PORTAL SCATTER TO PRIMARY DOSE RATIO OF 4 TO 18 M V PHOTON SPECTRA INCIDENT ON HETEROGENEOUS PHANTOMS By Siobhan R. Ozard B.Sc. (Hon), University of Victoria, 1995 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF D OCTOR OF PHILOSOPHY in T THE FACULTY OF GRADUATE STUDIES DEPARTMENT ~0F; PHYSICS AND ASTRONOMY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 2001 © Siobhan R. Ozard> ZOO \ In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Physics and Astronomy The University of British Columbia 6224 Agricultural Road Vancouver, Canada V6T 1Z1 Date: A B S T R A C T Electronic portal imagers designed and used to verify the positioning of a cancer patient undergoing radiation treatment can also be employed to measure the in vivo dose received by the patient. This thesis investigates the ratio of the dose from patient-scattered particles to the dose from primary (unscattered) photons at the imaging plane, called the scatter to primary dose ratio (SPR). The composition of the SPR according to the origin of scatter is analyzed more thoroughly than in previous studies. A new analytical method for calculating the SPR is developed and experimentally verified for heterogeneous phantoms. A novel technique that applies the analytical SPR method for in vivo dosimetry with a portal imager is evaluated. Monte Carlo simulation was used to determine the imager dose from patient-generated electrons and photons that scatter one or more times within the object. The database of SPRs reported from this investigation is new since the contribution from patient-generated electrons was neglected by previous Monte Carlo studies. The SPR from patient-generated electrons was found here to be as large as 0.03. The analytical SPR method relies on the established result that the scatter dose is uniform for an air gap between the patient and the imager that is greater than 50 cm. This method also applies the hypothesis that first-order Compton scatter only, is sufficient for scatter estimation. A comparison of analytical and measured SPRs for neck, thorax, and pelvis phantoms showed that the maximum difference was within ± 0 . 0 3 , and the mean difference was less than ± 0 . 0 1 for most cases. This accuracy was comparable to similar analytical approaches that are limited to homogeneous phantoms. The analytical SPR method could replace lookup tables of measured scatter doses that can require significant ii time to measure. In vivo doses were calculated by combining our analytical SPR method and the con-volution/superposition algorithm. Our calculated in vivo doses agreed within ± 3 % with the doses measured in the phantom. The present in vivo method was faster compared to other techniques that use convolution/superposition. Our method is a feasible and satisfactory approach that contributes to on-line patient dose monitoring. iii CONTENTS Abstract ii List of Figures ix List of Tables xii Acknowledgements xiii 1 Introduction 1 1.1 Aim of this Work 1 1.2 Structure of this Thesis 2 1.3 Thesis Highlights 3 1.4 Accuracy Required in Radiotherapy 4 1.5 Clinical Linear Accelerator 5 1.6 Portal Imager 6 1.7 Patient Density Data 9 1.7.1 X-ray Computed Tomography 9 1.7.2 Phantoms 11 1.8 Sources of Scatter Dose in Portal Images 13 1.8.1 Compton Scattering and Pair Production 14 iv 1.8.2 Bremsstrahlung 17 1.8.3 Annihilation 18 1.8.4 Rayleigh Scattering 19 1.9 Quantities to Describe a Radiation Beam 20 1.9.1 Depth Dose Curves 20 1.9.2 Dose Profiles 21 1.10 Motivation to Calculate the Imager Dose from Scatter 22 2 Literature Review 24 2.1 Background: Portal Scatter Dose 25 2.2 Scatter Estimates From Treatment Planning Systems 27 2.2.1 Delta Volume Dose Algorithm 27 2.2.2 Convolution/Superposition Method 29 2.3 Theoretical Calculation of the Scatter Dose 32 2.3.1 Scatter to Primary Dose Ratio (SPR) Model 32 2.3.2 Slab Derived Scatter Kernels 36 2.3.3 Monte Carlo Calculation of the Total Imager Dose 39 2.4 Empirical Scatter Dose Estimation 39 2.4.1 Uniform Scatter Dose Approximation 40 2.4.2 Slab Derived Scatter Kernels 43 2.4.3 Empirical Scatter Fluence Function 46 2.5 Summary 47 3 Materials 49 3.1 Ionization Chambers 49 3.2 The Portal Imager 51 3.2.1 Liquid Film 53 v 3.2.2 Readout Electronics 54 3.2.3 Computer 55 3.2.4 Calibration for Dosimetry 56 3.3 Summary 59 4 Theory: Analytic SPR Calculation 60 4.1 History 61 4.2 Current Development: Analytical Imager Dose Calculation 61 4.2.1 Imager Dose from Primary Radiation 62 4.2.2 Imager Dose from First Order Compton Scatter 67 4.2.3 Scatter to Primary Dose Ratio 72 4.2.4 Examples 72 4.3 Summary 79 5 Monte Carlo Study and Validation 80 5.1 Monte Carlo Simulation Time for Dose Calculation 81 5.2 The Monte Carlo Code: SDOSXYZ 82 5.3 Simulation Parameters 87 5.3.1 Homogeneous Phantoms 87 5.3.2 Anthropomorphic Phantoms 88 5.4 Results 91 5.4.1 Scatter to Primary Dose Ratios 91 5.4.2 Validation of the Analytical SPR Calculation 99 5.4.3 Monte Carlo Simulation Times and Uncertainties 104 5.5 Summary 106 vi 6 Experimental Validation 107 6.1 Clinically Relevant Cases : . . 107 6.2 Photon Beam Characteristics 108 6.2.1 Photon Energy Spectra 108 6.2.2 Collimator Scatter Factor, SC(FA) I l l 6.3 Scatter to Primary Dose Ratio Measurements 112 6.3.1 Phantoms 112 6.3.2 Tissue Substitutes 114 6.3.3 Detector 119 6.3.4 Measurement Methods 120 6.4 Analysis Method 123 6.5 Results and Discussion 124 6.6 Summary 130 7 Application - In vivo Dosimetry 131 7.1 Materials and Methods 135 7.1.1 An Illustrative Example 135 7.1.2 Dose Calculation Methods 137 7.1.3 Accuracy of the Photon Source Model 141 7.1.4 Test Phantoms 142 7.1.5 Imager Dose Calibration 143 7.1.6 Ionization Chamber Measurements 147 7.1.7 Analysis 147 7.2 Results 148 7.3 Discussion 154 7.4 Summary • • • • 156 vii 8 Conclusions 158 8.1 Summary of Work 158 8.2 Future Research 161 8.3 Summary 162 A SDOSXYZ 163 B SPRs from Monte Carlo Simulation 166 C Measured SPRs 172 Bibliography 176 Index 187 viii LIST OF FIGURES 1.1 Diagram of a radiotherapy linear accelerator 7 1.2 Photon energy spectra from radiotherapy linear accelerators 8 1.3 A sample portal image 9 1.4 Diagram of a clinical linear accelerator with a portal imager 10 1.5 The liquid matrix portal imager 11 1.6 X-ray computed tomography images of the chest 12 1.7 Percent energy transferred to water by Compton and pair production. . . 14 1.8 Illustration of Compton scattering and pair production 15 1.9 Differential Klein-Nishina cross-section versus photon scattering angle. . . 16 1.10 Energy spectra for electrons produced by monoenergetic photons 17 1.11 Bremsstrahlung yield for water and bone 18 1.12 Relative dose versus depth in water 21 1.13 Relative dose versus off-axis distance in water 22 2.1 The extended phantom concept 30 2.2 Portal images computed with convolution/superposition 31 2.3 Phantom geometry used in the SPR model 33 2.4 Overview of the Netherlands Cancer Institute in vivo dosimetry method. 41 2.5 Phantom setup for empirical slab derived portal scatter kernels 45 ix 3.1 Cross-sectional view of a typical thimble-type ionization chamber 50 3.2 Cross-section of the liquid matrix portal imager 52 3.3 Schematic diagram of the readout electronics for the portal imager. . . . 54 4.1 Variables for the analytical scatter calculation 65 4.2 Mass attenuation and mass absorption coefficients for water 66 4.3 Relationship between K E R M A and dose 75 4.4 Imager dose profiles (primary and scatter) for homogeneous phantoms. . 77 4.5 Imager dose profiles (primary and scatter) for heterogeneous phantoms: . 78 5.1 Monte Carlo simulation geometry 82 5.2 Verification of results from SDOSXYZ for separating the scatter dose. . . 85 5.3 Verification of scatter fraction data computed by SDOSXYZ 86 5.4 The anthropomorphic phantoms 89 5.5 Central axis SPRs from multiple photon scatter and electron scatter. . . 92 5.6 Monte Carlo SPRs for the homogeneous water phantoms 93 5.7 Composition of the SPR versus SDD, beam area, and energy. 94 5.8 Monte Carlo calculated SPRs versus off-axis distance, neck phantom. . . 96 5.9 Monte Carlo calculated SPRs versus off-axis distance, thorax phantom. . 97 5.10 Monte Carlo calculated SPRs versus off-axis distance, pelvis phantom. . . 98 5.11 Comparison of Monte Carlo and analytical SPR profiles for the neck case. 101 5.12 Comparison of Monte Carlo and analytical SPR profiles for the thorax case. 102 5.13 Comparison of Monte Carlo and analytical SPR profiles for the pelvis case. 103 6.1 Comparison of measured and M C calculated percentage depth doses. . . I l l 6.2 Design of the experimental anthropomorphic phantoms 114 6.3 Comparison of the mass attenuation coefficients for the tissue substitutes. 116 6.4 Mass attenuation coefficients for the phantom materials 119 6.5 The extrapolation method for deriving the dose from primary photons. . 122 6.6 Comparison of analytical and experimental SPRs, homogeneous cases. . . 125 6.7 Measured and analytical SPRs for the anthropomorphic phantoms. . . . 127 6.8 Difference between analytical and measured SPRs, anthropomorphic cases. 128 6.9 Comparison of Monte Carlo and measured SPRs for the 18 M V beam. . . 129 7.1 Location of the measurement planes for the IC measurements 133 7.2 In vivo dosimetry with diodes 134 7.3 Illustration of the imager dose from primary photons and scatter radiation. 136 7.4 Comparison of CS calculated doses to measured doses 144 7.5 Schematic diagram of the phantoms 145 7.6 Dose calibration curve for the liquid matrix portal imager 145 7.7 Correction for the commercial flat field calibration 146 7.8 Extracted doses for a 25 cm water phantom irradiated with a 6 M V beam. 150 7.9 Extracted doses for a 25 cm water phantom irradiated with a 10 M V beam. 151 7.10 Extracted doses for the cork slab phantom irradiated with a 6 M V beam. 152 7.11 Extracted doses, aluminum slab phantom irradiated with a 10 M V beam. 153 xi LIST OF T A B L E S 4.1 Physical properties of the heterogeneities 73 4.2 Scatter to primary dose ratios for the examples 76 5.1 Comparison of Monte Carlo and analytical SPRs, heterogeneous cases. . 104 5.2 Monte Carlo C P U times and histories for the homogeneous phantoms. . . 105 6.1 Physical properties of the phantom materials 117 6.2 Effective atomic numbers for the phantom materials 119 6.3 Agreement between experimental and analytical SPRs, homogeneous cases. 126 7.1 Statistical analysis of the extracted phantom doses 149 B . l SPRs calculated with Monte Carlo simulation for a 6 M V beam 166 B. 2 SPRs calculated with Monte Carlo simulation for an 18 M V beam 169 C l SPRs measured for a 4 M V photon beam 172 C. 2 SPRs measured for a 6 M V photon beam 173 C.3 SPRs measured for a 10 M V photon beam 174 C.4 SPRs measured for an 18 M V photon beam 175 xii A C K N O W L E D G E M E N T S I would like to thank my supervisor, Ellen Grein (El-Khatib), for her guidance and encouragement throughout this research project. Her insight and experience were major contributors to the success of my thesis. Thanks also to each member of my supervisory committee (B. Clark, T. Keane, and D. Measday) for their ideas and invaluable feedback on radiation oncology and research. Many people in the Radiation Therapy Program at the B C C A have freely given their time and expertise towards my thesis research and I sincerely thank them. Special thanks go to L. Watts and C. Zankowski for assistance with Linux and EGS4 as well as A. Calleja for helping to schedule meetings. I would also like to thank K. Luchka, V. Strgar, and J. Wolters for technical support on the medical linear accelerators and related imaging and dosimetry equipment, especially the portal imagers. I also thank A. Jirasek and K. Otto for willingly answering my questions about Word and radiation therapy, and as well for the good company. I would also like to extend my gratitude to the faculty and staff in the Department of Physics and Astronomy at U B C for their support of my thesis research and supervision during my teaching assistantships, especially F. Bates, J. Eldridge, C. Waltham, and J. Young. Special mention goes to J. Johnson and L. Wong who filled several last minute, often after hours requests. Sincere thanks to H. Hubball and the Centre for Teaching and Academic growth for providing courses on teaching. To all my students - your willingness to work hard was inspiring. A sincere thanks to those students and faculty at U B C who provided guidance and friendship, especially E. Brief, S. McFarland, and M . Strimbold. This thesis benefited greatly from the criticism of many people, including: G. Wheeler xiii who corrected the thesis for grammatical errors, K. Yuen and W. Kwa for reviewing the abstract, H. Liu and P. Charland who read chapter 7, the anonymous reviewers for the paper on the analytical portal scatter to primary dose ratio calculation, and my father who provided many valuable comments and discussion on the entire thesis. I also thank H. Liu for providing the convolution/superposition codes and A. Ahnesjo for advice on how to write the Monte Carlo simulation code for this thesis. Finally, I thank my family and friends for their continual encouragement: my aunt for lending a sympathetic ear, P. Charland for advice on medical physics and graduate research, and my brother for his humour. Lastly, I would like to thank my parents. I am very grateful to both of you. xiv C H A P T E R 1 I N T R O D U C T I O N 1.1 A I M O F T H I S W O R K Radiotherapy portal images are analogous to planar X-ray films since the patient is positioned between the radiation source and the flat imager. The megavoltage treatment beam serves as the photon source. Portal imaging was originally developed to verify the position of a cancer patient relative to the external photon beam used for treatment. Portal images could also be used for patient dose verification immediately after treatment. Furthermore, the treatment accuracy increases when deviations between planned and measured doses are identified and corrected. The majority of the imager signal is from primary photons that pass through the patient without interacting. The remainder of the imager signal comes from scatter. Scatter includes photons that interact one or more times within the patient as well as patient-generated electrons. Scatter is a problem when verifying in vivo patient doses from portal images since novel algorithms are required to estimate the radiation dose from scatter. The goal of the current work is to develop, validate, and apply a method to calculate absorbed dose in the patient from absorbed dose measured at the portal imaging plane. 1 Chapter 1. Introduction 1.2 S T R U C T U R E O F T H I S T H E S I S 2 This thesis contains eight chapters having the common theme,.scatter dose in radio-therapy portal images. Chapter 1 provides background information on radiation therapy with photon beams, portal imaging, and sources of scatter dose in portal images. As well, the clinical linear accelerators that produce the photon beams are described and an example of the resulting dose distribution in water is presented. A literature review on portal scatter dose estimation methods is given in chapter 2. These methods are divided into three broad categories: (i) those that use the same cal-culation algorithms as for dose calculation within the patient, (ii) theoretical approaches, and (iii) empirical techniques. This review focuses on the advantages and disadvantages of each method, accuracy of the resulting dose data, and ways in which the data have been used within the radiotherapy process. Chapter 3 describes the operation and calibration of the imager used in this thesis for measurement of portal dose images. The imager is a two-dimensional array of 256x256 liquid ionization chambers and has a total imaging area of 32.5x32.5 cm 2. Chapter 4 presents the analytical method developed here for calculating the dose from scatter in the portal image. The analytical scatter calculation is a theoretical approach and applies the equations for photon attenuation, divergence, and Compton scatter within tissue. To illustrate the technique for portal scatter dose calculation, several examples are included to show the effect of photon energy and heterogeneous scattering objects on the scatter dose. Validation of the analytical method for calculation of the dose from scatter is provided in two separate chapters. Chapter 5 documents comparison of the analyticalal results and Monte Carlo simulation data for homogeneous and anthropomorphic scattering objects. Chapter 6 gives the details of an experimental validation of the analytical method where Chapter 1. Introduction 3 measurements of the scatter dose were carried out for homogeneous and heterogeneous scatterers over a wide range of radiation beam energies and beam areas. Statistical analysis of the results are included in both chapters 5 and 6. In chapter 7 the analyticalal scatter method is applied to the problem of extracting the phantom dose using a pair of measured and calculated portal dose images. The method described to compute the portal dose images does not require measured data to predict the total dose at the imager. This technique is advantageous compared to empirical methods for imager dose calculation that can require a significant amount of time to measure the data needed for the scatter computation algorithm. Chapter 8 concludes the thesis. It provides a summary of the major results and potential avenues for future work. 1.3 T H E S I S H I G H L I G H T S • Monte Carlo simulation results and experimental measurements of the scatter to primary 1 dose ratio (SPR) at the portal imager are reported for a wide range of clinically relevant cases. • The equations for photon attenuation and Compton scattering were applied to ana-lyticalally calculate the SPR in radiotherapy portal images. • Analyticalally calculated SPRs show good agreement with Monte Carlo simulation results and experimental measurements. • The analytical method has the following advantages: - since the imager dose from scatter is approximated by a uniform distribution, the calculation is only performed at the centre of the field, which reduces the 1Primary photons pass through the object (patient) without interacting or scattering. Chapter 1. Introduction 4 computation time - the method is based on an X-ray computed tomography scan of the patient, and thus is suitable for heterogeneous cases such as the thorax - the method does not rely on a database of scatter dose measurements - the method can account for the detector response as a function of photon energy. • Application of the analytical method is illustrated: - calculation of portal dose images normalized to the dose at the centre of the phantom. Quantitative comparison of calculated and measured portal dose im-ages can provide a quality assessment of the treatment. - extraction of the in vivo phantom dose. The method for extracting the phantom dose is faster than several similar techniques. 1.4 A C C U R A C Y R E Q U I R E D I N R A D I O T H E R A P Y Normal tissue can become nonfunctional after exposure to radiation and irradiation of normal tissue inevitably occurs during external beam radiotherapy. The probability of normal tissue complication (NTCP) versus dose follows a sigmoidal curve. This prob-ability can also be considered as the percentage of patients who experience treatment complication versus the total dose to the normal tissue. In clinical practice, the pre-scribed radiation dose is chosen to correspond to an N T C P value of 5%. Since the slope of the N T C P curve versus dose is steep, accurate dose delivery is important to avoid in-creasing the possibility of normal tissue injury. The steepness of the N T C P curve means that changes in delivered dose of either ±10% can give marked changes in the probability of normal tissue damage. Chapter 1. Introduction 5 The tumour control probability (TCP) as a function of tumour dose (that is, the percent of patients whose tumour was controlled) has also been experimentally deter-mined to be sigmoidal. The slopes of the T C P curves are shallower than for the N T C P curves because of the radiobiological variation in the tumours for different patients (see for example reference [87]). Practical experience with radiation therapy has shown that the dose to control microscopic disease ranges from 40 to 50 Gy, 2 while gross tumours are controlled by doses from 60 to 65 Gy. The recommended accuracy in absorbed dose for radiotherapy varies. Mijnheer et al. [78] propose that the accuracy should be 3.5% of the combined uncertainty for random and systematic errors, given as one standard deviation. In many cases, larger values are accepted and in a few cases an even smaller value is desired. The International Commission on Radiation Units and Measurements [88] concluded that an accuracy of ± 5 % is needed. The ability to fulfill such accuracy requirements depends partly on the control of random and systematic errors; human, software, and hardware mistakes; and tumour dose homogeneity [28, 88]. The reproducibility of patient setup for each fraction of the irradiation is one possible source of inaccuracy. Portal imaging is used to verify the accuracy of daily setup and has the potential to verify the dose delivered to the patient. 1.5 C L I N I C A L L I N E A R A C C E L E R A T O R The components of a radiotherapy linear accelerator are shown in figure 1.1 (a review of medical electron accelerators is given by Karzmark et al. [50]). In a medical electron accelerator, an electron beam is accelerated to megavoltage energies. This electron beam is then converted via the bremsstrahlung process to a photon beam in the X-ray target. The target is made of a high-atomic number metal such as tungsten to improve the 2The unit of radiation dose is the gray, Gy, and 1 Gy=l J kg - 1 . Chapter 1. Introduction 6 efficiency of bremsstrahlung photon production. The maximum energy of the photon energy spectrum is equal to the energy of the incident electron beam. If the energy of the electrons striking the target is 6 MeV, then the nomenclature for the resulting photon spectrum is 6 M V . Sample photon energy spectra for 6 and 18 M V beams are given in figure 1.2: these spectra were taken from [80] and [127], respectively. Movable collimator jaws define the size of the square or rectangular photon beam. The collimators, which are usually made of tungsten, attenuate the X-ray beam by several orders of magnitude and are designed to cleanly cut-off the radiation beam with minimal penumbra. 1.6 P O R T A L I M A G E R A portal image is analogous to an X-ray image used for diagnosis of bone fractures. Portal images are obtained with the same photon source as for the radiation treatment: a sample image is given in figure 1.3. The main purpose of portal imaging is to guide the repositioning of the patient between treatment fractions3 and to ensure that the patient is positioned as intended. Portal images can be recorded on X-ray film or with a wide range of two-dimensional, electronic detectors for immediate on-line display. Compared to electronic detectors, film has several disadvantages for portal imaging. For example, the optimal film exposure dose is lower than the typical dose received by the film while a patient is treated, and therefore the treatment has to be interrupted to remove the film. As well, the time to develop and read the film prevents intervention to correct patient set-up before treatment. Finally, the X-ray image must be digitized first if image enhancement is required, while a portal image is already digitized so that image enhance-ment can be carried out on-line. Munro [81] and Boyer et al. [18] review electronic portal 3 T h e probability of normal tissue damage is decreased by delivering the radiation dose in small fractions rather than in one large dose. The total radiation dose is typically delivered to the patient in approximately one minute exposures given five days a week over five to seven weeks. Each exposure is termed a fraction, and the dose per fraction is RS1.8 to 2 Gy. Chapter 1. Introduction 7 Accelerator guide Electron beam Bending magnet Electron gun Waveguide Klystron Stand • ! Gantry Target Flattening Filter Collimators Photon beam Treatment couch Figure 1.1. Cross-sectional diagram, of a radiotherapy linear accelerator. Electrons, created by thermionic emission, are injected into the accelerator guide by the electron gun. Microwaves from the klystron provide power to accelerate the electrons, and the bending m,agnet rotates the electron beam, to hit the brem,sstrahlung target. The resulting photon beam is made uniform, in intensity across the beam, area by the flattening filter, and then collimated by primary and secondary collim,ators. Chapter 1. Introduction _ _ 8 ~ 10u > I 1 0 - 1 > co CD 0) 10 2 O rz d) 5= o 10"3 CL 0 i—1—i—1—i—1—i—1—i—1—r J i L -I I l_ J i L 7 9 11 Energy (MeV) 14 16 18 Figure 1.2. Photon energy spectra at the centre of the beam, for linear accelerators with nominal accelerating potentials of 6 MV (—) and 18 MV ( ). imaging devices, and Webb [128] provides a review of portal imaging. Figure 1.4 shows where the portal imagers are located with respect to the patient treatment couch. This figure also defines the air gap between the patient and the imager that will be discussed throughout this work. Figure 1.5 is a photograph of the liquid matrix portal imager (this imager was used for measurement of the portal dose images discussed in chapter 7). The detector is mounted on a mechanical arm so that the imager can be retracted out of the way of the radiotherapists who set-up and treat the patient. Electronic portal imagers were designed for imaging, rather than the measurement of radiation dose. However, several groups have applied these imagers for measurement of the dose to the patient, or in vivo dosimetry. The application of electronic portal imagers for dosimetry is reviewed in chapter 2. Chapter 1. Introduction 9 Figure 1.3. A sample portal image of a head phantom taken with a photon beam, for radiation therapy. The contrast in the im.age is lower than that for diagnostic X-ray images. To better visualize the patient anatomy the im.age was digitally processed to enhance the contrast. (Im,age reprinted from, page 373 of [124], with permission from, Elsevier Science.) 1.7 P A T I E N T D E N S I T Y D A T A 1.7.1 X - R A Y C O M P U T E D T O M O G R A P H Y In radiation therapy, the patient's physical density is measured in a set of axial images using X - r a y computed tomography ( C T ) . Figure 1.6 shows an example of an axial C T image of the chest. Each area element (or pixel) of the image corresponds to a volume element (voxel) within the patient. The third dimension corresponds to the slice thickness. This data is used when planning the course of radiation therapy for the patient. In this section, the method for measuring C T images and the interpretation of the measured data are briefly reviewed. A n introduction to C T technology and image reconstruction methods can be found in [19]. For C T the internal structure of the patient is reconstructed from multiple projections obtained wi th a kilovoltage X - r a y tube. During each axial slice acquisition, the X - r a y Chapter 1. Introduction 10 Patient Air Gap Portal imager Figure 1.4. Schematic diagram of a clinical linear accelerator with a portal imager. The position of som,e portal imagers is fixed, while for other imagers the distance between the patient and the imager can be varied. In the current work, the size of the air gap between the patient and the imager is a key parameter for calculating the portal dose images. tube circles the patient and X-rays that pass through the patient are absorbed by a ring of detectors surrounding the patient. The intensity of X-rays reaching the detector depends on absorption of the beam by the tissues, which the beam passes through. Image reconstruction methods are then used to analyze the multiple projections to obtain the density and position of the different structures contained within each slice. The C T reconstruction process results in a two-dimensional matrix of numbers in the range from near 0.0 up to values near 1.0. These numbers correspond to the average linear attenuation coefficient of the tissue contained in each voxel. To display these numbers on a computer screen, they are scaled to a larger range, and also normalized to the attenuation coefficient of water: C T Number = 1000 x ^ x e l ~ ^water ( l l } A'-water Water, therefore, has a C T number of zero; lung C T numbers are « -800 and bone C T numbers range from +300 to +1000. These C T numbers can be converted to phys-Chapter 1. Introduction, Figure 1.5. The liquid m,atrix portal imager mounted on a Varian, linear accelerator. In (a), the imager is retracted into the gantry, while (b) is a multi-expo sure photograph and shows several different positions of the im,ager behind the patient treatment couch. An, advantage of this imager for portal dosimetry applications is that large air gaps between the patient and the imager can be used, which simplifies the calculation of the imager dose from, patient scatter. (Images reprinted from, page 123 of [81], with permission from, the W. B. Saunders Com,pany.) ical density [37] and electron density [23] as required for the patient dose calculation algorithms. 