstruction [Pang et al., 2008].
Similar investigations in other groups have found similar results; a clinical study
at Duke University found that on-board DT with a kilovoltage imager provided for
better visibility of many soft tissues (prostate gland, liver, kidneys, head and neck
tissues, etc.) and bone when compared to kilovoltage radiographs. This study also
found that DT was fast enough to acquire an image while the patient held their
breath, thus eliminating respiratory motion artefacts [Godfrey et al., 2006b]. DT
investigations performed with Varian OBI kilovoltage imagers mounted on treatment
linacs have found that acquisition arcs of 20◦ to 30◦ e offer an ideal combination of
slice selectivity and acquisiton speed [Wu et al., 2007] [Kriminski et al., 2007]. These
groups confirmed that kV DT allowed identification of a variety of organs not readily
visible in single radiographs, and that respiration-correlated DT produced less motion
blur than seen in the equivalent CT scans.
CHAPTER 2. LITERATURE REVIEW
2.3
28
Cobalt Therapy Equipment
Cobalt-based external beam radiotherapy machines fell from favour in the 1980s as
advancements in linear accelerator technology outstripped development on the cobalt
units. Cobalt machines remain common in the developing world, though, and are
likely to continue to play a major role in those countries for the foreseeable future
[Ravichandran, 2009]. While cobalt units are still produced today, none are currently equipped with image guidance systems, and MLCs have only been added in
recent years. It is possible, though, to outfit an existing conventional cobalt machine
with multileaf collimators and to use it for IMRT delivery. Clinical IMRT treatment
plans calculated for a MIMiC binary MLC on a Theratron 780-C cobalt unit indicate dose distributions that are comparable to those obtained with a 6 MV linac
[Joshi et al., 2009]. Treatment deliveries to film using thin pencil beams from the
cobalt unit have yielded dose distributions that match predictions to better than 5%
and 5 mm [Schreiner et al., 2009].
First-generation CT with a translate-rotate benchtop jig was demonstrated on this
same cobalt unit in 1999 [Salomons et al., 1999]. The images obtained were found
to be of sufficient quality to localize small, high-contrast objects within a phantom
[Schreiner et al., 2003a]. Further investigation revealed a highly promising characteristic of Co-60 CT imaging: extremely good linearity between the calculated CT
number and the true electron density of the material, a trait not shared by kilovoltage
CT for high electron densities [Hajdok et al., 2004].
Portal imaging has also been demonstrated on Kingston’s Co-60 machine, using both a scanning liquid ion chamber (SLIC) and an amorphous silicon panel
CHAPTER 2. LITERATURE REVIEW
29
[McDonald, 2010][Rawluk, 2010]. The contrast and noise characeristics of the portal images are quite poor in comparison to kilovoltage radiographs. Due to the high
energy of the Co-60 beam, very little subject contrast is provided by the photoelectric interactions that give kV images their high contrast. The dominant Compton
interactions depend mainly on electron density, which varies only marginally between
different soft tissues; as a result, images taken with the Co-60 beam show almost no
contrast between different soft tissues. A further limitation is the markedly non-point
nature of the cobalt source; the cobalt pellets fill a 2 cm diameter cylinder, which
therefore casts a geometric penumbra in projection images. The presence of this
penumbra gives the Co-60 imaging system a greatly reduced resolution, compared to
systems that use a point-like source.
Tomosynthesis on the cobalt unit has been previously studied, using the SAA
method and SLIC detector [McDonald, 2010]. The results were promising, but the
images produced by the SAA algorithm are visually quite different from both planning
CT scans and conventional radiographs, so clinical staff who are used to other imaging
modalities may have difficulty interpreting SAA tomosynthesis images. Furthermore,
the long readout times of a SLIC would make it difficult to use on a continuously
rotating gantry. Stopping the gantry every few degrees to take an image would
increase the total imaging time, and since the cobalt source cannot be turned off or
quickly pulsed, would also increase the imaging dose; acquiring the image data as
quickly as possible in a continuous rotation is therefore preferable.
More recently, a full Co-60 cone beam CT (CoCBCT) system, using third generation rotational geometry, has been built using the cobalt source and an amorphous
silicon detector panel. Using clinically realistic geometry, a limiting resolution of
CHAPTER 2. LITERATURE REVIEW
30
slightly better than 2.0 line pairs per centimetre was measured with the CatPhan
CTP528 resolution test phantom; in other words, aluminum objects as small as 2.5
mm were distinctly visible against a water-equivalent material. Contrast sensitivity
down to a relative electron density difference of +5% / -4% between feature and background was observed, with an effective imaging dose of 24 cGy, using a Gammex 467
contrast phantom. High contrast features as small as 1.8 mm have been observed at
an effective imaging dose of 17 cGy [Rawluk, 2010].
The practical imaging dose for CoCBCT, however, remains high. Although complete CoCBCT images can be acquired with an effective imaging dose (counting only
panel-on time) as low as 3 to 4 cGy, considerably more dose would have to be given in
practice. For safety reasons, the treatment gantry’s rotation cannot exceed approximately 1 RPM, and CBCT requires that all possible ray paths through the object be
sampled- in other words, the gantry must rotate through at least 180◦ plus the width
of the beam. Therefore, the cobalt source would have to be exposed for at least 30
seconds to collect enough data for a full CT reconstruction. Typical reference dose
rates for a fresh cobalt source are on the order of 300 to 400 cGy/min. Even near the
end of a source’s useful life, the reference dose rate is still over 150 cGy/min. These
values would put the dose for a CoCBCT scan with a bare source in the range of 75
to 200 cGy, an order of magnitude too high to be practical.
Possible ways to reduce the imaging dose include attenuating the beam to reduce
its intensity, using a limited-angle DT method to reduce the total exposure time,
or switching to an X-ray tube or a weaker radioisotope source for imaging. In the
present work, we will focus on DT techniques using the Co-60 machine’s treatment
beam. Some preliminary results with an Ir-192 source will also be presented.
Chapter 3
Theory
In this chapter, we will review the underlying physics and mathematics that make
radiographic imaging and tomographic reconstruction possible.
3.1
Photon Attenuation
Co-60 computed tomography (CT) and digital tomosynthesis (DT) imaging, like other
radiographic imaging modalities, depend on photon attenuation. Attenuation is the
result of photon interactions with the material of the object being imaged. The
interaction of high-energy photons with matter is primarily through one of three
processes, each of which has an energy-dependent cross section that varies with atomic
number (denoted as Z). These dominant processes are as follows:
• The photoelectric effect, in which an incident photon transfers all of its energy
to an electron, causing that electron to be ejected from the atom. This effect is
dominant at low energies (below 0.5 to 1 MeV). The probability of photoelectric absorption per atom is approximately proportional to Z n E −3.5 , where n is
31
CHAPTER 3. THEORY
32
between 4 and 5 [Knoll, 2010].
• The Compton effect, in which an incident photon scatters off an electron, transferring some energy (and usually ejecting the electron from its atom) before
continuing on a new (scattered) trajectory. Compton scattering is typically
dominant from a bit less than 1 MeV to about 10 MeV in materials of biological interest. The Co-60 gamma beam used for most of the present work, with
a mean energy of 1.25 MeV, is attenuated primarily by Compton interactions.
The probability of Compton scattering is dependent on the number of electrons
per unit volume (i.e. the electron density ρe ), and the probability on a per-atom
basis therefore increases linearly with Z; it also exhibits a gradual decrease as
the photon energy is increased [Knoll, 2010].
• Production of electron-positron pairs can occur when photons in excess of 1.02
MeV interact with the nuclear Coulomb field; the pair production effect becomes
dominant above 7 to 15 MeV. Pair production can be a dominant factor in
therapeutic beams from linear accelerators, but is a relatively small player at
the Co-60 energy. The pair production probability scales approximately with
Z 2 and increases dramatically at higher energies [Knoll, 2010].
In addition to the three dominant interaction processes, several other effects contribute to the attenuation of a photon beam:
• The coherent Rayleigh scattering effect changes the photon’s path without reducing its energy, and plays a small but measurable role at energies below
approximately 1 MeV; it is typically one to two orders of magnitude less likely
than photoelectric absorption.
CHAPTER 3. THEORY
33
• Thomson elastic scattering, in which a photon scatters off a bound electron.
• Photonuclear interactions, analogous to photoelectric interactions but with nucleons in place of electrons, can come into play at very high photon energies.
The photonuclear effect is of no measurable consequence in the 1 MeV range
at which the present work is conducted.
• A high-energy photon may produce an electron-positron pair in the Coulomb
field of an individual electron; the resulting momentum transfer is sufficient
to eject the target electron from its atom. This triplet production effect is
a small but not negligible contributor to the total attenuation in high energy
linac beams; it is of no significance in the 1.25 MeV gamma beam from a Co-60
source, which is below the threshold energy for this effect to occur.
Each of these processes has a certain probability of occuring, for a particular
photon energy and target material, and there is a substantial body of literature surrounding the measurement of these probabilities [Podgorsak, 2004]. They can often
be derived on sound theoretical grounds [Jackson, 1999]. It is possible, although computationally intensive, to make a complete accounting of the possible interactions of
an individual photon or electron using Monte Carlo methods. For practical purposes,
though, it is often sufficient to combine all photon attenuation into a single linear attenuation coefficient. Denoted µ, it represents the probability (per unit path length)
that a photon will interact with the material by one of the mechanisms described
above. As the individual cross-sections depend on both photon energy and atomic
number, µ is a function of both E and Z ; furthermore, µ must also be dependent
on the density of the material. To remove this density dependence, it is common to
CHAPTER 3. THEORY
34
Figure 3.1: Dominant interaction processes for photons interacting with matter, over
a range of photon energies and atomic numbers. The Co-60 beam, at 1.25 MeV mean
energy, is dominated by Compton scattering over the entire range of stable nuclei.
Red lines indicate loci of equal probability for the adjacent interactions.
compute and tablulate the mass attenuation coefficient, µ/ρ, which depends only on
photon energy and target composition.
Consider a narrow photon beam, monoenergetic with energy E, incident on a
uniform attenuator of thickness x and with linear attenuation coefficient µ(E) at
the beam energy. If the beam’s initial intensity is I0 , the intensity I(x) after passing
through thickness x of the absorber is given by the Beer-Lambert law [Podgorsak, 2005]:
I(x) = I0 eµ(E)x
(3.1)
In practice, the objects we wish to image, such as human anatomy, are usually not
homogeneous. To account for the many different materials that photons may pass
through, the Beer-Lambert law can be integrated along a ray through the phantom.
If the attenuation coefficient is µ(E, r) at each point r in the object, the observed
CHAPTER 3. THEORY
35
intensity I1 is [Attix, 1986]:
R
I1 = I0 e
µ(E,r)dr
(3.2)
Several additional complications arise in the practical case. We assume that µ
depends on the overall probability that a photon will interact, and thus not be observed at the detector. A photon that is Compton scattered, though, might reach the
detector even though the original (primary) photon did interact. If, as is usually the
case for imaging, there are multiple detector elements, each element can and will observe scattered photons that originated on different rays. The finite size of the cobalt
source adds an additional issue; namely, that while the co-ordinates at which a ray
intersects the detector are known to within the size of a pixel (typically less than one
millimetre), the source of the ray could be anywhere within the relatively large source.
Furthermore, this treatment neglects scattering from the beam collimators or from
within the source itself. The reconstruction methods used for the present work, described in Sections 3.4 through 3.6, generally do not account for these complications,
resulting in certain artefacts that reduce the overall quality of the images.
3.2
Detector Physics
For X-ray or gamma ray imaging purposes, a large array of closely-spaced, identical detectors is desirable. These detectors should also be efficient, i.e. they should
minimize the number of photons and the total energy needed to produce an image.
For many decades, the standard medical radiology detector was a silver halide solution suspended in a gelatinous emulsion on film. In recent years, film has been
CHAPTER 3. THEORY
36
largely replaced by electronic detectors. The detector panels used for this work, a
Varian PortalVision aS500 and a PerkinElmer XRD1640, are semiconductor devices
fabricated on amorphous silicon wafers.
The task of a flat-panel detector is to translate the photon energy fluence incident
on it to a series of binary numbers representing the intensity observed by each detector
pixel. The first step in this conversion is one or more metallic “build-up” layers,
which present a large number of interaction targets to the incoming primary photons.
Primary (incident) photons, scattered photons and secondary electrons liberated from
the build-up layer then interact with a scintillator layer. The resulting cascade of
optical-energy photons strikes the electrically biased semiconducter layer, causing
a charge buildup in the detector cells. The readout circuitry scans through these
cells, shunting that charge through an analog-to-digital converter to get a binary
number proportional to the radiation intensity striking that cell during the acquisition
period. Figure 3.2 illustrates several possible interactions that occur in the Varian
PortalVision aS500 panel.
3.3
Forward Projection and the Radon Transform
We will now mathematically describe the process of taking a single radiographic
projection. The forward projection operation results in the familiar X-ray images used
in diagnostic medicine. These images also form the raw data for digital tomosynthesis
(DT) and cone beam computed tomography (CBCT) reconstructions. This can be
done in a two-dimensional slice, as is the case in many common CT scanners, or
in a three-dimensional volume for DT, cone beam CT, or conventional projection
radiography.
CHAPTER 3. THEORY
37
Figure 3.2: Some possible interaction histories for several high-energy photons striking an amorphous silicon flat-panel detector (not to scale). The diode layer and
scintillator layer are common to all α-Si detectors, but each manufacturer uses different overlying materials, the choice of which is determined primarily by the expected
energy of the incident radiation beam.
1. The photon is Compton scattered; the lower-energy scattered photon continues
onward and an electron is liberated at the interaction site.
(1a) As an energetic electron travels through matter, it transfers some of its energy
to other electrons, ejecting some of them from their atoms.
(1b) Secondary electrons excite the scintillation layer, which releases visible photons
as it relaxes to a lower-energy state; these visible photons strike the silicon photodiodes.
2. An incident photon undergoes photoelectric absorption, transferring its energy to
an electron, that then continues as previously described.
3. A high-energy photon directly excites the scintillator, which then releases visible
photons.
4. A high-energy photon deposits its energy directly in the silicon photodiode, liberating electrons that are then measured by the readout electronics.
CHAPTER 3. THEORY
38
What we observe on the detector is the result of attenuation according to the BeerLambert law (Equation 3.2). When an object is placed between a detector panel and
a radiation source, the intensity measured by each pixel of the detector is related to
the ray integral of the attenuation coefficients at each point in the object along the
ray from source to pixel. (Scattering is, for the moment, ignored.) We will denote
the measured two-dimensional image by I, the corresponding two-dimensional set
of attenuation coefficient ray integrals by R, and the measured value corresponding
to zero attenuation by N . If a CT or DT reconstruction will be performed, the
measured image should be normalized relative to the zero attenuation (air only, no
object) reading and the exponentiation in the Beer-Lambert law should be reversed:
R = − ln
I
N
(3.3)
The mathematical representation of the forward-projection process was derived by
Radon in 1917 and now bears his name [Radon, 1917]. Consider a compactly supported continuous function µ(r) = µ(x, y) in a two-dimensional plane, representing
the attenuation coefficient at each point. (A compactly supported function is zero
outside some defined region; for radiographic purposes, this represents an object surrounded by air or vacuum.) The space of straight lines in the plane is denoted by L,
and any such line can be parametrized as (x(s), y(s)). The Radon transform R, then,
is simply the integral of µ(x, y) along each line:
Z
Z
+∞
µ(r) |dr| =
R(L) =
L
µ(x(s), y(s)) ds
−∞
(3.4)
CHAPTER 3. THEORY
39
In three or more (n) dimensions, it is customary to reserve the Radon name for the
case where the integration is over an n − 1 dimensional hyperplane. In the case of
X-ray imaging, where we integrate along lines in 3-space, this integral is referred to
as the X-ray transform, or the John transform [John, 1938].
The task of an image reconstruction algorithm is to find the original function
µ(x), representing the attenuation coefficients at each point in the object, from the
set of projections R. Although Radon proposed an inverse for the Radon transform
[Radon, 1917], it is generally not used in practical applications. The inverse Radon
transform assumes that no noise is introduced during the forward projection process,
an idealized case that cannot be achieved in practice. Other reconstruction algorithms
are both more computationally efficient and better able to handle the non-ideal case in
which noise is present in the projections. In the following discussion, we will (for the
most part) constrain ourselves to the third-generation, full fan or cone beam geometry
(Figures 2.2 and 2.3) in which the majority of the present work was conducted.
