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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 3 9 12 Literature Review . . . . . . . . . . . . . . . Tomography . . . . . . . . . . . . . . . . . . . . . . . . Image Guidance in Radiation Therapy . . . . . . . . . Cobalt Therapy Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 13 24 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 31 35 36 39 49 52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . iv Chapter 4: 4.1 4.2 4.3 4.4 Experimental Methods Imaging Apparatus . . . . . . . Image Reconstruction . . . . . . Image Analysis . . . . . . . . . Dose Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 53 59 64 80 Results . . . . . . . . . . . . . . . . . . . . . Radiation Dose . . . . . . . . . . . . . . . . . . . . . . Spatial Filtering . . . . . . . . . . . . . . . . . . . . . . Resolution . . . . . . . . . . . . . . . . . . . . . . . . . Contrast Sensitivity . . . . . . . . . . . . . . . . . . . . Geometric Considerations in DT . . . . . . . . . . . . . Appearance of Anthropomorphic Phantoms . . . . . . Image Guidance Accuracy . . . . . . . . . . . . . . . . Cone Beam CT . . . . . . . . . . . . . . . . . . . . . . Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 82 84 86 95 101 108 112 116 122 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 . . . . . . . . . . . . . . . . . . . . v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 140 141 141 List of Tables 5.1 Imaging dose and failure rates for aligning Co-60 images to planning images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 vi List of Figures 1.1 1.2 1.3 Co-60 gamma ray spectrum . . . . . . . . . . . . . . . . . . . . . . . Modern linear accelerator (photograph) . . . . . . . . . . . . . . . . . Multi-leaf collimator . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 8 2.1 2.2 2.3 Principle of conventional tomosynthesis . . . . . . . . . . . . . . . . . CT scanner geometry generations . . . . . . . . . . . . . . . . . . . . Cone beam imaging geometry for portal, DT and CBCT images . . . 15 18 21 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 37 41 42 43 44 47 51 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 58 68 70 71 73 76 76 78 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 85 85 86 89 91 vii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 92 93 96 98 100 102 103 104 107 110 111 113 114 115 119 121 123 124 125 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 CHAPTER 5. RESULTS 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. Bibliography [Var, 2000] (2000). PortalVision aS500 Reference Manual. Varian Medical Systems, Palo Alto, CA. Report 6.0.05. Cited on page 55. [Per, 2010] (2010). XRD1640 manual. PerkinElmer Optoelectronics, Fremont, CA. Cited on page 56. [TPL, 2011] (2011). RANDO Phantom Data Sheet RAN100 / RAN110. The Phantom Laboratory, Salem, NY. http://www.phantomlab.com/library/pdf/rando_ datasheet.pdf. Cited on page 75. [Vie, 2011] (2011). ViewRay — MRI-Guided RT. http://www.viewray.com/. Cited on page 132. [Almond et al., 1999] Almond, P. R., Biggs, P. J., Coursey, B., Hanson, W., Huq, M. S., Nath, R., and Rogers, D. (1999). AAPM’s TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams. Medical Physics, 26(9):1847–1870. Cited on page 80. [Andersen and Kak, 1984] Andersen, A. and Kak, A. (1984). Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm. Ultrasonic Imaging, 6:81–94. Cited on pages 23 and 52. [Attix, 1986] Attix, F. H. (1986). Introduction to Radiological Physics and Radiation Dosimetry. John Wiley & Sons, New York. Cited on page 35. [Baydush et al., 2005] Baydush, A. H., Godfrey, D. J., Oldham, M., and Dobbins, III, J. T. (2005). Initial application of digital tomosynthesis with on-board imaging in radiation oncology. Proc. of SPIE, 5745:1300–1305. Cited on page 26. [Beckmann, 2006] Beckmann, E. (2006). CT scanning: The early days. British Journal of Radiology, 79(937):5–8. Cited on page 16. [Boin and Haibel, 2006] Boin, M. and Haibel, A. (2006). Compensation of ring artefacts in synchrotron tomographic images. Opt. Express, 14:12071–12075. Cited on page 63. 133 BIBLIOGRAPHY 134 [Colsher, 1976] Colsher, J. G. (1976). Iterative three dimensional image reconstruction from tomographic projections. Computer Graphics and Image Processing, 6:513–537. Cited on page 23. [Coltman, 1954] Coltman, J. W. (1954). The specification of imaging properties by response to a sine wave input. Journal of the Optical Society of America, 44(6):468– 471. Cited on pages 66 and 69. [Després et al., 2007] Després, P., Sun, M., Hasegawa, B., and Prevrhal, S. (2007). FFT and cone-beam CT reconstruction on graphics hardware. Proc. of SPIE, 6510:65105N–1–65105N–7. Cited on page 23. [Dobbins, 2009] Dobbins, III, J. T. (2009). Tomosynthesis imaging: At a translational crossroads. Medical Physics, 36(6):1956–1967. Cited on page 22. [Feldkamp et al., 1984] Feldkamp, L., Davis, L., and Kress, J. (1984). Practical conebeam algorithm. J. Opt. Soc. Am., 1(6):612–619. Cited on pages 19, 23, 39, 40, 46, and 49. [Godfrey et al., 2006a] Godfrey, D. J., McAdams, H., and Dobbins, III, J. T. (2006a). Optimization of the matrix inversion tomosynthesis (MITS) impulse response and modulation transfer function characteristics for chest imaging. Medical Physics, 33(3):655–667. Cited on page 24. [Godfrey et al., 2003] Godfrey, D. J., Rader, A., and Dobbins, III, J. T. (2003). Practical strategies for the clinical implementation of matrix inversion tomosynthesis (MITS). Proc. of SPIE, 5030:379–390. Cited on page 24. [Godfrey et al., 2001] Godfrey, D. J., Warp, R. J., and Dobbins, III, J. T. (2001). Optimization of matrix inverse tomosynthesis. Proc. of SPIE, 4320:696–704. Cited on page 24. [Godfrey et al., 2006b] Godfrey, D. J., Yin, F.-F., Oldham, M., Yoo, S., and Willett, C. (2006b). Digital tomosynthesis with an on-board kilovoltage imaging device. Int. J. Radiation Oncology Biol. Phys., 65(1):8–15. Cited on page 27. [Gopal and Samant, 2008] Gopal, A. and Samant, S. (2008). Validity of the linepair bar-pattern method in the measurement of the modulation transfer function (MTF) in megavoltage imaging. Medical Physics, 35:270–279. Cited on pages 66 and 69. [Grant, 1972] Grant, D. G. (1972). Tomosynthesis: A three-dimensional radiographic imaging technique. IEEE Transactions on Biomedical Engineering, BME-19(1):20– 28. Cited on page 16. BIBLIOGRAPHY 135 [Groh et al., 2002] Groh, B., Siewerdsen, J., Drake, D., Wong, J., and Jaffray, D. (2002). A performance comparison of flat-panel imager-based MV and kV conebeam CT. Medical Physics, 29:967–975. Cited on page 20. [Hajdok, 2002] Hajdok, G. (2002). An investigation of megavoltage computed tomography using a radioactive cobalt-60 gamma ray source for radiation therapy treatment verification. Master’s thesis, Queen’s University at Kingston. Cited on pages 59 and 122. [Hajdok et al., 2004] Hajdok, G., Kerr, A., Salomons, G., Dyke, C., and Schreiner, L. J. (2004). The