1.7.2 P H A N T O M S To calibrate radiation therapy devices and verify dose calculation algorithms, the radiation doses must be measured in settings that mimic actual treatments. Th i s is achieved by placing the dosimeter in a volume of material that is radiologically tissue-equivalent. Such a volume of material is called a phantom. The important radiological properties for tissue equivalence are scattering and absorption of ionizing radiation. A tissue-equivalent material should have the same density and number of electrons per gram as the tissue it replaces [112, 113]. Tissue-equivalence between a given tissue and tissue substitute may be verified by comparing the density, mass energy absorption Chapter 1. Introduction 12 9 (b) (a) Figure 1.6. X-ray computed tom.ography images of the mediastinum, and pulmonary parenchyma. The images in (a) and (b) are the same but, use different gray-scale ranges to view the various tissues. In (a), the fat, lymph nodes, and vascular structures in the mediastinum can be differentiated. In (b), the fine details of the pulmonary parenchyma can be seen. coefficients, p,ab/P, and restricted collision stopping powers, 4 L/p, of the two media for al l energies of interest. Water is readily available, inexpensive and is an ideal phantom material to replace muscle [3, 54,120]. Since water is fluid, computer controlled movement of the dosimeter wi th in the phantom is possible, which saves considerable time when measuring the doses at more than one point. When verifying or commissioning dose algorithms, the doses are usually measured in a 40x40x40 c m 3 water phantom, called a watertank or standard phantom. 4 Stopping power quantifies the average energy loss of an incident charged particle per unit track length and is given the symbol dT/dx (units MeV/cm) . Energy loss by electrons occurs from bremsstrahlung (a radiative process) as well as ionization and excitation (collisional losses). Consequently, the total stopping power is the sum of the radiative and collisional parts: The restricted collisional stopping power, L , only includes collisional energy losses by the electron along its path that are below a given threshold energy. Above this threshold, the electrons that are knocked out as a result of the collision create tracks of their own called delta rays. The mass restricted collisional stopping power is the ratio of the restricted collisional stopping power L and the mass density, p. (1.2) Chapter 1. Introduction 13 Suitable tissue substitutes for muscle, lung, bone, bone marrow, and other tissues have been designed and verified [21]. A heterogeneous phantom can be as simple as a stack of rectangular slabs of different tissue substitutes, known as a slab phantom. Anthropomorphic phantoms are designed to conform more closely to the shape and size of the standard human body [22]. For this thesis, phantom materials are of interest to ensure that the scatter model correctly accounts for the scattering and absorption in different tissues. The Monte Carlo simulation software package EGS4, which will be used later for the Monte Carlo validation of the scatter model, comes complete with files specifying the restricted mass stopping powers and mass attenuation coefficients for a variety of tissues, common phantom ma-terials, and materials found in dosimeters [83]. For the experimental validation, tissue substitutes will be chosen from those listed in the International Commission on Radia-tion Units and Measurements Report 44 [21] based on their degree of tissue equivalence, availability, cost, and ease of use. 1.8 S O U R C E S O F S C A T T E R D O S E I N P O R T A L I M A G E S Medical linear accelerators produce a spectrum of photon energies as described in section 1.5. The maximum photon energy in the spectrum is approximately equal to the energy of the electrons exiting the accelerator waveguide. Typical spectra for treating subcutaneous tumours have a maximum photon energy between 4 to 24 MeV. Within tissues, the most important mode of photon interaction over this energy range is by Compton scattering. At the higher photon energies, pair production also becomes im-portant. Figure 1.7 shows the relative importance of these two interaction modes [49]. At radiotherapy energies, photoelectric and photonuclear events can be ignored [8]. Comp-ton scattering, pair production, bremsstrahlung, annihilation, and Raleigh scattering are Chapter 1. Introduction 14 120 0 6 12 18 24 Energy (MeV) Figure 1 .7 . Percentage of the energy transferred to water by Com,pton scattering (—) and by pair production (- - -) versus the energy of the incident photon. The range of incident photon energies encompasses the energies from, m,edi,cal linear accelerators for treating tumours located beneath the skin. described briefly in this section as they are important for portal scatter dose studies. 1.8.1 C O M P T O N S C A T T E R I N G A N D P A I R P R O D U C T I O N Compton scattering is the most important interaction between photons and soft tissue for radiotherapy. For a 2 MeV photon interacting in water, 99.3% of the total cross-section is accounted for by this type of scatter. Figure 1.8 illustrates both Compton scattering and pair production. In Compton scattering, the incident photon scatters off an atomic electron and changes direction. Some of the energy of the incident photon is transferred to the electron, ejecting the electron from the shell. The interaction cross-section per unit mass (or Compton mass attenuation coefficient) is independent of the atomic number, Z, of the scattering medium [8]. Chapter 1. Introduction 15 a) b) Figure 1.8. Illustration of (a) Compton scattering and (b) pair production. The Klein-Nishina cross-section for Compton scattering is given by: ^ W = 7 ( l + « * 2 « ) { 1 + a ( 1 1 _ C 0 8 ( ? ) } { ^ [ i + a ^ ^ ^ f + c x * ^ ) } ( L 3 ) where Q, is the solid angle of the scattering cone ra is the classical electron radius 6 is the photon scattering angle (see figure 1.8) a is the initial energy of the photon divided by the rest mass energy of the electron. This cross-section is graphed as a function of photon scattering angle 0 in figure 1.9. Equation (1.3) assumes that the electrons are free and stationary. To correct for the electron binding energy and motion of the electron, the Klein-Nishina cross-section is multiplied by the incoherent scattering function, S [49]. In pair production, a photon is absorbed within the electromagnetic field of a nu-cleus and gives rise to an electron/positron pair. The photon requires a minimum energy Chapter 1. Introduction 16 Figure 1.9. Differential Klein-Nishina cross-section versus angle of the scattered pho-ton (6), for initial photon energies of 0.5 MeV (—), 2 MeV (- - -), and 6 MeV (•••)• This shows that Com,pton scattered photons, at radiotherapy energies, are preferentially scattered in the forward direction. of 1.022 MeV. At values that are well above this minimum threshold energy, the elec-tron/positron pair are strongly forward directed. The energy of the incident photon minus the threshold energy is not necessarily split equally between the kinetic energy of the electron and positron. The mass attenuation coefficient for pair production is approximately proportional to the atomic number of the medium, Z [8]. Electrons generated from Compton and pair production events within the patient can also deposit dose at the imaging plane. Figure 1.10 is a graph of the energy spectra for Compton electrons set in motion by monoenergetic photons. From figure 1.10, one can see that electrons are set in motion with energies almost as great as the maximum photon energy present in the beam. Electrons and positrons from pair production events can have energies between 0 and (E7-1.022) MeV, where E 7 is the energy of the incident photon. Electrons lose energy at the rate of ~2 MeV c m - 1 in water. Thus the highest Chapter 1. Introduction 17 o CO O c o o CD C/) V) (/} o o c 1000 v 100 > CD CD 10 LU 1 LU b 0.1 0.01 -TTTTTEy =0.2 MeV rrrp E =0.089 MeV e, max Ey =2 MeV E =1.77 MeV e, max; J E y = 6 M e V E =5.75 MeV e, max [ Ey =24 MeV E =23.7 MeV e, max -i • • I iL 0.01 0.1 1 10 Electron energy (MeV) 100 Figure 1.10. Distribution of the electron energies produced by m,onoenergetic photons. Each curve is labeled by the photon energy, Elt and the maximum, electron energy the recoil electron m,ay acquire, Ee>max- (Adapted from, a similar figure in [49].) energy electrons will pass through up to ?sl2 cm of water. This was the reason for tracking the patient-generated electrons in the current study. 1.8.2 B R E M S S T R A H L U N G The electrons set in motion by Compton scattering or pair production can give rise to scattered photons through bremsstrahlung radiation. In this process, the electrons are scattered and therefore accelerated by the electrically charged nuclei and consequently radiate energy in the form of bremsstrahlung photons. The fraction of the incident electron energy that is radiated as bremsstrahlung, called the bremsstrahlung yield, depends on the initial energy of the electron and the atomic number of the material [8]. The bremsstrahlung yield for water, which is radiologically comparable to soft tissue such as muscle, is plotted in figure 1.11. The yield for cortical bone is also shown in the graph since cortical bone has a higher effective atomic number Chapter 1. Introduction 18 I—i—i • • • • • 11 T T T T I I I I 111 2 10"1 CO E 10 ,-5 i i 11111 nl ill 0.001 0.01 0.1 1 10 100 Energy (MeV) Figure 1.11. Comparison of the bremsstrahlung yield for water (—) and bone ( ) for incident electron energies from, 0.01 to 25 Me V. Over the energy range for radiation, therapy, the bremsstrahlung yield for bone is approximately 1.5 times that for water. (Data from [8]). than water. It can be concluded from this graph that the bremsstrahlung yield for bone is « 1 . 5 times the yield for water. 1.8.3 ANNIHILATION Positrons formed through pair production lose kinetic energy as they ionize and excite molecules along their trajectory. At the end of their track, the positron slows down enough so that electron capture can occur [8, 49]. The two particles annihilate each other, their charges are neutralized, and their masses are converted into 1.022 MeV of energy. This energy is radiated in the form of two 0.511 MeV photons that leave the annihilation site in opposite directions. If the positron annihilates in flight while it still has kinetic energy, the kinetic energy is passed on to the annihilation photons. According to Berger [9], as cited in Attix [8], the average fraction of the positron's kinetic Chapter 1. Introduction 19 energy that is converted to annihilation radiation is comparable to the fraction going into bremsstrahlung radiation. 1.8.4 R A Y L E I G H S C A T T E R I N G In Rayleigh or coherent scattering the scattered photons are forward peaked and no energy is lost by the incident photon. For low-Z materials like water, Rayleigh scatter is negligible. For example, the ratio of the coherent-to-incoherent cross-section for water at 2 MeV is only 0.0003. Nevertheless, since Rayleigh scattering was a significant problem when validating the portal scatter model in Spies et al. [114], a brief review of the physics of this interaction is included here. The differential cross-section per unit solid angle is given by [49] ^ = | ( l + cos2c9)[F(x^)]2 (1.4) where F(x, Z) is the atomic form factor, x = sin(f?/2)/A, and Z is the atomic number of the material. For small values of 6, F(x, Z) ~ Z , while for large values of 9, F(x, Z) approaches zero. The portal scatter study in [114] used copper phantoms (Z=29) and found that coherent scatter contributed approximately 16% of the total dose on the central beam axis. In the current work, coherent scatter was neglected for the following reasons. First, the total scatter dose here is small. Second, the materials used in the current study that have high atomic numbers [bone and aluminum (Z=13)], are not as extreme as copper (Z—29). Third, the volume of the high atomic number materials exposed to the photon beam is much less than the total phantom volume, unlike the study by Spies et al. [114] where the entire exposed volume was composed of copper. Chapter 1. Introduction 1.9 Q U A N T I T I E S T O D E S C R I B E A R A D I A T I O N B E A M 20 Throughout this thesis, comparison is often carried out between different methods for estimating the dose. For example, the measured dose could be compared to the dose calculated analyticalally or through Monte Carlo simulation. This section briefly describes two methods to present the doses for this work, as well as the normalization of this data. 1.9.1 D E P T H D O S E C U R V E S If the dose is measured in a tank of water versus depth for photon beams, curves as shown in figure 1.12 result. These depth dose curves are characterized by a steep dose buildup region from the surface to the maximum dose, and then show an exponential fall-off past the depth of maximum dose. The exponential decrease occurs due to the attenuation of the primary photon beam. The reason for the rapid buildup of dose within the first few centimeters of the water surface can be explained by examining the range of the secondary electrons. Consider first the case where the electrons have a very short range, as for a very low-energy photon beam. In this situation, the dose is deposited very near the photon interaction site. For each centimeter layer in the water, the same number of photons interact (neglecting attenuation of the photon beam and photon backscatter), and all the electrons lose all their kinetic energy in the layer from where they originated. In this case, if photon attenuation is included, the maximum dose occurs at the surface. For higher energy beams, the electrons traverse several centimeters of water before coming to rest. If the same number of photons interact at each depth, within the first few centimeters, the number of electrons in motion per centimeter will increase with depth. Consequently, the dose rises. At some depth, due to the attenuation of the photon beam, equilibrium is reached between the number of electrons starting and Chapter 1. Introduction 21 1.6 1—r 6MV 10 MV 0.3 0.0 0 5 10 Depth (cm) 15 20 Figure 1.12. Graph of the relative dose measured in water as a function of depth for 6 (—) and 10 MV ( ) photon beams. The depth of m,axim,um. dose is 1.5 cm, for the 6 MV beam and 2.5 cm for 10 MV. The data is for a 10x10 cm? radiation field. the number stopping, and the maximum dose will occur at this depth. This depth is known as the depth of maximum dose. In figure 1.12, the curves were normalized at a depth of 10 cm. The dose from contaminant electrons created by photons interacting with components in the treatment head is no longer clinically significant at a depth of 10 cm for high energy photon beams [111], with the exception of the 50 M V racetrack microtron [40]. In our work, this normalization facilitates comparison of depth dose curves measured experimentally and calculated from Monte Carlo simulation, since the simulation omitted the contaminant electrons. 1.9.2 D O S E P R O F I L E S The plot of the dose as a function of distance from the centre of the beam is termed the dose profile, and a sample is shown in figure 1.13. In this case, the normalization Chapter 1. Introduction 22 1.2 i i . | i i i | i i i i i . | i i . | i i i _ 1.0 r f -. dose 0.8 \ \ \ \ CD .> 0.6 '- I '-+—< CO I \ CD 0.4 0.2 0.0 . . 1 . . . 1 • , , • i i 1 i i i 1 i i r»--6 -4 -2 0 2 4 6 Off-axis distance (cm) Figure 1.13. Relative dose versus off-axis distance from the centre of the beam, in a water phantom,. The data is for a 6 MV beam, and a 10x10 cm2 field at a depth of 10 cm. dose is the dose on the central beam axis (zero off-axis distance) at this depth. Since the profile was calculated at the isocentre,5 where the beam size is defined, the 50% dose points occur at the geometric beam edge at -5 and +5 cm. The dose just outside the geometric field edges is nonzero since the electrons scatter laterally along their path and some photon transmission occurs through the collimators. 1 . 1 0 M O T I V A T I O N T O C A L C U L A T E T H E I M A G E R D O S E F R O M S C A T -T E R The slopes of the normal tissue complication probability curves are steep. Precise dose delivery for each fraction is therefore important. Portal imagers may be calibrated 5 T h e isocentre is a point located at the intersection of the central beam axis and the axis of rotation of the gantry. For the linear accelerators in the current work, the isocentre is at 100 cm from the bremsstrahlung target in the treatment head. Chapter 1. Introduction 23 to record the dose at the imaging plane, and this information may be used as part of the quality assurance of the treatment. The total dose at the imager is the sum of the dose from primary (unscattered) photons and scattered particles. Chapter 2 reviews current methods for calculating the imager dose. While some centres have developed their own algorithms for computing the imager dose from scatter, solutions to this problem are still of interest since existing solutions suffer from limitations that will be discussed in the next chapter. C H A P T E R 2 L I T E R A T U R E R E V I E W An important challenge to the widespread use of on-line in vivo dosimetry with portal imagers has been the development of accurate portal scatter dose calculation methods for patients. Portal scatter estimation methods have evolved from using the same algorithms as those used for patient dose calculation [76, 130], to advanced Monte Carlo methods [26]. The physicists' time investment to implement the scatter calculation algorithm is still a significant problem, for example, using approaches that depend on a database of measured scatter doses for predicting the portal scatter dose. In this chapter, existing scatter estimation methods are described and classified into three categories. First are those approaches that use exactly the same calculation algo-rithm as used for dose calculation within the patient. The second group contains those techniques based on theoretical treatment of the transport and scatter of the photons through the patient, air gap, and portal imager. The third class includes methods that are based on experimental measurements of the portal scatter dose. Within each cate-gory the review is chronological. The areas of interest include the limits, accuracy, uses, and theory. A brief background is provided at the start of the chapter to provide general information on the physical characteristics of portal scatter. 24 Chapter 2. Literature Review 2 . 1 B A C K G R O U N D : P O R T A L S C A T T E R D O S E 25 Estimates of the scatter from patients are also important when considering the con-struction of radiotherapy facilities, since the thickness of the concrete to shield staff and the public from unintentional irradiation depends on these scatter estimates. Re-ports summarizing the methods and results of scatter estimates are available and provide background information on patient scatter. When calculating shielding requirements, the patient scatter is estimated by measuring a quantity defined as the scatter fraction of dose (SF). A definition of SF is required for this discussion, however, the exact definition for SF in shielding purposes is irrelevant here. Therefore, for this study, a definition of SF is chosen that is more relevant to portal dosimetry. In portal dosimetry, the SF of dose is the ratio of the scatter dose to the total dose, both measured at the imaging plane. The works by Taylor et al. [122] and Shobe et al. [110] are complementary Monte Carlo and experimental studies for shielding calculation that provide comprehensive SF data for a wide range of scatter angles. Although the SFs were not studied at zero degrees,1 which would have been of interest here, several features of the author's re-search are worth mentioning. The maximum value of the scatter fraction occurs with the minimum amount of buildup material over the ionization chamber or scoring voxel. This occurs because of the low energy of the scattered photons as well as the presence of electrons originating from the phantom. The SF decreases with increasing thickness of material over the detection layer. This decrease is rapid at first because of the higher attenuation of the low energy scattered photons. The SF then decreases more slowly due to the attenuation of the primary and scattered photons. The variation of the SF versus buildup thickness was also reported by Droege and Bjarngard [27]. 1Zero degrees was defined as the direction of the central axis of the beam. Non-zero angles were defined by the beam central axis, the isocentre, and the (off-axis) position of the dose scoring voxel (or ionization chamber). Chapter 2. Literature Review 26 Taylor et al. [122] computed SF data with the Integrated Tiger Series Version 3.0 Monte Carlo simulation code. This code required several hours to several days to obtain an accuracy of 4% or better when using a Hewlett Packard series 9000/model 735 UNIX workstation. They chose cutoff energies2 of 0.1 MeV for electrons and 0.01 MeV for photons. Agreement between measured and Monte Carlo results for the SF data was on average 0.83 (expressed as a ratio) with a standard deviation of 40%, which was satisfactory for shielding calculation. Reports on Monte Carlo estimates of scatter for portal dosimetry include those by Jaffray et al. [47], McCurdy and Pistorius [70], Swindell and Evans [117], and Partridge and Evans [95]. Jaffray et al. [47] provide data for a single phantom thickness (17 cm thick polymethacrylate) and show that the SFs decrease with increasing beam energy (from 6 to 24 MV) on the central beam axis, and also show good agreement between measured and calculated SF data at 6 M V . McCurdy and Pistorius [70] reported the scatter fraction for a photon counting detector3 for singly and multiply scattered photons over a wide range of air gaps, field sizes, phantom thicknesses, and beam energies. Jaffray et al. [47] showed that with no air gap, the first-order Compton scatter fluence. dominated the SF of photon fluence for monoenegetic photon beams from 2 to 20 MeV. McCurdy and Pistorius [70] reported the SF of photon fluence for singly and multiply scattered photons for 6 and 24 M V photon beams and showed that first-order Compton scatter continues to dominate the SF as the size of the air gap increases. Swindell and Evans [117] provide extensive Monte Carlo results for the portal scatter to primary dose ratio4 (SPR) for a 6 M V beam. They reported SPRs on the central axis 2 W h e n a particle's energy falls below the cutoff energy, the particle is no longer tracked and the history is terminated. 3 F o r a photon counting detector, the detector response is independent of energy. The detector signal is the sum of the number of incident photons and the photon energy has no influence on the response. 4 T h e portal scatter to primary dose ratio is the ratio of the dose from scatter radiation to the dose from primary photons, both measured at the imaging plane. Chapter 2. Literature Review 27 for circular beams with areas up to 320 cm 2, homogeneous water phantoms ranging from 5 to 35 cm thick, and isocentre to detector distances from 10 to 100 cm. The magnitude of the SPR varied from less than 0.005 to over 0.30, and the number of photon histories required per SPR varied from several million to several hundred million. They showed good agreement between measured and Monte Carlo results, with root mean squared absolute differences of less than 0.01 (for example, the absolute difference between an SPR of 0.21 and 0.25 is 0.04). This work was extended by Partridge and Evans [95] who reported SPRs for a beam energy of 10 M V . 2.2 S C A T T E R E S T I M A T E S F R O M T R E A T M E N T P L A N N I N G S Y S T E M S Two portal scatter calculation methods that use patient treatment planning systems5 are described in this section. The first is the Delta Volume algorithm, which is based on ray-tracing the primary and scattered photon paths. The second is the convolu-tion/superposition method that uses dose kernels computed with Monte Carlo simula-tion. 2.2.1 D E L T A V O L U M E D O S E A L G O R I T H M Wong et al. [130] described the use of the Delta Volume dose calculation algorithm for computing portal dose images for heterogeneous phantoms and patients. The calculated portal doses agreed within 3% with film and ionization chamber measurements. Although . only a 6 0 C o beam was investigated, extension of the method to higher photon energies was expected to be feasible. In the Delta Volume method [104, 129, 131], the dose computation space was divided into voxels, each of which was assigned a physical and electron density equal to the 5 A treatment planning system consists of computer software that calculates the dose to the patient from a limited amount of data on the radiation beams as well as the patient contour and density data. Chapter 2. Literature Review 28 average for that voxel. For a 6 0 C o beam, most of the dose deposited in a voxel comes from electrons set in motion by photons that interact (or Compton scatter) for the first time within that voxel: this component of the dose is termed primary dose. The remainder of the dose is mainly from photons that scatter first outside of the dose deposition voxel, and then interact again within the dose deposition voxel: this part of the dose is called scatter dose. The Delta Volume algorithm accounted for the dose from primary, first and second order Compton scatter, as well as photons scattered more than twice (which was classified as multiple scatter). The dose from primary, first, and second order scatter was calculated by ray-tracing through the volume and computing the photon attenuation along the ray paths. The Klein-Nishina coefficient was used to calculate the probability of Compton scattering. The multiple scatter dose component was computed with an empirical formula. The Delta Volume method assumed that the photon source was a point source, which was a limitation of their approach since real photon sources have a finite extent. This mostly affects the primary dose near regions of major density changes (for example, near bone), and will tend to give a sharper transition between the two areas than will exist in reality. It was expected that an improved model for the photon source could be designed from an array of point sources, and that it would be sufficient to consider the extended source for the primary calculation only. Ying et al. [133] calculated portal images using the planning C T data and the Delta Volume method. Discrepancies between measured and predicted portal dose images can arise from several sources, including: (i) changes in patient anatomy during treatment, (ii) errors in beam delivery, and (iii) inaccuracies in the treatment planning algorithm. Ying et al. [133] assumed that changes in patient anatomy during treatment caused the differences between the predicted and measured images. They proposed correcting the planning C T data using the measured portal dose image and an iterative algorithm Chapter 2. Literature Review 29 to modify the C T data. Convergence was obtained when the measured and calculated portal dose images agreed sufficiently well. The patient dose was subsequently calculated from the altered C T data. This approach was demonstrated using computer simulation for a chest phantom, where the density and size of the lungs was allowed to vary. McCurdy and Pistorius [72] investigated an analytical approach for portal scatter dose calculation that is similar to the Delta Volume Algorithm. They used Compton kinemat-ics and ray tracing to determine the fluence of first-order Compton scattered photons at the portal imaging plane. Results for homogeneous and heterogeneous phantoms showed good agreement with predictions of the first scatter fluence calculated using Monte Carlo simulation. 2.2.2 C O N V O L U T I O N / S U P E R P O S I T I O N M E T H O D Another method that estimates the patient scatter dose with a treatment planning system6 is the approach developed by McNutt et al. [73, 74, 75, 76] based on earlier work by Papanikolaou [91]. This technique applies the convolution/superposition algorithm [67, 68, 106, 107, 108] to calculate the dose within the patient and the portal imager. A discrete, voxelized description of the phantom is used with uniform physical and electron densities in each voxel. In the convolution/superposition method, the dose is calculated by convolving the total energy released per unit mass (TERMA) in each voxel with pre-calculated three-dimensional dose deposition kernels. The total dose at each voxel is computed by superimposing the dose contributed by interactions within each voxel in the phantom that is irradiated. Dose deposition kernels have been calculated in a spherical water phantom by scoring the dose deposited in spherical coordinates from a forced photon interaction at the centre of the phantom. 