3.4
Filtered Backprojection
Inverting the Radon transform, using real-world data, is not a simple task. The
projection data measured by a detector array cannot be perfect; they are always
corrupted by noise. Using the exact, analytical form of the inverse Radon transform
on noisy data often results in very poor quality images. Other algorithms, that are
more noise-tolerant and more computationally efficient, are used in practice. Of these,
the filtered backprojection class is likely the most common, and an algorithm of this
type, the FDK cone beam backprojection [Feldkamp et al., 1984], was used for the
majority of the current work.
CHAPTER 3. THEORY
40
Exhaustive mathematical treatments of the filtered backprojection cone beam
algorithm are plentiful [Feldkamp et al., 1984] [Kak and Slaney, 1988] [Hsieh, 2009].
The purpose of this section is not to repeat the existing mathematics, but rather to
summarize the key features of the algorithm and to comment on its applicability for
limited-angle DT.
3.4.1
Fourier Slice Theorem
Consider an arbitrary object whose attenuation coefficients are given by µ(x). We
will take the X-ray transforms R of this object at several different angles β relative
to a Cartesian co-ordinate frame (x,y) of our choice. The usual way of obtaining R is
to apply Equation 3.3 to images acquired with a detector array. We will assume, for
the moment, that the rays used to generate a particular projection Rθ are parallel.
The spatial frequency components of the projection, then, are the spatial frequency
components of the object itself in the plane of projection; in other words, the Fourier
transform of the projection at angle β corresponds to a line at angle β through
the two-dimensional Fourier transform of the object, the frequency domain being
specified in the co-ordinate frame (u,v). This result can be proven mathematically
[Kak and Slaney, 1988] and is known as the Fourier slice theorem. This relation is
illustrated in Figure 3.3.
One line segment in the frequency domain is not sufficient to reconstruct the
original object. Consider the case, though, where projection data can be acquired
at many different angles around the object. Each projection, after being Fourier
transformed, gives another unique line through the frequency domain. Once we have
acquired projections over a 180◦ arc, we have sampled the entire frequency domain
CHAPTER 3. THEORY
41
Figure 3.3: The Fourier slice theorem, illustrated in a 2D plane where we are looking
along the rotation axis. If we take the Radon transform (i.e. a projection image),
then take the Fourier transform of that projection, the resulting values correspond to
a line through frequency space at the same angle as the original projection.
(Figure 3.4). We may then interpolate from polar to Cartesian co-ordinates and take
the inverse two-dimensional Fourier transform. Given enough such projections, one
might expect the result to be a close approximation to the original object function
µ(x). This is not quite the case, however. Consider the density of measurement
points in the frequency domain; we are clearly over-sampling at the origin and undersampling at the high spatial frequencies. A weighting filter must be applied on each
line through the frequency domain in order to correct this imbalance. The required
filter is a ramp or wedge, whose value at spatial frequency w is 2π|w|/N if we have a
total of N projections equally spaced over 180◦ [Kak and Slaney, 1988].
In DT acquisitions, we do not sample all posssible angles, instead choosing a
set of projections spanning a small arc βtot < 180◦ (Figure 3.4). There is little
information about the spatial frequencies in the v direction, particularly the lower
spatial frequencies. When such a data set is returned to the spatial domain by a 2D
CHAPTER 3. THEORY
42
Figure 3.4: If we take projections over at least 180◦ of rotation (left), the frequency
space is fully sampled; this is the computed tomography (CT) case (left). The filtering
operation weights the data points according to their distance from the origin (zero
spatial frequency) to compensate for the sparser spacing at high spatial frequencies.
In DT, the rotation arc is limited (right), and the frequency space is not fully sampled.
inverse Fourier transform, features will be blurred out in the y direction, and only the
X-Z planes can be presented as meaningful images. If we use the same ramp filter as
for CT, what little data is available for the low spatial frequencies is suppressed. New
filters must therefore be designed to correct the DT frequency space for particular
applications.
The linearity of the Fourier transform affords us a convenient choice. We may
choose to Fourier transform the projections, filter them, place the resulting data
in frequency space, and then take the 2D inverse Fourier transform to recover the
original object. We may instead choose to Fourier transform the projections, filter
them, and then use a 1D inverse Fourier transform to recover filtered projections,
which can then be “back-projected” and summed as shown in Figure 3.5. These two
procedures are mathematically equivalent, but the latter is easier to implement in an
CHAPTER 3. THEORY
43
Figure 3.5: Projection images, having been filtered individually, are backprojected
into the reconstruction volume (left). As the number of projections becomes large, the
sum of the backprojected images converges to the original function µ(r), representing
the attenuation coefficients at each point in that slice through the patient: a CT
image (centre). In the DT case (right), the imaging arc is limited, and features remain
blurred in the direction for which spatial frequency components are not known; this
corresponds to the second case in Figure 3.3. It is obvious by inspection that the
size of the DT blurring, i.e. the effective slice thickness, depends on the width of the
feature being studied.
accurate and computationally efficient manner and so has been historically favoured
[Kak and Slaney, 1988]. Notably, the filtered backprojection approach is easier to
adapt for use with diverging beams, and it allows reconstruction to begin before
data acquisition is complete; furthermore, polar-to-Cartesian interpolation errors in
the spatial domain affect only small areas, instead of disrupting the entire image as
frequency domain errors are prone to do [Hsieh, 2009].
3.4.2
Fan Beam Filtered Backprojection
Clinically useful X-ray and gamma ray sources are usually point-like sources, in which
case the rays of the imaging beam are not parallel, but instead form a diverging fan.
To illustrate this, we will work in the geometry shown in Figure 3.6. We will use the
CHAPTER 3. THEORY
44
Figure 3.6: In a 2D fan beam (left), each ray in the fan corresponds to a different
θ. We perform the spatial filtering operation on the weighted projection images,
then backproject each of them along their corresponding fans and take the sum of
the resulting backprojections. The cone beam algorithm used for this work treats
the 3D case as a series of tilted 2D fan beams(one of which is shown at right), each
corresponding to one row of the detector. Summing the backprojections for all rows
of all detector positions yields the final image.
variable β for the angle from the y-axis to the central ray of the fan, and describe an
individual ray in the fan beam by its angle γ relative to the central ray. The central
ray is the same in the fan beam case as in the parallel beam case, but the other rays
are not: each ray in the fan beam corresponds to an angle β +γ. If we wish to produce
a CT image, all ray paths through the object must be sampled; it is evident from the
geometry that sampling all ray paths requires that βtot ≥ 180◦ + γm .
For mathematical convenience, it is desirable to treat the detector line (or plane,
in 3D) as passing through the origin, rather than being set back by some distance.
The required transformation is a simple scaling of the pixel size, and we are left with
Rβ at the origin (point O in Figure 3.6).
Given appropriate choices of the angular positions β at which the images are
CHAPTER 3. THEORY
45
acquired, it is possible to rearrange the fan beam data to correspond to a parallelbeam equivalent [Kak and Slaney, 1988]. Consider once again the geometry of Figure
3.6. We have associated the ray passing through point A on the image with angle β,
but in the parallel-beam case, this ray would correspond to point C on the image at
angle β + γ. Let s be the distance from the origin to the detector pixel of interest,
i.e. the length OA. Then the distance t from the origin to point C is t = s cos γ. By
finding θ and s for each ray in each projection, we might reassemble a parallel-beam
set from fan-beam data.
This is, however, unnecessary if we exploit the linearity of the Fourier transform
and choose to backproject individual filtered projections, rather than combining the
projections in the frequency domain. The backprojection process must account for
the divergence of the beam, and we must first weight the raw data to account for the
fact that, with a flat imaging panel, we are using equally spaced colinear detectors,
rather than sampling at equiangular intervals along an arc.
The fan-beam filtered backprojection algorithm can be summarized as follows:
1. Logarithmically transform the measured image data to yield line integrals, and
scale the pixel size so that the image data lie on lines through the origin.
2. Weight the data to correct for the use of flat, equidistant detector elements
instead of equiangular elements.
3. Transform each line of data to the frequency domain, apply a ramp filter to
correct the spatial frequency weighting, and transform it back to the spatial
domain.
4. Backproject each line of filtered data along its corresponding fan, recording the
CHAPTER 3. THEORY
46
resulting image value at each point on the reconstruction grid. Take the sum of
all the backprojections.
5. Normalize the resulting 2D image with respect to the attenuation coefficient of
water to yield a CT image calibrated in Hounsfield units.
Complete mathematical descriptions of this class of algorithms are plentiful, and the
interested reader is referred to previous literature on the subject [Kak and Slaney, 1988]
[Hsieh, 2009] [Feldkamp et al., 1984].
3.4.3
Cone Beam Filtered Backprojection Algorithm
In many cases, including the present work, a cone beam geometry (Figure 2.3) in three
dimensions is convenient to use in a clinical setting. Should we choose to reconstruct
in the spatial domain, the filtered backprojection approach can be adapted to correct
for the cone angle, the extra dimension, and the use of a plane of equally spaced detector elements instead of measuring at equiangular intervals [Feldkamp et al., 1984].
A computationally practical algorithm for this process was published by Feldkamp,
Davis and Kress in 1984, and now bears their initials.
The 3D cone beam algorithm is conceptually and mathematically similar to the 2D
fan beam algorithm, and is identical for one central fan passing through the isocentre.
Outside of that central plane, the cone beam case is approximated by a series of
tilted fan beams. The geometric weighting factor, which corrects for the use of a flat
array of detectors, is modified to account for the new third dimension. The filtering
operation is the same as for the fan beam case, and is applied only in the direction
of movement, i.e. the p direction in Figure 3.7. Finally, the backprojection process
is modified to incorporate the third dimension; each row of a filtered projection is
CHAPTER 3. THEORY
47
Figure 3.7: Imaging geometry and co-ordinate frames for cone beam image acquisition
and reconstruction with the Feldkamp-Davis-Kress algorithm. Images Iβ (p, q) are
acquired at many angles β relative to the object’s co-ordinate frame (x, y, z) before
being transformed to Rβ (p, q) according to Equation 3.3. The system’s rotation axis
is the object’s z axis, and the beam axis is coincident with the y axis when β = 0. In
DT, β = 0 defines the centre of the acquisition arc.
backprojected along the tilted fan beam corresponding to that row. The algorithm
can be summarized as follows, for the geometry illustrated in Figure 3.7.
Consider a series of two-dimensional radiographs Iβ (p, q) corresponding to X-ray
transforms Rβ (p, q) of a three-dimensional object whose attenuation coefficients are
described by a compactly supported continuous function µ(x, y, z). The detector
records a value N corresponding to zero attenuation when no object is in the beam.
The co-ordinates (x, y, z) describe points in the object; the co-ordinates (p, q) describe
points on the detector plane when the detector lies at angle β to the object’s Cartesian
co-ordinate frame. The p and z axes are parallel and the z axis is the rotation axis.
The object, its X-ray transforms, and the measured images can then be related by
CHAPTER 3. THEORY
48
integrating along each of the rays s from the source to each of the detector pixels:
Z
Iβ (p, q)
) = µ(x, y, z) ds
(3.5)
Rβ (p, q) = − ln(
N
s
The corners of the flat detector are farther from the source than the centre of the detector, and subtend different solid angles; it is therefore necessary to apply a weighting
factor as discussed earlier for the fan-beam case. The acronyms SAD and SDD refer
to the source-to-axis and source-to-detector distance, respectively, measured normal
to the detector plane.
SAD
Rβ0 (p, q) = Rβ (p, q) p
SAD2 + p2 + q 2
(3.6)
The weighted data are filtered in the frequency domain to account for the oversampling of low spatial frequencies and the under-sampling of high spatial frequencies.
Filter design will be discussed later; for now, consider the filter H(q 0 ) to be the ramp
function 2π|w|/N described above, multiplied with the projection in the frequency
domain. The transform and filter are applied to each row of pixels on the detector
(constant p) and operate only in the direction of rotation, i.e. the q axis. We will
denote the one-dimensional Fourier transform operator in the q direction as Fq and
its inverse as Fq−1 .
Qβ (p, q) = Fq−1 (Fq [Rβ0 (p, q)] · H(q 0 ))
(3.7)
The weighted, filtered projections are now back-projected into the reconstruction
grid to determine µ0 (x, y, z), the reconstructed approximation to the original density
function µ(x, y, z). The backprojection is performed using the substitutions t =
CHAPTER 3. THEORY
49
x cos β + y sin β and s = −x sin β + y cos β to move between the (s, t) plane (parallel
to (x, y) but rotated by β) and the reconstruction co-ordinate system (x, y, z):
Z 2π
SAD2
SADz
SADt
0
,
dβ
(3.8)
µ (x, y, z) =
Qβ
(SAD − S)2
SAD − s SAD − s
0
For further mathematical background on this algorithm, the reader is referred to chapter 3 of [Kak and Slaney, 1988] or to [Feldkamp et al., 1984]. The in-house MATLAB
implementation used for the present work is described in [Rawluk, 2010].
The FDK algorithm can be used for both CBCT and DT. In the former case,
a total sampling arc of 180◦ plus the total cone beam angle is required in order to
sample all ray paths through the object, and therefore to fill the entire sampling
region in the frequency domain. Additional data can reduce noise, but provides no
new information that would improve resolution or accuracy. In the DT case, the total
sampling arc is much less than 180◦ , leaving huge gaps in the frequency domain; the
net result is that, after backprojection, features are blurred or smudged out in the
direction for which data is missing.
3.5
Shift-and-Add Digital Tomosynthesis
The conventional film tomosynthesis method of Figure 2.1 can be implemented as a
software algorithm. This is known as shift-and-add digital tomosynthesis (SAA DT).
The first step is to transform the actual data measured on the flat-panel imager
to a virtual detector plane, lying parallel to the plane we wish to view. This step
is equivalent to converting from the isocentric geometry used for acquisition on a
rotating gantry, to the linear translation geometry of conventional tomosynthesis.
CHAPTER 3. THEORY
50
The resulting simulated projection images are then shifted, overlaid, and summed
to produce a DT image. In the SAA implementation used for the present work,
we consider only the image data I, and not the logarithmically transformed data R
described by Equation 3.3.
In this reconstruction algorithm, the projection process is implemented as follows.
We consider a flat-panel detector whose pixel pitch (distance between sensor elements)
is S. The detector is held normal to the beam axis, at a fixed distance SDD from
the source, as the source and detector rotate around the patient. We will consider an
individual pixel, in column U and row V of the image taken at angle β.
We create temporary indices p and q to indicate the position of pixel U, V relative
to the detector midpoint, which lies on the beam axis. The position (p, q) thus found
is the same as that used for filtered backprojection, in Section 3.4 and Figure 3.7. For
column indices higher than the midpoint, we define p = S(U − Umid ) and for column
indices below the midpoint, we define p = S(Umid − U ). The row index q is defined in
the same manner. Our pixel then appears in column X and row Y of the simulated
(virtual) detector plane after the projection:
p × SDD cos β 1
X=
SDD ± p sin β S
!
p
q (XS)2 + SAD2
1
Y = p
(SDD × p sin β)2 + (p cos β)2 S
(3.9)
(3.10)
The choice of sign for the ± operator in the equation for X depends on which side
of the detector midpoint p is on, and on the value of β relative to the middle of the
imaging arc. This projection is illustrated in Figure 3.8 for the plane containing the
U (and thus p) axes of the physical detector and the X axis of the virtual detector
CHAPTER 3. THEORY
51
Figure 3.8: Geometry for shift-and-add digital tomosynthesis using isocentric motion.
The source and detector panel rotate together around the isocentre, such that the
distances SDD and SAD are constant. At each angle β within the total imaging
arc, a projection image is taken, then transformed to a virtual detector plane that is
normal to the β = 0 beam axis and that intersects the physical detector panel on the
beam axis for that particular value of β. The magnification SDD/SAD is constant,
and it is evident that the virtual-detector images are equivalent to the conventional
film tomosynthesis planes from Figure 2.1.
plane.
We now find the horizontal distance by which each simulated projection image
must be shifted to bring a plane at distance p from the isocentre into focus. Let the
distance from source to isocentre be A, and the distance from source to detector be
SDD as before. Then, the simulated detector image corresponding to angle β must
be shifted by K pixels, where for p < 0,
K(β, p) = SDD sin β
1
SAD cos β
−1
SAD cos β + p
S
(3.11)
CHAPTER 3. THEORY
52
and where p > 0,
K(β, p) = SDD sin β 1 −
SAD cos β
SAD cos β + p
1
S
(3.12)
After each backprojected image has been shifted by K(β, p) pixels, we take the
average of the stack of shifted images and are left with a DT image of plane p
[McDonald, 2010].