potential for cobalt-60 tomotherapy II: Initial Co-60 MVCT performance evaluation. Med. Phys. Cited on page 28. [Hall, 2000] Hall, E. (2000). Radiobiology For The Radiologist. Lippincott Williams & Wilkins, Philadelphia, PA. Cited on pages 5 and 9. [Hsieh, 2009] Hsieh, J. (2009). Image Reconstruction, pages 55–117. Computed Tomography. SPIE Press, Bellingham, WA. Cited on pages 40, 43, and 46. [IAEA, 2003] IAEA (2003). A Silent Crisis: Cancer Treatment in Developing Countries. International Atomic Energy Agency, Vienna. http://www.iaea. org/Publications/Booklets/TreatingCancer/treatingcancer.pdf. Cited on pages 1 and 3. [Islam et al., 2006] Islam, M. K., Purdie, T. G., Norrlinger, B. D., Alasti, H., Moseley, D. J., Sharpe, M. B., Siewerdsen, J. H., and Jaffray, D. A. (2006). Patient dose from kilovoltage cone beam computed tomography imaging in radiation therapy. Medical Physics, 33(6):1573–1582. Cited on page 26. [Jackson, 1999] Jackson, J. D. (1999). Classical Electrodynamics 3rd Edition. John Wiley & Sons, Hoboken, NJ. Cited on page 33. [Jaffray and Siewerdsen, 2000] Jaffray, D. and Siewerdsen, J. (2000). Cone-beam computed tomography with a flat-panel imager: initial performance characterization. Medical Physics, 27:1311–1323. Cited on page 19. [John, 1938] John, F. (1938). The ultrahyperbolic differential equation with four independent variables. Duke Mathematical Journal, 4(2):300–322. Cited on page 39. [Joshi et al., 2009] Joshi, C., Dhanesar, S., Darko, J., Kerr, A., Vidyasagar, P., and Schreiner, L. J. (2009). Practical and clinical considerations in cobalt-60 tomotherapy. Journal of Medical Physics, 34(3):137–140. Cited on pages 2, 10, and 28. BIBLIOGRAPHY 136 [Kak and Slaney, 1988] Kak, A. and Slaney, M. (1988). Principles of Computerized Tomographic Imaging. IEEE Press, New York. Cited on pages 23, 40, 41, 43, 45, 46, 49, 52, and 64. [Kalendar, 2006] Kalendar, W. (2006). X-ray computed tomography. Phys. Med. Biol., 51:R29–R43. Cited on page 17. [Knoll, 2010] Knoll, G. F. (2010). Radiation Detection and Measurement. John Wiley & Sons, Hoboken, NJ. Cited on page 32. [Koren, 2011] Koren, N. (2011). Understanding resolution and MTF. http://www. normankoren.com/Tutorials/MTF.html. Cited on page 65. [Kriminski et al., 2007] Kriminski, S., Lovelock, D., Mageras, H., and Amols, H. (2007). Evaluation of respiration-correlated digital tomosynthesis in the thorax and abdomen for soft tissue visualization and patient positioning. Med. Phys., 34(6):2608–2608. Cited on page 27. [McDonald, 2010] McDonald, A. (2010). Investigation of megavoltage digital tomosynthesis using a Co-60 source. Master’s thesis, Queen’s University at Kingston. Cited on pages 21, 29, 52, 59, and 63. [Morin et al., 2009] Morin, O., Aubry, J., Aubin, M., Chen, J., Descovich, M., Hashemi, A., and Pouliot, J. (2009). Physical performance and image optimization of megavoltage cone-beam CT. Medical Physics, 36:1421–1432. Cited on page 20. [Nelms et al., 2010] Nelms, B. E., Rasmussen, K. H., and Tomé, W. A. (2010). Evaluation of a fast method of EPID-based dosimetry for intensity-modulated radiation therapy. J. App. Clin. Medical Physics, 11(2):140–157. Cited on page 26. [Niklason et al., 1997] Niklason, L., Christian, B., Niklason, L., Kopans, D., Castleberry, D., Opsahl-Ong, B., Landberg, C., Slanetz, P., Giardino, A., Moore, R., Albagli, D., Dejule, M., Fitzgerald, P., Fobare, D., Giambattista, B., Kwasnick, R., Liu, J., Lubowski, S., Possin, G., Richotte, J., Wei, C.