6McNutt et al. [73] worked with the ADAC Pinnacle treatment planning system (ADAC, Milpitas, CA) which is now available from Philips (Philips, Amsterdam, Netherlands). Chapter 2. Literature Review 30 Air Gap Dose deposition point Figure 2.1. The extended phantom, concept. A photon interaction at f' will generate a shower of photons and electrons. Som,e of these shower particles may lead to dose deposited at r. The dose at the imager is calculated by stretching the dose deposition kernel A across the air gap between the phantom, and imager. (Adapted from [73] and [76]). The air gap between the patient and the portal imager is a very large, low density heterogeneity. In heterogeneous regions the dose deposition kernels are scaled by the electron density of the medium relative to the electron density of water. This scaling is known as radiological pathlength scaling. Figure 2.1 illustrates the extended phan-tom concept where the dose deposition kernels are scaled between the patient and the imager. Figure 2.2 illustrates primary and scatter images calculated with the convolu-tion/superposition algorithm. McNutt et al. [76] found that the imager dose profiles calculated with the convolution/superposition algorithm agreed within 4% with mea-sured dose profiles. For their comparison they normalized the profiles to the dose at the central axis of the imaging plane. Therefore, only the relative amplitudes of the measured and calculated profiles were compared. Chapter 2. Literature Review 31 Figure 2.2. Portal images computed with convolution/superposition, (a) The neck phan-tom, for this example showing the left lateral field (indicated by the solid diverging lines) and the central axis of the field (dashed line). The im.ages provide a qualitative illustra-tion of the (b) primary dose and the (c) scatter dose. The bright, band in the prim,ary image corresponds to the photon path through the trachea, while the dark band (far left) in this image aligns with the photons that, have traversed the spinal column. M c N u t t et, al. [74, 75] reconstructed the doses wi thin heterogeneous phantoms using a measured portal image. A drawback of their dose reconstruction method is the time required to compute the patient dose using a measured image. The most computation-ally intensive part of their technique was the convolution of the reconstructed primary energy fluence wi th in the phantom with the dose deposition kernels. The number of computations for this step was approximately proportional to O oc NFNDNV (2.1) where Np is the number of fields for the treatment, Np the number of points wi th in the phantom at which the in vivo dose is to be calculated, and Ny is the number of voxels exposed to the primary beam. The symbol O in equation (2.1) stands for 'order of ' . 7 7 T h e estimate of the order assumes that the dose in the patient is calculated from the dose deposition point of view, rather than with the dose interaction method (see for example [106]). Chapter 2. Literature Review 32 2 . 3 T H E O R E T I C A L C A L C U L A T I O N O F T H E S C A T T E R D O S E The theory of photon and electron transport is well established and accurate esti-mates of the portal scatter dose are possible with Monte Carlo simulation. To reduce the. sometimes prohibitive time required for theoretical calculation, simplified cases are studied to derive straightforward rules for predicting the scatter dose. The theoretical approaches reviewed here vary dramatically in complexity, from a powerful hand calcu-lation (simple scatter to primary dose ratio model of Swindell and Evans [117]) to full Monte Carlo simulation of the treatment that requires parallel computer processors. 2.3.1 S C A T T E R T O P R I M A R Y D O S E R A T I O (SPR) M O D E L Swindell and Evans [117] derived a simple model from first principles for the portal scatter to primary dose ratio (SPR) on the central axis for homogeneous scattering ob-jects. This group used Monte Carlo simulation to show that the scatter to primary dose ratio is uniform across the imager for large air gaps between a homogeneous scattering object and the portal imager. This result was applied in their SPR model. At their in-stitution the portal imager was located at a fixed source to detector distance of 200 cm, which satisfied the requirement of a large air gap. The physical model of the SPR was developed by examining the photon fluence at the portal imager from primary photons as well as first and second order Compton scatter. The model predicts that for a cylindrical, homogeneous slab of water of thickness t, placed symmetrically about the isocentre and irradiated by a circular radiation field of area A at the isocentre, SPR = M * ( l + M ) ( l + M ) (2.2) where k0 = 0.0266 (In + L 2) 2 ( W 2 ) 2 (2.3) Chapter 2. Literature Review 33 Field diameter plane Isocentre Phantom L2 Detector Figure 2.3. Phantom, geometry used in the SPR model. A circular beam of area A is incident upon, a circular water phantom, of thickness t located symmetrically about the isocentre. The isocentre is at distance L\ from, the photon source, and the detector is at a distance Li from, the isocentre. This figure is based on a similar figure in [117]. L\ is the source-to-isocentre distance, L2 is the isocentre-to-detector distance, and K is the mean energy of the 6 M V photon beam expressed in units of 0.511 MeV (that is, 1.81 MeV/0.511 MeV). Figure 2.3 illustrates the phantom geometry used for their model. Since there is no simple expression for fci, this constant was optimized by comparing equation (2.2) to an extensive set of Monte Carlo data. Constant k\ depends weakly on Li and for 60< Li <100 cm, k\ « 0 . 0 0 2 c m - 1 . As Li decreases below 50 cm, k,\ increases, which is understandable since k,\ was interpreted to be proportional to the ratio of the number of twice-scattered detected photons to the number of once-scattered detected photons. The first term in equation (2.2), koAt, states that as a first approximation, the SPR is proportional to the irradiated volume (for example, the SPR is « 1 % per liter of irradiated scatterer for L\ = L2 =100 cm). The agreement was better than 0.01 between their Monte Carlo data and their experimental SPR measurements, as well as between the model and the Monte Carlo data. Their Monte Carlo code included Compton scattering and pair production, but not Chapter 2. Literature Review 34 coherent scattering and bremsstrahlung production. The scored quantities at the detector were the energy E and status (denoted by superscripts P for primary and S for scattered) of every photon that arrived in a particular area. The SPR was calculated from SPR = E f i R(;El\ (2.5) where R(E) is the detector response, which describes the efficiency with which detected photons are converted into the detector output signal. Three types of detector responses (photopeak, photon counter, and Compton) were studied and the corresponding response functions are: photon counter = constant (2.6) Compton detector R(E) = electron recoil energy (2.7) photopeak detector R(E) = E. (2.8) Most detectors used in portal imaging devices are Compton detectors, since the dominant interaction is a single Compton scattering, for which the signal is proportional to the average energy imparted to the recoil electron. Thus R(E) can be calculated from the appropriate Klein-Nishina cross-section. The SPR model for a 6 M V photon beam is in use in a clinical trial testing missing tissue compensators8 for tangential breast radiotherapy. Compensators are designed from portal images to determine the thickness of the breast along the source-ray lines. This model has been used with two detectors, a purpose-built detector consisting of a linear array of scintillating crystals [36], and the liquid matrix ionization chamber electronic portal imaging device [35]. 8 A missing tissue compensator is designed to attenuate the photon beam so that the resulting dose within the tumour volume is more homogeneous. The compensator is constructed from high density ma-terial (for example, lead shot) and is inserted between the patient and the photon source. The thickness of the lead shot at each point in the two-dimensional grid depends inversely, to a first approximation, on the thickness of the tissue along the ray line between the photon source and the dose computation point. Chapter 2. Literature Review 35 Since a more uniform dose to the breast for large patients was observed with a 10 M V beam than with a 6 M V beam, Partridge and Evans [95] validated the SPR model at 10 M V , again using Monte Carlo data. They showed that the model was accurate at 10 M V for L 2 greater than 60 cm and for all field areas A up to 625 cm 2. Moreover, they concluded that the model was sufficiently accurate to use in the design of missing tissue compensators for breast radiotherapy with a 10 M V beam. Hansen et al. [42] incorporated an approximate form of the SPR model of Swindell and Evans [117] into a method to calculate the in vivo dose within the patient. In vivo doses in an anthropomorphic phantom agreed with measurements within 3%. In vivo doses were calculated by deriving the primary energy fluence (PEF) within the phantom using a measured portal image, and then convolving this P E F with the convolution/superposition dose deposition kernels. The P E F at the imaging plane was computed by dividing the total dose by SPR/(1+SPR). The P E F within the phantom was calculated by back-projecting the P E F at the imaging plane to the phantom plane (the back-projection accounted for the inverse square law and attenuation of the primary photon beam). The order of their algorithm for calculating in vivo doses was approximately proportional to O oc NFNDNV (2.9) where Np, ND, and Ny were defined in equation (2.1). Spies et al. [114] developed a rapid analytical method to calculate the first and second order Compton scatter fluence at the detector. One important simplification was that the second order Compton scatter was assumed to be isotropically distributed around a centre located at the midplane of the phantom. Integrals over the energy spectra were replaced with the average value of the function. As well, it was assumed that the incident primary photon fluence was a parallel beam, and therefore the divergence of the photon beam from the linear accelerator was ignored. Spies et al. [114] also hypothesized that for Compton Chapter 2. Literature Review 36 style detectors [see equation (2.5) and discussion of that equation] the description of scattering by first-order Compton scatter alone may be sufficient in practice. Spies et al. [114] examined the scatter from small, solid copper cylinders irradiated with radiosurgical9 fields. They demonstrated absolute differences within 0.02-0.03 be-tween analytical SPRs and SPRs calculated with an in-house developed Monte Carlo simulation code. Direct experimental measurements of the scatter (away from the cen-tral beam axis) were also carried out using an in-house developed portal imager consisting of 128 Csl scintillation crystals optically coupled to silicon photodiodes. Although diffi-culties were present in reconciling the experimental and Monte Carlo results, the Monte Carlo model was concluded to be good for describing the portal scatter to primary dose ratio using small air gaps. 2 . 3 . 2 S L A B D E R I V E D S C A T T E R K E R N E L S Perhaps the most promising methods for portal scatter dose calculation are those that apply slab derived scatter kernels computed from Monte Carlo simulation [43]. In this approach, cylindrically symmetric scatter kernels are calculated by scoring the scatter dose at the portal imager resulting from a pencil beam traversing a homogeneous water phantom and an air gap. A database of kernels k(t) is generated for a range of phantom thicknesses t, air gaps, and photon beam energies. Originally, the method was to be applied for measuring the radiological tissue thickness of breast tissue with portal images by Hansen et al. [43]. Their original research was limited to 6 M V photon beams. The radiological thickness is then used to design cus-9Radiosurgical fields are usually less than 4 cm in diameter as measured at the isocentre. These fields are used to treat inoperable small malignant and non-malignant lesions of the brain. 1 0 T h e radiological tissue thickness for a single voxel in the phantom is the product of the electron density of the voxel and the photon pathlength through the voxel. The radiological thicknesses for a column of tissue along the photon source to detector ray line is the sum of the radiological thickness for each voxel along the ray. Chapter 2. Literature Review 37 tomized tissue compensation to improve the dose homogeneity within the breast. Portal images were used to determine the tissue thickness rather than C T densitometry since these patients do not fit into the bore of standard C T scanners when they are in the treatment position (the arm on the same side as the treated breast is raised over the patient's head). To determine the tissue thickness, an iterative method was developed based on mea-sured portal images with I and without O the patient in the photon beam, and the database of scatter kernels k(t) indexed by tissue thickness, t. The image without the patient in the beam gives the photon fluence distribution incident on the patient, which is nonuniform. Although the method was intended to be iterative, one iteration was found to extract the tissue thickness accurately enough. Consequently, only the non-iterative approach is discussed here. First, / is taken as the initial estimate of the dose from primary photons, P. Then the tissue thickness t(r) at a point f is calculated using the relationship where /J is the mean attenuation coefficient for the photon beam and O is the portal image taken without the patient in the beam. For example, in breast tissue the mean attenuation coefficient for adipose tissue could be used. The tissue thickness is then used to estimate the scatter dose at the imager, S(r): This estimated scatter is then used to provide a better estimate of the primary dose assuming that the total imager signal is from primary and scatter dose, P(r) = 0(r) exp[-7Zt(r)] (2.10) (2.11) I{r) = P(r) + S(r). (2.12) Chapter 2. Literature Review 38 Finally, equation (2.10) is solved a second time for t(r') using the estimate for the primary dose P(r) from equation (2.12). This approach was validated for homogeneous water phantoms and several heterogeneous phantoms in [43] with an accuracy of better than 1.5% for the dose from primary radiation and 2.8 mm (one standard deviation) of the true radiological thickness. The slab derived scatter kernel approach for scatter estimation was extended for air gaps less than 40 cm and photon energies up to 24 MeV by McCurdy and Pistorius [69, 70, 71]. To use the scatter kernels for heterogeneous cases, the C T data was converted into an equivalent homogeneous phantom (EHP). The EHP was calculated by converting each column of C T data (along the source to imager pixel ray line) into an equivalent thickness of water by summing the radiological thickness of each voxel in the column. The maximum deviation between the predicted and Monte Carlo results for beam energies of 6 and 24 M V and air gaps of 10 to 40 cm was 0.5±0.6%, expressed as a percent of the total fluence on the central beam axis. Since the EHP concept was developed by Pasma et al. [97], the EHP concept will be defined in section 2.4.2 when discussing the experimentally derived slab kernels measured by Pasma et al. [97]. One of the main drawbacks of using Monte Carlo codes to develop scatter dose esti-mation models and to calculate portal scatter kernels is the lack of standard codes that separately score the primary and scatter fluence, or dose at the imager. Consequently, several researchers have developed and validated their own code for this purpose (for example, Jaffray et al. [47], Swindell et al. [118], and McCurdy and Pistorius [70]). All of these codes examine only photon scatter. An advantage of Monte Carlo approaches for developing scatter models is that the scatter dose can be separated according to the scat-ter mode (single versus multiple scattering, for example). This is important to determine the dominant scatter modes. Chapter 2. Literature Review 39 2 . 3 . 3 M O N T E C A R L O C A L C U L A T I O N O F T H E T O T A L I M A G E R D O S E Descalle et al. [26] calculated portal images with the P E R E G R I N E Monte Carlo code for a phantom used in contrast studies that contained holes of varying diameter and depth. They achieved an accuracy of 1% for the total dose using a lateral grid resolution of 1 mm. This feat is still only possible with computer systems that network a large number of processors to carry out the computations in parallel to reduce the real time for the computation. Good agreement between the measured and calculated images was seen when comparing the contrast and resolution. Measured images were taken with the liquid matrix ionization chamber portal detector. While Monte Carlo simulation represents the most accurate method for calculating portal scatter, the time for the simulation limits use of this technique to a very small number of research centres. More practical approaches are required for widespread im-plementation of in vivo dosimetry with portal imagers. 2 . 4 E M P I R I C A L S C A T T E R D O S E E S T I M A T I O N The scatter calculation methods presented in this section are all based on (i) a database of measurements of the scatter at the imaging plane, and (ii) an assumed functional form for the scatter. The first technique is the simplest and applies the ex-perimental finding that the scatter dose is uniform across the imager for large air gaps. The second method derives measured scatter kernels as a function of the thickness of homogeneous polystyrene phantoms, analogous to the slab derived scatter kernels calcu-lated with Monte Carlo simulation by Hansen et al. [43]. The third approach assumes a functional form for the change in scatter fluence between the patient and the imager. Chapter 2. Literature Review 40 2.4 .1 U N I F O R M S C A T T E R D O S E A P P R O X I M A T I O N Investigators at the Netherlands Cancer Institute (NCI) developed a method for cal-culating the midplane dose within the patient using the measured portal image [11, 12, 14, 30, 31]. Currently, their method is applied to in vivo dosimetry for lung radiation therapy at their institute. In this section the aspects of their technique that are relevant here will be briefly reviewed, including terminology, problems, and the consequences of the drawbacks and limits of their approach. An overview of their method is shown in figure 2.4. To convert the measured portal image to the portal dose image, the pixel values are converted to dose (in step two) with a nonlinear calibration curve relating pixel value to dose. The calibration curve is measured for homogeneous phantoms of varying thickness [31]. In step three, a correction is performed to account for an incorrect commercially applied algorithm to compensate for the differing sensitivity of each detector pixel [31]. The NCI group of Boellaard et al. [12] investigated the portal scatter dose as a function of field area, phantom thickness, air gap, and source-to-phantom surface distance for homogeneous phantoms and a beam energy of 8 M V . The primary dose for each phantom thickness was calculated by extrapolating the total dose versus field area to zero field area, for an air gap of 90 cm. For smaller air gaps, the scatter was computed by subtracting the primary dose (as measured at an air gap of 90 cm and then corrected for beam divergence) from the total dose. At air gaps of less than 50 cm, the scatter dose distribution was approximately Gaussian, with an increasing width as the air gap increased. At the centre of the beam, the scatter dose increased by a factor of 25 when the air gap decreased from 50 cm to 5 cm. At air gaps larger than 50 cm, the portal scatter dose was uniform across the imager. This finding is applied in step four of the NCI in vivo dosimetry method, where the portal scatter dose is approximated by a uniform Chapter 2. Literature Review 41 Measure portal image 2. Convert pixel values to dose: Portal Dose Image Compensate for commercial flat field correction 4. Apply look-up table to remove portal scatter dose Apply inverse square law: Primary Exit dose Apply convolution model using transmission: Exit Dose Image Compare planned and extracted exit dose images Calculate Midplane Dose Image Compare planned and extracted midplane dose images Figure 2.4. Overview of the Netherlands Cancer Institute in vivo dosimetry method. Step six in the chart requires a measurement of dose with and without the patient in the beam to estimate the scatter within the patient. distribution. The portal scatter dose for patients is estimated using a look-up table [14] of the total to primary dose ratio on the central beam axis measured for homogeneous phantoms. This look-up table is measured for a range of field areas, air gaps, and homogeneous phantom thicknesses. To estimate the portal scatter dose for a patient, the field area, air gap, and thickness11 of the patient are used to look-up the ratio of the total to primary 1 1 I n this case the thickness t was calculated from the beam transmission T through the patient: t — — InT/Ji. The transmission was defined as the ratio of the central axis doses with and without the patient in the beam. The data used for calculating the transmission was measured from portal dose images. Chapter 2. Literature Review 42 dose ratio. The primary dose for the patient portal image is then calculated by dividing the measured total dose for that patient by the ratio of the total to primary dose found from the look-up table. The scatter dose is then equal to the difference of the total and primary dose. Finally, the scatter dose is subtracted from each pixel in the portal dose image. A drawback of the look-up table approach is the time needed for measuring the total to primary dose ratios for a range of field sizes, air gaps, and phantom thicknesses to create the look-up table. In step five, the inverse square law is applied to calculate the primary exit dose in the patient using the primary portal imager dose (the exit plane is within the patient and is a distance dmax from the where the beam exits the patient). In step six, the total exit dose is calculated by adding the patient scatter dose at the exit plane to the primary exit dose. The patient scatter dose is estimated using the transmission through the patient, which was defined as the ratio of the primary dose measured with and without the patient in the beam [14]. Measuring a portal image without the patient in the beam for each field requiring in vivo dosimetry is a significant drawback of their method, since it extends the time needed for each treatment, which becomes yet more significant for treatments with multiple fields. In step seven the in vivo doses at the exit plane are compared over the whole field to the intended doses calculated with their treatment planning system. A better location to compare the intended and in vivo doses is at the tumour plane, which may coincide with the midplane of the patient in some cases. For step eight, estimation of the midplane dose, Boellaard et al. [11] developed a novel method for calculating the midplane dose from the exit dose, patient thickness, and patient transmission. The accuracy of this method was poor (differences of 5 to 10% for a 6x6 cm 2 field and 4 to 18 M V beams) for small radiotherapy fields and heterogeneous phantoms irradiated with single fields. While their method for calculating the midplane in vivo dose does not require C T data, it was Chapter 2. Literature Review 43 recognized in their work that a more accurate estimate of the midplane dose would be achieved with C T data and a treatment planning algorithm that partially accounted for electron transport. Their midplane in vivo dose calculation technique was independent of the C T data to provide an overall check of the treatment planning calculation. The accuracy of their exit in vivo doses using the uniform portal scatter dose approximation and the convolution model for the patient scatter was 2.5% (one standard deviation). 2.4 .2 S L A B D E R I V E D S C A T T E R K E R N E L S Pasma et al. [97, 99] measured slab derived scatter kernels and applied these kernels to predict the portal scatter dose for heterogeneous phantoms and patients. The scatter kernels were extracted from measured ionization chamber data at the imaging plane for homogeneous polystyrene phantoms. In this section, the method for predicting the portal dose is briefly reviewed. The notation used here is a simplification of that used in the original papers in order to highlight the important features of their algorithm. Pasma et al. [98] calibrated their Philips SRI-100 portal imager so that a portal image could be converted to the dose D(x,y) as measured by an ionization chamber in a buildup cap 1 2 at the imaging plane. Buildup material is added on top of the imager to filter out electrons generated within the patient. This added buildup material, however, is heavy (for example, the 1 mm sheet of steel used weighed 1.3 kg, while the portal imager originally weighed 15 kg). Over one year, the added weight caused sag of the imager and a change in the position of the central axis by 3%, which had to be corrected for during daily calibration of the imager. In their method to measure the scatter kernels, first the primary dose P(x,y), and then the scatter dose S(x,y) is calculated. To calculate the primary dose, the total 1 2 A buildup cap is a sleeve with a water-equivalent thickness equal to the depth of maximum dose in water for the beam. This sleeve is placed over a radiation detector (for example, an ionization chamber). Chapter 2. Literature Review 44 dose D(x,y) at position (x,y) was measured with an ionization chamber as a function of field area (FA) for each phantom thickness, resulting in a function D(FA,x,y) for each thickness. This function was then extrapolated to zero field area for each thickness. The extrapolated value of D(FA,x,y) at FS=0 theoretically contains no scatter dose, and is therefore equal to the primary dose. Although this method has been criticized since the extrapolation is subjective, the function D(FA, x, y) was shown to be linear at 6 M V for field sizes less than 144 cm 2 at the isocentre. The scatter dose kernels were derived in a more complex manner. Figure 2.5 illustrates the notation used to index the scatter kernel s(r, t, L) as a function of position r, tissue column thickness t, and air gap L. The scatter kernel is assumed to be spatially invariant and rotationally symmetric. The total scatter dose S is assumed to be equal to the sum of the scatter kernels for each tissue column in the irradiated volume of the patient: S(X>V)= I, B ^s[r(x'-x,y'-y),t(x',y'),L(x,,y')}dx'dy'. (2.13) J(x',y')eiiela The scatter kernels are derived by solving equation (2.13) for S(x = 0, y — 0) (that is, S at the central axis) using a method similar to that described by Storchi and Woudstra [115, 116]. Since the scatter kernels were derived from measurements for homogeneous water phantoms a method is needed to allow calculation of the scatter dose for heterogeneous cases. Pasma et al. [97] solved this problem by converting the patient computed tomog-raphy data (that is , the three-dimensional matrix of densities relative to water) to an equivalent homogeneous polystyrene phantom (EHP). Each column in the E H P is calcu-lated by finding the total radiological thickness of the patient along the source to detector ray, and then dividing this total by the electron density of polystyrene. As well, the dis-tances between the centre of mass and detector plane are equal for the corresponding columns in the patient and the EHP. Chapter 2. Literature Review 45 s[r=(x '-x,y '-y),t,L] (a) (b) Figure 2.5. Phantom, setup for empirical slab derived portal scatter kernels, (a) The total scatter dose in the image under the point (x, y) is equal to the sum of the scatter contributions from, each, column of tissue [for instance, at (x',y')J in the irradiated part of the field. The field boundaries are indicated by the heavy divergent lines, (b) Scatter kernels s[r = (x1 — x,y' — y),t,L] are derived for a clinically applicable range of tissue column, thicknesses t(x', y') and air gaps L(x', y') between the exit surface of the phantom, and the portal image plane. This figure was adapted from, figures in [97]. This approach was verified for the prediction of portal dose images, and the agreement between predicted portal images and ionization chamber measurements was 1% (one standard deviation) for anthropomorphic phantoms [97]. The method has also been used to predict the fluence under dose compensators as a quality assurance check for the inverse dose calculation algorithm and mil l ing machine that design and m i l l the compensators [99]. The portion of the code that predicts the primary dose component has also been used to verify intensity modulated beams [96]. No patient or phantom was placed between the photon source and portal imager for this verification, so that only the primary dose was required. Pasma et al. [99] calculated the in, vivo dose for prostate cancer patients by scaling the total imager dose by the ratio of the dose at the isocentre in the patient to the dose Chapter 2. Literature Review 46 at the imager. This group limited their in vivo dosimetry to a single point at 5 cm depth within the patient on the central beam axis. The ratio applied for the clinical calculation was measured on the central axis with a 25 cm homogeneous polystyrene phantom. A significant drawback of their scatter computation approach is the large workload for measuring the data to derive the scatter kernels. It was estimated that the minimum time required to measure this data was 4 hours per beam energy for a single linear accelerator [97]. Setting up and levelling the watertank13 takes approximately two hours. At present, at the Vancouver Cancer Centre, thirteen individual photon beam energies are used. Therefore, a minimum of 58 hours would be needed to measure the data to apply this method. 