3.6
Algebraic Reconstruction
A radically different, but equally valid, approach to the reconstruction problem is
to treat it as a large system of linear equations. The mathematical basis for this
approach originated in the late 1970s, and it is commonly used in ultrasonic tomography [Kak and Slaney, 1988] [Andersen and Kak, 1984]. The algebraic approach is
very flexible; it can be combined with ray-tracing algorithms to handle refracting or
diffracting rays, and there are many solvers from which to choose.
Algebraic reconstruction may be a promising option for Co-60 DT. Algebraic
algorithms have proven highly amenable to parallel processing on computer graphics
hardware, so it is likely that the computational advantages of filtered backprojection
will soon cease to be a significant factor in the choice of algorithm for a particular
problem. Because of time and resource constraints, though, algebraic approaches
were deemed to be outside of the scope of the present work.
Chapter 4
Experimental Methods
4.1
Imaging Apparatus
The imaging apparatus described here was designed to facilitate cone beam CT and
DT imaging in the treatment beam of a Co-60 teletherapy machine. The key parts of
the system are shown in Figure 4.1. It is already well established that a linac gantry
can be fitted with a kilovoltage X-ray system, largely independent of the treatment
machine itself, and this is common practice on commercially available therapy linacs.
There is no reason to suspect that such a system would behave any differently on a
Co-60 machine than on a linac, so kilovoltage systems were not studied in the present
work. Treatment beam imaging, though, is quite different on a cobalt machine, due
to the large physical size of the source, its energy spectrum, and its continuous beam.
A linac, by comparison, has a nearly point-like source, and produces short, frequent
pulses of radiation, to which the imaging panel electronics can be synchronized.
53
CHAPTER 4. EXPERIMENTAL METHODS
54
Figure 4.1: Experimental imaging system for Co-60 CT and DT studies. Key components are: (A) Amorphous silicon imaging panel, (B) Motor-driven rotation stage
supporting the phantom being imaged, (C) Beam collimator of Theratron T780-C.
4.1.1
Radiation sources
The radiation source used for the majority of the present work was the Co-60 source
of a Theratron T780-C (Best Theratronics, Kanata, ON). The Cancer Centre of
Southeastern Ontario (CCSEO) is equipped with such a machine, and many cancer
clinics in the developing world rely on similar or identical technology. The source
consists of many small pellets of Co-60 sealed inside a stainless steel cylinder, 2 cm
in diameter and approximately 5 cm high. The activity of a new Co-60 teletherapy
source is typically on the order of 400 to 500 TBq, and drops by half every 5.7 years.
Its beam (Figure 1.1) is dominated by two energies, 1.1732 MeV and 1.3325 MeV,
and for many purposes it can be thought of a 1.25 MeV monoenergetic source.
For some experiments, a much smaller and weaker source was desired in order to
reduce the radiation dose to the patient and to alleviate the effects of the geometric
penumbra cast by a large source. The Nucletron Ir-192 Flexisource, intended for
CHAPTER 4. EXPERIMENTAL METHODS
55
high-dose-rate brachytherapy, was part of the CCSEO’s standard clinical inventory,
and was chosen for these experiments. The active part of this source is 0.6 mm in
diameter by 3.5 mm long, and is sealed with a 0.125 mm thick stainless steel sheath.
The half-life of Ir-192 is only 74 days, so the source must be replaced regularly, and the
Ir-192 imaging experiments described here had to be conducted within the first month
of a source’s life to yield sufficient beam intensity. A range of energies are present in
the Ir-192 beam; it is dominated by clusters of peaks near 300 keV, 480 keV and 600
keV but also includes weaker components at many other energies. While numerous
other radioisotopes could conceivably be used as imaging sources, the options for the
present work were constrained to hardware that was already available at the CCSEO.
4.1.2
Detector panels
Two detector panels were used for this work. Both are of the amorphous silicon type,
relying on the interaction principles illustrated in Figure 3.2 to produce electrical
signals in silicon photodiode arrays.
The Varian PortalVision aS500 (Varian Medical Systems, Palo Alto, CA) uses
a 30 cm by 40 cm (384 by 512 pixel) silicon detector array with a 0.784 mm pixel
pitch [Var, 2000]. The active layer of silicon photodiodes is 0.1 mm thick; this is
overlaid with a 0.48 mm phosphor layer, a 1.0 mm copper build-up layer, and finally
a 9 mm protective layer of Rohacell polymethacrilimide foam with an aluminum skin
[Siebers et al., 2004]. This panel was originally designed for use in the treatment
beam of a 6 MV linac, and its structure was optimized accordingly.
The most recent experiments were conducted with a PerkinElmer XRD1640 detector (PerkinElmer Optoelectronics, Fremont, CA) provided by Best Theratronics.
CHAPTER 4. EXPERIMENTAL METHODS
56
This panel uses a 40.9 cm by 40.9 cm (1024 by 1024 px) detector array with a 0.4
mm pixel pitch. Its silicon photodiodes are affixed to a glass substrate and supported
by a printed circuit board made from 3 mm carbon-fibre laminate. Above the image
sensors are a scintillator layer (Kodak LANEX), a 0.5 mm graphite layer, and a 0.75
mm aluminum top plate [Per, 2010], with the sensor top set back by 9.35 mm below
the top plate. The manufacturer claims an operating energy range of 40 keV to 15
MeV; the lack of a dense metal build-up layer suggests that the device is optimized
for the lower end of that range.
The PerkinElmer panel has a notable field-of-view advantage and almost twice the
linear resolution of the Varian panel, but it lacks a dense metal build-up layer and so
is optimzied for lower energies. The choice of this panel was primarily one of availability and convenience, as it was provided by Best Theratronics. The PerkinElmer
panel’s sensitivity to lower energy X-rays also offers the possibility of using the same
imaging panel for the cobalt treatment beam and for a second, lower energy X-ray
or radioisotope source mounted on the same gantry. Although the Varian panel’s
construction is potentially better suited to treatment beam imaging, the unit used
for the present work was old and its control electronics were beginning to fail with
age.
4.1.3
Motion and control system
In order to create a CT or DT image, it is necessary to acquire projection images
at many angular positions around the patient. In a clinical setting, the patient or
phantom lies stationary while the radiation source (and, in some geometries, the
detectors) rotate. In the lab setting, it is often more convenient to hold the source
CHAPTER 4. EXPERIMENTAL METHODS
57
and detectors stationary, and rotate the phantom. The two options are equivalent.
For the present work, the cone beam geometry illustrated in Figure 2.3 was used.
A three-axis (up/down, left/right, rotation) motion stage with stepper motor
drives was built for previous dose delivery and imaging research on the cobalt unit,
and the rotation part of this system (shown in Figure 4.1) was re-used for the present
work. The motion stage was controlled by custom software written in LabView
[Salomons et al., 1999]. Computer control of the imaging panels was performed using
their respective manufacturers’ interface software on a Windows XP computer. The
system integration and automation code was implemented in AutoHotKey; the code
used for the present work is the author’s updated version of an in-house automation
script written several years ago for CoCBCT studies [Rawluk, 2010]. In its current
state, the system can acquire a complete scan with minimal user intervention, except
for periodic resetting of the source timer. It is quite a bit slower than would be expected from a fully integrated system that could communicate directly with both the
stage and the panel at the same time, an acceptable trade-off to facilitate day-to-day
reconfiguration of the experimental system, but one that would have to be corrected
in a clinical implementation.
4.1.4
Phantom alignment system
The bunker in which the Theratron T780-C is installed is equipped with alignment
lasers mounted on the walls on either side of the cobalt gantry. Each wall laser
projects a horizontal and a vertical plane of red laser light; an additional pair of
laser beams are projected from the ceiling. A single laser is mounted high on the
wall opposite the gantry. The cobalt unit includes a lamp that projects through the
CHAPTER 4. EXPERIMENTAL METHODS
58
(a) Laser alignment of a test object, the QC3 phantom, (b) Primary beam collimators of the Therin the imaging system
atron T780-C Co-60 unit
Figure 4.2: The Co-60 system uses intersecting laser beams to identify the machine
isocentre, and a visible light source to allow the user to set the size of the field. When
treating, the light bulb moves out of the way and the radioactive source slides into
position at the apex of the collimators.
same collimator as the treatment beam, and this field light has cross-hairs to project
a centre mark. The beams are aligned so that all laser beams, along with the field
light centre mark, intersect within 2 mm of the machine isocentre. The intersection
of these laser beams was used as the reference origin for aligning the apparatus.
To align the imaging system, the gantry was rotated to the 90◦ position to provide
a horizontal beam. The experiment table was then positioned manually so that the
left and right edges of the surface of the detector panel were at the specified distance
from the isocentre, as determined by using a tape measure with respect to the ceiling
lasers. The detector panel was centred with respect to the field light. The rotation
stage was positioned manually using a tape measure with respect to the ceiling lasers.
Fine alignment of the detector panel in the remaining two rotation axes, and the
CHAPTER 4. EXPERIMENTAL METHODS
59
rotation stage in its two constrained rotation axes, was performed using a spirit level
and shimming wedges.
The uncertainty in the isocentre-to-panel-surface distance and in the isocentreto-stage-axis distance was approximately ± 2 mm. Mechanical tolerances and the
flexibility of some of the mounting hardware prevented further improvement of the
alignment accuracy. It is worth noting that the uncertainties in alignment are on the
order of one-tenth of the diameter of the cobalt source. The imaging system proved
to be particularly sensitive to errors in the alignment of the rotation axis with the
panel’s vertical readout axis; any measurable misalignment of these axes resulted in
images that were heavily blurred outside of the central fan beam. Small errors in
the source-to-axis and source-to-detector distance appeared to have relatively little
effect on the overall image quality, resulting in a slight scaling and loss of geometric
accuracy but no qualitative change in the image appearance.
4.2
Image Reconstruction
The image reconstruction system used here was implemented in-house in Matlab
(Mathworks, Natick, MA). Parts of the system were written by the author specifically for the present work; the reconstruction algorithms themselves had already been
implemented by previous researchers at the CCSEO [Hajdok, 2002] [McDonald, 2010]
[Rawluk, 2010] and those codes were updated and modified by the author for integration into the current system.
CHAPTER 4. EXPERIMENTAL METHODS
4.2.1
60
Pre-Processing
After acquiring each image, but before saving it, three correction operations were
performed by the imaging panel control software.
• A “dark field” or “offset” image was subtracted from the raw image data. The
dark field image was acquired before the scan, with the beam off, and describes
the systematic image noise that is due to leakage currents and other irregularities in the detector electronics. Subtracting it from each image removes these
contributions to the image noise. This correction was small and relatively consistent for the PerkinElmer panel; it was larger and less stable with time on the
older Varian panel.
• The image was normalized with respect to a “flood field” or “gain” image, also
acquired before the scan, this time with the beam on and no object in the
scanner. Each pixel was normalized individually. This step corrects for any
minor differences in the relative response of individual image sensor elements,
thereby reducing another systematic contributon to image noise. This also has
the effect of “flattening” the field, which would otherwise appear darker at the
edges due to their greater distance from the source.
• On the PerkinElmer panel, a “dead pixel” correction was performed. Using a
map of the known manufacturing defects in this particular panel, provided by
the manufacturer, the dead pixels were masked out and replaced by an average
of the surrounding pixels. (The Varian panel’s controller did not perform such
a correction; a similar effect was achieved in the Matlab code by subtracting
some multiple of a pattern of known troublesome pixels from each image.)
CHAPTER 4. EXPERIMENTAL METHODS
61
The recorded image I is related to the dark field image Mdarkf ield , the flood field
image Mf loodf ield and the raw image sensor data M by:
I=
M − Mdarkf ield
Mf loodf ield
(4.1)
Further pre-processing was performed on the raw data in Matlab:
• An optional 2D spatial filtering step could be performed, using a custom kernel
or a moving average filter, to smooth the data in an attempt to reduce noise.
This option was rarely used in the present work.
• The axis offset was found and corrected; i.e. the distance by which the panel’s
centre was offset from the rotation axis. An automated approach to this problem was implemented in which two images separated by 180◦ were taken, one
image was mirrored left-to-right, and the offset necessary to minimize the difference between these two images was determined. This approach worked very
well for many objects; however, it occasionally failed for highly asymmetrical
objects. In these cases, the offset was found manually by minimizing the “halo”
in reconstructed central slices.
• The image data were normalized with respect to a blank-field (zero attenuation) value and, optionally, logarithmically transformed. The log transform is
essential for the filtered backprojection algorithm, as described in Section 3.4,
and is optional for shift-and-add. This step reverses the exponentiation in the
Beer-Lambert law (eq. 3.2) and the normalization assigns a (log transformed)
value of zero to a pixel whose corresponding ray had zero attenuation.
• The image data were, optionally, downsampled to a lower resolution, often 256
CHAPTER 4. EXPERIMENTAL METHODS
62
by 256 or 512 by 512 pixels. The PerkinElmer panel’s native 1024 by 1024 resolution, at 0.4 mm/pixel, was far finer than anything that could be resolved with
the 2 cm diameter cobalt source. A 2- to 4-fold downsampling of the raw data
sacrificed little or no usable resolution, but cut reconstruction times and final
data set sizes by a factor of 8 to 64. Unless otherwise noted, the downsampling
was performed using a standard antialiased bicubic algorithm, i.e. a weighted
average of the pixels in the nearest 4-by-4 neighbourhood. This introduced a
slight smoothing effect, similar to the moving average filter mentioned earlier,
reducing noise at the expense of a slight increase in blur.
• An optional pre-cleaning was performed using a variation of the Radon-Prell
anti-ring algorithm [Prell et al., 2009]. Differences in sensitivity between the
columns of the Varian detector did not always show up in the flood-field correction, and sometimes changed over the course of a long scan session. This
algorithm attempts to smooth out differences between columns, reducing vertical streaking in the raw images and thereby reducing ring artefacts in the
reconstructed 3D volumes. The PerkinElmer detector did not exhibit this flaw
when properly calibrated, making this correction unnecessary.
4.2.2
Reconstruction
Several existing CBCT reconstruction codes based on the FDK algorithm were modified by the author to allow for the arbitrary central angle, projection spacing, filter
design, and total arc necessary for DT reconstruction. The essential components of
the algorithm are described in Section 3.4.
The FDK algorithm calls for a filter to be applied in frequency domain; the natural
CHAPTER 4. EXPERIMENTAL METHODS
63
form of this filter is a ramp or wedge (see Section 3.4). As the random noise in a
detector panel contains mainly higher spatial frequency components, a ramp filter
would enhance this noise. A further complication, in the case of DT, is that the
ramp filter goes to zero at low spatial frequencies; thus, features with a large spatial
extent in the direction of filtering can be artificially suppressed. (In CT, where the
frequency space is fully sampled, this does not pose a problem.) The noise problem
can be addressed by multiplying the ramp filter with a sinc function to produce the
Shepp-Logan filter, which nearly satisfies the Fourier Slice Theorem requirements for
most spatial frequencies but flattens out at the very highest frequencies in the image.
For DT, a filter that does not go to zero at zero spatial frequency is called for; several
possible candiate filters were investigated as part of the present work. The filters
developed for this work will be presented in Figure 5.2 of Section 5.2.
An existing shift-and-add tomosynthesis code (Section 3.5, [McDonald, 2010]) was
refactored and modified by the author to be compatible with the imaging equipment
used for the present work.
4.2.3
Post-Processing
Third-generation CT geometry is inherently prone to ring artefacts. A faulty detector
element will appear at the same relative position to the source over the entire imaging arc; when backprojected, the data from this faulty element leaves a ring in the
reconstructed image. The problem has been studied extensively in previous literature
[Raven, 1998] [Sijbers and Postnov, 2004] [Boin and Haibel, 2006] [Prell et al., 2009].
A ring reduction algorithm based on Prell’s work was implemented on the CCSEO’s
cobalt CT system in 2010 [Rawluk, 2010] and it was used, where appropriate, in the
CHAPTER 4. EXPERIMENTAL METHODS
64
present work. The PerkinElmer panel’s control software corrects for known defects
before saving the data, so ring correction was often not necessary when using data
from this panel.
Pixels near the centre of the imaging panel are known to pick up more scattered radiation from the phantom than pixels near the edge of the panel [Kak and Slaney, 1988].
As a result, the panel may record higher than expected intensities near the middle of
the image when an object is in the beam. When used as inputs to a reconstruction algorithm, such images falsely imply that there is less attenuation through the centre of
the object. The result is an overall “cupped” appearance to the reconstructed image;
the CT number appears lower in the middle than it should be. Cupping corrections
for Co-60 cone beam CT have been studied previously [Rawluk, 2010] and, while minor cupping artefacts were visible in many of the images used here, the details of
their correction were not a major consideration in the present work.