-Y., and Wirth, R. (1997). Digital tomosynthesis in breast imaging. Radiology, 205:399–406. Cited on page 22. [Pang, 2005] Pang, G. (2005). Cone beam digital tomosynthesis (CBDT): An alternative to cone beam computed tomography (CBCT) for image-guided radiation therapy. Med. Phys., 32(6):2126–2126. Cited on page 27. [Pang et al., 2006] Pang, G., Au, P., O’Brien, and Bani-Hashemi, A. (2006). Quantitative evaluation of cone beam digital tomosynthesis (CBDT) for image-guided radiation therapy. Med. Phys., 33(6):1988–1988. Cited on page 27. BIBLIOGRAPHY 137 [Pang et al., 2008] Pang, G., Bani-Hashemi, A., Au, P., O’Brien, P., Rowlands, J., Morton, G., Lim, T., Cheung, P., and Loblaw, A. (2008). Megavoltage cone beam digital tomosynthesis (MV-CBDT) for image-guided radiotherapy: a clinical investigational system. Physics in Medicine and Biology, 53:999–1013. Cited on page 27. [Petersson et al., 1980] Petersson, C. U., Edholm, P., Granlund, G. H., and Knutsson, H. E. (1980). Ectomography- a new radiographic reconstruction method- II. Computer simulated experiments. IEEE Transactions on Biomedical Engineering, BME-27(11):649–655. Cited on page 22. [Podgorsak, 2004] Podgorsak, E. B. (2004). Radiation Physics for Medical Physicists. Department of Medical Physics, McGill University Health Centre, Montreal. Cited on pages 7 and 33. [Podgorsak, 2005] Podgorsak, E. B. (2005). Radiation Oncology Physics: A Handbook for Teachers and Students. International Atomic Energy Agency, Vienna. Cited on page 34. [Prell et al., 2009] Prell, D., Kyriakou, K., and Kalendar, W. (2009). Comparison of ring artifact correction methods for flat-detector CT. Physics in Medicine and Biology, 54:3881. Cited on pages 62 and 63. [Radon, 1917] Radon, J. (1917). On the determination of functions from their integral values along certain manifolds. Berichte der Sächsischen Akadamie der Wissenschaft, 69:262–277. Trans. P.C. Parks for IEEE Trans. Med. Im. MI-5(4), 1986. Cited on pages 14, 38, and 39. [Rajapakshe et al., 1996] Rajapakshe, R., Luchka, K., and Shalev, S. (1996). A quality control test for electronic portal imaging devices. Medical Physics, 23(7):1237– 1244. Cited on page 68. [Raju, 1999] Raju, T. N. (1999). The Nobel chronicles. The Lancet, 354:1653. Cited on page 16. [Raven, 1998] Raven, C. (1998). Numerical removal of ring artifacts in microtomography. Rev. Sci. Instrum., 69:2978–2980. Cited on page 63. [Ravichandran, 2009] Ravichandran, R. (2009). Has the time come for doing away with cobalt-60 teletherapy for cancer treatments. Journal of Medical Physics, 34:63–65. Cited on page 28. BIBLIOGRAPHY 138 [Rawluk, 2010] Rawluk, N. (2010). Implementation and characterization of conebeam computed tomography using a cobalt-60 gamma ray source for radiation therapy patient localization. Master’s thesis, Queen’s University at Kingston. Cited on pages 29, 30, 49, 57, 59, 63, 64, 70, 112, 116, 117, 118, and 122. [Röntgen, 1896] Röntgen, W. (1896). On a new kind of rays. Nature, 53(1369):274– 276. Cited on page 13. [Rossman, 1969] Rossman, K. (1969). Point spread-function, line spread-function and modulation transfer function. Radiology, 93:257–272. Cited on page 67. [Salomons et al., 1999] Salomons, G. J., Kim, B., Gallant, G., Kerr, A., and Schreiner, L. J. (1999). CT imaging with a prototype cobalt-60 tomotherapy unit. Proc. Annual Scientific Meeting of the Canadian Organization of Medical Physicists, pages 187–189. Cited on pages 28 and 57. [Sarkar et al., 