2.4.3 EMPIRICAL SCATTER F LUENCE FUNCTION Bogaerts et al. [15, 16] proposed a method for estimating the scatter dose on the central axis of the portal image for 6 M V beams and air gaps up to 40 cm. Central to their technique is a function that defines the change in scatter fluence between the exit and the imaging planes. This function was assumed to depend on the size of the air gap. This approach is analogous to the inverse square law for primary radiation. Specifically, they assumed that the functional form for the ratio of the scatter fluence between the exit and imaging planes Fs was given by: F . ( * , „ , g , « ) - 3 l = ' ^ (2.14) xy •* xy where g is the size of the air gap, (x, y) the length and width of the field at the exit plane (the exit plane is defined in figure 7.1), (x',y') the length and width of the field 1 3 A watertank is a 40x40x40 cm 3 acrylic tank filled with water within which an ionization chamber is moved under computer control. Measurements of the dose profiles and depth doses are possible by moving the chamber at constant velocity within the beam and by using a reference ionization chamber to monitor fluctuations in the beam output. Chapter 2. Literature Review 47 at the imager, and a is a parameter determined from experimental measurements of Fs. The value of a ranged from 0.6 to 1.0 and varied for different phantom thicknesses, heterogeneities, and field sizes. The maximum achievable accuracy for the calculated exit doses was estimated to be 2.4% (one standard deviation), and the maximum deviation for test phantoms was 4.5%. Although the accuracy of their method was less than that for conventional in vivo dosimetry, for example by using diodes, it was concluded that the technique was still useful. Reasons for this finding included satisfactory accuracy, a reduced workload for the radiation therapists administering the treatment, and a smaller increase in the treatment time to perform the in vivo dosimetry. 2 . 5 S U M M A R Y Obstacles still exist that must be overcome before there is widespread availability of scatter dose estimation algorithms for in vivo dosimetry with portal imagers. Our aim is to develop a scatter estimation technique that is an improvement over previous methods. The uniform portal scatter dose method appears to be a sound approximation both theoretically [117] and experimentally [12], and is efficient to implement. This method is limited to large' air gaps (defined as greater than 50 cm) and was applied successfully for patient in vivo dosimetry. The drawback to this approach is the additional time needed for measuring the data for the look-up tables. In the current work the portal scatter dose is approximated by a uniform distribution. The total scatter dose is approximated by the first-order Compton scatter dose, which may be sufficiently accurate for the total scatter dose [114]. The scatter is computed by ray-tracing through the patient, the air gap, and the imager in an approach that is similar to the Delta Volume algorithm [131] or the method described by McCurdy and Pistorius [72]. Chapter 2. Literature Review 48 While some of the previous methods have also focused on ways to calculate the dose from primary radiation, our intention is to use convolution/superposition for this com-putation. This direction would mean that portal dose images could be calculated with convolution/superposition by (i) modifying the convolution/superposition algorithm for the primary component and (ii) incorporating the analytical method for the scatter esti-mate. C H A P T E R 3 M A T E R I A L S The first section in this chapter briefly describes the operation of ionization cham-bers, which are used later for the experimental validation of the analytical method for calculating the SPR. In the second section, the construction, readout, and calibration of the liquid matrix portal imager are reviewed. This imager was used for the in vivo dose measurements in chapter 7. 3 . 1 I O N I Z A T I O N C H A M B E R S Ionization dosimetry is one of the most convenient and most widely used methods for measuring absorbed dose [51]. In most cases, it is also the most accurate. The ionization chamber is the central piece of equipment in this system. A typical thimble-type ionization chamber is shown in figure 3.1. The goal of ionizing dosimetry is to deduce the absorbed dose or energy absorption per unit mass in the medium surrounding the chamber. Cavity theories (for example, Spencer-Attix [17], Bragg-Gray [66], and Burlin [79]) have been developed to convert the charge measurement to absorbed dose. The particular cavity theory appropriate for a given chamber depends on the dimensions of the cavity and the atomic composition of the wall and the gas. The Bragg-Gray theory is used for small cavities.1 Provided that the composition of 1 For small cavity ionization chambers, the charged particles lose only a small fraction of their energy in crossing the cavity. The ranges of the electrons are assumed to be much larger than the cavity diameter so that most of the charged particles in the cavity originate from the wall or medium. 49 Chapter 3. Materials 50 Wall Guard electrode Electrode Insulation Gas Figure 3.1. Cross-sectional view of a typical thimble-type ionization chamber. A poten-tial difference exists between the inner surface of the wall and the central electrode. As charged particles cross the gas cavity they ionize air particles during transit. The charge is collected using an electrometer connected to the ionization chamber by a shielded cable. the chamber walls is similar to that of the medium, the absorbed dose in the medium surrounding the ionization chamber is given by the Bragg-Gray equation: dE — = WJg(Sm/S9) (3.1) where dE/dm, is the energy deposited per unit mass in the surrounding medium W is the average energy deposited in the gas per ion pair formed Jg is the number of ion pairs formed per unit mass of gas (Sm/Sg) is the mean ratio of the mass collision stopping powers of medium and gas, averaged over the energy distribution of the secondary charged particles crossing the cavity. The minimum energy required to ionize a gas molecule is considerably smaller than the average energy deposited in the gas per ion pair formed, W. This is explained by the secondary particles dissipating much of their energy in non-ionizing collisions and by the scattered electron from an ionizing collision that usually emerges with some surplus Chapter 3. Materials 51 kinetic energy. For electrons in dry air, the value of W is 33 .85±0.15 eV per ion pair. The measured quantity in absorbed dose calculation is usually the charge collected per unit mass, or volume, of the cavity. For absorbed dose measurements in water, the wall material ideally used is one that has similar properties compared to water or air. The physical properties that are impor-tant are the mass energy absorption coefficients, pen/p, and the mass collision stopping powers, S/p. The mass energy absorption coefficients determine the energy imparted to the medium by the photons, and the mass collision stopping powers determine the energy transfer from the charged particles to the solid or gas. Ion chambers are operated at high enough potentials so that most of the ions formed in the chamber are collected. The collection efficiency for a particular geometry of ionization chamber and cavity material can be derived by considering the recombination of the ions in the cavity during charge collection. In pulsed radiation, the pulses are typically short (a few microseconds or less) and the interval between pulses is long compared to the transit time of the ions between the electrodes (for example, in small air ionization chambers the transit time is typically 100 to 300 /JS). If these conditions are satisfied, then it may be assumed that the total ionization per pulse occurs instantaneously and that the ions produced by one pulse are collected before the next pulse starts. 3 . 2 T H E P O R T A L I M A G E R The electronic portal imaging device used for our work was a liquid matrix ioniza-tion chamber system (Varian Associates, Palo Alto, CA) installed on a Varian Clinac 2100C/D linear accelerator. This imager was chosen since we have the most experience with this particular model for portal dosimetry [92, 93, 94] compared to other types of Chapter 3. Materials 52 S £ rs Printed circuit board Foam Plastoferrite Printed circuit board Liquid ionization film Printed circuit board Foam Printed circuit board Figure 3.2. Diagram, of the cross-section of the liquid m,atrix ionization chamber portal imager showing the materials surrounding the liquid layer. (Figure adapted from, [31].) portal imagers at our centre. The technology was developed at the Netherlands Cancer Institute by H . Meertens and M . van Herk [77, 123]. The imager is mounted on the linear accelerator gantry wi th a motor-driven retractable arm, which allows motion in three-dimensions (see figure 1.5 in section 1.6). The sensitive area of the detector is 32.5x32.5 c m 2 . This area is partitioned into a matrix of 256x256 l iquid ionization chambers, each with a volume of 1.27x 1.27x0.8 m m 3 . The matr ix is formed by crossing two printed circuit boards, each etched wi th 256 parallel copper strip electrodes, at 90° to one another. The l iquid ionization film is sandwiched between the two circuit boards, as shown in figure 3.2. X- ray photons incident on the imager are converted to electrons, which then ionize the molecules in the l iquid. Once an equilibrium is reached between the rates of for-mation and recombination of these ions, the ionization current is measured from each chamber. The ionization current is amplified and corrections are applied to account for differences between individual electrometers and chambers. The image is then displayed on a terminal outside of the treatment room. Chapter 3. Materials 53 A 1 mm thick plate of plastoferrite2 is used to convert the X-ray photons into elec-trons. The foam, circuit boards, and plastoferrite in front of the liquid layer are equiv-alent to R*8±0.5 mm of water [13], while the material behind the liquid is equivalent to « 5 mm of water [31]. By adding material above the top-most circuit board (for example, polystyrene) so that electronic equilibrium is achieved at the liquid layer, the pixel3 signal and signal-to-noise ratio can be maximized. 3.2.1 L I Q U I D F I L M By using a liquid ionization medium rather than one of gas, the chambers can be very small since the liquid has a higher density and will therefore have a larger signal-to-noise ratio. This imager uses isooctane (2,2,4 trimethylpentane, CgHi 8) for the liquid film. Ionization chambers utilizing organic liquids may be classified as relying on ion transport or electron transport. In this imager, isooctane ions are formed and travel through the liquid to the electrodes. The mobility of these heavy ions is low and hence the transit time for an ion to cross the chamber from one electrode to the other is long: van Herk [123] calculated the transit time to be 0.5 s. Although the isooctane is pure when the imager is constructed (grade - spectro-scopic), impurities probably arise from water diffusing through the circuit boards as well as from interaction between the liquid and the chamber materials. Radiochemical reac-tions within the liquid will affect the concentration of impurities. Furthermore, a change in the level of purity may affect the signal collected if the impurity is charged, since this will affect the current collected by the electrometer. Since the image gray-scale values remain within 1% over three months [31], the purity of the liquid over time is not a significant problem. 2Plastoferrite is a mixture of plastic and barium ferrite (density, p=4.75 g c m - 3 ) . 3 A pixel is a small element of area. Chapter 3. Materials 54 The reason for the choice of isooctane for this imager was not apparent from the literature, however, this liquid has a relatively high free ion yield4 compared to other hydrocarbons [105]. 3.2 .2 R E A D O U T ELECTRONICS Readout of the ionization current for this imager proceeds pixel by pixel, and is shown schematically in figure 3.3. High voltage (typically 250-300 V) is switched from one row electrode to the next on the top printed circuit board. When one high voltage row electrode is switched on, the current is read out from each electrometer attached to the 256 column electrodes on the bottom circuit board. Activation of the high voltage switches and readout electrometers is synchronized with 4 T h e free ion yield, Gfi, is the average number of free ion pairs formed per unit of absorbed radiation energy. The value of Gfi is influenced by the recombination of ions formed along the ionization track of the secondary electron, the linear energy transfer of the radiation, and the electric field strength. High voltage row electrodes Signal column electrodes Electrometer 1 Figure 3.3. Schematic diagram of the readout electronics for the scanning liquid m,atrix ionization chamber electronic portal imaging device. A high voltage (HV) is switched from one row electrode to the next. The ionization current is read from each of the 256 column electrodes sequentially when, one row electrode is polarized. (Figure adapted from [123].) Chapter 3. Materials 55 the internal 60 Hz clock of the linear accelerator used for producing the radiation beam pulses [39]. The time for a single current measurement from all 256 column electrodes is ~2 ms, and current sampling commences ~8 ms after a beam pulse. An additional wait time is included before any measurements are taken to allow the ion concentration within the liquid to reach equilibrium. Equilibrium is reached within 1 s after turning the beam on [123]. The time to regain equilibrium after readout at the highest dose rates is « 4 0 ms [123], since only a small fraction of the ions are collected. With four current samples per pixel, the total time for image acquisition is [(2 ms sample - 1 row - 1 x 4 samples + 8 ms row - 1 ) x 256 rows + wait t i m e ] « 4 s. One of the drawbacks for this imager is the long scan time for image readout. The long scan time prevents integration of the signal as a function of time. 3.2.3 C O M P U T E R A computer located outside the treatment room and attached to the imaging elec-tronics serves several functions, including automatic position control of the detector and image display. Image analysis algorithms are available on the computer, including image enhancement, edge detection, basic statistics, and image matching. Raw images are corrected for differences in the pixel sensitivities, electrometer offsets, and leakage currents [18]. The first correction accounts for the electrometer offsets and leakage current and is given the symbol Ej, where the subscript j represents the jth electrometer. Measurement of Ej is carried out quickly without polarizing voltage prior to the acquisition of each image [31]. The magnitude of Ej is « 1 0 % [18] of the raw pixel intensity. Second, the ionization chamber offsets are determined from the bias field image or dark current image Bij, which is measured without radiation. This bias correction helps to cope with the artifacts caused by the fast switching of the high-voltage electrodes and its magnitude is ~1% [18]. Third, the variation in ionization chamber cell sensitivity Chapter 3. Materials 56 is approximately measured from the ratio of the individual pixel response to the average pixel response when the entire matrix is irradiated with a uniform field. The image of the uniform field is termed a flood field, Fij. Differences in chamber sensitivity are « 4 0 % in magnitude [18] and arise from differences in electrode shape and electrode surface heterogeneities. The commercially displayed image Wij is calculated from the raw image Iij using the equation Wij = (Iij — Ej - Bij)-^- (3.2) where F is the average pixel intensity in the flood field. 3 . 2 . 4 C A L I B R A T I O N FOR D O S I M E T R Y The differential equation governing the ion-pair concentration n(t) [105] when no polarizing pulse is applied is given by van Herk [123] dn(t) dt = Nin(t)-an2(t) (3.3) where Nin(t) is the ionization rate, a is the ion recombination constant, and t is the time. In both continuous and pulsed radiation beams the imager readout commences after the ion concentration has reached equilibrium. For continuous radiation, as from a 6 0 C o radiotherapy source, the ionization rate Nin(t) is constant. At equilibrium, the rate of change of the ion concentration dn(t)/dt is zero, and the equilibrium ion concentration neq is equal to [123] neq = \JNin/a. (3.4) For radiotherapy linear accelerators, having pulsed beams, the approximate solution for the average ion concentration navg between pulses is given by Boellaard et al. [13]: ra, a v g \ aAt •) - ( | ) a V 2 A i i / 2 A i V 3 / 2 ( 3 5 ) Chapter 3. Materials 57 where ANin is the number of free ions produced per pulse and At is the time between pulses. Boellaard et al. [13] showed that the first term of equation (3.5) was within 1% of the exact solution for navg for typical clinical dose rates (less than 400 cGy min - 1 ) . In this thesis, the portal image is converted to the dose as measured by an ionization chamber within a water-equivalent medium. The experimental relationship between the pixel intensity Wij and the dose rate as measured by an ionization chamber within a water-equivalent medium, D, has been confirmed by many authors (for example, [31, where a, and b are the calibration constants for dosimetry. This is in agreement with the theoretical predictions, given by equations (3.4) and (3.5). To determine a and b, the average pixel value in a small region of interest and the dose rate are measured under the same conditions for a range of dose rates. The dose is measured with an ionization chamber placed at the depth of maximum dose within a block of water-equivalent material (for example, polystyrene). The rectangular block has the same dimensions as the imager. The ionization chamber is placed at the same source to detector distance as the portal imager. Although water-equivalent material (for example, polystyrene) is added above the ionization chamber, this material is insufficient to stop all the patient-generated electrons. For example, for an 18 M V photon beam, a total thickness of 3.2 cm of water-equivalent plastic would be added above the ionization chamber. Since electrons lose energy at the rate of « 2 MeV c m - 1 in water, patient-generated electrons above s^ 6.4 MeV will pass through the buildup material and deposit dose in the ionization chamber. This was the reason for tracking the patient-generated electrons in the current study. When calibrating the pixel signal against the dose measured in a 30x30 cm 2 polystyrene plate, the calibration constants were found to be nearly independent of field size [30]. 132, 134]): (3.6) Chapter 3. Materials 58 The region of interest is defined as an area in the image over which the beam may be considered to be uniform. An outer housing for the imager is usually removed when the imager is applied for dose measurements. Sufficient buildup material is added to the imager to maximize the signal. If the commercially corrected images are used for dosimetry, then errors of several per-cent result [31], because the flood field produced by the linear accelerator is nonuniform and the commercial imager software assumes that the flood field is uniform. To solve this problem, the dose in the flood field is measured with an ionization chamber and the corrected pixel values Vij are calculated from ^ = WijG(biit flood) ( 3 ? ) where Fij is the flood field [see also equations (3.2) and (3.6)]. It is assumed that the calibration constants (a,b) measured on the central beam axis are a good approximation for all pixels in the image. At non-zero gantry angles (that is, when the beam is pointed in directions other than down), the calibration constants vary within the image, due to changes in thickness of the liquid layer across the detector [132]. The imager warm-up time, or the time to obtain a constant reading, is « 1 hour [31]. The amount of signal change for a chamber varies from pixel to pixel depending on the heat dissipated by nearby electronics. Only those pixels that are located near heat sources exhibit a change in their reading with time. The chamber sensitivity remains constant as long as the acquisition time between images is at least 5 min [31]. The accuracy of calibration is « 0 . 6 % and the calibration constants [a and b in equation (3.6)] remain stable within 1% for &3 months [31]. Chapter 3. Materials 3.3 S U M M A R Y 59 The most important part of this chapter was subsection 3.2.4, which presented the method for calibrating the liquid matrix portal imager for use as a dosimeter. When calibrating the imager, the gray-scale image is converted to the dose as measured by an ionization chamber placed at the depth of maximum dose within a water-equivalent rectangular block (for example, within a block of polystyrene). The pixel value to dose calibration curve was given by equation (3.6). In the following chapter, a new analytical method for calculating the scatter to pri-mary dose ratio is presented. This analytical method is validated against Monte Carlo simulation results and experimental measurements in chapters 5 and 6, respectively. C H A P T E R 4 T H E O R Y : A N A L Y T I C S P R C A L C U L A T I O N This chapter presents the analytical method for calculating the scatter to primary dose ratio (SPR) in radiotherapy portal images. In this method, the imager scatter dose at off-axis points is equal to the scatter calculated at the central beam axis. Hence the portal scatter dose is approximated by a uniform distribution, in accordance with the result found experimentally by Boellaard et al. [12] when measuring the scatter for large air gaps between the phantom and the imager. This approximation greatly reduces the calculation time, since the scatter dose is computed only at one point in the image instead of at each point in the image. The technique accounts for the photon spectrum, the patient tissue density data, and the detector response. Attenuation and divergence of the primary and scattered photons is calculated by ray-tracing from the photon source, through the patient, to the imager. It is assumed that the detector is composed of water-equivalent materials. Since the response of the liquid matrix portal imager used in the current work can be calibrated against the dose as measured by an ionization chamber, the assumption of a water-equivalent detector is appropriate here. Several examples of the analytical calculation for the dose from primary and scatter radiation, as well as the SPR, are presented. This work was published in [90]. 60 Chapter 4- Theory: Analytic SPR Calculation 4 . 1 H I S T O R Y 61 McCurdy and Pistorius [72] applied the theory of Compton scattering to predict the first-order portal scatter fluence component. Spies et al. [114] analyticalally modelled the first and second order Compton scatter from copper cylinders and achieved good agreement between the model and Monte Carlo data. The high-density phantom was chosen to test the model in extreme circumstances. Direct measurements of the scatter at off-axis points were compared to Monte Carlo and analytical results. Spies et al. [114] hypothesize that, in practice, portal scatter may be well approxi-mated by first-order Compton scatter alone for Compton detectors. Boellaard et al. [12] found that the scatter dose is uniform when the air gap is at least 50 cm: this approxi-mation is also used in the current work and so large air gaps (50 cm or larger) are used. Large air gaps also minimize the SPR from multiply scattered photons (McCurdy and Pistorius [70]). 4 . 2 C U R R E N T D E V E L O P M E N T : A N A L Y T I C A L I M A G E R D O S E C A L C U -L A T I O N In this chapter, we developed a new method for calculating the SPR on the central axis. First, the theory for calculating the dose from primary is presented, and then the computation of the dose from scatter is described. The units for each quantity are stated. When an approximation is used, the impact of this simplification on the final SPR is discussed. Chapter 4- Theory: Analytic SPR Calculation 62 4.2.1 IMAGER D O S E FROM PRIMARY RADIATION In this section the equation for the dose from primary photons at the portal detec-tor, PA, is presented. Throughout this work the superscript A denotes an analyticalally calculated quantity. The dose from primary radiation for a simplified parallel, monoen-ergetic photon source is discussed first, and then the more realistic case of a diverging, polyenergetic beam is examined. The simplified case applies to a broad, parallel-ray, monoenergetic photon source of energy E (units [MeV]) incident on a homogeneous absorber of constant thickness. The direction of the incident photons is parallel to the central axis throughout the beam. The phantom and detector are assumed to be homogeneous and composed of the same material. The dose from primary photons at the detector PA [MeV g - 1] can be calculated from the collision K E R M A 1 Kc [MeV g - 1] [49], PA = 8KC = $ exp[-(i(E)(t + dmax)]^EabtW(E)3 (4.1) where $ is the photon fluence or photon flux incident on the phantom [photons cm - 2 ] p(E) is the linear attenuation coefficient for photons of energy E, [cm - 1] t is the thickness of the homogeneous absorber [cm] p is physical density of the medium [g cm - 3 ] dma,x is the depth of maximum dose (see section 1.9.1) at the detector, [cm] X KERMA is the kinetic energy released per unit mass. Chapter 4- Theory: Analytic SPR Calculation 63 Eab,w(E) is the average energy absorbed per photon (average kinetic energy transferred to electrons that leads to ionization, excluding energy lost to bremsstrahlung) for water [MeV photon - 1] 8 accounts for differences between the collision K E R M A and the absorbed dose [7, 84] (dimensionless). The term &p/p gives the number of photons that interact per unit mass of material irradiated by a photon fluence $. The average energy absorbed per photon of incident energy E is given by [49] Eab(E) = ^ - E (4.2) where fiab is the absorption coefficient [cm - 1] for the detector material. The detector response function R(E) [MeV g - 1 cm 2 photon - 1] [see equations (2.6) to (2.8) in section 2] was included explicitly in equation (4.1), and was equal to the mean dose absorbed in water for an incident photon of energy E given by R(E) = ^-Eab,w(E)8. (4.3) Pw This particular response function was chosen since the portal imager is calibrated against the dose measured with an ionization chamber (see subsection 3.2.4). The transmission of the primary photons in equation (4.1) {specifically, the term exp[—p.(E)(t + dmax)]} was replaced by a discrete summation along the source to detector ray-line. The exponential transmission of the primary photons Tp(fd, E) at a particular point on the detector located by vector fa [illustrated in figure 4.1(a)] is thus given by Tp(fd, E) = exp • ]T Arn(rn,E) L f „ = o (4.4) where the lower limit of the sum (fn = 0) is located at the photon source. Vector fn is the index of the sum. In the calculation A r was approximated as Az (the thickness of Chapter 4- Theory: Analytic SPR Calculation 64 the voxel2 along the Z axis, which was 1 cm). The ray pathlength for the attenuation of the photons (primary and scattered) was calculated within approximately 1 mm for the homogeneous phantoms, and was exact along the central axis for all phantoms. Voxel coordinates along the ray path were calculated using the angles between the (X,Y) axes and the projection of the ray onto the X Y plane. This method of ray tracing accounts for beam divergence. Since the pathlength through the voxel A r was assumed to be equal to Az (that is, the voxel size along the Z axis), this ray-trace was approximate for the heterogeneous phantoms away from the central beam axis. For lung, muscle, and adipose tissue, the exponential transmission was accounted for in the analytical calculation by using an approximation to equation (4.4). In these cases, the mass attenuation coefficient for water pw(E)/pw [cm2 g - 1] was substituted for the tissue specific coefficient but it was then multiplied by the actual density of the tissue: Arp(rn,E) = Ar^f^-p(rn) (4.5) „ L^lArp(fn). (4.6) Pw This approach is reasonable for photon beam energies up to 24 M V . For bone, the atten-uation was calculated without using this approximation (that is, for a voxel composed of bone, the mass attenuation coefficient for bone was used when calculating the attenua-tion for that voxel). In the experimental validation described in chapter 6, aluminum is substituted for bone and the attenuation coefficient for aluminum is used for those voxels containing this metal. The mass attenuation and mass absorption coefficients for each material were cal-culated by linear interpolation using the data tabulated as a function of energy in [49]. These coefficients are plotted for water in figure 4.2. 2 A voxel is an element of volume. Chapter 4- Theory: Analytic SPR Calculation 65 (c) > p. x i ! Detector Figure 4.1. Variables for the analytical scatter calculation, (a) Vectors fd and fp are shown, (b) Vectors fv, R and Q as well as angle 9 are shown, (c) View from the top of the phantom, showing the beam, edges ( ) and the limits of integration for the calculation: xh xr, Vb, a,ndy f. These limits are depth dependent due to the divergence of the photon beam. The dose from primary radiation for a parallel photon source [equation (4.1)] can be modified for a point photon source by including the inverse square law that describes the decrease of the primary fluence wi th distance from the source. Since the fluence was defined at the phantom surface ( $ 0 ) for the Monte Carlo simulation, the primary fluence at the detector $ is given by [49] (4.7) where the SSD is the source to phantom surface distance and the S D D is the source to Chapter 4- Theory: Analytic SPR Calculation 66 Figure 4 . 