4.3
Image Analysis
Standard tests exist for measuring image quality in cone beam CT and for portal
imaging. DT is not used as widely as CT or portal imaging, so image quality in DT
is often reported qualitatively or by modifying tests originally intended for portal
imaging.
4.3.1
Resolution
In this and following sections, reference will be made to the “spatial frequency” of
a test pattern. Spatial frequency is simply a way to describe the size of features in
CHAPTER 4. EXPERIMENTAL METHODS
65
a test pattern. If we arrange a pattern of lead bars 0.1 cm wide, separated by light
plastic bars 0.1 cm wide, the spatial frequency of the pattern is (0.1 + 0.1)−1 = 5 line
pairs per centimetre (lp/cm).
Modulation Transfer Function
The modulation transfer function (MTF) of an imaging system is a way to describe the
spatial frequency response of the system. The MTF at a given spatial frequency is the
ratio of output modulation to input modulation at that spatial frequency. In terms of
what we see in an image, the MTF is essentially the contrast (the difference between
light and dark, relative to the average value) observed at that spatial frequency, and
is typically stated relative to the contrast at very low spatial frequencies. If the
MTF at a particular spatial frequency is 0.50, the contrast observed in the image
at that spatial frequency is half the contrast observed at very low frequencies. The
MTF describes the entire imaging system, and its definition does not depend on the
physics involved; given appropriate test patterns, the MTF is defined the same way
in optical photography as in digital tomosynthesis or conventional radiography.
A closely related resolution metric is distinguishable line pairs per centimetre. This
is a subjective assessment of the highest spatial frequency at which an alternating
light/dark pattern is visible. The relation between MTF and distinguishable line pairs
depends on image noise, viewing conditions and the observer’s visual acuity, but it
can be roughly stated that the distinguishable limit corresponds to an MTF of 2% to
5%, the latter value being widely accepted [Silverman, 1998] [Koren, 2011].
A distinction should be made between the case of a high-contrast test pattern,
CHAPTER 4. EXPERIMENTAL METHODS
66
which is essentially a square wave input, and a sinusoidal input whose Fourier transform is a pure single frequency. In the results presented here, we will consider the
relative modulation transfer function for a series of square wave inputs, normalized
to MTF = 1 at the lowest available spatial frequency in the bar patterns. If we
also measure the image values for a large light region and a large dark region, effectively giving us the contrast between uniform areas without any effect from the
blurring of the edges, we can calculate the sine wave MTF from the square wave MTF
[Coltman, 1954] [Gopal and Samant, 2008]. These sine wave MTF curves will also be
presented.
Point, Line and Edge Spread Functions
In response to a nearly point-like object, an ideal imaging system would produce a
one-pixel point on an otherwise unaffected background. In practice, there will be
some blurring between that one pixel and the background, and the point object will
appear “fuzzy”. The actual image recorded by the system in response to an infinitely
small point object is the point spread function (PSF) of the imaging system. A
similar procedure, taking a one-dimensional profile through a thin wire instead of the
tiny point, yields the line spread function (LSF). The PSF and LSF illustrate how
much blurring the imaging system introduces. In the case of Co-60 treatment beam
imaging, the PSF is dominated by the geometric penumbra that results from having
a non-point source.
A good approximation to a true point object can be made in optical photography,
where a sufficiently small black dot on white paper will suffice. In radiography, it is
not so simple, as an object must have mass– and therefore size– if it is to attenuate
CHAPTER 4. EXPERIMENTAL METHODS
67
a radiation beam. The closest we can come is to use wires or pellets of dense metals,
such as tungsten or gold. Even then, a pellet large enough to noticeably attenuate
the radiation beam will generally be at least as large as the sub-millimetre pixels of
the detector.
Instead of the point or line spread functions, it is therefore common to use the
edge spread function (ESF) to describe the blurring of features in radiography. The
ESF is found by looking at a profile of pixel values across a sharp edge between
a high-density material and a low-density one. The first derivative of the ESF is
approximately the LSF, and the Fourier transform of the LSF or PSF is the MTF
[Rossman, 1969]. Since the Fourier transform of a point object (a delta function) is
a constant function, the “ideal” MTF would also be a constant function. In practice,
the PSF or LSF is not a point, and its Fourier transform– the MTF– drops off as the
spatial frequency increases. A wider (blurrier) PSF corresponds to a faster fall-off of
the MTF.
Resolution of Cone Beam CT
The resolution of the Co-60 CBCT system was measured by scanning a CatPhan
CTP528 phantom module. The CTP528 consists of 21 groups of 2 mm thick aluminum bars embedded in a water-equivalent plastic. The spacing between the bars in
each group corresponds to spatial frequencies of 1 to 21 line pairs per centimetre. For
the present work, the limiting resolution was taken to be the highest spatial frequency
at which the separation between the aluminum bars could be visually distinguished.
CHAPTER 4. EXPERIMENTAL METHODS
(a)
68
(b)
Figure 4.3: The QC3 spatial resolution phantom from Standard Imaging. (a) Optical
photograph. (b)Portal image in Co-60 beam with PE XRD1640 panel, SAD 80 cm,
SDD 120 cm.
Resolution of Digital Tomosynthesis and Portal Images
The resolution of DT and portal images was quantified by finding the relative modulation transfer function according to the method of Rajapakshe et al, using images
of the PipsPro QC3 phantom [Rajapakshe et al., 1996].
The QC3 phantom, shown in Figure 4.3, is used in one common implementation of a quality assurance test used to check for problems with megavoltage X-ray
imaging systems [Rajapakshe et al., 1996]. The test object contains five groups of
lead/plastic strips, each resembling a zebra stripe pattern and each with a different
spacing between the strips. These groups are used to assess the relative modulation
transfer function of the imaging system at different spatial frequencies. The phantom
CHAPTER 4. EXPERIMENTAL METHODS
69
also contains solid lead segments of varying thicknesses. The phantom is placed at a
45◦ angle to the detector readout lines so that aliasing artefacts, due to sharp edges
lining up with pixel rows or columns, do not affect the results.
In this method, we consider an image of several sets of dark/light line pairs, for
example, the QC3’s stacks of alternating lead and plastic bars of varying thicknesses.
The spatial frequency f of each set of bars is the reciprocal of the spacing between
bars in a stack. For each of the five spatial frequency regions provided in the QC3
phantom, we define σ1 as the standard deviation of the pixel values in that region on
a test image A, and σ2 as the standard deviation of the pixel values in a reference
√
image B. We also consider σc , which is 1/ 2 times the standard deviation of the
pixel values in the difference image A − B. The relative modulation transfer function
for a square wave input can be found by taking:
p
RM T Fsquare (f ) = σ1 2 − σc 2
(4.2)
As this is a relative measurement only, it is usually normalized to RM T Fsquare = 1
at the lowest available spatial frequency. The resulting RMTF curves indicate how
quickly the system’s performance falls off at higher spatial frequencies, and their
use in conventional radiography is well established [Coltman, 1954]. The MTF for a
sine wave input was determined from the square wave relative MTF [Coltman, 1954]
[Gopal and Samant, 2008].
For edge spread measurements, a slab of solid lead (Figure 4.4) was used to produce
images with sharp, high-contrast edges in both the horizontal and vertical directions.
The lead slab was 10 mm thick and was supported in the central X-Z plane, i.e. the
plane of the DT image at the rotation axis. With one corner of the lead slab on the
beam axis, the slab extended beyond the edges of the field in two directions. It was
CHAPTER 4. EXPERIMENTAL METHODS
70
Figure 4.4: A square of lead sheet, 1.0 cm thick, used for determining edge spread
functions. The lead edge is a good approximation to a sharp, high-contrast edge when
imaging at megavoltage energies. A smaller cube of lead alloy holds the sheet upright
as the stage rotates during a DT image acquisition sequence.
surrounded only by air.
4.3.2
Contrast
Contrast in CoCBCT
The contrast characteristics of Co-60 cone beam CT have been studied previously
[Rawluk, 2010] and those experiments will not be repeated here. It was deemed
appropriate, however, to confirm that the results of [Rawluk, 2010] hold for the new
imaging panel and the more realistic geometry used for the current work. To this end,
the low-contrast sensitivity of the CoCBCT system was assessed using the CatPhan
CTP404 phantom (The Phantom Laboratory, Salem, NY). The phantom consists of a
water-equivalent plastic in which several holes are drilled. Plugs of various materials
CHAPTER 4. EXPERIMENTAL METHODS
(a) CatPhan
71
(b) Gammex 467
Figure 4.5: CatPhan CTP404 and Gammex 467 phantoms. The Gammex is shown in
the orientation in which it was scanned for the DT sensitivity measurements described
in Sections 4.3.2 and 5.4.2.
are inserted in these holes. The low-contrast sensitivity of the system was assessed
by finding the lowest contrast plugs that were visible against the water-equivalent
background, i.e. the plugs with a relative electron density closest to that of water.
Contrast in CoDT and Portal Images
The CTP404 and the Gammex RMI 467 (Gammex Inc, Middleton, WI), shown in
Figure 4.5, are designed for use with conventional CT scanners in which the imaging
apparatus can make a full 360◦ rotation around the phantom. This is not the case in
DT. For small imaging arcs, the slice thickness of DT becomes large, and features that
lie in one plane appear, with some blurring, in other planes. If these phantoms were
CHAPTER 4. EXPERIMENTAL METHODS
72
used in their normal orientations for small arc DT, the individual contrast cylinders
would appear to overlap and blend into each other for some viewing angles.
The method chosen for contrast sensitivity measurements in DT and portal imaging was to use the Gammex 467 phantom in an unusual orientation. The Gammex is a
cylindrical disc, and its axis is normally aligned with the Z-axis (rotation axis) of the
imaging system. For DT and portal image measurements, the Gammex phantom was
used with its axis coincident with the central imaging beam axis. As the phantom’s
sample cylinders are thicker than the main disc of the phantom, the contrast cannot
easily be assessed visually with the phantom in this orientation. The assessment was
therefore performed mathematically, by measuring the mean and standard deviation
of the image values for a small region in the centre of each sample cylinder. These
values were then compared to the known electron density of each cylinder.
4.3.3
Geometric Considerations
The filtered backprojection algorithm and the shift-and-add algorithm contain assumptions and approximations, and cannot be assumed to provide perfect DT reconstructions. The detector, likewise, is not perfect and introduces some blurring
that could conceivably have a preferred direction near the edges of the field. It is,
therefore, not possible to guarantee that a reconstruction will be free of distortions or
image artefacts. As a major potential use of this technology is for patient positioning, where geometric accuracy is critical, it was necessary to measure any distortions
introduced by the imaging and reconstruction process.
A new phantom was designed and built to allow for observation and measurement
of any geometric distortions introduced during the DT imaging and reconstruction
CHAPTER 4. EXPERIMENTAL METHODS
73
Figure 4.6: The DT geometric distortion phantom, shown in an excerpt from its fabrication drawings. The phantom is made from acrylic, i.e. poly(methyl methacrylate)
and is 50 mm thick, with the illustrated features lying 25 mm below the surface.
CHAPTER 4. EXPERIMENTAL METHODS
74
process. This phantom was also used to find the slice thickness profiles for each DT
method. The phantom is shown in Figure 4.6. Its main features, all of which are
embedded in solid polymethacrylate (acrylic) resin, are:
• A grid of 2 mm lead pellets, uniformly spaced at 2 cm intervals. The centre of
each pellet is located in the reconstructed image, and its observed co-ordinates
compared to the expected position. In this manner, any geometric distortion
introduced by the FBP (Section 3.4) and SAA (Section 3.5) algorithms could
be observed and measured.
• Two 2 mm tungsten rods in an X pattern. The X allows an observer to confirm
the flatness of the DT focal plane; should the focal plane be warped, the corner
of the X near the centre of the phantom will be in focus for one DT plane, while
the far corner of the X will be in focus at a different DT plane.
• Four tungsten rods in a box pattern. Two of these are used in conjunction with
the room lasers, and later with the imaging software, to verify the alignment
of the phantom. The horizontal rod serves to reveal any loss of low spatial frequencies during reconstruction, a possible problem with filtered backprojection
DT. Slice thickness profiles are extracted from the reconstructed image of the
vertical rod. The outermost rods are used to confirm field of view, and to reveal
possible edge-of-field effects.
• A grid of stainless steel wires, staggered at 2 cm intervals. These allow for
visual imspection of the direction of the tomosynthesis blur– for example, is it
purely horizontal, or does a particular reconstruction method introduce a radial
component to the DT blur.
CHAPTER 4. EXPERIMENTAL METHODS
75
The extraction of data from images of this phantom was partially automated in
Matlab. However, no automatic image segmentation routine was found to work reliably on the noisy, low-contrast lead pellet grid, so the pellet centroids were measured
manually for each image.
4.3.4
Anthropomorphic Phantoms
The image guidance system on a modernized clinical Co-60 machine would be used
primarily to image patients, so its performance on human-like (anthropomorphic)
phantoms is an important indicator of its clinical utility.
The RANDO phantom shown in Figure 4.7 (The Phantom Laboratory, Salem,
NY) is used as a surrogate for a live human in imaging and dosimetry experiments
where a close approximation to human anatomy is needed. It consists of a natural human skeleton, encapsulated in a urethane gel whose density and average atomic number are a close approximation to human muscle with randomly distributed fat. The
chest cavity contains a synthetic foam with similar density to lung tissue [TPL, 2011].
RANDO is cut into 2.5 cm transverse slices, of which only the necessary subset for a
particular experiment are used.
The CIRS pelvic phantom (CIRS Inc, Norfolk, VA) shown in Figure 4.8 contains
tissue-equivalent materials to simulate the prostate gland, bladder, pelvic bone and
rectum.
CHAPTER 4. EXPERIMENTAL METHODS
76
Figure 4.7: The head segment of the RANDO anthropomorphic phantom. It is made
of natural bone encapsulated in a tissue-equivalent urethane polymer.
Figure 4.8: The CIRS pelvic phantom. Synthetic polymers, with radiological properties similar to those of the various organs, are cast in place in a tissue-equivalent
gel.
CHAPTER 4. EXPERIMENTAL METHODS
4.3.5
77
Image Guidance Accuracy Test
A study was performed to compare the accuracy of image registration for three
methodologies: CoCBCT, CoDT using the FDK algorithm, and cobalt portal imaging. The purpose of this experiment was to determine whether images taken on the
cobalt machine could be accurately and consistently registered to corresponding images taken on a conventional CT scanner, and to determine the error involved in doing
so. As this experiment was meant to roughly simulate a clinical workflow, the RANDO
anthropomorphic phantom, which closely approximates real human anatomy, was
used.
A jig was fabricated to allow precise alignment of the RANDO head, torso or
pelvis sections with respect to the alignment lasers. With the head section mounted
in the jig, the zero position marks were aligned with the cobalt machine’s lasers and
a series of images were taken, using the Varian aS500 panel, at 1.5◦ intervals as the
phantom rotated about the Z axis. The jig and phantom were then shifted by a few
millimetres in each direction and the scan was repeated. In doing so, a position error
was introduced, the exact value of which was recorded but was not provided to the
observers who would attempt to register the images. Finally, the jig and phantom
were moved to a conventional planning CT scanner (Philips AcQSim), aligned to that
machine’s lasers, and scanned. This procedure was repeated for the torso and pelvis
sections of the RANDO phantom.
From each set of cobalt image data, three image sets were extracted. A CoCBCT
image was reconstructed, using the FDK algorithm (Section 3.4). This same algorithm was used on a subset of projections spanning a 12◦ arc to produce a digital
tomosynthesis image. Finally, the projection images at 0◦ and 90◦ were used as-is.
CHAPTER 4. EXPERIMENTAL METHODS
78
Figure 4.9: Aligning a Co-60 CBCT image of the RANDO head phantom to the
corresponding planning CT image.
In the CoCBCT and CoDT cases, the raw 3D image from the planning CT scanner
was used as a reference. The orthogonal portal images were matched to digitally
reconstructed radiographs (DRRs); DRRs are simulated projection images calculated
by taking the X-ray transform (Section 3.3) of the planning CT data.
Matching of the images was performed using a modified version of the CERR
radiotherapy research toolbox for MATLAB. Six clinical physicists, two physics residents and two QA technologists were recruited to perform the matching. They were
asked to manually move a cobalt image, overlaid on top of a planning image as depicted in Figure 4.9, until the two images appeared to match. The software then
reported the displacement in each Cartesian axis, which was later compared to the
known shifts that had been introduced when the phantoms were scanned.