2009] Sarkar, V., Shi, C., Rassiah-Szegedi, P., Diaz, A., Eng, T., and Papanikolaou, N. (2009). The effect of a limited number of projections and reconstruction algorithms on the image quality of megavoltage digital tomosynthesis. Journal of Applied Clinical Medical Physics, 10(3):155–172. Cited on page 23. [Schiwietz et al., 2010] Schiwietz, T., Bose, S., Maltz, J., and Westermann, R. (2010). A fast and high-quality cone beam reconstruction pipeline using the GPU. Proc. of SPIE, 6510:65105H–1–65105H–12. Cited on page 23. [Schreiner et al., 2009] Schreiner, L. J., Joshi, C., Darko, J., Kerr, A., Salomons, G., and Dhanesar, S. (2009). The role of cobalt-60 in modern radiation therapy: Dose delivery and image guidance. Journal of Medical Physics, 34(3):133–136. Cited on pages 2, 10, and 28. [Schreiner et al., 2003a] Schreiner, L. J., Kerr, A., and Salomons, G. (2003a). The potential for image guided radiation therapy with cobalt-60 tomotherapy. Proc. Int’l Conf. on Medical Image Computing and Computer-Assisted Intervention (MICCAI), page 2879. Cited on page 28. [Schreiner et al., 2003b] Schreiner, L. J., Salomons, G., Kerr, A., Joshi, C., Hsu, A., Dyck, C., and Gallant, G. (2003b). The potential for cobalt-60 tomotherapy I: Dose delivery studies. Unpublished manuscript. Cited on page 2. [Siebers et al., 2004] Siebers, J., Kim, J., Ko, L., Keall, P., and Mohan, R. (2004). Monte carlo computation of dosimetric amorphous silicon electronic portal images. Medical Physics, 31:2135–2146. Cited on page 55. BIBLIOGRAPHY 139 [Sijbers and Postnov, 2004] Sijbers, J. and Postnov, A. (2004). Reduction of ring artefacts in high resolution micro-CT reconstructions. Physics in Medicine and Biology, 49:N247. Cited on page 63. [Silverman, 1998] Silverman, P. (1998). CT– A practical approach to clinical protocols. Lippincott Williams & Wilkens, Philadelphia, PA. Cited on page 65. [Stewart and Thomson, 2011] Stewart, M. and Thomson, E. (2011). 2011 ontario budget– controlling growth in health-care spending is key to budget commitment to balance the books. http://www.conferenceboard.ca/topics/economics/ budgets/ontario_2011_budget.aspx. Cited on page 2. [Traitor, 2007] Traitor (2007). Gamma spectrum of 60co, observed with a germanium detector. https://en.wikipedia.org/wiki/File:60Co_gamma_spectrum_ energy.png, licensed GFDL/CC. Cited on page 5. [Van Dyk, 1999] Van Dyk, J. (1999). Radiation oncology overview. The Modern Technology of Radiation Oncology, pages 1–17. Medical Physics Publishing, Madison, Wisconsin. Cited on page 17. [Van Dyk and Battista, 1996] Van Dyk, J. and Battista, J. J. (1996). Cobalt-60: An old modality, a renewed challenge. Cited on pages 2 and 10. [Verellen et al., 2008] Verellen, D., Ridder, M., and Storme, G. (2008). A (short) history of image-guided radiotherapy. Radiother. Oncol., 86:4–13. Cited on page 17. [Webb, 2001] Webb, S. (2001). Intensity-Modulated Radiation Therapy. Institute of Physics Publishing, Bristol. Cited on pages 8 and 25. [Wu et al., 2007] Wu, Q., Godfrey, D. J., Wang, Z., and Zhang, J. (2007). On-board patient positioning for head-and-neck IMRT: Comparing digital tomosynthesis to kilovoltage radiography and cone-beam computed tomography. Int. J. Radiation Oncology Biol. Phys., 69(2):598–606. Cited on page 27. [Ziedses des Plantes, 1932] Ziedses des Plantes, B. G. (1932). Eine neue methode zur differenzierung in der roentgenographie (planigraphie). Acta. Radiol., 13:182–192. Cited on page 15. 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.