2 . Mass attenuation (•, left vertical axis) and muss absorption (o, right vertical axis) coefficients for water. Data from Johns and Cunningham. [49]. The smooth curve between the data points is for visual guidance only. detector distance. In the analytical calculation, both the source to surface distance and the source to detector distance were measured along the central beam axis, which is an approximation for points away from the central axis. This approximation introduces a negligible error for the cases considered in this thesis. Since realistic radiotherapy beams from clinical linear accelerators emit photons over a range of energies, the dose from primary photons is summed over all energies present in the primary photon energy spectrum. The energy spectra used in this work were previously discussed in section 1.5. In the analytical calculation, the photon source was modeled as an isotropic, point source and the photon spectrum was assumed to be invariant across the beam. Jaffray et al. [47], Partridge and Evans [95], and Swindell and Evans [117] used the same approximate photon source model and obtained good agreement between calculated and measured scatter to primary dose ratios or scatter fraction data. Chapter 4- Theory: Analytic SPR Calculation 67 By using equations (4.6) and (4.7) to modify equation (4.1), the expression for the dose from primary photons becomes P V , ) = / ? ( | ^ ) 2 XT (4-8) Ei=Emin "w This expression is for (i) an isotropic, polyenergetic, point source, (ii) a heterogeneous phantom or patient, (iii) a detector assumed to be composed of materials with similar attenuation, scattering, and absorption properties as water, and (iv) a photon source with an energy spectrum that is invariant across the beam. The summation limits for the outer sum (Emin, Emax) are from the minimum photon energy to the maximum photon energy present in the photon beam incident on the phantom or patient and Ei is the index of summation. 4 . 2 . 2 I M A G E R D O S E F R O M F I R S T O R D E R C O M P T O N S C A T T E R The total dose from scatter S at a pixel on the portal detector can be expressed as. the sum of the dose from each scatter mode, S(fd) = SF(rd) + SMS(rd) + SCP(fd) (4.9) where Sp is the dose from photons that scatter once within the scattering object and then interact with the detector, which is also termed the dose from first-order Compton scatter is the dose from photons that scatter more than once with the scatter object, and includes the dose from bremsstrahlung and annihilation photons that originate within the scatter object Chapter 4- Theory: Analytic SPR Calculation 68 Sep is the dose from charged particles (electrons and positrons) that are set in motion within the scattering object, cross the air gap between the object and the detector, and then deposit dose within the detector. McCurdy and Pistorius [70] showed that the first-order scatter dominates the scatter fluence for a wide range of beam energies, field sizes, and air gaps. Furthermore, Spies et al. [114] hypothesized that the total scatter dose could, in practice, be approximated by the first-order Compton scatter dose. In the current work, the portal scatter dose from multiply scattered particles (photons and patient-generated electrons) was neglected, which can be stated as: SA(fd) « SA(rd). (4.10) Further, air gaps are used that are 50 cm or larger, since Boellaard et al. [12] showed that the scatter dose was uniform for large air gaps. The scatter dose at off-axis points is approximated by the first-order Compton scatter dose at the central beam axis. The total dose from first-order scatter, SA(fd), was calculated from the probability that a photon originating from the photon source scatters once within the phantom and then deposits dose within the detector. The total scatter dose from first-order scatter for each pixel on the detector was evaluated by summing the contribution from each scattering voxel within the irradiated volume of the phantom. In this section, the primary photon source is approximated by a model of the energy spectrum that is invariant across the beam. The equation for the scatter dose is for a heterogeneous scattering object (patient or phantom). As well, the detector materials are assumed to have similar radiological properties compared to water. The photon path for a photon that scatters once and reaches the detector was shown in figure 4.1(b): the primary photon travels from the source to the voxel along fv, scatters at the voxel at fv, and then the scattered photon travels along vector R to the detector pixel Chapter 4- Theory: Analytic SPR Calculation 69 located at fd. A mono energetic source of primary photons (energy E) is considered first. The detector scatter dose at fd from first-order Compton scattered photons generated within a scattering voxel located at, fv is expressed as [MeV g - 1 ]: S${fd,rv,E) = ^0(E)F(fv)Tp(fv,E)e(R,e,E)^^Ts(fv,fd,Ei) (4.11) Pe,w where F(fv) is the inverse square law that accounts for the divergence of the photons from the phantom surface to the scattering voxel, F(fv) — (SSD/F„) 2 Tp(rv, E) is the transmission of the primary photons to the scattering voxel e(R, 0, E) is the monoenergetic scatter kernel [MeV g - 1 photon - 1 cm2] Pe(rv)/Pe,w is the ratio of the electron density of the voxel to the electron density of water (units of electron density, [electrons cm - 3]) Ts(rv, fd, Ei) is the transmission of the scattered photons between the scattering voxel at fv and the detector point at fd Ei is the energy of the scattered photon that originates at the scattering voxel, and is given by EX(E, 6) = E/{1 + a[l - cos(0)]} a is the energy of the incident primary photon divided by the rest mass energy of the electron, a = E/(0.511 MeV) 6 is shown in figure 4.1(b) and is the angle between the incident primary photon direction (given by vector Q) and the direction of the scattered photon (vector Q terminates at the same location as vector fd). The photon fluence $0(E) was defined at the phantom surface. Chapter J,.- Theory: Analytic SPR Calculation 70 In equation (4.11), the transmission of the primary photons between the incident phantom surface and the scattering voxel, Tp(fv, E), is given by Tp(fv, E) = exp - £ Arp{fn,E) r „ = 0 ,(4-12) For voxels containing water-like tissues, the same approximation was made as previously discussed for equation (4.6). The monoenergetic scatter kernel in equation (4.11), e(R,9,E), gives the dose per unit incident primary photon fluence at the detector pixel at fd from primary photons of energy E that travel from the incident photon source, scatter at the voxel located at fv, and then interact with the detector at fd- The scatter kernel is expressed as au W 2 pw aA where do(a, 6) I du is the differential Klein-Nishina cross-section per electron per steradian, which gives the probability that an incident photon of energy E will scatter at an angle 9, [cm2 electron - 1 steradian -1] pe>w is the electron density of water, [electrons cm - 3 ] 8V is the volume of the scattering voxel at fv [cm3] R is the three-dimensional distance between the scattering voxel at fv and the detector pixel at fd, R = fd — fv, and is present to account for the solid angle dVt = dA/\R\2 dA is the pixel area on the detector located by the vector fd, shown in figure 4.1. Chapter 4- Theory: Analytic SPR Calculation 71 To calculate the scatter from a voxel composed of a specific tissue with electron density pe(fv), the scatter kernel is multiplied by the electron density relative to water for the voxel, Pe(rv)/pe,w, in equation (4.11). In the analytical calculation the differential cross-section da(a,9)/dfl was calculated directly from the formula stated in [49]. Angle 9 is given by 9 = arccos R-Q (4.14) }R\\Q\_ In the calculation, the scatter volume SV was chosen to be 0.25 cm 3 (0.5 cm along the X and Y axes, 1 cm along the Z axis). This choice was based on the result that the absolute error in the scatter to primary dose ratio, due to the size of the voxel, was approximately <5SPR=0.01<5V (for SPRs equal to « 0 . 1 0 ) . In equation (4.11) the transmission of the scattered photons between the scattering voxel at fv and the detector pixel at fd was calculated from: T8(fv,fd,Ei) = exp Td - Y, A r A i ( r „ , £ ; 1 ) fn—fv (4.15) Again, for voxels with water-like tissues, the approximation presented in equation (4.6) was made, and for voxels containing bone, no approximation was used. Each voxel in the scattering object is assigned a uniform physical and electron density, and hence the description of the phantom or patient is discrete. Since each voxel within the irradiated part of the phantom or patient contributes scatter dose to each pixel on the portal detector, the total scatter dose (for a monoenergetic incident beam) at the detector pixel fd is the sum of the scatter contribution from each scattering voxel, SA(fd,E)= E E E SA[fd,fv = (x,y,z),E} (4.16) z-za y=yb x=xt where the (x,y) limits of summation are shown in figure 4.1(c). The limits of summa-tion in the Z direction are from the entrance phantom surface zs to the exit phantom Chapter 4- Theory: Analytic SPR Calculation 72 surface zm. Since radiotherapy beams are polyenergetic, the total scatter dose at fd was calculated by summing over the entire incident primary photon energy spectrum Vf Xr Emax S$(fd) = £ £ £ £ S ^ P ^ i x ^ z l E i ] . (4.17) z=zs y=yb x=xt Ei=Emin The energy bin width for the sum over energy varied from 0.20 to 0.25 MeV (the bin widths chosen were the same as the widths for the published photon energy spectra, and hence differed for each spectrum). 4.2.3 S C A T T E R TO PRIMARY D O S E RATIO The scatter to primary dose ratio (SPR) was computed by taking the ratio of equations (4.17) and (4.8), which is expressed as SPR(f d ) = (4.18) £ £ £ £ sF[fd,fv = (x^z\Ei}/ z=zs y=yb x=xt Ei=En ( f ^ ) 2 E ^(EMf^E^^KUEi). Ei—Efni-fi In this expression, the 3 term in the numerator and denominator are not shown since they are assumed to cancel. This approximation, although not explicitly stated, was also used in the work of Jaffray et al. [47], Partridge and Evans [95], and Swindell and Evans [117]. The contribution to the SPR from photons that pass through the secondary photon collimator jaws was found to be negligible. Jaw transmission is « 0 . 5 to 1% of the primary photon beam intensity. This effect was also ignored in [47], [95], and [117]. 4.2.4 E X A M P L E S The analyticalal forms for the dose from primary and scatter radiation [see equa-tions (4.8) and (4.17) respectively] were evaluated for homogeneous water phantoms and Chapter 4- Theory: Analytic SPR Calculation 73 Table 4 .1 . Physical and electron density relative to water (p/pw, pe/Pe,w respectively) for the simulated lung and bone tissues used in the analytical and Monte Carlo calculation. The effective atomic number, Z, is also listed. For lung, the value of Z is approximated by the value for water. Heterogeneity P/Pw Pe/Pe,w Z Lung 0.250 0.248 7.51 Bone 1.850 1.73.7 12.31 water phantoms containing lung or bone slabs. The terms to account for beam diver-gence (SSD/SDD) and (SSD/fv) were not included since these examples used a parallel source. These cases were chosen to show briefly how the primary photon energy and the presence of heterogeneities within the phantom affect the portal scatter to primary dose ratio. The lung and bone slab phantoms were chosen since they are low and high density heterogeneities, respectively. The physical and electron densities for the lung and bone are listed in table 4.1 and were taken from [21]. In all cases, the photon sources were broad, parallel, monoenergetic beams and the air gap between the phantom and the imager was equal to 50 cm. This air gap size was chosen since the imager dose from scatter has been shown to be uniform both theoretically [117] and experimentally [12] (for point sources) when the air gap is larger than or equal to 50 cm. In all cases the analytical results were compared to data from Monte Carlo simulation (code SDOSXYZ, which is described later in chapter 5) to evaluate the validity of the analytical approach. Two photon beam energies were selected for the examples to illustrate the behaviour of the SPRs for low and high energies of the radiotherapy beam. The mean energy for a polyenergetic beam is approximately one third of the accelerating potential. For example, a 6 M V beam has a mean energy of 1.9 MeV, and as a rough guide, the 6 M V beam behaves like a 2 MeV monoenergetic photon source. For the SPR examples here, monoenergetic energies equal to 2 and 8 MeV were chosen since 6 M V and 24 M V are Chapter 4- Theory: Analytic SPR Calculation 74 common low and high-energy beams, respectively. Relatively large field sizes were used for these examples (16x16 cm 2 and 20x20 cm2) since the scatter was significant, whereas for smaller fields (for example, 5x5 cm 2) the SPR was « 0 . 0 1 . In the analytical method, the dose D from primary and scatter radiation was cal-culated from the collision K E R M A Kc, multiplied by the quantity 8, which accounts for the fact that the dose is affected by secondary electrons generated upstream of the dose deposition point [63]. 8 depends on the photon beam energy and beam type (for example, parallel versus point source), the field size, the depth within the phantom, and the phantom material. 8 can be estimated from first principles [63] and through Monte Carlo simulation [41]. The latter approach was chosen for our work since the former approach is restricted to available published data. 8 was calculated on the central axis at the depth of maximum dose from the ratio 8 = D/KC (4.19) where the total dose per incident photon fluence D/Q was computed with the Monte Carlo simulation code DOSXYZ [103]. The collision K E R M A per incident photon fluence Kcf $ was found at the depth of maximum dose dmax using Kc(dmax)/$ = exp[-fi{E)dmax}^-Eab<w{E). (4.20) The value for 8 calculated at the depth of maximum dose within the imager was assumed to be applicable for the dose from primary as well as scatter. For example, for an 8 MeV photon beam collimated to a 5x5 cm 2 field, /5=1.058±0.008: figure 4.3 shows the absorbed dose calculated with Monte Carlo simulation, the collision K E R M A , and the product of 8 and the collision K E R M A . The photon cross section data used was the same for the collision K E R M A calculation and the Monte Carlo simulation. Chapter 4- Theory: Analytic SPR Calculation 75 In figure 4.4 the dose profiles across the imager for the scatter and primary radiation are illustrated for the homogeneous 20 cm thick water phantom. For both the 2 and 8 MeV photon beams, the scatter dose is uniform and increases with increasing field size since a larger volume is exposed to the primary photon fluence. The dose from both primary and scatter radiation are higher for the 8 MeV beam than for the 2 MeV beam.' Table 4.2 tabulates the scatter to primary dose ratios, which shows that the SPRs are slightly lower for the higher beam energy. The probability of Compton scattering at non-zero scattering angles decreases with increasing photon beam energy (see figure 1.9), which is probably why the SPRs are lower for 8 MeV compared to 2 MeV. The heterogeneous phantoms contained slabs of bone or lung within a 20 cm thick water phantom. The lung slab was 8 cm thick, while the bone slab was 3 cm thick. Figure 4.5 and table 4.2 show the results for the heterogeneous cases. The graphs show that the lung and bone heterogeneities have a strong affect on the dose from primary photons but very little effect on the dose from scattered particles. In the presence of a Depth (cm) Figure 4 . 3 . Graph illustrating the relationship between KERMA (—) and dose (his-togram,) per unit incident photon fluence. The KERMA was calculated for a monoener-getic 8 Me V photon, beam, incident on water. The dose was computed using Monte Carlo simulation, (DOSXYZ) with, a monoenergetic, parallel photon beam of energy 8 MeV. Field size 5x5 cm2. 6 was calculated by comparing the dose and KERMA from, 3.2 to 4.2 cm in. depth; B=1.058±0.008. KERMA multiplied by 6 (- - -). Chapter 4- Theory: Analytic SPR Calculation 76 Table 4 . 2 . Scatter to primary dose ratios calculated on the central axis from the Monte Carlo simulation results for a parallel beam incident on a 20 cm, thick phantom. The im,ager was represented as a rectangular block of water and the doses were scored at the depth of maximum dose for the respective beam, energy. Case Energy Field size S P R M C (MeV) (cm2) Homogeneous 2 16x16 0.035 20x20 0.050 8 16x16 0.025 20x20 0.034 Lung slab 2 20x20 0.035 Bone slab 2 20x20 0.053 Lung slab 8 20x20 0.032 Bone slab 8 20x20 0.045 low density inhomogeneity (lung), the SPR decreases compared to a homogeneous water phantom of the same physical thickness mainly because the dose from primary photons increases due to the decreased attenuation of the primary photon beam. Conversely, in the presence of a high density inhomogeneity (bone), the SPR increases compared to a homogeneous water phantom of the same physical thickness mainly because the dose from primary radiation decreases due to the increased attenuation of the primary beam. Chapter 4- Theory: Analytic SPR Calculation 77 CD O c CD +-» C CD •g "o c c i— 0 Q_ CD CO O Q CN * 3 E o o » o jr a. >> O Q. — i — i — i — i — i — r (a) l_ ooooooooooo 2 2 0 -12-8 -4 0 8 12 8 4 4 Off axis distance (cm) T~7i i i I I r (b) _ [XXKXXXXX>CK>OQ _ 0 -12-8 -4 0 4 8 12 Off axis distance (cm) 15 CD O c CD 13 C CD •g o c 12h c L_ CD Q. CD CO O Q E o 9 o o •cl 6 CD I 1 I 1 I 1 I 1 I 1 I 1 I (C) - f > i - . q - H t o g .12-8 -4 0 4 8 12 Off axis distance (cm) 0 b^-T^i-Pi- .^r -12-8 -4 0 4 8 12 Off axis distance (cm) Figure 4.4. Dose profiles at the detector for homogeneous phantoms. The dose profiles from, primary photons as calculated from, Monte Carlo simulation (—) and using the analytical equations (o) are shown as well as the dose profiles from, scatter, Monte Carlo (-- -), analytical (O). In all cases, the phantom, was 20 cm, thick (water) and a parallel photon source was used in the simulation and calculation. The photon energies and field sizes for each part in the figure are: (a) 16x16 cm? field, 2 MeV photons; (b) 20x20 cm2, 2 MeV; (c) 16x16 cm2, 8 MeV; and (d) 20x20 cm2, 8 MeV. Chapter 4- Theory: Analytic SPR Calculation 78 CD O c CD 3 t£= +-» C CD •g "o c c v— CD Q . CD tf) O Q I 1 I 1 I 1 I 1 I 1 I 1 I r (a) p o o o o o o o o o o o a E o o o CD CL 0 n 1 - F - | - , S - r P t s 8 -12-8 - 4 0 4 8 12 Off axis distance (cm) 1 0 I 1 l 1 l 1 l 1 I 1 I 1 I (b) ^ T n l - p l - . ^ - . - P t S g •12-8 - 4 0 4 8 12 Off axis distance (cm) CD O c CD 13 c CD •g 'o c c 13 L— CD Q . CD CO O Q 18 \ (c) 15r- ~ I 12h 1 9^ D_ CL I 1 I 1 I 1 I 1 I 1 I t o i - p - i - . q --12-8 - 4 0 4 8 12 Off axis distance (cm) 18 15 12 9 0 I 1 I 1 I 1 I 1 I 1 I 1 l (d) C X X J O O O O O C r O C r O O - t Q i - P i - . H - , --12-8 - 4 0 4 8 12 Off axis distance (cm) Figure 4 .5 . Dose profiles at the detector for heterogeneous phantoms. The dose profiles from primary photons as calculated from Monte Carlo simulation (—) and using the ana-lytical calculation (o) are shown as well as the dose profiles from, scatter, Monte Carlo (- --), analytical (U). In all cases, the field size was 20x20 cm?, the total physical thickness of the phantom, was 20 cm, and a parallel photon source was used in the simulation and model calculation. The photon energy and inh,om,ogeneit,y for each part, of the figure are: (a) 2 MeV photons, lung slab phantom.; (b) 2 MeV, bone slab; (c) 8 MeV, lung slab; and (d) 8 Me V, bone slab. Chapter 4- Theory: Analytic SPR Calculation 79 In all of the examples the Monte Carlo results for the scatter to primary dose ratio at the central axis was accurately predicted by the analytical approach. The mean absolute difference between the analytical and Monte Carlo SPRs on the central beam axis was 0.003, and the maximum absolute difference was 0.006. 4.3 S U M M A R Y A method was described in this chapter to calculate the imager dose from primary photons as well as from first-order Compton scattered photons. For a simple parallel photon source the analytical method accurately predicted the SPR in comparison to Monte Carlo results. In equation (4.18), multiply scattered particles were neglected and the portal scatter dose was approximated by a uniform distribution. The accuracy of equation (4.18) is unknown. Therefore, it was necessary to validate the equation with both Monte Carlo simulation and with experimental measurements to ensure that the cumulative affect of each approximation is acceptable. A computer program was written to calculate the dose from primary radiation in equation (4.8), the dose from scatter in equation (4.17), and the scatter to primary dose ratio. In this program the scattering object was described as a three-dimensional matrix with a voxel size of 0.25 cm 3, and the detector dose was computed on a rectangular grid with variable pixel spacing. The dose from primary photons, equation (4.8), was evaluated at each pixel on the detector for heterogeneous phantoms and at the central beam axis for homogeneous cases. The scatter dose in equation (4.17) was evaluated at the central beam axis for all cases. When comparing the doses calculated by this analytical method to the Monte Carlo simulation results, the doses from the analytical calculation were converted to dose per photon in units of [Gy photon - 1] by applying the unit conversion [MeV g - 1]=[1.602xl0 - 1 0 Gy] to equations (4.8) and (4.17). C H A P T E R 5 M O N T E C A R L O S T U D Y A N D V A L I D A T I O N In this chapter, the accuracy of the analytical scatter to primary dose ratio (SPR) calculation presented in chapter 4 is examined. Monte Carlo (MC) simulation was chosen for the validation of the analytical method since with its use the detector dose can be separated into different components according to particle type and interaction history, which cannot be determined experimentally. The first section of this chapter briefly reviews current M C simulation times for calculating the dose within body phantoms. Second, the M C code SDOSXYZ that was written and verified for this work is described. While previous reports have shown that the first-order scatter dominates the pho-ton scatter fluence [47, 70], an estimate of the portal scatter to primary dose ratio from first-order Compton scatter and from multiply scattered particles is lacking. The third section of this chapter presents the simulation to score the SPRs from each scatter mode (first-order Compton, multiple photon scatter, and patient-generated electrons) for ho-mogeneous and anthropomorphic phantoms. In the fourth section, both the M C simulation results and the validation of the ana-lytical method are discussed. The results for the homogeneous cases cover a wide range of beam energies, phantom thicknesses, field areas, and source to detector distances. A summary of the M C validation of the analytical SPR method is given in the fifth and final section. This work was published [90]. 80 Chapter 5. Monte Carlo Study and Validation 81 5 . 1 M O N T E C A R L O S I M U L A T I O N T I M E F O R D O S E C A L C U L A T I O N The Electron Gamma Shower (EGS4) M C package for simulating photon and elec-tron/positron transport [10] (Rogers and Bielajew, 1989) was chosen for the study since EGS4 is an extensively verified set of codes for simulating radiotherapy beams. The Monte Carlo code written for this work, S D O S X Y Z , is a variant of the EGS4 code D O S X Y Z . The first S in S D O S X Y Z stands for scatter. SDOSXYZ (see section 5.2) uses the same description of the phantoms and photon source as DOSXYZ. Typically, our simulation consists of a phantom representing the patient, a large air gap between the phantom and the detector, and a homogeneous water slab for the portal detector (see figure 5.1). The phantom and detector are defined by a set of voxels, or cubes, of variable length in the X, Y , and Z planes. When the computation time (or C P U time) required to achieve results of acceptable accuracy with M C simulation is long, as was the case here, the C P U time and methods to minimize this time are important. Therefore previously reported C P U times and techniques to reduce that time are included here. Total C P U time depends on the size of the dose scoring voxels, overall volume of the simulation phantom, number of photon histories, energy of the incident photon beam, and accuracy desired in the final result. The Stanford M C group [25, 65] reported simulation times for photon beam dose calculation within a body phantom using a network of 22 Pentium Pro 200 MHz personal computers (PCs). A rough estimate of the C P U time for photon beams [65] was stated as ~30 minutes using the 22 PC network. This estimate was for dose scoring voxels from 2-5 mm on a side, beam energies from 4 to 15 M V , and uncertainties of 1% (one standard deviation). In the present work, five 333 MHz processors were used to reduce the overall computation time. The aim of the P E R E G R I N E project [24, 126] is to provide rapid, accurate M C cal-Chapter 5. Monte Carlo Study and Validation 82 Point photon source .X Y / A Li i Source to isocentre distance 100 cm for all simulations Phantom A i thickness ^ f Water Slab / \ i r r t "\ 1 J Field area / L _ -I v Source to detector distance r Detector plane Scoring Bin Figure 5.1. The geometry for the Monte Carlo simulation. All field sizes were specified at the isocentre, which was at 100 cm. from, the photon source. The dose scoring bin was located on the central beam, axis at the depth of m,axim,um dose in the detector. culation. This goal is achieved using multiple computer processors and techniques to increase the efficiency at the expense of reduced accuracy in certain areas. For example, the electrons generated from photons interacting with the secondary collimator jaws are ignored in the simulation. This approximation leads to a loss of fine detail in the tail of the beam profiles under the collimator jaws but the absolute dose estimates from the simulation with this approximation are in good agreement with experimental measure-ments up to beam energies of 18 MV. In the current M C validation the transmission and scatter from the collimator jaws were ignored to decrease the C P U time. 5 . 