This resulted in nine tables of data: for each of the three imaging modalities,
and for each of the three phantom sections, a series of measured shifts were recorded
for several attempts by several observers. The measured shifts were first adjusted
CHAPTER 4. EXPERIMENTAL METHODS
79
so that the average of all observed shifts for the case where shift=(0,0,0) was zero;
this compensated for any misalignment of the lasers, and the resulting correction was
applied to all measured shifts. The data were then manually culled to remove cases
of clear operator error. Any observed shift in excess of 10 mm was automatically
deemed to be due to operator error; in addition, a few cases were culled where a clear
pattern in the data indicated a particular user’s unfamiliarity with the software (for
example, getting the exact same large error in one axis for three consecutive tries at
the same data would imply that the user did not know how to move the image in
that axis). The fraction of cases culled in this way was recorded as the operator error
rate for each modality. The remaining data were analyzed to find, for each modality
and phantom section:
• The mean error in each Cartesian axis;
• The mean absolute 2D vector error in the XZ and YZ (“beam’s eye view”)
planes;
• The mean absolute 3D vector error;
• The range of variation of each of these errors, to one standard deviation.
In the case of DT, where only one set of planes was viewed, the 3D error was estimated
by assuming that the magnitude of the error in the X-direction would be the same as
that in the Y-direction, and that the same Z shift would be measured in either view.
CHAPTER 4. EXPERIMENTAL METHODS
4.4
80
Dose Estimates
A major concern when imaging with a high-energy treatment beam is the radiation
dose delivered to the patient for imaging purposes.
The decay rate, and therefore the radiation intensity, of a radioisotope source is
very predictable. It is therefore not necessary to perform a dose measurement for
every experiment. The measurement can be made once, under carefully controlled
conditions, and the dose involved in an actual experiment can be calculated based
on that measurement, the geometry involved, the half-life of the source, and the time
elapsed since the measurement.
A convenient reference condition is established in the TG-51 dosimetry protocol
[Almond et al., 1999]. We consider a radiation beam, 10 cm by 10 cm square at the
machine isocentre, incident on a water tank that extends well beyond the edges of
the beam. The reference dose rate is the dose rate to water at the isocentre, with the
isocentre at a depth of 10 cm below the surface of the water, under these standard
conditions.
Tables listing the reference dose rate for these standard conditions at monthly
intervals, spanning the expected lifetime of the source, were prepared when the source
was installed. The dose calculated for a particular scan was based on the reference
dose rate from these tables for the date of the scan.
4.4.1
Imaging Dose
We will define the imaging dose to be the total dose to water, at the CT or DT rotation
axis, under the reference conditions described above, during the time in which images
are actually being taken.
CHAPTER 4. EXPERIMENTAL METHODS
81
The reference dose Dref (cGy/min) is measured at a distance dSI from the source;
the imaging rotation axis is at a distance dSO from the source. If we acquire N images
in total, and the detector is active for T milliseconds for each image, the imaging dose
Dimg is:
Dimg = N Dref
4.4.2
dSI
dSO
2 T
60 × 1000
(4.3)
Total Dose
The cobalt source requires a transit time of approximately two seconds to move
between the shielded and exposed positions, and a shutter capable of blocking the
beam would be extremely heavy. It is therefore not possible to interrupt the beam
between consecutive frames of an image sequence, as is done with X-rays produced by
a linac or conventional tube. The total dose delivered while imaging with the cobalt
beam will in general be somewhat higher than the imaging dose. If we consider a
gantry that rotates at ω revolutions per minute, and we image over a total arc of βtot
degrees, the total dose Dtot is:
Dtot = Dref
dSI
dSO
2 βtot
360 × ω
(4.4)
Chapter 5
Results
5.1
Radiation Dose
Applying the calculations described in Section 4.4 to the imaging system used for
the present work, we find that under appropriate operational constraints, the total
dose due to imaging will be that shown in Figure 5.1. The gantry rotation speed is
restricted to 1 rpm, as is the case on clinical machines. Increasing the spacing dβ
between projections reduces the imaging dose, but since the source cannot be pulsed
off quickly, the total dose shown in Figure 5.1 is not affected– the extra dose is simply
wasted. Knowing the gantry rotation speed and the time needed for the imaging
panel to take one image, we can determine the spacing dβ that yields no wasted dose;
this spacing is 0.80◦ for the fastest frame (133 ms) of the PerkinElmer XRD1640
detector, and 0.60◦ for the 100 ms frame of the Varian aS500.
It is clear from Figure 5.1 that, without some form of attenuation to reduce the
beam intensity, the dose due to imaging is high enough that Co-60 cone beam CT
cannot be used on a clinical machine. Collecting enough image data for CBCT
82
CHAPTER 5. RESULTS
(a) CoCBCT
83
(b) CoDT
Figure 5.1: Radiation dose due to (a) CoCBCT and (b) CoDT imaging, as a function
of the total acquisition arc, for a fresh and an old source. The frame time is 133
ms, and dβ = 0.80◦ , chosen so that the panel is never sitting idle while radiation is
being delivered. The SAD is 80 cm. For comparison, the radiation dose due to CBCT
imaging with a kilovoltage X-ray tube is typically on the order of 1.6 to 3.5 cGy.
reconstruction would require the source to be exposed for at least half a minute on a
1 rpm gantry. The resulting radiation dose would be far too high, leading to adverse
side effects well in excess of those normally associated with radiotherapy. Speeding
up the gantry rotation would reduce the dose, but not enough for safe imaging, and
would risk serious injury if part of the fast-moving gantry were to bump into the
patient.
The following sections, therefore, will focus on Co-60 DT techniques, in which the
very small total arc allows a dramatic reduction in the total dose due to imaging. It
is likely that beam attenuators or collimator apex modifications would be necessary
to reduce the dose to clinically acceptable levels, but the arc angle alone yields an
order-of-magnitude improvement in dose over CoCBCT.
CHAPTER 5. RESULTS
5.2
84
Spatial Filtering
In Section 3.4.1, we saw that when performing a CT reconstruction, it is necessary to
apply a spatial filter to the raw images to compensate for the non-uniform sampling
of the frequency space. A simple ramp function should suffice for CT; in practice,
the Shepp-Logan filter, which weights the highest spatial frequencies somewhat less
heavily so as to avoid amplifying the image noise, is often preferred. The choice of
an appropriate filter for DT, though, is not so obvious. A ramp or Shepp-Logan
filter would produce the desired weighting at higher spatial frequencies, but nearly
eliminates the lowest spatial frequencies, a range that is already under-sampled by the
nature of the limited-arc acquisition. Therefore, three different spatial filters (Figure
5.2) were used for these experiments. One is the standard Shepp-Logan (SL) filter.
The others, designed by the author for this work, are a modified Shepp-Logan filter
(SLLF) with the lowest spatial frequencies kept, and a modified Shepp-Logan filter
(SLNZ) with a constant, non-zero offset added to all spatial frequencies equally.
The effects of each of these filters on the sharp lead edge phantom, along with the
unfiltered case used by the shift-and-add algorithm, are shown in Figure 5.3. There is
a clearly visible difference between the SL filter and the other three cases; the loss of
the lowest spatial frequencies in the horizontal direction is obvious. In CT, this would
be compensated for by projections from other angles, but in DT, it poses a significant
problem. It is also immediately clear that the resolution of the FBP DT system using
the Shepp-Logan filter will be quite different in the vertical and horizontal directions.
CHAPTER 5. RESULTS
85
Figure 5.2: Spatial filters used for DT reconstruction with the filtered backprojection
algorithm.
(a) FDK algorithm, (b) FDK, Shepp-Logan (c) FDK, Shepp-Logan
Shepp-Logan filter (SL) filter plus constant off- with lowest frequencies
set (SLNZ)
kept (SLLF)
(d) SAA algorithm
Figure 5.3: The effect of different reconstruction filters on the appearance of DT
images of the lead plate described in Section 4.3.1. The lead plate is 1.0 cm thick and
its edge lies on the rotation axis. Under the (horizontal-only) Shepp-Logan filter used
in CBCT, the vertical edge is enhanced in this DT image, but large uniform areas
corresponding to low spatial frequencies are not rendered faithfully. Variations on
the Shepp-Logan filter in which low frequencies are kept yield DT images that more
faithfully reproduce the true object. In SAA DT, no spatial filtering is used. For all
images, dβ = 1◦ , βtot = 40◦ and 10-frame averaging was used to yield 1330 ms/frame.
CHAPTER 5. RESULTS
86
Figure 5.4: Edge spread functions in the horizontal (X) and verical (Z) directions,
measured across a sharp lead edge, for filtered backprojection DT with three different
spatial filtering methods.
5.3
Resolution
The measurements described in this section summarize the spatial resolution of the
prototype Co-60 DT imaging system for a range of total imaging arcs, using acquisition geometry chosen to provide sufficient clearance to scan a patient.
5.3.1
Edge Spread Function
The images in Figure 5.3 include sharp edges in both the horizontal and vertical
directions. From these, we can extract edge spread functions, which are useful for
comparing the resolution and the blur characteristics of the four methods.
If the total imaging arc is fixed at 10◦ , the edge spread functions of the three filtered backprojection methods are as shown in Figure 5.4. In the horizontal direction–
CHAPTER 5. RESULTS
87
the direction of movement and of filtering– the SL filtered reconstruction exhibits the
sharpest edge of the three, but does not faithfully reproduce the large, uniform regions
of air and lead on either side of the edge. The high-pass filter has almost completely
cancelled these very low frequency components. The other two filters, developed by
the author for use with this DT system, show an edge that is nearly as sharp, but
without losing the low frequency components. The exact shape of the transition from
the edge to the uniform region varies slightly, but the increase in blurring that would
result appears to be minimal. Looking at the vertical direction, we see that with the
SL filter, the edge is noticeable but nearly lost in the noise, the loss of contrast being
due once again to the horizontal high-pass filter. The SLNZ and SLLF filters yield
a Z-direction edge spread function that is generally similar to their X-direction ESF,
apart from a slightly different shape to the knee region.
Direction-dependent variations in the response of an imaging system are undesirable. If a system responds to horizontal edges in a very different way than it responds
to vertical edges, the resulting images will be difficult for a radiologist or radiation
therapist to interpret. With this in mind, the SLLF and SLNZ spatial filters are particularly appealing, whereas the unmodified Shepp-Logan filter is likely to produce
images that would cause some confusion for viewers unfamiliar with its particular
characteristics.
An important parameter in a DT acquisition is the total imaging arc, βtot , through
which the source and detector rotate. It would not be unreasonable to expect some
change in the appearance of edges as βtot is changed. Sweeping through a range of
possible arcs for three of the algorithm/filter combinations under study, we find the
edge spread functions shown in Figure 5.5. It would appear that, apart from the
CHAPTER 5. RESULTS
88
previously mentioned case of the Shepp-Logan filter, the ESF varies only slightly
with the total imaging arc over the range of angles used for DT. The SAA algorithm,
which has no spatial filter, exhibits the same ESF (Figure 5.5, bottom row) for any
choice of total arc.
5.3.2
Downsampling
When using the PerkinElmer XRD1640 detector panel, it was necessary to either crop
the images significantly, or downsample them to a lower resolution, in order to perform
reconstructions in a reasonable amount of time. When an image is downsampled to a
lower resolution, some information is lost. If we wish to downsample the raw images,
we must demonstrate that the information that is lost is not important information.
To confirm this, the modulation transfer function of a raw portal image was measured
using the QC3 phantom described in Section 4.3.1. The resulting MTF curves were
compared to MTF curves calculated from downsampled versions of the same portal
image, as shown in Figure 5.6.
From these charts, it is clear that downsampling from 0.4 mm/pixel to 0.8 mm/pixel
is not detrimental to resolution. The resolution loss introduced by the downsampling
operation is evidently negligible compared to the blurring created by the imaging system itself (mainly the large diameter of the source). Only at the very highest spatial
frequencies is any difference observed, in which case the downsampled images appear
slightly superior- but still at the threshold of visibility, and therefore not significantly
different. As a practical consequence, money could be saved by using a lower resolution detector– one with 512x512 resolution and 0.8 mm pixels, for example– without
CHAPTER 5. RESULTS
89
Figure 5.5: Edge spread functions for Co-60 DT images at SAD 80 cm, SDD 120
cm. Top row: Filtered backprojection, Shepp-Logan filter. Middle row: Filtered
backprojection, SLLF filter. Bottom row: Shift-and-add.
CHAPTER 5. RESULTS
90
any real sacrifice in image quality. The point at 0.227 lp/mm is a peculiar one, producing a much lower MTF than might be expected. This is due to the large physical
size of the Co-60 source, and the geometric penumbra that is therefore produced.
At this spatial frequency and distance, the width of the penumbra matches up with
the line pair spacing in such a way as to cancel out much of the image contrast.
(An optical ray-tracing illustration of this effect is shown in Figure 5.7.) By most
standards, though, these are very poor MTF curves, being severely limited by the
large penumbra that results when the source size is large and the detector is held far
from the object. Previous work and theoretical considerations indicate that better
spatial resolution is achievable if the detector is very close to the rotation axis, but
it is probably not feasible to reduce the axis-to-detector distance below 30 to 40 cm
without risking collision with the patient.
5.3.3
MTF of DT images
With 0.5x bilinear downsampling deemed acceptable, MTF measurements were made
using the QC3 phantom for two sets of DT images. The first set was produced
using the FDK filtered backprojection algorithm (Section 3.4) and a Shepp-Logan
spatial filter. The second set used the SAA algorithm (Section 3.5) and no filter.
Total acquisition arcs ranging from 4◦ to 20◦ , with a 1◦ projection spacing, were
used for both algorithms. An additional measurement was made for a quarter-circle
acquisition in 5◦ increments. The results are illustrated in Figures 5.8 and 5.9
The filtered backprojection case shows a significant improvement in resolution over
the basic portal image. While the penumbra-blurred 0.25 lp/mm point remains unaffected, higher spatial frequencies are dramatically clearer in FBP DT images. The
CHAPTER 5. RESULTS
RMTFsquare
91
MTFsine
Figure 5.6: Modulation transfer function, as measured using the QC3 phantom, for
Co-60 portal images using the PerkinElmer XRD1640 detector at SAD 80 cm, SDD
120 cm. Frame time 1330 ms. MTF curves are shown for raw 1024x1024 pixel images
and for images downsampled to 512x512 resolution using two standard image resizing
algorithms.
Figure 5.7: Simulated ray-traced shadows of a 0.227 lp/mm bar pattern in the beam
of a 2 cm diameter light source. Certain combinations of spatial frequency and distance cause an interference effect between the penumbras cast by each bar, so MTF
measurements in this region may not reflect the true resolution of the system. A
similar effect can occur for gamma rays from a large-diameter source.
CHAPTER 5. RESULTS
92
(a) SL filter
(b) SLLF filter
(c) SLNZ filter
(d) SAA DT
Figure 5.8: Relative modulation transfer function, as measured using the QC3 phantom, for Co-60 DT images using the PerkinElmer XRD1640 detector at SAD 80 cm,
SDD 120 cm. Frame time 1330 ms, dβ = 1◦ except as noted.
CHAPTER 5. RESULTS
93
(a) SL filter
(b) SLLF filter
(c) SLNZ filter
(d) SAA DT
Figure 5.9: Sine wave modulation transfer function, as measured using the QC3
phantom, for Co-60 DT images using the PerkinElmer XRD1640 detector at SAD 80
cm, SDD 120 cm. Frame time 1330 ms, dβ = 1◦ except as noted.
CHAPTER 5. RESULTS
94
high-pass spatial filter is responsible for much of the improvement. The filter’s purpose, per Figure 3.4, is to compensate for the uneven sampling of the frequency space.
The Shepp-Logan filter was designed, though, for the CT case in which βtot > 180◦ ,
and when used for limited-arc DT it adds an edge-enhancement effect in the direction
of filtering. This edge enhancement greatly increases the contrast of medium to high
spatial frequency patterns, improving the spatial resolution of FBP DT compared
to simple portal images. At high βtot (i.e. cone beam CT), the edge enhancement
of a projection from one direction is cancelled by a projection from an orthogonal
direction, improving slice selectivity at the cost of in-plane spatial resolution.
The use of a Shepp-Logan spatial filter, which approaches zero for very low spatial
frequencies, produces an interesting side effect in the sine wave MTF curve. The
lowest spatial frequency in the QC3 phantom, 0.1 lp/mm, shows a nearly 2.5-fold
MTF enhancement relative to the “very low” spatial frequencies (actually about 0.01
to 0.02 lp/mm) used for the comparison. Generally speaking, an imaging system’s
highest MTF is at very low spatial frequencies, but in this case, the filtering operation
partially suppresses those very low frequencies and emphasizes the higher ones. The
frequencies that are nearly lost correspond to objects much larger than the elements
of the widest bar pattern in the phantom.
Filters specifically modified for DT use, in which the lowest spatial frequencies
are not lost, yield interesting results. The SLLF filter (a Shepp-Logan filter adapted
to be non-zero at low frequencies) exhibits very similar MTF characteristics to the
standard Shepp-Logan filter at high spatial frequencies. However, the lowest spatial
frequencies are not wiped out, so the overall appearance of the phantom (Figure 5.10)
lacks the odd-looking edge enhancement artefacts and is rather more realistic. The
CHAPTER 5. RESULTS
95
SLNZ filter, in which a uniform offset is added to the Shepp-Logan filter, produced
MTF results that were generally much closer to unfiltered SAA DT than to those
produced by the algorithms in which a strong high-pass character was inherent in the
filter design. Evidently, there exists a set of spatial filters which may offer superior
resolution for DT without destroying the low-frequency components or creating edge
enhancement artefacts. Such filters are generally based on the simple ramp filter, but
that are non-zero at zero spatial frequency. The SLLF filter used here would seem to
be an appropriate starting point from which to refine the spatial filter design.
The SAA results are quite comparable to the raw portal image results– indeed,
they are virtually indistinguishable. This is not unexpected; an SAA DT image is an
average of several portal images, and while the contrast between features in different
planes is affected by the reconstruction, the portal images themselves are not changed.
A significant loss in resolution is seen in the last case, where βtot = 90◦ . It is likely
that the large projection spacing in this case is at least partly to blame. We will soon
see (Figure 5.17) that distinct duplication of features and ringing of edges becomes
evident at large dβ, undoubtedly to the detriment of spatial resolution.
5.4
Contrast Sensitivity
An important measure of a radiographic imaging system’s performance is its ability
to distinguish between objects that are very close in density, and therefore exhibit
very low contrast relative to each other. In this section, we will consider the contrast
in Co-60 DT images.
CHAPTER 5. RESULTS
(a) FBP(SL) βtot = 4◦
96
(b) FBP(SL) βtot = 8◦ (c) FBP(SL) βtot = 20◦ (d) FBP(SL) βtot = 95◦
(e) (SLLF) βtot = 4◦
(f) (SLLF) βtot = 8◦
(g) (SLLF) βtot = 20◦
(h) (SLLF) βtot = 95◦
(i) SAA βtot = 4◦
(j) SAA βtot = 8◦
(k) SAA βtot = 20◦
(l) SAA βtot = 95◦
Figure 5.10: DT images of QC3 line-pair phantom. Top row: FBP DT with SheppLogan (SL) filter. Middle row: FBP DT with SLLF filter. Bottom row: SAA DT, no
spatial filter. These are the images from which Figures 5.8 and 5.9 were calculated.
SAD 80 cm, SDD 120 cm, dβ = 1◦ .
CHAPTER 5. RESULTS
5.4.1
97
Linearity in DT
The Gammex 467 phantom described in Section 4.3.2 was used, with the axis of the
Gammex disc aligned with the beam axis, to produce DT images at a range of total
arcs. Because the phantom’s sample plugs are thicker than the disc itself, most of
them appear lighter than the disc in these images, and the usual method of visually
assessing contrast relative to the background– as is done for CT– does not work.
Instead, the mean image value of each plug was measured, along with an estimate of
the standard deviation (i.e. the noise) of the image of each plug.
In the photon energy range being considered here, Compton interactions are dominant over all others. As the Compton effect depends on electron density but not on
atomic number, we would expect the measured attenuation of the beam to be linearly dependent on electron density. If we plot the image value as a function of the
electron density of the corresponding sample plug, we find (Figure 5.11) that while
the relationship is not perfectly linear, it is sufficiently close to not cause confusion
when the images are viewed.
In X-ray imaging, we usually have to contend with a “beam hardening” effect:
the object being imaged preferentially absorbs the lower energy photons, leaving a
higher proportion of high-energy photons by the time the beam reaches the detector.
The Co-60 beam, though, is effectively monoenergetic when it enters the object.
Higher-density materials cause more Compton scattering, and therefore have a higher
proportion of low-energy scattered photons leaving them. The detector used for these
measurements, the PerkinElmer XRD1640, lacks a dense metal build-up layer and is
therefore somewhat more sensitive to lower photon energies than to high ones. This
may be the reason for the slight deviations from linearity at higher electron densities.
CHAPTER 5. RESULTS
98
(a) FBP DT image with relative electron densities marked
(b) SAA image
(c) Linearity of FBP DT
(d) Linearity of SAA DT
Figure 5.11: Linearity of Co-60 DT images using the FBP algorithm (SLNZ filter) and
the SAA algorithm on the Gammex 467 phantom. The individual sample cylinders
each have a diameter of 3 cm. The results presented are for an 8◦ arc at SAD 80 cm,
SDD 100 cm, dβ = 1◦ . No appreciable dependence on total arc was found over the
range 4◦ ≤ βtot ≤ 32◦ .
CHAPTER 5. RESULTS
5.4.2
99
Contrast in DT
An observer’s ability to distinguish between two different regions that are very close
in density and image level depends on the contrast between those regions, relative to
the noise in those regions. If we consider the image value as a function of electron
density over a very narrow range of electron densities representative of human soft
tissues, we get Figure 5.12. For two tissues to be distinguished, there should be no
overlap between their corresponding noise bars, and ideally a significant gap between
those bars.
From these measurements, we can estimate the limits of the Co-60 DT system’s
ability to distinguish between low-contrast soft tissues. Under highly idealized conditions, with no overlying anatomy and with all soft tissues being the exact same
thickness, it is possible to identify soft tissues with an electron density difference of
at least 2%.
A notable outlier, at a relative electron density of 1.00, is the Gammex phantom’s
pure water cylinder. Because of this cylinder’s neck and cap, it is thicker than the
solid plugs, and therefore appears darker in DT images. This data point has been left
in these graphs to emphasize an important point: soft tissue contrast in DT depends
quite dramatically on the thickness of a feature, as well as on its electron density
and its size in the plane being viewed. This is a notable difference from CT, where a
feature that is appreciably thicker than the slice thickness will appear essentially the
same in a particular slice regardless of how many slices it spans.
If we consider the effects of varying feature thickness and overlying anatomy, the
low-contrast sensitivity of DT will be greatly reduced. While lung, tissue and bone
can of course be clearly distinguished, it is probably not reasonable to expect to be
CHAPTER 5. RESULTS
100
(a) FBP DT image, relative electron densities labelled
(b) SAA image
(c) Sensitivity of FBP DT
(d) Sensitivity of SAA DT
Figure 5.12: Low-contrast sensitivity of Co-60 DT images using the FBP algorithm
(SLNZ filter) and the SAA algorithm on the Gammex 467 phantom. The images
correspond to those in Figure 5.11, windowed to match the Y-axis scale of the corresponding graphs. The results presented are for an 8◦ arc at SAD 80 cm, SDD
100 cm, dβ = 1◦ . No appreciable dependence on total arc was found over the range
4◦ ≤ βtot ≤ 32◦ .
CHAPTER 5. RESULTS
101
able to rely on accurate identification of soft tissue boundaries, such as the edge of
the prostate gland, in a Co-60 DT image.
5.5
Geometric Considerations in DT
The main potential use of a Co-60 DT system is for accurately positioning a patient
on a treatment machine. If we expect to rely on these images for geometric alignment,
we must first confirm that the imaging and reconstruction process is not introducing
additional geometric errors.
5.5.1
Distortion
In this section, we will address the question of whether a feature at a particular
position in a physical object appears at the correct position in a DT image of that
object. The phantom described in Section 4.3.3 was used for this assessment. DT
reconstructed images of this phantom appear generally as shown in Figure 5.13.
We will begin by considering the magnitude of the distortion vector at each point
on the phantom’s lead pellet grid. This is illustrated in Figure 5.14.
The total distortion in the filtered-backprojection case was found to be an approximately linear function of the distance from the beam axis, with no appreciable
dependence on the total imaging arc. We note that, with the reconstruction volume
at 80 cm from the source, the ray passing through a point 16 cm from the beam axis
diverges from that axis by 11.3◦ . An observed total distortion of approximately 2 mm
at the edge of the field therefore corresponds quite closely to the difference in the field
size at the front and back faces of the detector sandwich (9.35 mm thick × tan(11.3◦ )
CHAPTER 5. RESULTS
(a) FBP with SL filter, βtot = 25◦
102
(b) SAA, βtot = 24◦
Figure 5.13: Overview images of the DT distortion phantom. Blue circles represent
the true positions of the lead pellets; red stars indicate their observed positions in the
image. The green stars on the vertical tungsten rod are the locations at which slice
thickness images (Figure 5.16) were taken. Note the Shepp-Logan filter’s near-deletion
of the horizontal tungsten rod; this study was performed prior to the development
of the dedicated DT spatial filters. A different choice of filter would modify the
appearance of some features, but would not change their locations.
CHAPTER 5. RESULTS
103
SAA DT Central Plane Distortion
0.35
0.3
0.3
0.25
βtot=5°
βtot=15°
βtot=25°
βtot=95°
Fit 5°
Fit 15°
Fit 25°
Fit 95°
0.2
0.15
0.1
0.05
0
Magnitude of Distortion (cm)
Magnitude of Distortion (cm)
FBP DT Central Plane Distortion
0.35
0.25
βtot=4°
βtot=14°
βtot=24°
βtot=94°
Fit 4°
Fit 14°
Fit 24°
Fit 94°
0.2
0.15
0.1
0.05
0
0
5
10
15
Radius from Beam Axis (cm)
(a)
0
5
10
15
Radius from Beam Axis (cm)
(b)
Figure 5.14: DT distortion by radius from beam axis
= 1.87 mm); in other words, this distortion could be explained as a simple scaling due
to the strongest response of the detector occurring at some depth below its surface.
The SAA case shows a similar radius-dependent distortion as observed for FBP
DT, but adds a significant dependence on total arc angle. The pellets were harder to
identify in these images, leading to more scatter in the measurements, but the trend
is clear: SAA DT exhibits increasing distortion as we increase the total arc.
By separating the distortion into lateral and vertical components, the cause of the
distortion can be studied in more detail. This is illustrated in Figure 5.15 for both
algorithms.
For both algorithms, the lateral distortion increases with lateral distance from the
beam axis, and exhibits no appreciable dependence on the total arc. This result would
appear to support the idea that much of the distortion is a simple scaling due to the
thickness of the detector sandwich. In FBP DT, the vertical distortion exhibits a
similar trend, although the vertical distortion is approximately double the horizontal
CHAPTER 5. RESULTS
104
SAA DT Central Plane Lateral Distortion
0.3
0.25
0.25
0.2
βtot=5°
βtot=15°
βtot=25°
βtot=95°
Fit 5°
Fit 15°
Fit 25°
Fit 95°
0.15
0.1
0.05
0
-0.05
Lateral Distortion (cm)
Lateral Distortion (cm)
FBP DT Central Plane Lateral Distortion
0.3
0.2
βtot=4°
βtot=14°
βtot=24°
βtot=94°
Fit 4°
Fit 14°
Fit 24°
Fit 94°
0.15
0.1
0.05
0
-0.05
-0.1
-0.1
0
5
10
Lateral Distance from Beam Axis (cm)
0
SAA DT Central Plane Vertical Distortion
0.3
0.3
0.25
0.25
0.2
βtot=5°
βtot=15°
βtot=25°
βtot=95°
Fit 5°
Fit 15°
Fit 25°
Fit 95°
0.15
0.1
0.05
0
-0.05
-0.1
Vertical Distortion (cm)
Vertical Distortion (cm)
FBP DT Central Plane Vertical Distortion
5
10
Lateral Distance from Beam Axis (cm)
0.2
βtot=4°
βtot=14°
βtot=24°
βtot=94°
Fit 4°
Fit 14°
Fit 24°
Fit 94°
0.15
0.1
0.05
0
-0.05
-0.1
0
5
10
Vertical Distance from Beam Axis (cm)
0
5
10
Vertical Distance from Beam Axis (cm)
Figure 5.15: DT image distortion, separated into lateral and vertical components.
CHAPTER 5. RESULTS
105
distortion– a reminder that the FDK cone beam algorithm is only an approximation,
albeit a close one, for vertical positions far away from the beam axis. The vertical
distortion for SAA reveals the arc angle dependence that was observed in the total
distortion figures for this algorithm. We can therefore identify the culprit: the vertical
component of the conversion from the real to the virtual detector plane in Equation
3.10, in which restricting ourselves to integer values of the pixel position co-ordinates
(a necessary approximation in the current implementation of the code) may cause
a loss of precision as β becomes large. Adding a sub-pixel interpolation step before
rounding off the co-ordinates in the virtual detector plane might alleviate this error.
5.5.2
Slice Thickness
The chief advantage of DT reconstructed images, compared to simple projection images, is the slice selectivity that DT offers: features lying outside the plane of interest
appear blurred out, rather than being superimposed over the anatomy we wish to
study. An important metric of the performance of a DT system, then, is the thickness of the slices– in other words, how far does a particular feature appear to extend
into adjacent planes.
We can see from Figure 3.4, a direct consequence of the imaging geometry, that
the slice thickness in DT will be a function of spatial frequency. We have little
knowledge of the spatial frequencies in the Y-direction that correspond to features
with a low spatial frequency in the plane of interest, i.e. large features. In other
words, a large feature will extend over many adjacent planes in the reconstructed
image. For smaller objects, which are dominated by higher spatial frequencies, we
have plenty of information about spatial frequencies in the Y direction, and these
CHAPTER 5. RESULTS
106
features do not extend very far into adjacent planes of the DT image set. Hence, it is
not meaningful to speak of a single slice thickness for DT, as what we observe would
be dependent on the size of the feature in question
One way to study this plane-to-plane blur in DT is to consider a very small, high
contrast feature, such as a thin tungsten wire, in an otherwise homogeneous medium.
As the total arc angle is increased, we gain additional information about spatial
frequencies in the Y direction (along the beam axis), and the spatial resolution in
the Y direction is improved. The feature therefore exhibits less overlap into adjacent
planes. If we look along the Z (rotation) axis at an XY plane, instead of the XZ plane
that DT images are usually viewed in, a thin wire appears as shown in Figure 5.16
and the blurring into adjacent planes, at different Y values, can be seen. It is also
important to consider the characteristics of the blurred region: ideally, the DT blur
should blend smoothly into the background as we move away from the feature.
The largest improvements in slice thickness come when we move from portal images and very small DT arcs to an arc of about 25◦ . A 5◦ arc is barely different
from a single portal image; small features might be visible in a plane five or more
centimetres away. At 25◦ , though, a 2 mm tungsten wire is visible in DT planes up
to 1.4 cm from its true location, and it is blurred beyond recognition at more than 2
cm– sufficient selectivity in the Y-direction to offer a useful improvement over portal
images. Beyond 25◦ , we encounter diminishing returns, as an increase in total arc
(and therefore radiation dose) yields smaller and smaller reductions in slice thickness. Even approaching the CBCT limit βtot ≈ 180◦ , the slice thickness (full width at
half maximum) for the 2 mm tungsten wire never goes below approximately 5 mm.
This is approximately what would be expected, considering that the edge spread
CHAPTER 5. RESULTS
107
βtot =
5◦
15◦
25◦
35◦
45◦
55◦
65◦
75◦
85◦
95◦
175◦
βtot =
4◦
14◦
24◦
34◦
44◦
54◦
64◦
74◦
84◦
94◦
Ideal
Figure 5.16: DT slice thickness images over a range of total imaging arc angles. These
images are cross-sections of a 2 mm tungsten wire, looking down along the rotation
(Z) axis to view an X-Y plane, instead of the X-Z planes we normally look at in DT.
Top row: FDK filtered-backprojection method, Shepp-Logan filter, 5◦ ≤ βtot ≤ 175◦ .
Bottom row: Shift-and-add method, 4◦ ≤ βtot ≤ 94◦ . SAD 80 cm, SDD 140 cm,
dβ = 1◦ . As βtot increases, the effective slice thickness decreases until, in the CBCT
limit βtot > 180◦ , no preferred direction would be evident. At lower right is the true
size of the wire.
CHAPTER 5. RESULTS
108
function measurements described in Section 5.3.1 indicated considerable blurring of
sharp-edged objects due to the penumbra of the cobalt beam.
If we look along the X direction in the 0 cm plane, the same edge-enhancement
effect described in Section 5.2 can be seen for the FBP case using the Shepp-Logan
filter. The SAA algorithm, lacking a spatial filter, exhibits no such enhancement. It
does, however, introduce an overall gradient in the Y direction at high βtot , which
would have to be compensated for with window and level settings when viewing the
images. The SAA algorithm appears to produce a smoother, less noisy blur region
than the FBP algorithm, as would be expected considering that the spatial filter in
the FBP algorithm enhances high spatial frequencies, and image noise tends to occur
at high spatial frequencies.