2 T H E M O N T E C A R L O C O D E : S D O S X Y Z S D O S X Y Z scores the total dose per unit incident fluence in a Cartesian geometry for a specified particle source. Details of the code are given in appendix A. S D O S X Y Z scores the primary dose P and the scatter dose S at the portal detector. Separation of the Chapter 5. Monte Carlo Study and Validation 83 primary and scatter dose was performed by examining the first interaction of each photon. If a photon interacted first in the detector, then the dose from the Compton scattered electron (or electron/positron from pair production) was scored as dose from primary. If a photon interacted first in the patient phantom, then the entire dose in the detector from the resulting particle shower was scored as dose from scatter. S D O S X Y Z also separates S according to particle type and history: charged particles (CP), singly scat-tered photons (F), and multiply scattered photons (MS). The multiple scatter component includes photons from bremsstrahlung, annihilation, and multiple Compton scattering. SDOSXYZ scores the dose per primary photon [Gy photon - 1] and results are presented as SPRs (for example, S P R # £ ) . SDOSXYZ, like DOSXYZ, divides the total number of photon histories for the simula-tion into ten equal batches. In this work the superscript MC indicates an M C calculated quantity. After all the photon histories are simulated, the average S P R M C and standard deviation S P R ^ C of the total S P R M C for the ten batches are computed. As well, the average and standard deviation are also computed for each component of the SPR (that is, for S P R ^ C , S P R ^ , and SPRjgg). The standard deviation of the SPR, S P R ^ C , was calculated from where N is the number of batches (N=10). The results from the code SDOSXYZ were verified by comparing simulation results to data from D O S X Y Z as well as data reported by Ahnesjo [1]. Each comparison is documented here. To verify that S D O S X Y Z recorded the same total dose as compared to D O S X Y Z , the total dose along the central beam axis for a stack of eleven tissue slabs was calculated by both codes and compared. This geometry is 25.6 cm thick and consists of slabs of (5.1) Chapter 5. Monte Carlo Study and Validation 84 cortical bone, adipose tissue, lung, and muscle. The simulation was run for a parallel beam collimated to a 10x10 cm 2 field using beam energies of 4 M V and 24 M V [80]. This particular slab geometry and photon source were chosen since the results could be compared to results in [1], as discussed below. The voxels were 0.2 cm in the depth direction and l x l cm 2 in area, which is only a small difference from that used in [1] (cylindrical geometry with voxels of radius 0.2 cm). The larger area voxels used here did not affect the results and significantly reduced the simulation time. The total dose along the central beam axis, as computed from S D O S X Y Z , is shown in figure 5.2. The root mean square deviation between the total dose from S D O S X Y Z and D O S X Y Z was found to equal 0.0001%, which was accurate enough for the current investigation. To validate the separation of the dose from the different scattering modes, the results from S D O S X Y Z , just described for the eleven slab thorax phantom, were compared to published results [1]. In this comparison, the dose from primary, first scatter, and multiple scatter were compared along the central beam axis and are shown in figure 5.2. Good quantitative agreement was found between our results and [1] for both 4 and 24 M V . Differences may have arisen between this work and Ahnesjo's [1] because of the use of an earlier version of the simulation code [10, 83] in [1]. The results from SDOSXYZ were also verified for calculation of the portal scatter dose by calculating the scatter fraction of dose (SF) 1 and comparing these values to data reported by Jaffray et al. [47]. This comparison is shown in figure 5.3. The data of [47] was chosen since the scatter fraction data covered a wide range of beam energies (6 and 24 MV) , while other sources of scatter data for portal dosimetry were limited to lower beam energies (see for example [95] and [117]). The scatter fraction data calculated here used the same photon energy spectra as 1The scatter fraction of dose was denned as the ratio of the dose from scatter to the total dose, both measured on the central beam axis at the portal imaging plane. Chapter 5. Monte Carlo Study and Validation 85 Jaffray et al. [47], and the simulation setup was a point photon source incident on a 17 cm thick polymethacrylate slab. The field size was 30x30 cm 2 and the photon spectra were from [80]. In the current work, the doses were computed by SDOSXYZ, while in [47], photon fluences were converted to scatter fractions assuming a Compton style detector [see equation (2.5) in section 2.3.1]. In [47] the detector dose from patient-(a) 3 F 2 h 1 h (b) (J C 3 d u C o Q S o > o FA 4 h M B i—i—i—i—|—i—r L Total Total scatter M t t t t i M 3 B M 20 25 0 5 10 15 Depth (cm) Figure 5.2. Verification of results from the code SDOSXYZ for separating the scatter dose. In the graphs the letters A, M, B, and L stand for adipose tissue, muscle, hone, and lung respectively, (a) Dose along the central beam axis as computed by SDOSXYZ (—) for a stack of slab phantoms irradiated with a 10x10 cm2 parallel 4 MV photon beam. The total dose is separated into the primary, total scatter, and first scatter dose components. Good agreement is obtained with previous results reported by Ahnesjo [1] (•). (b) Same as in (a) except for a 24 MV photon beam. The doses from, primary and first scatter were omitted in (b) for clarity. Chapter 5. Monte Carlo Study and Validation 86 generated electrons was neglected in the SFs. Since the magnitude of the SF from charged particles was ^0.03 as calculated by SDOSXYZ for the 24 M V beam, this component of the SF was not included in the SFs from SDOSXYZ presented in figure 5.3 to allow for a meaningful comparison with the published data. 0.30 0.25 h | 0.20 h o LJ- 0.15 h CD 1 0.10 CO 0.05 0.00 I Beam energy 6 MV I I I L (a) 0 10 50 60 0 10 20 30 40 Air gap (cm) 50 60 20 30 40 Air gap (cm) Figure 5.3. Verification of scatter fraction data computed by SDOSXYZ. The scatter fraction is plotted versus air gap for (a) 6 MV and (b) 24 MV photon beams incident on a 17 cm, thick polym,ethacrylat,e slab. The field area was 30x30 cm2. The scatter fraction data calculated using SDOSXYZ (•) are compared to measured (B) and calculated (A) results reported in Jaffray et al. [47]. Jaffray et, al. [47] did not report measured scatter fraction data for the 24 MV beam,. Figure 5.3 shows that our SF results agree well with the measured and calculated data from [47] for both beam energies. In summary, our results from the M C code SDOSXYZ are in good agreement with previously published data both within heterogeneous slab phantoms and at the portal imaging plane. Chapter 5. Monte Carlo Study and Validation 5.3 S I M U L A T I O N P A R A M E T E R S 87 A point source model was chosen as the photon source for the portal scatter dose simulation. The photon energy spectra used here for beam energies equal to 4, 6, 10, and 24 M V were taken from [80] while the spectrum for the 18 M V beam was from [127]. This is consistent with the choices by previous authors in portal dosimetry, for example [47, 95, 117]. For all cases, the simulation was performed with default- values for the Parameter Reduced Electron Step Algorithm (PRESTA) [10] (Bielajew and Rogers, 1989) to reduce the computation time while maintaining accuracy in the model of the physics of the charged particle transport. A photon history was terminated when the energy of the photon fell below PCUT=10 keV, while electrons/positrons were tracked until their total energy fell below ECUT=521 keV. The following subsection provides a description of the simulation for the homoge-neous and anthropomorphic phantoms. Simulation results for these phantoms provided benchmarks with which to debug the code for the analytical SPR method described in chapter 4 and quantitatively assess the accuracy of the analytical SPR approach. Het-erogeneous phantoms were chosen to investigate the influence on the SPRs of tissues and body cavities with physical properties that are significantly different from those of water (for example, bones and air gaps). 5.3.1 HOMOGENEOUS PHANTOMS Figure 5.1 showed the geometry for the M C simulation of the homogeneous phantoms. We calculated the SPRs (total SPR, as well as the SPR for each of the three scatter modes) for a wide variety of cases for homogeneous phantoms. This data set is unique since patient-generated electrons were included in the SPRs. The SPRs were calculated Chapter 5. Monte Carlo Study and Validation 88 for a single voxel on the central axis at the depth of maximum dose for a 10x10 cm 2 field. A single, square voxel on the central beam axis with a length that was 20% of the field length as projected onto the scoring plane was used to be consistent with data reported by previous authors [117, 118] and to be able to obtain accurate results within a reasonable C P U time. The thickness of the voxel was such that the dose remained within ± 1 % of the maximum dose throughout this depth. The thickness and depth of the dose scoring voxel was 0.5 cm and 1.5 cm, respectively, for the 6 M V beam, and 0.8 cm and 4.2 cm for the 18 M V beam. The analytical approach approximates the portal scatter dose by a uniform distri-bution across the imager, which occurs when the air gap between the patient and the imager is at least 50 cm [12]. Consequently, large source to detector distances (SDDs) were used for the M C studies; the SDDs varied from 150 to 230 cm. Since the tumour volume is usually placed at a distance of 100 cm from the photon source, and the min-imum air gap for the analytical method was 50 cm, the minimum SDD for simulation of the homogeneous phantom was selected as 150 cm. A maximum SDD of 230 cm was chosen since this is the source to floor distance. SPRs were calculated for 6 and 18 M V photon spectra, for field areas from 3x3 cm 2 to 20x20 cm 2 at the isocentre, and for homogeneous water slab thicknesses from 10 to 30 cm thick. 5.3.2 ANTHROPOMORPHIC P H A N T O M S Three heterogeneous anthropomorphic phantoms were simulated as part of the M C validation (figure 5.4). The treatment sites chosen (neck, thorax, and pelvis) cover a representative range of tissue thicknesses and beam energies encountered clinically. The beam energy, field area, and irradiation setup for each phantom were based on standard patient treatments. The atomic composition of each tissue was taken from the Interna-Chapter 5. Monte Carlo Study and Validation 89 (a) (b) (c) Z LZZl Air Figure 5.4. The anthropomorphic phantoms: (a) neck, (b) thorax, and (c) pelvis. Dis-tances are in centimeters. Each phantom, is shown, in an axial view. Field areas (measured at the isocentre) and beam, orientations were: neck, 8x8 cm? lateral; thorax, 12x12 cm? anterior; and pelvis, 10x10 cm2 lateral. For each, case, the beam position is illustrated by the divergent solid lines and the central beam axis is indicated by the dashed lines. t ional Commission on Radiat ion Units and Measurements Report 44 [21] and the sizes of the phantoms and heterogeneities were taken from an anatomical C T atlas [20]. A n S D D of 185 cm was selected for the anthropomorphic phantoms as (i) this S D D was the largest that could be used wi th our commercial portal imagers on extendible mechanical arms, and (ii) a large S D D optimizes the conditions for the analytical S P R calculation since the S P R from mult iply scattered photons and charged particles decreases wi th increasing S D D . The voxel size at the detector was set to 1 cm along the X axis and 2 cm along the Y axis. The anthropomorphic phantoms were symmetric about the Y axis to allow the volume of the voxels to be doubled, which reduced the C P U t ime 2 by a factor of y/2. 2 T h e uncertainty in the dose computed within a voxel is proportional to the square root of the number of photon histories for the simulation. Therefore, by doubling the volume of the voxel, the number of histories can be reduced by a factor of \/2. Chapter 5. Monte Carlo Study and Validation 90 A neck phantom was selected since the imager scatter dose from this phantom would be minimal due to the relatively small fields used for neck treatments and the short beam path through the tissue. Lower beam energies (4 and 6 MV) are typically applied for head and neck treatment sites since the depths of the tumours are small. Therefore, the neck phantom was simulated with 4 and 6 M V beam energies (that is, two separate results were obtained, one with the 4 M V beam and another with the 6 M V beam). The field area for the neck case was 8x8 cm 2 and this was a lateral field passing through the spine and trachea as shown in figure 5.4(a). A thorax phantom irradiated with an anterior beam through one of the lungs was selected since this treatment configuration involves a large, low-density organ (lung). In [89], the lung density relative to water for cancer patients undergoing radiotherapy was reported to vary from 0.15 to 0.45, with a mean of 0 .28±0.03. Lower lung densities are found in emphysema patients, while patients with pneumonia have higher lung densities. Three results were obtained for the thorax phantom to cover the range of lung densities found clinically; the lung densities simulated were 0.1, 0.24, and 0.5 g c m - 3 . A beam energy of 6 M V and a field area of 12x12 cm 2 were used for these cases. The third phantom chosen simulated lateral irradiation of the pelvis with the beam passing through the femoral heads. This site was chosen since, for the higher photon energies used for these cases, attenuation of the primary photon beam is greatest due to the large photon path through the tissue and high density bone. As a result of the attenuation of the primary beam, the SPRs from multiple photon scatter and charged particles are large and therefore, this phantom tests the validity of the analytical approach for an extreme case. Tumours within the pelvis are treated with 10, 18 and 24 M V beams. The pelvis phantom was simulated for these three beam energies (10, 18, and 24 MV) with a 10x10 cm 2 lateral field. Chapter 5. Monte Carlo Study and Validation 91 5.4 R E S U L T S In this section, the M C SPR results are described in three parts. First, the central axis SPRs calculated using M C simulation for the homogeneous phantoms are presented. The first subsection also examines the SPR for each scatter mode as a function of off-axis distance at the detector for the anthropomorphic phantoms. Second, the accuracy of the analytical method as compared to the M C data is tabulated. In the third subsection, the M C simulation uncertainties and computer simulation times are reported and briefly discussed. 5.4.1 S C A T T E R TO PRIMARY D O S E RATIOS In figure 5.5, the sum of the SPR from multiply scattered photons and the SPR from patient-generated electrons, (SPR^^+SPR^ 7 ) , is shown for an SDD of 185 cm. Figure 5.6 presents the total SPRs on the central axis as a function of field area, SDD, and beam energy as calculated with SDOSXYZ for the homogeneous water phantoms. This figure shows that the SPR decreases (in almost all cases) with increasing beam energy. Figure 5.7 reports S P R ^ C , SPRj^g, and SPR^? as a function of SDD, beam energy, and field area for a 20 cm thick water phantom. The following observations can be made from this figure: (i) S P R ^ C decreases most in magnitude with increasing SDD - this decrease is more dramatic for the 6 M V beam; (ii) S P R ^ 0 is greater at the lower beam energy; and (iii) SPRj$s is slightly larger at 6 M V than 18 M V . The trends just described in figures 5.6 and 5.7 are due to the increasing probability of Compton scattering at larger scattering angles as the incident photon energy decreases. The results for SPR^p* using the 6 and 18 M V beams show that the increase in scoring voxel depth with beam energy was insufficient to compensate for the increased energy of patient-generated electrons. Chapter 5. Monte Carlo Study and Validation 92 0.05 5 0.04 Pi PH ™ 0.03 + % 0.02 Pi PH M 0.01 0.00 —i 1 r Beam energy 6 M V Water phantom thickness (cm) *t30 500 Beam area (cm ) 500 Beam area (cm ) Figure 5.5. The sum of the scatter to primary dose ratio for multiply scattered photons and patient-generated electrons, (SPR^s+SPR(?p')', as calculated using Monte Carlo for an SDD of 185 cm. The data is shown for beam energies of (a) 6 MV and (b) 18 MV incident on homogeneous water phantoms. SPRcfi is greater at the higher b e a m energy in figure 5.7 due to the increase in the energy of the scattered electrons (and hence, p a t h of travel) w i th increasing p h o t o n b e a m energy. Chapter 5. Monte Carlo Study and Validation 93 0.08 0.06 h 0.04 H 0.02 0.00 0.16 1 1 1 Beam energy 18 MV l -Jl50 _Water thickness 10 cm — / /J200 r i i i (d) 1 0.00 H 0.04 0.00 0.25 A 0.20 0.15 0.10 H 0.05 0.00 1 1 1 1 Beam energy 18 MV _Water thickness 20 cm / J 1 5 0 --1170 ^ 2 0 0 -r 1 1 1 (e) 1 1 1 1 Beam energy 18 MV — Water thickness 30 cm 1 -1150 - £ 1 7 0 ~ — ^ ^ ^ ^ ^ -5200 4K \ 1 1 (f)~ 1 0 100 200 300 400 500 0 100 200 300 400 500 Beam area (cm ) Beam area (cm 2) Figure 5.6. Scatter to primary dose ratios on the central beam axis calculated using Monte Carlo simulation for the homogeneous water phantoms as a function of the area of the square field at the isocentre. SDDs varied from. 150 to 230 cm. Beam energies and water phantom, thicknesses shown: (a) 6 MV, 10 cm.; (b) 6 MV, 20 cm.; (c) 6 MV, 30 cm.; (d) 18 MV, 10 cm.; (e) 18 MV, 20 cm, and (f) 18 MV, 30 cm.. In parts (d), (e), and (f) the data for SDDs equal to 160, 185, and 230 cm, were omitted for clarity. Chapter 5. Monte Carlo Study and Validation 94 o VB 2 o B •c a. o O 00 0.15 0.12 0.09 0.06 0.03 0.00 0.05 0.04 0.03 0.02 0.01 0.00 0.05 0.04 0.03 0.02 0.01 0.00 1 1 f , First Compton scatter only |J8eam energy 6 MV Source to detector distance (cm) ' ^ T 1 1 1 1 Multiply scattered photons only Beam energy 6 MV ^Sl50 _ - § 1 7 0 - ^ ^ ^ ^ ^185 _ . ® 1 | _ Charged particles only Beam energy 6 M V T T T x150 7-170 185" 0.15 0.12 0.09 0.06 — i 1 1 r First Compton scatter only Beam energy 18 MV - \ 0.03 0.02 0.01 0.00 0.05 1 1 1 I Multiply scattered photons only Beam energy 18 MV — J 5 0 _ -^170 _ ^ i S ^ - - =1185 1 ^ 0.04 | _ Charged particles only Beam energy 18 M V T T T *185-^ 100 200 300, 400 500 Beam area (cm 500 Beam area (cm L ) Figure 5.7. Contribution of SPRf0, SPR$g and SPR^g to the total SPRMC as a func-tion of SDD and field area as calculated using Monte Carlo simulation for a 20 cm thick water phantom,. From the top left,: (a) SPR^C, 6 MV; (b) SPR$%, 6 MV; (c) SPR^g, 6 MV; (d) SPR^C, 18 MV; (e) SPR%CS, 18 MV and (f) SPRgj?, 18 MV. Chapter 5. Monte Carlo Study and Validation 95 Figure 5.8 shows the off-axis SPRs for the neck phantom M C results. The SPR profiles were taken along the X axis across the simulated detector at an SDD of 185 cm for all the anthropomorphic phantoms: the coordinate system for the simulation was given in figure 5.4. The simulated detector is always perpendicular to the photon beam as shown in figure 5.1. At each voxel within the detector the scatter and primary doses were scored, and then the SPR calculated. Since the scatter dose is relatively uniform, the structure seen in the SPR is due to changes in the primary dose. For these cases, the SPR from multiply scattered photons and electrons was negligible. Therefore treatment sites involving the neck are potentially good candidates for the analytical SPR method, which accounts for only the first-order scatter dose. In figure 5.9, the off-axis SPRs for the lateral irradiation of the thorax phantom are plotted. Due to the difference in density between lung and muscle, the edge between the lung and muscle is visible as a jump in the SPR at an off-axis distance of ^5 cm. Changing the lung density from 0.1 to 0.5 relative to water increased the total SPR by only « 0 . 0 1 . The SPR from first-order scatter is within « 0 . 0 0 5 of the total SPR, so that approximating the total scatter dose by that from first-order Compton scatter is a good approximation for this case. Figure 5.10 shows the off-axis SPRs for the pelvis phantom. As the beam energy increased from 10 to 24 MV, the total SPR increased for this phantom. The SPR from charged particles was larger than the SPR from multiply scattered photons for all ener-gies. The SPR from charged particles increased with increasing beam energy, however, the SPR from first and multiple photon scatter were indifferent to beam energy. The total SPR is within «0 .02-0 .03 of that from first-order scatter. Chapter 5. Monte Carlo Study and Validation 96 0.05 0.04 h 0.03 h 0.01 0.00 0.05 0.00 o 2 CD CO o T3 CO E 'K 0.02 h o -*—* CD CO O 00 o "co 1_ Ci) CO o •a co E 0.02 h o -*—< CD CO O CO I I _ ( a ) I I I I I • Total First order Compton / /y Multiply scattered photons -/ y Charged particles —r£n 1 1 r = ( = \ r & 1—,=1 1 1 1— 0.04 V 0.03 h 0.01 h T T T Total First order Compton Charged particles Multiply scattered photons -8 -4 8 -2 0 2 4 6 Off-axis distance Figure 5.8. Scatter to primary dose ratio calculated using Monte Carlo as a function of off-axis distance along the X-axis for the neck phantom, at a beam, energy of (a) 4 MV and (b) 6 MV. The off-axis distance is measured along the detector, which, was at a source to detector distance of 185 cm,. Chapter 5. Monte Carlo Study and Validation 97 o -4—' CO 1_ CD CO O T J ^ CO E CL o -*—' l _ CD ±2 CO O CO o CO 0 CO o T J CO E CL O k— CD CO o CO o 2 CD co o T J CO E CL O L— CD ro o CO 0.05 0.04 0.03 0.02 0.01 0.00 0.05 0.04 0.03 0.02 0.01 0.00 0.05 0.04 0.03 0.02 0.01 0.00 n 1 r Total First order Compton Charged particles Multiply scattered photons (a) I I I Total v . 1 l First order Compton \ ^ — Charged particles \ N , ~ Multiply scattered photons \ \ I (b) _____ i — - 1—• — i ^ i i i Total v . 1 1 First order Compton Charged particles v "Multiply scattered photons A ^ - • (c) __ | = £ •—1 ^ -15 -10 -5 0 5 10 Off-axis distance 15 Figure 5.9. Scatter to primary dose ratio as a function of off-axis distance along the X-axis for the thorax phantom, at a beam energy of 6 MV for lung densities relative to water of (a) 0.5, (b) 0.25 (normal density), and (c) 0.1. The SPR changes by less than, one percent when the relative lung density changes from 0.1 to 0.5. The SDD was equal to 185 cm,. Chapter 5. Monte Carlo Study and Validation 98 0.10 0.08 0.06 g "co i _ CD co o TJ Cf CO E g. 0.04 o 1_ CD ti CO O co CO t_ CD CO o CO E i _ CL o CD CO O 00 O V-* CO l_ CD CO o T J CO E CL o H—» CD CO o CO 0.00 0.10 0.08 0.06 0.04 0.02 0.00 0.10 0.08 0.06 0.04 0.02 0.00 (a) Total First order Compton Charged particles 0.02 I- Multiply scattered photons (b) Total First order Compton • Charged particles . |- Multiply scattered photons (c) 1 1 -Total First order Compton Charged particles Multiply scattered photons -10 -5 0 Off-axis distance 10 Figure 5.10. Scatter to primary dose ratio as a function of off-axis distance along the X-axis for the pelvis phantom, at a beam, energy of (a) 10 MV, (b) 18 MV, and (c) 24 MV. The SPR from, multiply scattered photons increases negligibly with increasing beam energy compared to the change in the SPR from charged particles. The SDD was equal to 185 cm. Chapter 5. Monte Carlo Study and Validation 99 5.4.2 VALIDATION OF T H E A N A L Y T I C A L S P R CALCULATION Comparison of the SPRs calculated using the analytical method described in chap-ter 4 to the total SPR from the M C simulation for the neck phantom cases are given in figure 5.11. In the analytical calculation, the scatter dose across the imager was ap-proximated by that on the central beam axis and the primary dose was calculated for each voxel at the detector. As expected from figure 5.8, the analytical method is a good approximation for the total SPR across the X axis for the neck phantom irradiated with a 4 or 6 M V beam. The differences between the analytical and the M C results are mostly due to the main approximation in the analytical approach: multiply scattered particles (photons and electrons) were neglected in the analytical method whereas they are included in the M C data. Similarly, the results for the thorax cases are shown in figure 5.12 and the analytical SPR is also in good agreement with the M C results. The pelvis cases are illustrated in figure 5.13. For the pelvis cases, the SPR from multiply scattered particles is larger than for the neck and thorax phantoms. In turn, the large SPR from multiple scatter for the pelvis cases is due principally to insufficient buildup material on the imager to stop the patient-generated electrons before they reach the scoring voxel within the detector. Three quantities were computed when comparing the analyticalally calculated SPRs to the M C SPRs: (i) the maximum difference between the two sets of SPRs, ASPRmax, (ii) the mean difference, A S P R = ^ £ ( S P R £ 7 ; - S P R ? ) (5.2) and (iii) the root mean square of the differences, ASPR<7 = ^ E i _ ! (SPR^ - S P R f c ) - A S P R (5.3) N — I Chapter 5. Monte Carlo Study and Validation 100 where N was the number of SPRs compared. For the results from the homogeneous phan-toms, the SPRs were compared only on the central beam axis. The data for homogeneous cases were analyzed by grouping all the results for one beam energy together (total num-ber of SPRs per beam energy: JV=72), and then calculating ASPRmax, ASPR, and A S P R a . For the anthropomorphic cases, the M C results were analyzed for each simula-tion separately and the SPRs were compared for each pixel on the detector; N was equal to the number of pixels on the simulated detector (AT=98, 200, and 162 for the neck, thorax, and pelvis cases respectively). Good agreement was obtained between SPR^ and S P R ^ C for the homogeneous wa-ter phantoms: at 6 M V , ASPR ± ASPR C T =0 .000±0 .003 and ASPRmax=0.009 while at 18 M V , A S P R ± A S P R C T = 0 . 0 0 1 ± 0 . 0 0 3 and ASPRmax=0.010 [see equations (5.2) and (5.3)]. Table 5.1 summarizes the quantitative comparison between S P R M C and SPR$ for the anthropomorphic phantoms. The mean difference between S P R M C and SPR^ is equal to the mean difference over the field between SPRMC and S P R ^ C (see figures 5.8, 5.9, and 5.10). The mean difference between S P R M C and SPR$ was mainly due to approximating the total scatter dose by the first-order Compton scatter dose only. From table 5.1 the mean difference between the analytical and M C results, ASPR, was 0.005 or less for both the neck and thorax cases. For the pelvis cases, ASPR was 0.03 or less. The accuracy of the current analytical method is comparable to that of similar tech-niques. The SPR model of Swindell and Evans [117] was shown to have a mean experi-mental difference of 0.005 or less for an SDD of 200 cm, water phantom thicknesses up to 30 cm, beam areas up to 400 cm 2, and beam energies of 6 and 10 M V [95]. The analytical SPR model of Spies et al [114] agreed within 0.02 to 0.03 with M C results for off-axis SPRs using air gaps from 6.3 to 18.3 cm, a 6 M V radiosurgical field, and copper phantoms up to 3.5 cm thick. Chapter 5. Monte Carlo Study and Validation 101 -8 -4 -2 0 2 4 Off-axis distance (cm) Figure 5.11. Graph of the scatter to primary dose ratio as a function of off-axis distance along the X-axis calculated from, Monte Carlo simulation (—) and analyticalally (•) for the neck phantom. Results are shown for beam energies of (a) 4 MV and (b) 6 MV. Chapter 5. Monte Carlo Study and Validation 102 0.05 -15 -10 -5 0 5 Off-axis distance (cm) Figure 5.12. Graph of the scatter to primary dose ratio as a function of off-axis distance along the X-axis calculated from, Monte Carlo simulation (—) and analyticalally (•) for the thorax phantom,. Results are shown for lung densities relative to water equal to (a) 0.5, (b) 0.25, and (c) 0.1. Chapter 5. Monte Carlo Study and Validation 103 2 CD CO o TJ CO E Q. O H—» i_ CD co o CO 0.10 0.08 -0.06 -0.04 0.02 0.00 0.10 • ••••••••• m • • • • • • (a) -10 -5 0 5 Off-axis distance (cm) Figure 5.13. Graph of the scatter to primary dose ratio as a function of off-axis distance along the X-axis calculated from Monte Carlo simulation (—j and analyticalally (•) for the pelvis phantom,. Results are shown for beam energies of (a) 10 MV, (b) 18 MV, and (c) 24 MV. Chapter 5. Monte Carlo Study and Validation 104 Table 5.1. Agreement between the scatter to primary dose ratios calculated from, Monte Carlo simulation (SPRMC) and analyticalally (SPRF) for the anthropomorphic phantoms. The second column, lists the number of pixels at the detector used in the analysis of the accuracy of the predicted scatter doses, N. Case Number of pixels (N) ASPR ± ASPR C T ASPRmax Neck, 4MV 98 0.000±0.001 0.003 Neck, 6MV 98 -0.002±0.001 0.005 Thorax, low density lung 220 -0 .004±0.003 0.014 Thorax, normal density lung 220 -0 .005±0.003 0.013 Thorax, high density lung 220 -0 .005±0.003 0.013 Pelvis, 10 M V 162 -0 .014±0.007 0.029 Pelvis, 18 M V 162 -0 .018±0.007 0.038 Pelvis, 24 M V 162 -0.027±0.008 0.050 5.4.3 M O N T E C A R L O S I M U L A T I O N T I M E S A N D U N C E R T A I N T I E S Minimizing the C P U time for the M C simulation was important for the validation described in this chapter. The total simulation time for the homogeneous and anthro-pomorphic phantom results described in section 5.3 alone required thirteen weeks using a single 333 MHz processor. This estimate neglects the C P U time for debugging and validating the SDOSXYZ results, debugging the simulation files, and the time to obtain simulation results for other parts of this thesis. Several methods were used to minimize the total C P U time. For the heterogeneous cases, the voxels at the detector were twice as wide along the Y axis (that is, along the axis of symmetry for these phantoms) as that along the X axis. This was possible because of the symmetry of the phantoms. Making use of this symmetry reduced the total number of photon histories by a factor of For the homogeneous cases, the SPR was calculated for a single, large voxel on the central axis. The thickness of the dose scoring voxel at the detector along the source to detector ray line was maximized for Chapter 5. Monte Carlo Study and Validation 105 Table 5.2. Monte Carlo CPU times and total number of photon histories for the ho-mogeneous water phantoms. This table contains a representative sample of all the cases, since there are too many to list individually. The source to detector distance for these results was 200 cm, and the field area was 14x14 cm?. Beam Phantom Number of Number of C P U Absolute energy thickness histories histories/hour time uncertainty (MV) (cm) (millions) (millions/hour) (hours) in the SPR 6 10 25 4.1 6 0.002 20 40 2.3 17 0.004 30 45 1.7 26 0.005 18 10 8 2.4 3 0.003 20 12 1.3 9 0.003 30 18 1.0 18 0.004 all cases, which increases the volume of the voxel. Maximizing the dose scoring voxel volume increased the probability of dose deposition within the voxel, and thus, reduced the simulation time. Each M C simulation was run until the absolute uncertainty in the total SPR was less than or equal to 0.01 (for example, if the SPR was equal to 0.20 and the absolute uncertainty was 0.01, then the SPR was 0.20±0.01) . Appendix B lists the M C calculated SPRs for the homogeneous water phantoms: these tables include the total SPR, as well as the SPR from each scatter mode (first-order Compton, multiple photon scatter, and patient-generated electrons). Absolute uncertainties are reported for the total SPR and each component of the SPR. The mean M C uncertainties for the SPRs (averaged over the field at the detector) for the anthropomorphic phantoms were 0.001, 0.003, and 0.006 for the neck, thorax, and pelvis cases respectively. Table 5.2 gives the C P U times and the total number of photon histories for a rep-resentative sample of the M C results for the homogeneous phantoms. These times were obtained using a 333 MHz Pentium II processor and the Linux operating environment. Chapter 5. Monte Carlo Study and Validation 5.5 SUMMARY 106 In this chapter, the accuracy of the analytical method was examined. The analytical method was found to be a good approximation for the neck and thorax phantoms, since the SPR from multiply scattered particles in these cases was small. For the pelvis case, the mean difference between the analytical SPR was within 0.015-0.030 of the total SPR calculated using M C simulation. To improve the accuracy of the analytical method for such cases, it would be necessary to include the portal scatter dose from patient-generated electrons, multiple Compton scattering, bremsstrahlung, and annihilation. Since the sensitive area of the imager is fixed and the analytical SPR method requires a 50 cm air gap, application of the analytical method is limited by the maximum area that the imager can measure when using a 50 cm air gap. Reducing the air gap allows larger field areas to be used, however the accuracy of the analytical method will decrease since the SPR from multiply scattered particles increases with decreasing air gap. The advantage of the analytical method, compared to the semi-empirical method of Boellaard et al. [14], is that the SPRs were calculated for heterogeneous cases without measuring data for a look-up table. If the analytical SPRs are valid for experimen-tal phantoms, then another institution can use the analytical method and reduce the implementation time for calculating the portal scatter dose for heterogeneous cases. Since the primary energy spectra for the analytical method are different from the experimental photon energy spectra, an experimental validation of the analytical SPR approach is presented in the following chapter. In reality, the mean energy of the photon spectra can decrease by « 6 to 15% from the central axis to 10 cm off axis [80], as measured at the isocentre. This change in energy is termed off-axis softening. The analytical method ignores off-axis softening, therefore the experimental validation is necessary to determine the accuracy of the method. C H A P T E R 6 E X P E R I M E N T A L V A L I D A T I O N An experimental validation is also necessary since the description of the linear acceler-ator for the Monte Carlo (MC) simulation was also incomplete. For example, the photon source was modeled for the simulation as an isotropic point source. For the clinical linear accelerators, the photon sources are spatially variant and diffuse. This chapter describes the experiments carried out to measure the SPRs on the cen-tral axis for homogeneous and anthropomorphic phantoms. These measurements are quantitatively compared to the predicted SPRs from the analytical method, which was presented in chapter 4. First, the choice of field sizes and phantom thicknesses for the experimental validation are discussed. Second, the beam characteristics of the clinical linear accelerators are reviewed to understand the limits of the photon source models for the analytical SPR calculation. Third, the phantom designs, tissue substitutes and measurement techniques for the experimental validation are discussed. The fourth section presents the results from the quantitative analysis of the agreement between the experimental and analytical SPRs. A summary is given in the fifth and final section. This work was published [90]. 