5.6
Appearance of Anthropomorphic Phantoms
The ultimate goal of this project is to evaluate the suitability of Co-60 treatment beam
imaging for use in a clinical setting. Geometric phantoms are useful for characterizing
the performance of the system, but ultimately, the images that matter are those of real
anatomy. Of particular concern are any imaging artefacts that might be introduced by
the DT reconstruction process, and could create confusion about the anatomy being
viewed. A suitable surrogate for a real patient is the RANDO phantom (Section
4.3.4). In this section, we will consider the appearance of the RANDO head phantom
in DT images, for a range of possible choices of the acquisition arc βtot and the
projection spacing dβ.
It has already been established (Section 5.1) that a large spacing between successive projection images would waste dose unless the source can be pulsed on and
CHAPTER 5. RESULTS
109
off quickly, which is not practical with the current hardware. Nevertheless, it is instructive to consider the artefacts that would result if we did take widely spaced
projections, pulsing the source off between images. Looking at Figure 5.17, we see
that as the spacing dβ becomes large, features are replicated, rather than blurred,
by DT. Instead of an out-of-plane feature appearing in a particular plane as a faint
blur, it appears as a series of distinct, faint copies at varying distances from its true
position. This is as would be expected from theory, and illustrates that a good clinical
DT protocol should use relatively closely spaced projections. The improvements in
slice selectivity that result from a large total arc are not worth the additional image
artefacts that result from using too large a spacing between projections.
It has already been shown (Section 5.5.2) that increasing the total arc reduces the
slice thickness and increases the degree to which out-of-plane features are blurred.
This effect is illustrated in Figure 5.18 for a range of total arc angles, including the
full CBCT case. The images shown here are excerpts from a parametric series of
reconstructions. In this series, all possible choices of βtot and dβ with a total arc
6◦ ≤ βtot ≤ 90◦ , using 5 ≤ N ≤ 31 projection images, for dβ ≥ 1.5◦ were considered,
and only a small subset are shown here. In Section 5.5.2, it was found that the
greatest gains in slice selectivity came when we moved from single images, or very
small imaging arcs, to using an arc of 20 to 30 degrees. With the anthropomorphic
phantom, it appears that once again, the most dramatic gains in slice selectivity
have been made by the time we reach 20 degrees; the full CBCT case clearly offers a
selectivity advantage, but at a huge cost in radiation dose.
For comparison purposes, Co-60 images of the three main regions of the RANDO
CHAPTER 5. RESULTS
110
(c) N=13, dβ = 3◦
(d) N=9, dβ = 4.5◦
(e) N=7, dβ = 6◦
(f) N=5, dβ = 9◦
Figure 5.17: Effects of the projection spacing dβ on the appearance of FBP DT
images of two stainless steel pins embedded in different sagittal planes of the RANDO
head phantom. The total imaging arc βtot is a constant 36◦ for all images. As
we increase dβ, the out-of-plane features contributed by each individual projection
become evident, rather than blurring together. This effect is more pronounced when
we consider planes farther from the central axis. The CBCT Shepp-Logan filter was
used for all images.
CHAPTER 5. RESULTS
111
(a) N=5, βtot = 6◦
(b) N=7, βtot = 9◦
(c) N=9, βtot = 12◦
(d) N=11, βtot = 15◦
(e) N=15, βtot = 21◦
(f) N=21, βtot = 30◦
(g) N=31, βtot = 45◦
(h) N=240, βtot = 360◦
Figure 5.18: Effects of the total imaging arc βtot on the appearance of FBP DT images
of two stainless steel pins embedded in the RANDO head phantom. The projection
spacing dβ is a constant 1.5◦ for all images. For small βtot , the DT image appears
similar to a high-pass filtered portal image. As βtot increases, the out-of-plane pin is
blurred out and the in-plane one is enhanced, along with the corresponding anatomical
features. In the limit βtot > 180◦ , DT becomes cone beam CT.
CHAPTER 5. RESULTS
112
phantom are presented in Figure 5.19 for each of three radiographic imaging modalities. Raw portal images, CoCBCT images produced with the filtered backprojection
algorithm, and FBP (SL filter) CoDT images for a 12◦ arc are shown for the head,
pelvis and torso regions. Qualitiatively, CoDT represents a considerable improvement over portal imaging, but it lacks the anatomical selectivity of true cone beam
CT. These images, and additional similar ones, are from the image guidance study
described in Sections 4.3.5 and 5.7.
5.7
Image Guidance Accuracy
As the primary purpose of a Co-60 imaging system would be for positioning patients
on a treatment machine, a measurement of the accuracy of such an image guidance
system is desirable. The methods used are described in Section 4.3.5. The images for
this experiment were taken on the Varian aS500 panel at SAD 100 cm, SDD 125 cm,
the choice of geometry being made for consistency with previous work [Rawluk, 2010]
and to match the geometry of the Best Theratronics Equinox machine that would
likely be the first candidate to be fitted with such an imaging system.
In Figure 5.20, we see the total error in the alignment of the Co-60 images to the
planning images, in three-dimensional space. To understand this graph, consider the
first point, for CT imaging of the head phantom. We interpret this as saying that, on
average, the user’s measurement of the shift in the phantom’s position was off by 1.8
mm from the true magnitude of that shift, and that 68% of the time (one standard
deviation), the user’s measurement was off by between 0.3 mm and 3.2 mm.
Cone beam CT imaging shows a marked advantage for all three anatomical regions.
This is not surprising, as there is far more data in a CBCT image than in a DT
CHAPTER 5. RESULTS
113
(a) Head, CoCBCT
(b) Head, 12◦ CoDT
(c) Head, portal image
(d) Torso, CoCBCT
(e) Torso, 12◦ CoDT
(f) Torso, portal image
(g) Pelvis, CoCBCT
(h) Pelvis, 12◦ CoDT
(i) Pelvis, portal image
Figure 5.19: Appearance of coronal images of RANDO head, torso and pelvis phantoms using three Co-60 treatment beam imaging techniques. These images were used
for the image guidance accuracy study described in Sections 4.3.5 and 5.7.
CHAPTER 5. RESULTS
114
Figure 5.20: Estimated 3D vector errors in manual alignment of Co-60 images to
corresponding planning images. For CT, this is the true observed error in 3D. For
DT, where only a 2D view was available, the error shown here is an extrapolation to
the 3D case with the assumption that the magnitude of the error in the horizontal
direction is the same in any view. For portal images, the error was estimated by
individually aligning two orthogonal views. “Failed” attempts (Table 5.1) are not
included here.
image or a pair of portal images. Notably, CBCT images allow rotations, as well
as translations, to be measured in all three dimensions. An additional contributing
factor is that all the volunteer users were at least somewhat familiar with CBCT
imagery prior to this study, but were generally less familiar with DT or with the
particular characteristics of Co-60 portal images.
If a patient is out of position by a few millimetres along the direction from which
the beam is coming, the net effect on the treatment is relatively small- the dose
calculations might be thrown off slightly, but the tumour will still be hit. However,
if the patient is misaligned by a few millimetres in a direction perpendicular to the
treatment beam, we would expect a dramatic effect on the treatment outcome: normal
tissue on one side of the tumour will be irradiated, while part of the other side of
the tumour will not recieve enough dose. It is therefore important to consider the
misalignment in the “beam’s-eye view”, especially since it was established in Section
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115
Figure 5.21: Observed 2D vector errors (beam’s-eye views) in manual alignment of
Co-60 images to corresponding planning images. In cases where data was available for
both sagittal and coronal views, both views were included in these results. “Failed”
attempts are once again excluded.
5.3.1 that the resolution of a DT image may be quite different in the vertical and
horizontal directions. Considering only the misalignment in the 2D beam’s-eye view
plane, we find (Figure 5.21) that while the 2D error is less than the 3D error, the
order of preference of the three imaging modalities is not changed.
From these results, we may conclude that Co-60 cone beam CT, referenced against
standard kilovoltage CT, provides the ability to identify patient misalignment to an
accuracy of approximately 1.5 mm 50% of the time, and usually to within 3 mm or
better. However, we saw in Section 5.1 that the dose from CoCBCT is far too high
for use on a patient. CoDT, referenced against kilovoltage CT, yielded somewhat
less favourable results, particularly for the pelvic region. Portal images on the Co-60
machine, referenced against simulated portal images calculated from kilovoltage CT
data, appear at first glance to be slightly superior to DT in some cases and slightly
inferior in others. When we take into account the failure rates (Table 5.1), portal
imaging loses any advantage it may have had: one out of every nine attempts to
match a Co-60 portal image to the corresponding simulated planning image results
CHAPTER 5. RESULTS
Modality
CoCBCT
CoDT 12◦
2x CoDT 12◦
2x Portal
Imaging Dose
40 cGy
1.5 cGy
3.0 cGy
0.3 cGy
116
Total Dose
99 cGy
3.3 cGy
6.6 cGy
0.4 cGy
# of Cases
261
262
263
# Cut
3
11
31
Failure Rate
1.1%
4.2%
11.8%
Table 5.1: Imaging doses for each modality and failure rates for manually aligning
Co-60 images to planning images. The failure rate, or user error rate, includes all
cases where the user could not align the images to within 10 mm or better, and cases
where obvious patterns in the data implied that a lack of familiarity with the software
was to blame for the error in at least one direction.
in failure. Failure here is defined to be anything indicating a shift of more than 10
mm, along with cases where particular patterns in the data indicate that a user was
using the software incorrectly.
It is worth noting that the DT protocol used for these experiments was an early
one, using the Shepp-Logan filter and a relatively large dβ of 1.5◦ . Furthermore, the
CoDT images were aligned with respect to CT images from a kilovoltage scanner used
for treatment planning, which appear quite different from DT images. Refinements
made to the imaging protocol since this study have yielded visible improvements in
the quality of the DT images, and if combined with appropriate reference images
and user training, could be reasonably expected to yield an improvement in image
guidance accuracy.
5.8
Cone Beam CT
Co-60 cone beam CT with the equipment used for the present work has already been
well studied [Rawluk, 2010]. Although CoCBCT was found to yield remarkably good
images, the radiation dose remains far too high for clinical use. Nevertheless, a small
CHAPTER 5. RESULTS
117
selection of CoCBCT imagery will be presented here for comparison to previous work,
the major differences being a new detector panel (PerkinElmer XRD1640 instead of
Varian aS500) and a clinically realistic geometry with sufficient clearance to fit a
full-size adult.
Some preliminary work was also conducted on cone beam CT using a much
weaker, lower energy source: the Nucletron Ir-192 Flexisource used for high-doserate brachytherapy at the CCSEO. IrCBCT offers three theoretical advantages over
CoCBCT: lower energy photons (and therefore the possibility of getting improved
contrast from Z-dependent photoelectric interactions instead of just ρe -dependent
Compton interactions), a much lower beam intensity (therefore lower dose), and a
smaller source to reduce the penumbral blurring.
5.8.1
Limiting Resolution of CBCT Images
A comprehensive discussion of the spatial resolution of Co-60 CBCT is presented in
[Rawluk, 2010], in which it was found that the limiting resolution for high contrast line
pairs was 0.27 to 0.30 lp/mm, which corresponds to objects 1.8 mm across separated
from each other by 1.8 mm. The geometry used for those measurements, at SAD 100
cm / SDD 125 cm, offers enough clearance to scan a head or a limb, but not a body.
For comparison, a line pair phantom (CatPhan) scanned with CoCBT at SAD 80 cm
/ SDD 120 cm is shown in Figure 5.22d; the limiting resolution here, due to the larger
penumbra, is at best 0.20 lp/mm.
One way to reduce the total dose due to imaging is to use a weaker source. A
weaker source is also likely to be smaller, reducing the penumbra and improving spatial resolution. Three views of the CatPhan resolution slice are presented in Figure
CHAPTER 5. RESULTS
118
5.22 for scans with the 1mm x 3mm Ir-192 source of the Flexitron brachytherapy
machine. A dramatic improvement in resolution for Ir-192 CT is evident when compared to Co-60 CT, with a segment at 0.5 lp/mm being quite visible on a 512x512
reconstruction grid. Downsampling too far, to a 256x256 grid, cuts the limiting resolution to 0.4 lp/mm, and if we reconstruct from the raw data without downsampling–
a 1024x1024 grid– everything beyond 0.4 lp/mm is lost in the noise.
Noise is a major problem in Ir-192 CT using the present setup. For these scans, the
detector gain was set as high as possible, the frame time extended to 666 ms, and 20fold averaging of raw image frames was used to extend the effective time per projection
image to 13 seconds. Nevertheless, the images remain quite noisy. A potentially
greater concern is that under these conditions, the detector panel was operating at
its design limits, and the dark current correction alone was over twice the magnitude of
the final signal. Thus, tiny irregularities in the correction data that would ordinarily
be unnoticeable become a major factor, resulting in thick ring artefacts corresponding
to different blocks of detector readout electronics. An order-of-magnitude increase in
the beam intensity, or a similar improvement in the sensitivity of the detector at low
intensities, would be needed to resolve this issue.
5.8.2
Contrast in CBCT
The contrast sensitivity characteristics of CoCBCT using the PE XRD1640 detector
and the new, clinically realistic geometry are not appreciably different from those
found in [Rawluk, 2010]. In that work, it was found that for organs of at least 3
cm in diameter, an electron density difference of 4% to 5% was needed to tell soft
tissues apart. The present results for CoCBCT are generally similar to those found
CHAPTER 5. RESULTS
119
(a) IrCT, 256x256
(b) IrCT, 512x512
(c) IrCT, 1024x1024
(d) CoCT, 512x512
Figure 5.22: Cone beam CT resolution using the line pair slice of the CatPhan.
Iridium images were taken at SAD 55 cm, SDD 80 cm, 666 ms frames averaged 20x
at dβ = 1.2◦ and downsampled to 256x256 or 512x512 resolution, or left raw, before
reconstructing. Cobalt image was taken at SAD 80 cm, SDD 120 cm, 133 ms frames
averaged 10x at dβ = 1◦ . The overall diameter of the phantom is 20 cm.
CHAPTER 5. RESULTS
120
previously, despite the different geometry and new imaging panel.
Iridium-192 cone beam CT appears to offer generally similar contrast sensitivity
to Co-60 CBCT, but as discussed in Section 5.8.1, a great deal of information is
lost in the noise in the current implementation of the system. The Co-60 beam is
effectively monoenergetic at 1.25 MeV, while the Ir-192 beam includes many lowerenergy gamma rays, the most prominent being a group of three energies near 300 keV
and several more near 200, 480 and 600 keV. On theoretical grounds, therefore, one
might expect the iridium beam to have a higher probability of photoelectric absorption
than the Co-60 beam, and since the photoelectric effect is strongly dependent on
atomic number, an Ir-192 beam should have the potential to offer superior contrast
to a Co-60 beam. The contrast to noise ratio, though, is rather poor in the current
images, as the detector is simply not designed to function in such a low intensity
beam.
5.8.3
Anthropomorphic Phantoms in CBCT
For comparison to previous work and for qualitative assessment of image quality, a
selection of Co-60 cone beam CT images of anthropomorphic phantoms will now be
presented.
If the quantum efficiency of the detector could be increased by a factor of ten– say,
up to 40% from the current 4% to 5%– it may be possible to accurately identify at
least a few soft tissues in CoCBCT images. The CIRS prostate phantom described in
Section 4.3.4 includes a simulated bladder, prostate gland and other organs. Figure
5.24 illustrates this phantom in CoCBCT imagery, with 10-fold averaging to simulate
a more efficient detector, compared to its appearance on a GE Lightspeed planning
CHAPTER 5. RESULTS
121
(a) IrCT Raw
(b) IrCT Ring reduced
(c) CoCT
(d) CoCT, narrowed window
Figure 5.23: Contrast-detail slice of the CatPhan phantom. IrCT: at SAD 55 cm,
SDD 80 cm, 666 ms frames averaged 20x at dβ = 1.2◦ . CoCT: SAD 80 cm, SDD 120
cm, 133 ms frames averaged 10x at dβ = 1◦ . The overall diameter of the phantom is
20 cm.
CHAPTER 5. RESULTS
122
CT scanner with a 120 kVp X-ray beam. The bladder is clearly visible in both
sets of images, and the bones are of course also visible. None of the other soft tissue
boundaries can be seen in the CoCBCT images, though, despite the high imaging dose
and 10-fold frame averaging. These images and others made under similar conditions,
combined with the existing literature on clinical experience with MV imaging on
linacs, suggest that we will not be able to reliably identify some important soft tissue
boundaries in CoCBCT imagery, even with an excessively high imaging dose. Bony
anatomy, or implanted fiducial markers, must be used as surrogates to localize the
anatomy of interest.
A common anthropomorphic phantom that has been presented in previous work
is the RANDO head phantom. For illustrative and comparative purposes, a CoCBCT
image of this phantom, taken at the same geometry (SAD 80 cm / SDD 120 cm) as
most of the DT work described previously, is shown in Figure 5.25. Some increase in
blurring is observed, relative to [Rawluk, 2010], as a result of the geometric changes
and the resulting increase in penumbra size. The imaging dose here is on the order of
20 to 30 cGy, but the total dose– allowing for the rotation of the gantry, as described
in Section 5.1– is about 90 cGy, more than an order of magnitude too high to be
clinically useful.
5.9
Other Applications
The high beam energy and nearly monoenergetic nature of the Co-60 source give Co60 imaging remarkable linearity characteristics in very high density materials, without
the image artefacts that occur when dense metals are scanned with kilovoltage CT
[Hajdok, 2002]. This makes CoCBCT it a potentially appealing option for non-clinical
CHAPTER 5. RESULTS
123
(a) Cobalt cone beam CT, central sagittal plane (b) 120 kVp multi-slice CT, central sagittal plane
(c) Cobalt cone beam CT, transverse plane (d) 120 kVp multi-slice CT, transverse plane
through bladder
through bladder
Figure 5.24: Comparison of CoCBCT to kilovoltage planning CT for the CIRS pelvic
phantom. Co-60 images were taken at SAD 80 cm, SDD 120 cm, 133 ms frames
averaged 10x at dβ = 1◦ . Planning CT images were taken on a GE Lightspeed RT
multi-slice scanner at 120 kVp.
CHAPTER 5. RESULTS
(a) Coronal
124
(b) Sagittal
(c) Transverse
Figure 5.25: RANDO head phantom imaged using CoCBCT. Imaged at SAD 80 cm,
SDD 120 cm, 133 ms frames averaged 1x at dβ = 1◦ , PE panel.
applications, such as archaeology and industrial testing, where a non-destructive 3D
imaging modality is desired.
The geometric penumbra of the cobalt beam can be reduced by greatly extending
the source-to-axis distance, and by placing the detector as close as possible to the
axis. In the CCSEO’s cobalt facility, we are limited to a SAD of 200 cm and SDD
of 220 cm, for a geometric penumbra of 2.0 mm. To compensate for the reduced
beam intensity at these large distances, longer frame times are used, with 10-fold
or 20-fold frame averaging to reduce noise. Remarkably fine details can be resolved
with this system; note the resistors ( 2 mm diameter) and the solder traces on the
circuit board of the position encoder shown in Figure 5.26. The solid iron armature
of the motor in those images exhibits none of the streaking or distortion artefacts
that occur when such large, dense metal objects are scanned at kilovoltage energies.
Many other items have now been scanned with this system, including artifacts from
CHAPTER 5. RESULTS
125
(a)
(b)
(c)
(d)
(e)
(f)
Figure 5.26: CoCT for non-destructive testing: a rotary encoder and stepper drive
motor. SAD 200 cm SDD 220 cm.
archaeological sites and samples of concrete shielding from a recent expansion of
the CCSEO’s radiotherapy facilities. Smaller, weaker Co-60 sources are already in
common use in industrial radiography, and CT or DT techniques have considerable
potential in that field.
Chapter 6
Summary and Conclusions
6.1
Summary
The difficulties involved in deploying complex, infrastructre-intensive linear accelerator technology in remote areas mean that Co-60 radiation therapy machines are
likely to play a major role worldwide for the foreseeable future. Cobalt technology is
less expensive than linacs. Cobalt units can be run from portable generators, while
linacs demand clean, high-voltage grid power. Cobalt units require little maintenance,
while linacs need periodic calibration and relatively frequent servicing. It is easy to
keep spares on hand for the handful of breakable parts in a cobalt machine, while
many linac-based facilities cannot afford to stockpile all the spare parts that these
machines could need, and must instead rely on fast courier service from the manufacturer’s warehouse. Where the cobalt machine falls short is in versatility, as it is
restricted to a single beam type and energy (a modern linac typically offers several
energies and a choice of photons or electrons), and to date has not been fitted with the
multi-leaf collimators and image guidance systems necessary for modern conformal,
126
CHAPTER 6. SUMMARY AND CONCLUSIONS
127
intensity-modulated and image-guided radiation therapy.
If we are to upgrade Co-60 machines to deliver tightly conformal dose distributions,
we must also provide some means of imaging the patient on the treatment machine
to ensure that the beam is in fact aimed at the tumour and not at a nearby region of
healthy tissue.
Previous work has indicated that portal, DT and CT imaging using the cobalt
machine’s treatment beam is possible. The radiation dose to the patient must be
dramatically reduced, though, in order for it to be clinically useful. In the present
work, we have explored several reconstruction methods and image acquisition protocols for Co-60 digital tomosynthesis. These techniques offer relatively good in-plane
resolution along with some of the selectivity of CT imaging, and with an order of
magnitude reduction in dose.
Two DT algorithms were studied in the present work, shift-and-add (SAA) and
filtered backprojection (FBP). In the FBP DT case, the question of spatial filter design
is an important one, and appropriate filters are not immediately obvious as they are
for FBP CT. It was found that a favourable class of spatial filters for DT use can be
obtained by modifying the standard CT filters to be non-zero at the lowest spatial
frequencies. The resulting filters can preserve much of the resolution enhancement
that FBP DT offers over SAA DT or portal imaging, without introducing undesirable
image artefacts. “Zebra stripe” line-pair patterns at spatial frequencies up to 0.45
lp/mm were clearly visible in DT images, implying that features as small as 1 mm can
be identified, as long as they offer sufficient contrast and are separated by more than 1
mm. A slight fall-off of in-plane resolution and a significant reduction in effective slice
thickness was found as the total imaging arc increased, in agreement with previous
CHAPTER 6. SUMMARY AND CONCLUSIONS
128
results.
The possibility of discerning soft tissue contrast from CoDT images was explored,
and it was found that under ideal conditions, the difference in electron density between
two geometrically similar tissues must be greater than 2% to 3% in order to distinguish
between them. The image values in DT, though, depend on the thickness of a feature
as well as on its density, a notable distinction from CT in which objects of identical
density ideally yield identical values in the image. We conclude that the ability to
distinguish low contrast soft tissue boundaries in CoDT images should not be relied
upon in practice. Bony anatomy, or implanted metal fiducial markers, must be used
instead.
Small but measurable distortions were found in the DT images studied here. Some
of these distortions are likely due to approximations in the reconstruction algorithms,
but the major contributing factor appear to be the slight scaling that results from
the detector’s active layer being at some depth beneath its surface. In future experiments, the detector should be set a few millimetres closer to the source, or the
source-to-detector distance in the reconstructed code adjusted, so that the detector’s
most sensitive point and the SDD coincide. This implies that any gantry-mounted
implementation of such a system would have to be mechanically stable to a tolerance
somewhat less than the detector sandwich thickness, i.e. a few millimetres, to avoid
introducing a gantry-position-dependent distortion.
Further effort is required to improve the system’s accuracy for image guidance
purposes, although results to date appear promising. Users can register Co-60 cone
beam CT images to their corresponding planning images with an average accuracy of
1.9±1.2 mm. The corresponding figure for aligning CoDT images to planning CT is
CHAPTER 6. SUMMARY AND CONCLUSIONS
129
3.5±2.0 mm, and for portal images to simulated portal images based on planning CT
data, 3.4±1.8 mm. Improvements to the DT imaging protocol, combined with user
training and more suitable planning images, would likely improve this accuracy. The
use of implanted fiducial markers to provide obvious, high-contrast alignment targets
would be helpful when targeting organs, such as the prostate, that can shift position
slightly relative to the nearby bones.
6.2
Future Work
There are several possible sets of constraints that will be used to guide these recommendations for future work. In the first case, we will restrict ourselves to Co-60
treatment beam imaging without modifications to the head of the cobalt machine. In
the second case, the possibility of using a separate imaging source will be added, but
without modifications to the machine head and with only one imaging panel being
used to reduce cost. In the final case, the possibility of modifying the treatment
machine itself, or investigating new detector technologies, will be discussed.
If we restrict ourselves to bolt-on additions for Co-60 treatment beam imaging,
CoDT imaging is the logical choice for further development. Further refinements
to the FBP spatial filter designs, using the SLLF filter desrcribed in Section 5.2,
are undoubtedly possible. A more robust and versatile implementation of the FDK
cone-beam reconstruction algorithm, ideally using parallel GPU processing to speed
up computation, would be a useful tool in this work. The possibility of adding a
physical filter in the beam, to reduce the dose rate, should also be explored. Some
preliminary work done by the author during the course of this project indicated
that it may be possible, given sufficient quantitative knowledge of the point spread
CHAPTER 6. SUMMARY AND CONCLUSIONS
130
function for a particular geometry, to partially deconvolve the PSF from the raw
portal images. This could be used to improve the resolution of the portal images,
and therefore of the reconstructed DT images. Another avenue that may be worth
exploring is the algebraic reconstruction methods. An algebraic reconstructor can
be split into two nearly independent parts: a sparse matrix solver, many of which
are readily available for different applications, and a forward projection model, which
represents the geometry of the imaging system and can be tailored to a particular
application. Knowing the size and shape of the Co-60 source and of the detector
elements, a forward projection model could be created that inherently includes the
source size effects, and might therefore offer an improvement in resolution. Finally,
the test system will have to be modified to allow image acquisition during a continuous
rotation, rather than stopping to shoot as is currently done. Since the order in which
the imaging panel reads its pixels is known, it may be possible to identify and record a
different angular position for each region of the panel. This would add complexity and
require significant modifications to the reconstruction code, but should compensate
for any artefacts introduced by the continuous rotation of the gantry.
The Co-60 source is far from ideal as an imaging source. It is too large, far
too strong, and produces photons at a much higher energy than would be ideal for
imaging. A particularly appealing option, then, is to bolt a second, dedicated imaging
source on the cobalt gantry, and if possible to use the same detector panel for both
the treatment beam and the imaging beam. Iridium-192 was investigated here as a
possible imaging source; several other radioisotopes might be suitable and a highcurrent X-ray tube operating at 100 kV or so could also be used. The PerkinElmer
XRD1640 panel used for some of the present work is claimed to be usable in beam
CHAPTER 6. SUMMARY AND CONCLUSIONS
131
energies from 40 keV to 15 MeV, and might therefore be an appropriate candidate.
The challenges here lie in mechanical design. A mechanism would have to be designed
to move the panel between the two beams, without allowing it to move under its
own weight as the gantry rotates. The performance of the detector at high energies
would likely be improved by the addition of a thin, dense metal build-up layer, so it
may be worthwhile to investigate the trade-offs in silicon imaging panel design more
thoroughly so that an optimized dual-energy panel could be found.
Modifying the head of the treatment machine is currently not a desirable option,
largely because such modifications would lead to the machine being declared a new
design, with associated regulatory and licensing complications in many jurisdictions.
Nevertheless, such modifications should at least be entertained as possibilities for
the next generation of cobalt machines. One conceptually simple, but mechanically
complex, modification would be to add adjustment capability to the apex of the
primary collimator, which is currently a constant 2 cm opening at all field sizes. If
the collimator apex could be narrowed for imaging, the dose rate would be reduced
and the resolution improved. The collimator apex would then be widened to expose
the entire source for treatment. Since we are considering modifications to the machine
itself, we may also consider embedding an X-ray source or small radioisotope source
in the head, where it would share the same collimators as the treatment source and
would retract out of the way when the treatment source is in use. More efficient
detector technologies should also be investigated. The amorphous silicon panels used
here have a quantum efficiency on the order of 5% at the cobalt beam energy. In other
words, 95% of the photons reaching the detector never interact with it to produce
a signal, and 95% of the dose is effectively wasted. There is considerable room for
CHAPTER 6. SUMMARY AND CONCLUSIONS
132
improvement here, if continued efforts on megavoltage imaging are deemed preferable
to bolt-on kilovoltage systems. Finally, if we remove all restrictions relating to the
use of existing equipment (along with all restrictions on cost), it is not that great
a leap to the proposed ViewRay machine [Vie, 2011], which integrates three Co-60
treatment heads with a magnetic resonance imaging system for real-time, 3D imaging
of the patient as the treatment is being delivered.
It is the opinion of this author that the most promising option is to use a second,
weaker imaging source mounted on the side of the treatment unit’s head assembly
at the same source-to-axis distance as the main source, with a single detector panel
mounted so that it can be moved between the low-energy imaging beam and the
high-energy main beam. Such a setup would allow portal imaging, DT and CBCT in
either beam, and would avoid the large expense associated with the use of multiple
imaging panels.
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Appendix A
Glossary
A.1
Imaging & Reconstruction
CT: Computed tomography, a technique in which projection data from many positions around a patient or object is used to reconstruct a map of the X-ray attenuation
coefficients at various points inside the patient. The radiation beam type may be included in the acronym: kVCT (kilovoltage CT), MVCT (megavoltage CT), CoCT
(cobalt-60 CT).
CAT: Computerized axial tomography, an early name for axial geometry CT scanners.
CBCT: Cone beam computed tomography, a particular type of CT geometry in which
a two-dimensional detector array records projections created with a single source.
DT: Digital tomosynthesis. This term includes computerized implementations of the
techniques used in conventional (film-based) tomosynthesis, along with techniques
that are mathematically similar to CT but that acquire image data at only a small
number of positions around the patient.
ESF: Edge spread function, the output produced by the imaging system in response
to an input that is a radiographically sharp edge.
FBP: Filtered backprojection algorithm.
FDK: Feldkamp-Davis-Kress (cone beam filtered backprojection) algorithm.
MTF: Modulation transfer function, the contrast of the imaging system as a function
of spatial frequency.
Portal image: A conventional radiographic projection image that is taken using a
therapy beam as the radiation source.
PSF: Point spread function, the output produced by the imaging system in response
to an input that is an infinitesimally small, very high contrast point.
SAA: Shift-and-add algorithm.
SL, SLLF, SLNZ: Spatial filters used in filtered backprojection. SL = Shepp-Logan,
140
APPENDIX A. GLOSSARY
141
SLLF = Shepp-Logan plus Low Frequencies, SLNZ = Shepp-Logan plus Non-Zero
offset.
Tomography: Imaging and reconstruction techniques that produce images of particular slices through a patient or object.
Tomosynthesis: Any of several techniques in which a set of projection images are
combined so that features in one plane are emphasized while features in other planes
are blurred or suppressed.
A.2
Equipment
Collimators: Pieces of shielding material, usually a dense metal such as tungsten
or lead, that are used to define the edges of a radiation field.
EPID: Electronic portal imaging device, an imaging panel that uses the therapy
beam as its source.
Gantry: The rotating support structure of a teletherapy machine or CT scanner.
MLC: Multi-leaf collimator. An array of dense metal leaves that can be moved under
computer control to define the edges of a radiation beam.
OBI: On-board imager, an X-ray imaging system mounted on a radiotherapy machine’s gantry, commonly used to verify the position and alignment of the patient.
Phantom: A test object used in a radiation experiment. Phantoms may be designed
with geometric patterns for image analysis, or they might simulate part of the human
body, or they could be made with particular dimensions and materials for dosimetric
experiments, among other possibilities.
SAD: Source to axis distance.
SDD: Source to detector distance.
SSD: Source to surface distance.
A.3
Radiation Therapy
Brachytherapy: Radiation therapy that uses a source that is inserted into the
tumour, or placed on its surface.
Conformal therapy: A class of treatment techniques in which the edges of the
beam are shaped, usually by an MLC, to conform to the edges of the target (i.e. the
tumour) for each position of the source.
Dose: The energy deposited by a radiation beam in a particular target of interest,
often stated in joules of energy deposited per kilogram of target mass (grays, 1 Gy =
1 J/kg).
IMRT: Intensity modulated radiation therapy, a form of conformal therapy in which
the MLC leaves are moved during the treatment to effectively produce different beam
APPENDIX A. GLOSSARY
142
intensities at various points in the field.
Inverse planning: The use of computerized optimization algorithms to determine
beam and collimator settings that will satisfy the user-specified dose constraints for
the various organs in the region of interest. Inverse planning is an essential part of
IMRT.
Teletherapy: Radiation therapy that uses a source located at some distance away
from the patient.
Tomotherapy: A form of IMRT that is delivered slice-by-slice using a fan-like beam
of radiation.