6 . 1 CLINICALLY R E L E V A N T CASES Clinical linear accelerators can produce radiation field sizes up to 40x40 cm 2 at the isocentre and the physical thickness of the patient can vary by up to 40 cm. While 107 Chapter 6. Experimental Validation 108 it may be possible to produce a 40x40 cm 2 field and a specific treatment site may be 10 cm thick, one would never encounter such a combination clinically for the treatment of solid, localized tumours. The experimental validation was carried out for a wide range of clinically relevant cases. The largest field areas for the validation corresponded to the largest areas used for each treatment site. The neck region is treated with 4 and 6 M V photon beams and the maximum field area is 14x14 cm 2. Tumours in the thorax are typically treated with a 6 M V beam; the maximum field area is usually 20x20 cm 2 , although the field can be larger. Tumours in the pelvis are treated with anterior, posterior, and lateral fields; the beam energies applied range from 10 to 24 M V . The anterior and posterior fields are typically smaller than 20x20 cm 2 , while the lateral fields are smaller than 16x16 cm 2. 6 . 2 P H O T O N B E A M CHARACTERISTICS This section briefly reviews several features of clinical linear accelerator photon beams and how these features influence the experimental validation of the analytical SPR calcu-lation method. The topics covered include the photon energy spectra and the collimator scatter factor. 6.2.1 P H O T O N E N E R G Y S P E C T R A The photon energy spectrum is probably the most important feature of the linear accelerator for dose calculation. For the Monte Carlo validation in chapter 5 the photon energy spectra were assumed to be invariant across the beam. Since complete, accurate spectra for real linear accelerators are difficult to obtain or calculate, this section briefly discusses the photon source models that other investigators have applied for portal scatter estimation and the accuracy of each study. Chapter 6. Experimental Validation 109 Jaffray et al. [47], Partridge and Evans [95], and Swindell and Evans [117] all measured SPRs or scatter fraction data on the central beam axis at the position of the portal detector, and these studies have several points in common. In these cases, the measured SPR or SF data for 6 or 10 M V beams showed good agreement with M C calculated values computed using the assumptions that (i) the experimental photon source was a point source, and (ii) generic photon energy spectra, such as those reported in Mohan et al. [80], were adequate to describe the photon spectra. Measured SPR or SF data for 6 or 10 M V beams showed good agreement with M C calculated values. Jaffray et al. [47] and Partridge and Evans [95] showed that the experimental and M C data agreed within the uncertainties in the data, and Swindell and Evans [117] report the mean difference between the calculated and measured SPRs to be 0.005. The comparison by Jaffray et al. [47] was carried out for air gaps from 10 to 60 cm and a 17 cm polymethacrylate slab phantom. The source to detector distance for the data reported by Partridge and Evans [95] and Swindell and Evans [117] was 200 cm. Since these previous studies assumed that the photon energy spectra was invariant across the beam and they obtained good agreement between calculated and measured SPRs or SFs on the central axis, this approximation was also made in the current analytical SPR calculation. In this chapter, measured SPRs are reported for three linear accelerators (all Varian): a Clinac 600C, which produces a 4 M V photon beam; a Clinac 2100C (6 and 10 MV); and a Clinac 21EX (18 MV). The corresponding photon energy spectra for the analytical computation were from Mohan et al. [80] for 4, 6, and 10 M V , and Waggener et al. [127] for 18 M V . The experimental validation was restricted to SPRs measured on the central beam axis because these generic spectra specify the photon spectrum on the central axis only and the mean energy of the primary photons can decrease by ^6 to 15% between the collimator axis of rotation and 10 cm off-axis [80] (this change in beam energy is known as off-axis softening). The energy spectrum was assumed to be invariant across Chapter 6. Experimental Validation 110 the beam for the analytical calculation. The 4, 6, and 10 M V spectra were averaged over a beam radius of 3 cm (measured at the isocentre) (Mohan et al. [80]). The 18 M V spectrum was measured on the central axis using a field of diameter 0.2 cm (Waggener et al. [127]). Off-axis softening was not included in the analytical calculation and therefore introduces an error into SPR^. To determine the validity of using these generic spectra for our accelerators, per-centage depth doses were computed using these spectra (with the EGS4 Monte Carlo simulation code DOSXYZ) and compared to experimentally measured depth doses. To maximize the agreement between the depth doses calculated with D O S X Y Z and the mea-sured doses, a small field (3x3 cm2) was chosen since the spectra are averaged over a circular beam with a radius of 3 cm [80] (for the 18 M V spectrum the beam was 0.2 cm in diameter [127]). An ionization chamber (IC10, Wellhofer Dosimetric, Schwarzenbruck, Germany) was used for the measurements, which has a diameter of 0.6 cm. For the simulation, the dose scoring voxels were chosen to be 0.6 cm laterally and 0.5 cm along the depth axis to match the size of the ionization chamber. The simulation phantom was 10x10x40 cm 3 and the source to detector distance was 100 cm to correspond to the measurement setup. The standard deviation of the Monte Carlo calculated doses relative to the total dose was less than 2%. Percent depth doses calculated from M C simulation and measured experimentally are shown in figure 6.1. These curves were normalized to a depth of 10 cm (see section 1.9.1 for choice of normalization depth). Good agreement is seen between the experimental and simulated depth doses for all energies up to a depth of 35 cm, therefore the generic spectra are a good approximation on the central axis for the linear accelerators used here. Chapter 6. Experimental Validation 111 " " 0 5 10 15 20 25 30 35 """0 5 10 15 20 25 30 35 Depth (cm) Depth (cm) Figure 6.1. Comparison of the percentage depth doses measured experimentally (—) and calculated from Monte Carlo simulation (histogram,) for photon, beam, energies of (a) 4 MV, (b) 6 MV, (c) 10 MV, and (d) 18 MV. 6 . 2 . 2 C O L L I M A T O R S C A T T E R F A C T O R , S C ( F A ) In the Monte Carlo simulation, the beam collimation was assumed to be perfect. With perfect collimation, all of the photons outside of the defined field size would be completely-absorbed. In reality, however, photons scatter within the treatment head, which leads to a field size dependence of the dose per monitor unit.1 This effect is included in photon 1A monitor unit is the unit for the radiation dose measured by the ionization chambers in the treatment head of the linear accelerator. Chapter 6. Experimental Validation 112 treatment planning systems by measuring a quantity known as the collimator (or head) scatter factor, Sc [48, 109, 125]. The collimator scatter factor depends on the photon source, field area (FA) at the isocentre, and the components in the treatment head (for example, the flattening filter, the monitor ionization chamber within the treatment head, and the collimator blocks). Measurement of 5C(FA) is carried out using an air ionization chamber in a buildup cap or using a beam-coaxial narrow cylindrical phantom. The collimator scatter factor is defined as where -D a j r is the dose measured by the ionization chamber. The value of 5C(FA) increases nonlinearly from ~0.9 to w l . l as the field area increases [the range of values for SC(FA) quoted are from the Varian Clinac 2100C linear accelerator at our centre, 6 and 10 M V photon beams]. The analytical method for the SPR calcula-tion neglected collimator transmission since the SPR measurement technique of Swindell and Evans [117] was used, which removes the collimator scatter effect by normalizing each dose to the dose measured in the same configuration but without the phantom in the beam. 6.3 S C A T T E R TO PRIMARY D O S E RATIO MEASUREMENTS In this section, the phantom designs and choice of tissue substitutes for the experi-mental validation are discussed. Following this, the measurement methods for the SPR on the central beam axis for homogeneous and anthropomorphic phantoms are presented. 6.3.1 P H A N T O M S One advantage of the experimental methods versus Monte Carlo approaches is that the measurement time for each SPR was constant and was much shorter than the time Chapter 6. Experimental Validation 113 for calculating an SPR with Monte Carlo simulation. Since (i) a benchmark data set of measured SPRs covering a wide range of radiotherapy energies, phantom thicknesses, and field sizes was unavailable, (ii) this data would be potentially useful in the future for validating absolute scatter dose calculation methods, and (iii) the measurement time for the SPRs was relatively rapid, there was strong motivation to compile a compre-hensive SPR database. Therefore, we measured SPRs for homogeneous water-equivalent phantoms using all the megavoltage beam energies at our centre (4, 6, 10, and 18 MV) and for field areas up to 28x28 cm 2. The water equivalent plastic blocks used for the measurements are discussed in section 6.3.2. SPRs were measured for water equivalent thicknesses up to 30 cm for 4 and 6 MV, and up to 40 cm for 10 and 18 M V . Three anthropomorphic phantoms were designed to represent the neck, thorax, and pelvis and are shown in figure 6.2. Measurements were performed for the neck phantom irradiated with a lateral field for beam energies of 4 and 6 M V . For the thorax phantom, an anterior 6 M V beam was used. The pelvis phantom was irradiated with 10 and 18 M V lateral beams. The differences between the phantoms for the Monte Carlo validation in chapter 5 and this chapter included: the position of the photon beams and the het-erogeneities, the atomic composition of the tissue substitutes, and the field areas. The position of the beams and heterogeneities was changed for the experimental validation to facilitate measurement of the SPRs; this method will be explained in section 6.3.4. The dimensions for the phantoms were measured from an anatomical C T atlas [20] and the Rando phantom2 (The Phantom Laboratory, USA). Section 6.3.2 discusses the choices of tissue substitutes for the experimental validation: aluminum was used to replace bone and cork was substituted for lung. The heterogeneities for each phantom were contained within a Lucite box with an open top and the box was filled with water. The density of 2The Rando phantom is a humanoid phantom constructed from a natural human skeleton cast inside material that has radiological properties similar to soft tissue. Lower-density material fills the rib cage, to simulate human lung at median respiratory state. Chapter 6. Experimental Validation 114 1 = 1 A i r Figure 6.2. Size (in cm,) and composition of the experimental anthropomorphic phan-toms: (a) neck, (b) thorax, and (c) pelvis. The radiation beams are indicated by the divergent lines. In each case the centre of the radiation field in the phantom, is shown, by the dotted line. The im,ages are axial, views. The beam, orientation for each case was: lat-eral for the neck and pelvis; anterior for the thorax. Every phantom consists of an, outer Lucite box (sides 3 mm or 9 mm, thick) with an open top. Permanent marks were made on the outside of the box for placement of the phantom, at the isocentre of the clinical linear accelerator. Heterogeneities were fixed in place with electrical tape. The blocks of cork were wrapped tightly with masking tape and then sealed in plastic bags. the Luci te walls was included in the analytical calculation. 6 . 3 . 2 T I S S U E SUBSTITUTES Ideally, phantom materials chosen to test the model would be highly tissue equivalent, readily available, and easy to cut or machine. In this section the reasons for using the chosen tissue substitutes are discussed. The properties of interest for the experimental validation are the attenuation and scattering properties, which are described by the attenuation coefficient and electron density of the material, respectively. To compare the tissue equivalence of the substitute with the tissue it replaces, two quantities were examined: the electron density of the tissue substitute relative to water, pe, and the mass attenuation coefficient ratio between the substitute and the tissue, substitute (9 (/VP)substitute 2) (/V P)tissue Chapter 6. Experimental Validation 115 Figure 6.3 shows graphs of the mass attenuation coefficient ratio for the tissue substitutes discussed in this section. Unless stated otherwise, material data presented here was from ICRU 44 [21]. Materials that were compared for muscle tissue substitutes included Solid Water (Gammex RMI, Middleton, WI), polystyrene, and water. Solid Water (or WT1) is an epoxy based material with fillers of polyethylene, phenolic microspheres, and calcium carbonate and was formed into 30x30x5 cm 3 or 40x40x5 cm 3 blocks. Solid Water was chosen as the tissue substitute for constructing the homogeneous phantoms since this material was available, is easier to handle than water, and the attenuation coeffi-cient is closest to that for muscle (see figure 6.3). Table 6.1 summarizes the elemental composition and physical density of water and Solid Water. Chapter 6. Experimental Validation 116 co 3 C CD *S CO CO CO CO 1.1 1 0.9 0.8 0.7 0.6 0.5 i—i—i i M i i i 1—i—i 11 T 1—i i i i 111 r Polystyrene/Muscle — — Water/Muscle Solid water/Muscle j i i i i i_ 0.9 0.8 1.1 0.9 0.8 0.7 i — i — i i 11111 1 — i — i i 11111 (a) i — i i i i i M Aluminum/Bone PVC/Bone (b) _j i " _j i 111111 0.6 i 1—i i i i 111 1 r n—i I I I I I I r Griffith lung/Lung LN10/Lung Cork/Lung (c) _i i i i 0.01 0.1 1 Energy (MeV) 10 Figure 6.3. The ratio of the mass attenuation coefficient for the tissue substitute to the muss attenuation coefficient for the tissue is plotted versus photon beam energy for alter-native tissue substitutes. These ratios are shown for (a) muscle, (b) bone, and (c) lung. As well, in (c), Griffith lung and LN10 (commercial lung substitutes) were included for comparison to cork. Chapter 6. Experimental Validation 111 Table 6.1. Physical properties of the phantom, materials. The physical densities were measured for these materials. The relative electron density for polyvinychloride (PVC) was from. ICRU 44 [21]- The physical and electron, densities for cork were calculated on the basis that, cork is a cellulose-based compound with a molecular weight, of 162.14 and a chemical composition of CQHIQO*,. The number of electrons per gram, for cork relative to water was calculated to be 0.956. Percent composition Physical Electron density by weight (%) density relative to water Material C H O Cl N Ca p (g/cm3) Water — 11.2 88.8 — — — 1.00 1.00 Solid Water 67.2 8.1 19.9 0.1 2.4 2.3 1.02 0.991 P V C 38.5 4.8 — 56.7 — — 1.32±0.01 1.24±0.02 Aluminum — — 2.70 2.35 Cork, lot 1 44.4 6.2 49.4 — — — 0.518±0.006 0 .495±0.006 Cork, lot 2 44.4 6.2 49.4 — — — 0.16±0.01 0 .15±0.01 For the bone substitute, polyvinylchloride3 (PVC) and aluminum4 were compared. The relative electron density of P V C (pe—1.2A) is between that for cortical bone (pe=1.78) and spongy bone (pe=1.15), and the relative electron density of aluminum (/oe=2.35) is higher than that for cortical bone. Aluminum was selected over P V C since bone is a high-density heterogeneity and aluminum would test the algorithm in an extreme case. Potential lung substitutes included woods (balsa and cork) [46] and expanded polyethy-lene foams [52]. Foamed materials with fillers, such as Griffiths lung or LN10/75, were also considered. The main challenge in selecting a lung tissue substitute was in ob-taining a material that matched the physical density of lung used for treatment plan-ning. Lung density in treatment planning varies from 0.15 to 0.45 g c m - 3 , with a mean of 0 .28±0 .03 g c m - 3 [89]. The physical density of Griffiths lung (p=0.26 g cm"3) and LN10/75 (p=0.31 g c m - 3 ) closely match the mean density of lung, however, these mate-industrial Plastics and Paints, Richmond 46061 Aluminum, Metal Supermarkets, Richmond Chapter 6. Experimental Validation 118 rials were not as readily available as balsa wood or cork. The density of balsa wood can be quite low (p=0.08 g cm - 3 ) , which eliminated this choice. Since it was initially desir-able to be able to measure the relative electron densities of the phantom materials with computed tomography, and we would have to apply corrections for beam hardening if using non-water equivalent material such as polyethylene [53], the expanded polyethylene foams were eliminated as choices. Cork was chosen as the best alternative for the lung substitute, and the mass attenu-ation coefficient between cork and lung is comparable to the foam mixtures as shown in figure 6.3. Two batches of cork were purchased, one with a high density5 of p « 0 . 5 g c m - 3 and one with a lower density6 of 0 .16±0.01 g c m - 3 . The lower density batch was used for the experimental validation since the lung is a low density inhomogeneity, and the lower density cork would test the algorithm in an extreme situation. The density of the cork was determined from the mass to volume ratio. The measurement uncertainty for the mass to volume ratio for the current work was « 2 % , and since the direct measurement of the density was faster than C T scanning the cork, the direct approach was used. Vari-ation in the density of the cork within a batch was the main source of uncertainty in the density for the low-density cork. The uncertainty in the density of cork when determined from C T data, as found by Kohda and Shigematsu [55] for 360 measurements of the same sample of cork, was « 4 % (measured density was 0.287±0.011) . The mass attenuation coefficients for the chosen tissue substitutes are shown in figure 6.4. The mass attenuation coefficient for cork was calculated from the weighted sum of the mass attenuation coefficients of the elements in cork, where the weights were equal to the percentage of the element by weight (see table 6.1 and reference [49]). Table 6.2 lists the effective atomic numbers Z for muscle and bone as well as for the 5 Cork flooring underlay, Banner Carpets, Burnaby. 6European Quality Cork Flooring, Port Coquitlam. Chapter 6. Experimental Validation 119 0.01 0.1 1 10 Energy (MeV) Figure 6.4. Graph of the mass attenuation coefficients for Solid Water, aluminum and cork. Table 6.2. Effective atomic numbers for the tissue substitutes used for this work and for the human tissues they replace. [49]. Material Z Muscle 7.64 Solid Water 7.89 Cellulose 6.97 Bone 12.31 Aluminum 13 tissue substitutes. 6.3.3 D E T E C T O R The radiation detectors available for measuring the SPRs included three different portal imagers as well as the ionization chambers at our centre. An ionization chamber was chosen for the measurement of the SPRs since the calibration of the portal imagers for Chapter 6. Experimental Validation 120 dose measurements is inexact [31], therefore measurement of the SPRs with an ionization chamber was more accurate than with a calibrated portal imager. A Farmer-type ionization chamber (PTW Freiburg, Germany, model N30001) was chosen for the experimental validation since this is expected to be the most accurate method for measurement of the SPRs. This chamber has a volume of 0.6 cm 3 . The inner electrode is made of aluminum and the wall is composed of 0.275 mm of polymethacrylate and 0.15 mm of graphite. The electrode is 21.1 mm long and the inner chamber diameter is 6.1 mm. The small variation of the value of the radiation quality factor for this chamber, UQ, versus beam energy means that the value of k,Q in the numerator of the SPR will cancel with k,Q in the denominator [121]. This ionization chamber was used in conjunction with a Victoreen 500 electrometer (Victoreen, Cleveland, Ohio). 6.3.4 M E A S U R E M E N T M E T H O D S In this section, the methods for experimentally measuring the SPRs for the homoge-neous and heterogeneous phantoms are presented. For homogeneous cases a published approach was used, while for the heterogeneous cases a novel technique for measuring the SPR on the central axis was developed. Large SDDs minimize the SPRs from multiply scattered photons and charged parti-cles. The largest SDD for our commercial imagers was 185 cm. Investigators at the Royal Marsden Hospital, which is an active centre for the development of portal scatter dose prediction methods [43, 95, 114, 117], use a fixed SDD of 200 cm; SPRs were measured here with an SDD of 200 cm for comparison with the latter studies. For the homogeneous cases, the SPRs were measured using the method presented by Swindell and Evans [117]. In this technique, the total dose on the central axis at the imaging plane is measured with and without the phantom in the beam. The ratio of the dose with the phantom divided by the dose without the phantom removes the effect Chapter 6. Experimental Validation 121 of the change in the machine output with changing field area (see the discussion on the collimator scatter factor in section 6.2.2). This ratio was denoted by TJV, where the T stands for total and the N for normalized. The dose from primary, P^, was calculated by extrapolating the total dose TN versus field area FA to zero field area, where the scatter signal should vanish. TN was fitted to a quadratic curve and the fitting was performed with the function minimization and error analysis program Minuit (CERN, Geneva, Switzerland). The physical interpretation of PJV is exp(—fit), where p, is the mean linear attenuation coefficient for the photon beam along the central axis and t is the thickness of the phantom. For each field area the SPR was then calculated using SFREXP{FA) = TN(FA)-PN_ ( G 3 ) FN This method for extrapolating the dose from primary from the total dose is illustrated in figure 6.5. The SPR database measured here for the homogeneous cases is included in appendix C for reference. The anthropomorphic phantoms were deliberately designed so that there were no heterogeneities along the central beam axis. This permitted measurement of the SPRs through a homogeneous section along the central axis (see figure 6.2). This was the main difference between the anthropomorphic phantoms for the experimental validation and those for the Monte Carlo validation discussed in chapter 5. The SPRs were measured in two steps. First, the Lucite tank only contained water (no heterogeneities) and the normalized dose from primary P^ was derived as previously described for the homogeneous cases. Second, the heterogeneities were placed in the tank and the normalized total dose TN was measured at the central beam axis for a range of field areas. The SPRs were then calculated according to equation (6.3). Since the SPR measurements were far faster than the Monte Carlo simulation, the field areas could be varied and ranged from 4x4 cm 2 up to a maximum field area (determined by Chapter 6. Experimental Validation 122 ( D CO •§ I—2 5 E o £ c d) CO J2 CD CD .C 0.64 h 0.60 h £ 0.56 h ( D o ° « 5 0.52 h •4—* O 0 100 200 300 400 Field area (cm2) 500 600 Figure 6.5. Illustration of the extrapolation method for deriving the dose from primary photons. Total measured dose TN (o) and the quadratic fit (—). The dose from primary radiation is equal to the total dose for a field area of zero. The error bars were omitted as they were too small to be seen. the maximum field area used for that treatment site) in 2 cm increments. The maximum field area was equal to 14x14 cm 2, 16x16 cm 2, and 20x20 cm 2 for the neck, pelvis, and thorax cases, respectively. Two measurements for each data point were taken to minimize the effect of random errors. The random error in the experimental SPRs for all cases is given approximately by c5SPR = o-TN + o-pNy fo-pN TN-P> N N 1/2 SPR 2V2~ = 0.006 T (6.4) where {orTN,o~pN) are the experimental uncertainties for T^ and PN, respectively, while T and uT are the total dose and standard deviation of the total dose, respectively. The maximum relative standard deviation of repeated measurements of the total dose was oT/T=0.002. The error bars for the experimental SPRs for all cases were equal to c5SPR«0.006. Chapter 6. Experimental Validation 6.4 ANALYSIS M E T H O D 123 Differences between the analytical and experimental SPRs arise from both random and systematic errors. The random error in the experimental SPRs is given by equa-tion (6.4). Systematic errors in the analytical SPR arise from neglecting the scatter from multiply scattered particles (multiple Compton scatter, bremsstrahlung, annihila-tion, and patient-generated electrons) and from assuming the photon energy spectrum is invariant across the beam. The analysis of the agreement between the analytical and ex-perimental SPRs was the same as the analysis for the Monte Carlo validation in chapter 5. For the readers convenience, the equations are repeated here. Three quantities were computed when comparing the analyticalally calculated SPRs to the experimental SPRs: (i) the maximum difference between the two sets of SPRs, ASPRmax, (ii) the mean difference, N ^ S P R = ± E ( S P R F , " S P R f X P ) , (6.5) i V i=i and (iii) the root mean square of the differences, E i l i [(SPR^ - S P R f * p ) - ASPR" A S P R , = |^ F ' 1 N _ [ >- (6.6) where N was the number of SPRs compared and EXP stands for experimentally mea-sured. For the homogeneous phantoms, these three quantities (ASPRmax, ASPR, and A S P R a ) were computed for each beam energy. N was different for each beam energy since the number of phantom thicknesses for which the SPRs were measured differed for each energy (see section 6.1). For example, for the SPRs measured using the homoge-neous phantoms irradiated with the 18 M V beam, N was equal to 48 (2 SDDs x 6 field areasx4 phantom thicknesses). Chapter 6. Experimental Validation 124 For the anthropomorphic phantoms, ASPRmax, ASPR, and ASPR f f were calculated for each phantom, beam energy, and source to detector distance. In these cases, N was the number of field areas for which the measurements were made. Since the SPRs were measured for (square) field areas in 2 cm increments, N was equal to 6, 7, and 9 for the analysis of the neck, pelvis, and thorax data, respectively. The field areas for the anthropomorphic cases were based on the typical field areas used for these sites as discussed in section 6.1. 6.5 RESULTS AND DISCUSSION In this section, the agreement between the experimental and analytical SPRs is pre-sented and discussed. Calculation of the analytical SPRs requires the patient density data, which can be obtained from a C T scan. Since the density of the phantoms was known in this work, C T scans of the phantoms were unnecessary. The analytical SPRs were computed according to equations (4.8) and (4.17) in chapter 4. SPRs were measured experimentally on the central axis for homogeneous Solid Water phantoms from 10 to 40 cm thick, beam energies from 4 to 18 M V , and SDDs of 185 and 200 cm. Figure 6.6 illustrates the majority of these SPRs for an SDD of 185 cm. Those SPRs that were omitted from the graphs (for example, SPRs for the 40 cm thick phantom irradiated with the 10 M V beam) exhibited poor agreement with the analytical SPR method. This lack of agreement probably occurred because neglecting multiply scattered photons in the analytical SPR calculation is a poor approximation in these cases. Good agreement is seen in figure 6.6 between SPR$ and SPR £ ' A ' P for all four beam energies; this agreement is quantified in table 6.3 [(see also equations (6.5) and (6.6)]. For the larger field areas and for the thicker phantoms, the analytical SPRs agree reasonably Chapter 6. Experimental Validation 125 well with the experimental data and are within £20.02 of the experimental SPRs. The analytical method could be improved by including higher order scattering. The drawback of including higher order scatter, for example second order Compton scatter, however, would be the increased time needed for the ray-tracing calculation. The SPRs were measured for air gaps equal to 50 cm and larger for the following five anthropomorphic phantom and beam energy configurations: the neck phantom, for Figure 6.6. Comparison of the analytical (—) and experimental (•) SPRs for the ho-mogeneous Solid Water phantoms. An SDD of 185 cm. was used. Beam energies shown: (a) 4 MV, (b) 6 MV, (c) 10 MV, and (d) 18 MV. Chapter 6. Experimental Validation 126 Table 6.3. Agreement between the scatter to primary dose ratio measured experimentally (SPREXP) and calculated analyticalally (SPRp) for the homogeneous water phantoms. Maximum field size was 20x20 cm2 for all cases. SDDs for this data were 185 and 200 cm,. Beam Max. energy thickness (MV) (cm) N ASPR ± ASPR C T ASPRmax 4 20 24 -0 .004±0.006 0.020 6 30 36 -0 .004±0.006 0.019 10 30 36 0.000±0.003 0.009 18 40 48 0.000±0.004 0.011 4 and 6 M V beams; the thorax phantom, 6 M V beam; and the pelvis phantom, 10 and 18 M V beams. Figure 6.7 shows the experimental and analytical SPRs for three of the anthropomorphic phantoms using an SDD of 185 cm. The agreement between the analytical and experimental SPRs was calculated for each source to detector distance using equations (6.5) and (6.6). Figure 6.8 displays the mean difference between the analytical and experimental SPRs, equation (6.5), for the anthropomorphic cases as a function of the source to detector distance. The error bars are equal to the standard deviation of the mean difference, given by equation (6.6). In figure 6.8 the analytical method is seen to be a good approach for the neck phantom for all SDDs and both 4 and 6 M V beams. These results confirm the M C data that showed that the SPR from multiply scattered particles was small for thin phantoms and small field sizes. For the thorax phantom, the agreement improves with increasing SDD - this also agrees with the M C results that show that the SPR from multiply scattered particles decreases with increasing SDD. For the pelvis case, the agreement between S P R £ X P and SPR^ improved with increas-Chapter 6. Experimental Validation 127 0.05 0.03 0.00 g ro 0.10 i_ CD 0.08 CO o 0.06 ro E "i_ 0.04 Q. O 0.02 CD ro 0.00 o CO 0.10 0.08 0.06 0.04 0.02 0.00 I I (a) l l i i i - • Neck phantom \ Beam energy 4 MV * t Lateral field I I I I I L (b) L (c) i l l i 1 r CP J I L Lung phantom Beam energy 6 MV J Anterior field I I I T T T f J_ Pelvis phantom Beam energy 18 MV. Lateral field _ i I I 0 50 100 150 200 250 300 350 400 Beam area (cm 2 ) Figure 6.7. Graphs of the measured (o) and analytical (•) SPRs for the anthropomorphic phantoms versus beam, area at the isocentre. Results are shown for the (a) neck phantom,, (b) thorax case, and (c) pelvis phantom,. The source to detector distance was 185 cm,. ing beam energy; this trend with energy was opposite to that found for the Monte Carlo results from the pelvis phantom (see figure 6.8 and table 5.1). From the Monte Carlo results in table 5.1 it was found that at 18 MV, S P R M C and SPR$ differed by «0 .02-0 .03 for the pelvis case because of the multiply scattered particles. However, the mean differ-ence between S P R ^ ^ and SPR^; was ~0.01 or less for the pelvis case when using the Chapter 6. Experimental Validation 128 Pelvis, 18MV ^Neck, 4 M V Neck, 6 M V i Thorax, 6 M V I Pelvis, 10 M V -0.03 150 160 170 180 190 200 210 Source to detector distance (cm) 220 Figure 6.8. Mean difference between the analyticalally calculated and experimentally measured SPRs on the central beam axis versus the source to detector distance. Each curve corresponds to a specific site and energy (labeled at right). Error bars represent the standard deviation of the mean difference (field areas ranged from. 4><4 c m ' 2 to the maximum, field size for that site. The m.axim,um field sizes were: 14x 14 cm2, 20x 20 cm2, and 16x16 cm2 for the neck, thorax, and pelvis cases, respectively). Only one error bar per curve is shown for clarity. The average standard deviation, for each site was: neck 4 MV, 0.001; neck 6 MV, 0.003; thorax 0.009; pelvis 10 MV, 0.003; and pelvis 18 MV, 0.003. 18 M V beam (see figure 6.8). S P R M C was also greater than S P R E X P by ?a0.02-0.03 for the 30 cm thick homogeneous phantom irradiated with an 18 M V beam (see figure 6.9). Off-axis softening of the primary photon beam would explain these results. Off-axis softening is due to the shape of the flattening filter in the treatment head of the linear accelerator. The flattening filter, which is composed of tungsten and copper, is thickest at the central beam axis and tapers off with increasing off-axis distance. Low-energy photons are absorbed in the flattening filter. Thus, the primary spectrum has a greater component of low-energy photons below the thinner part of the filter, which explains the softer primary X-ray spectrum off-axis. Since the filter is tapered, the primary photon fluence changes with off-axis distance. In turn, the softening of the primary spectrum affects the mean energy of the scattered photons that reach the central axis at the portal imaging plane. Chapter 6. Experimental Validation 129 I* 0.06 B 0.03 o s o.oo o G O 0 100 200 300 400 Beam area at isocenter (cm ) 500 Figure 6.9. Graph illustrating the effect of off-axis softening on the SPRs for the 18 MV beam,. Comparison, of the experimental (•) and Monte Carlo (A) scatter to primary dose ratios for a 30 cm, thick water phantom,, an, 18 MV photon beam,, and an SDD of 189.2 cm. The goodness-of-fit of the normalized total doses TN to a quadratic was assessed by examining the %2 values of the fit: where FAi is the ith field area and K is the number of field areas for the fit. In this case, the number of degrees of freedom was u=3 {y=K-M where K=6 is the number of data points per curve and M=3 was the number of parameters in the fit). The x2 value for 3 degrees of freedom and a level of significance of a=0.1 is x2,9(3)=6.25. Since the observed values for %2 were less than Xo.9(3), the quadratic model seems quite reasonable for these data. Figure 6.8 shows that the experimental SPRs on the central axis were modeled by the analytical SPR method to within « 0 . 0 3 for phantoms representing the neck, thorax, and pelvis. The accuracy of the current method is comparable with that of similar techniques. The SPR model of Swindell and Evans [117] was shown to have a mean experimental difference of 0.005 or less for an SDD of 200 cm, water phantom thicknesses up to 30 cm, beam areas up to 400 cm 2, and beam energies of 6 and 10 M V (Partridge and Evans [95]). The analytical SPR model of Spies et al. [114] agreed within 0.02 to 0.03 with Monte observed TN(FAj) - fitted TN(FAj) (6.7) Chapter 6. Experimental Validation 130 Carlo results for off-axis SPRs using air gaps from 6.3 to 18.3 cm, a 6 M V radiosurgical field, and copper phantoms up to 3.5 cm thick. 6.6 SUMMARY In this chapter, measurements of the scatter to primary dose ratio on the central axis of radiotherapy beams at the position of the portal imager were used to validate the analytical SPR method. Measurements were carried out for a wide range of clinically relevant treatment configurations involving homogeneous Solid Water phantoms as well as phantoms representing the neck, thorax, and pelvis. Tissue substitutes that mimic the attenuation and scattering from bone, muscle, and lung were discussed and selected. Experimental uncertainties were included for the measured SPRs. It was found that the analytical SPR method predicted the experimental SPRs to within « 0 . 0 3 . The agreement between the experimentally measured and analyticalally calculated SPRs was found to be comparable to similar approaches. The mean differences between the analyticalally calculated SPRs and the Monte Carlo calculated SPRs were also less than ~0.03, even though the simulation made several approximations for the clinical linear accelerator photon source models. The analytical SPR method can be applied in several ways. The application of the analytical SPR method to calculate the total portal imager dose is presented in the next chapter. The total dose at the portal imager is the sum of the dose from primary and the dose from scatter. Assuming an accurate method is used for calculating the primary component, P, the total T(x, y) at a point (x, y) in the image is the sum of P(x, y) and the scatter dose at the central beam axis, S = P(central beam axis) x SPR. C H A P T E R 7 A P P L I C A T I O N - In vivo D O S I M E T R Y In vivo dosimetry is the measurement of the dose delivered to the patient during a treatment session. Detectors can be placed on the patient's skin at the beam entrance and exit surfaces to measure the dose at the central beam axis. As well, measurements can be carried out within body cavities. Doses are then extrapolated in regions where direct measurement is impossible, such as in the tumour or in critical organs. By comparing the measured dose with the calculated or expected dose, errors can be found and corrected. Errors in dose delivery can occur from systematic and random causes. In vivo dosimetry is most useful for identifying systematic errors [38]. Leunens et al. [58] showed that it was possible to detect large systematic errors with one in vivo measurement, where a large error was defined as greater than 5%. Noel et al. [86] found that 16.7% of head and neck patients received doses that devi-ated 5-10% from the planned doses. In the same study, 1.3% of breast cancer patients had dose inaccuracies larger than 10%, and 6.5% had inaccuracies between 5-10%. The dose inaccuracies determined from in vivo dosimetry can result in important changes within radiotherapy departments. In vivo dosimetry has uncovered systematic errors in treat-ment planning algorithms that were subsequently corrected (for example, [44, 56, 58]). As well, data showing a reduction in errors when two, rather than one, radiotherapist work at a unit has supported the practice of having two radiotherapists cross-check each other's work to decrease mistakes [60]. 131 Chapter 7. Application - In vivo Dosimetry 132 Differences between the measured and planned doses can occur due to incorrect mea-surement of patient data, weight loss or gain during treatment, errors in patient setup, organ motion [2], problems with beam production, and errors in data transfer. Even with record and verify systems,1 Noel et al. [86] advocate the mandatory use of in vivo dosimetry for dose delivery verification. Entrance doses are measured using sufficient material over the detector to establish electronic equilibrium at the measurement layer (see figure 7.1 for the definition of the entrance plane). P-type semiconductor diodes are a common choice for in vivo dosimetry since they allow immediate readout, exhibit good reproducibility, and can be calibrated against an ionization chamber to measure dose [64, 85, 100, 101]. Entrance doses can verify the patient setup and accelerator performance, but alone, are insufficient to esti-mate uncertainty in the dose delivery. Exit doses correspond to a depth equal to dmax upstream of the exit surface of the patient (see figure 7.1), and give additional dose accuracy information related to patient data such as tissue thickness and tissue het-erogeneities. The photon beam transmission through the patient, which is defined as the ratio of the exit and entrance doses corrected for the inverse square law, is useful for measuring inaccuracies in the patient contour and heterogeneities used in the dose calculation. The midline dose can be estimated by assuming a linear [86] or exponential decrease [59] between the exit dose and entrance dose. A common approach for calculating the midline dose from entrance (or entrance and exit) doses is the method of Rizzotti [34, 44, 102] or slight variants of this method [32, 45, 57]. In this technique, depth dose data are used to convert the measured dose(s) to the dose at the patient midline. Figure 7.2 shows an example of an in vivo measurement with a diode. When the central axis passes through 1 Record and verify systems are software programs that check that the parameters entered by the radiotherapists for controlling the linear accelerator are within tolerance of pre-recorded data. Chapter 7. Application - In vivo Dosimetry 133 Isocentre A TS ' i f J ^ tP\ t 4 J Entrance plane Midplane Exit plane Imaging plane Figure 7.1. Location of the entrance, mid, exit, and imaging planes. The midplane and the isocentre coincided for measurements described in this chapter. The entrance plane was at the depth of maximum, dose (dmax) within the phantom, while the exit plane was at a depth of (t — dmax) where t was the phantom, thickness. For this chapter, measurements at the imaging plane were carried out at dmax within the imager. Doses were measured with both the portal imager and an, ionization chamber at the imaging plane. Ionization chamber readings were also recorded at the midplane and exit planes. Doses were normalized to the dose at the isocentre. heterogeneities, an equivalent pathlength in water is used rather than the physical depth between, for example, the entrance and midline points. In cases where the entrance and exit doses are used, the method in Rizzotti [34, 44, 102] is limited to situations with symmetric tissue heterogeneities with respect to the patient midline. Since the patient anatomy and dose information are automatically co-registered in a portal image, these imagers are superior to conventional in vivo dosimeters such as diodes [33]. Previous studies that applied the convolution/superposition (CS) algorithm for in vivo dosimetry with portal images are computationally intensive [42, 75]. It would be of interest to pursue faster methods of in, vivo dosimetry using the CS algorithm since an advantage of this approach is that the same convolution kernels can be used for computing the dose from primary photons, and so new dose kernels are unnecessary. This is the objective of this chapter. The method presented here uses the CS algorithm [61, 62, 106] for dose calculation within the phantom and for the imager dose from primary photons. Chapter 7. Application - In vivo Dosimetry 134 Figure 7.2. The diagram illustrates measurement of the in vivo dose to the breast with diodes. Diodes are placed at the central axis to measure the entrance and exit dose. The diode is covered by a hemispherical build-up cap with a water-equivalent thickness equal to the depth of maximum, dose for this photon energy. (Figure adapted from a similar diagram, in [45]). The imager dose from scatter is approximated by a uniform distribution across the imager and the scatter to primary dose ratio (SPR) on the central axis is estimated analyticalally from Compton kinematics [90]. The phantom in vivo doses were calculated by back-projecting the measured portal dose using pre-computed corrections calculated using the CS algorithm and the analytical SPR method. Calculated portal dose images were compared quantitatively to measured data obtained with (i) a liquid matrix portal imager calibrated to record dose, and (ii) a Farmer-type ionization chamber (IC). Homogeneous and heterogeneous phantoms were investigated. An illustrative example of the data is included as well as a discussion of the approximations for the technique. Chapter 7. Application - In vivo Dosimetry 135 7.1 MATERIALS AND METHODS 7.1.1 A N I L L U S T R A T I V E E X A M P L E An example of the experimental data used for this study is given in figure 7.3. The image in figure 7.3(b) was measured with the liquid matrix portal imager. Conversion of the image pixel values to dose is described in section 7.1.5. The phantom configuration for this example was a neck case irradiated with a lateral field as shown in figure 7.3(a). The total dose profile at the imager along the posterior-anterior direction of the phantom is graphed in figure 7.3(c). The dose from scatter was calculated by multiplying the total dose on the central axis by SPR/(SPR+1), where the SPR is the scatter to primary dose ratio on the central axis, as discussed in section 7.1.2. The air gap between the phantom and the imager was equal to 75 cm. For large air gaps (defined as greater than 50 cm), the dose from scatter is uniform [12, 117]. In figure 7.3(c) the doses from scatter and primary are graphed. In this chapter a method is described to calculate the total imager dose (at any point on the imager) normalized to the isocentre dose, which is then compared to measured data. Throughout this chapter, the isocentre was chosen as the normalization point for the dose profiles. Consequently, the current work examines both the relative amplitude and the intensity of the calculated imager dose, DT(fd). The profiles at the imaging plane could have instead been normalized to the dose on the central axis at the imager. If the normalization point had been located at the imaging plane, as was the case in [71] and [76], then only the relative amplitudes of the calculated profiles would have been investigated. Chapter 7. Application - In vivo Dosimetry 136 (a) Left Lateral Posterior Anterior (b) urn inum r Aii-111 Under Al Unde • -10 -5 0 5 10 Off-axis distance (cm) Figure 7.3. Illustration of the im,ager dose from, primary photons and scatter radiation. (a) The neck phantom, irradiation configuration for this example. The central beam, axis (-- -) as well as the boundaries of the lateral field (—) are indicated for the left, lateral field. (b) The portal image of the neck phantom for a 6 MV 8x8 cm? field. An air gap of 75 cm was used, (c) Dose profiles for the total dose, as well as the dose from primary and scatter. The direction of the profile is indicated by the horizontal line in part, (b). Chapter 7. Application - In vivo Dosimetry 137 7.1.2 D O S E C A L C U L A T I O N M E T H O D S The code chosen for calculation of the dose within the phantom is a set of state-of-the-art subroutines based on the convolution/superposition algorithm [61, 62] (see also [67, 68, 106]). These routines are suitable for computing the dose within heterogeneous phantoms when the atomic number of the heterogeneity is close to the effective atomic number for water [49]. This particular set of routines was selected for our work over another set2 since the former includes a more advanced model of the photon energy spectrum that is based on Monte Carlo simulation of the linear accelerator treatment head [62]. Dose computation using convolution/superposition has four basic steps. For simplic-ity, the dose deposited in one voxel (at the dose deposition site, r) by photons interacting in another voxel (at the interaction site, r') is considered (figure 2.1 illustrates vec-tors f and r'). First, the photon fluence spectrum is determined at the interaction site (r'), through knowledge of the fluence at the isocentre without the phantom present, <3?[(r' = 0,0,100)], and the transmission and divergence of the primary photons between the photon source and r'. Second, the total energy released per unit mass [TERMA, T(r')\, by photons interacting at r' is determined from the probability of photon interac-tion (that is, the attenuation coefficient) and the energy of the incident primary photon. Third, the product of the average electron density between the interaction and dose de-position sites, Pe> a n a " the distance between the interaction and dose deposition voxels, (r — r') is computed. Finally, the dose deposited at f is determined from a look-up table for the dose to water (or dose kernel, A) at the same value of pe\f— r'\ and angle (r — r') as calculated between the voxels at r and r'. The total dose at f is calculated by repeating this process for each voxel within the irradiated volume of the phantom. 2 Available from http://www-madrad.radiology.wise.edu/penbeam/index.html Chapter 7. Application - In vivo Dosimetry 138 Mathematically, the total dose D(r) [MeV g _ 1] can be expressed as £ c s ( r * ) = £ E E T(r')A[pe-\f-r'\,(f-r')} (7.1) z'=zs y'=yb x'=xi where the T E R M A T [MeV g _ 1] is given by Emax ..( rr.\ T(f}= E — Ek) (7.2) Ei=Emin P and A is the dose deposition kernel, which is discussed below. In equation (7.1) the three-dimensional summation is carried out for all interaction voxels r' = (x1, y', z') within the photon field. In equation (7.1), the term f — r' is the angle between f and r' while the term |r — r'| is the distance between the two vectors. Photon attenuation within the phantom causes the kernel to be variant with depth in the phantom. Calculating kernels at different depths within a water phantom, and then interpolating between the kernels can correct this. This technique is termed kernel hard-ening and TERMA-weighted [106] kernels at depths d=0, 20, and 40 cm were calculated for our work: A[(r = 0,0, d)} = ^E*-E™ t> l> 1 1 ; ' l i . (7.3) As well, the axis of the kernel was rotated to align the axis along vector r' (that is, along the ray joining the photon source and the interaction voxel) [61]. The kernels were originally calculated with a vertical axis. Since the photon source is a diverging source (rather than a parallel beam), the kernels are rotated so that they are aligned along r'. The remaining quantities in equations (7.1) and (7.2) are defined, as: zs, zm are the top and bottom surface of the phantom, respectively yb,y/ are the back and front limits of the radiation field, respectively, and depend on depth Chapter 7. Application - In vivo Dosimetry 139 the left and right limits of the field; also depth dependent p is the physical density [g cm - 3 ] pe is the average electron density between the interaction and dose depo-sition sites, relative to water E is the energy of the primary photon [MeV] Emin, Emax are the lower and upper energy limits for the photon spectrum [MeV] p(E) is the linear attenuation coefficient for photons of energy E, [cm - 1] $ is the photon fluence, [photons cm - 2 ] . In the calculation, the photon fluence was normalized to 1 at the isocentre: Emax £ $[(0,0,100),^] = 1. (7.4) Ei=Ernin E X T R A C T E D D O S E , DEX{fv) The extracted dose DEX at the point fv (see figure 4.1) within the phantom was given by: DEXFV) = DPI(fd)^^ (7.5) where Dpi was the dose measured by the portal imager at point fd, Des the phantom dose computed with CS using equation (7.1), and DT the total calculated dose at the portal imager [given by equation (7.6) below]. Vectors fd and fv were both co-linear with the same source to detector ray. Extracting the phantom dose in this manner is analogous to the method of Rizzotti [102], where the phantom dose is determined using (i) a measured dose at an external point outside the phantom, and (ii) the ratio of the dose at the internal point to the dose at the external point, which was predetermined. Chapter 7. Application - In vivo Dosimetry 140 I M A G E R D O S E , DT(fd) The total imager dose DT [MeV g - 1] at the point fd on the imager was calculated in two steps. First, the dose from primary Pcifd) was computed with the convolution algorithm using Monte Carlo calculated dose deposition kernels [61, 62, 106]. Second, the scatter to primary dose ratio on the central beam axis SPR[fd = (0, 0, SDD)] was computed with the analytical method described in [90] (the SDD is the source to detector distance). The total dose was then equal to DT{fd) = Pcifd) + Pc[rd = (0,0, SDD)] SPR[f_ = (0,0, SDD)]. (7.6) The dose from primary was given by [MeV g - 1 ]: zd,m Vf Xr Pcifd) = E E E ^ = (*', y', z')\ A[pe • \fd - r'\, (fd - r')} (7.7) z'=Zd,s y'=Vb x'=xt where zdtS, zdm are the top and bottom surface of the detector, respectively. For the cases investigated in this chapter, the mean and maximum difference between measured and analyticalally calculated SPRs were generally less than 0.01 and 0.03, respectively. P H A N T O M T R A N S M I S S I O N , TM(fd) A N D Tc(fd) The phantom transmission as measured at the imager, T^ifd)-, was computed from: „ J?p f |ph_11tom(^)/[1 + SPR(0,0>SDD)] J-M(rd) = r-rt (7.8) ^PI,no phantom' ^ where DPI phantom 1 S ^ e i m a S e r dose with the phantom and DPI n o phantom t u e i m a S e r dose without the phantom. The term in the denominator, D P I N Q phantom' w a s P r e s e n t to remove the effect of the change in the machine output factor with field area. The numerator was divided by the SPR to remove the scatter dose: T is then the transmission Chapter 7. Application - In vivo Dosimetry 141 of the primary beam through the phantom. The corresponding equation for the calculated phantom transmission Tc was m / - \ jPc,phantom(r^) , . T c ( d> = P 7 (iVi ( 7 - 9 ) c,no phantom V d> where Pc is the dose from primary calculated with equation (7.7). 7.1.3 A C C U R A C Y O F T H E P H O T O N S O U R C E M O D E L Liu et al. [62] analyzed the photon fluence at the isocentre as coming from two sources: (i) a primary source, for photons created through bremsstrahlung in the target, and (ii) an extra-focal source for photons that interact within the primary collimator and flattening filter. The primary source was modeled by a point distribution, while a Gaussian distribution modeled the extra-focal source. The effect of the electron target, primary collimator, flattening filter, monitor ionization chamber, and collimator jaws were included in the Monte Carlo simulation. The photon sources were radially symmet-ric, which is appropriate since the target, primary collimator, and flattening filter have cylindrical symmetry. The target, primary collimator, and flattening filter for our 2100C/D linear accelerator are the same as that used by Liu et al. [62]. The only difference between our linear accelerator and that modeled by Lui is the energy of the electrons that impinge on the target [119]. The percent depth doses and profiles are directly affected by the energy of the electron beam. It was important to determine the accuracy of these photon source models for our linear accelerators. If the doses we calculated using Liu's photon source models agreed well with our measurements, then the modeling of our linear accelerator treatment head with Monte Carlo simulation to generate the photon source model for the C S codes would be unnecessary. The accuracy of the doses calculated from Liu's models was determined from the Chapter 7. Application - In vivo Dosimetry 142 mean ratio R and standard deviation of the mean ratio Ra between the calculated Dcai and measured Dexv doses: R and Ra were calculated separately for each profile and depth dose; N was the number of data points for the depth dose curve or profile respectively. Our data was measured with an ionization chamber (IC10, Wellhofer, Schwarzen-bruck, Germany) in a 40x40x40 cm 3 water tank and compared to calculated data in a phantom of the same size. Percent depth doses were compared for field sizes from 3x3 to 20x20 cm 2 , while profiles were compared for radiation fields in the range 3x3 and 20x20 cm 2 . Representative results are graphed in figure 7.4. Depth doses were normal-ized at 10 cm depth [111]. Profiles were normalized on the central beam axis. For depths up to 25 cm, # ± . R C T = 1 . 0 1 ± 0 . 0 1 or better for the depth doses and 7 !± i? C T =0 .991 ± 0 . 0 0 4 at worst for the profiles. The good agreement between the two data sets is fortunate so that modeling of our 2100C/D clinical linear accelerator with Monte Carlo was unnecessary. The small deviation of #=1.01 from 1 for the depth doses most likely indicates that the electron energy in our case is slightly lower than the energy Liu et al. [62] used. 7.1.4 T E S T P H A N T O M S Figure 7.5 shows the phantoms designed to illustrate the methods described to cal-culate the total imager dose D^rd) and to extract the phantom dose Dpx(rv) using the measured portal image Dpi. Blocks of water equivalent plastic (Solid Water, Gammex RMI, Middleton, WI) were stacked to form the homogeneous phantoms. Figure 7.5(b) depicts the cork slab phantom, constructed from water equivalent blocks and a 12 cm (7.10) (7.11) Chapter 7. Application - In vivo Dosimetry 143 thick slab of low density cork (physical density relative to water equal to 0 .16±0.01; electron density relative to water equal to 0 .15±0.01) . A slab phantom containing a high density heterogeneity (aluminum, physical density relative to water 2.70 and electron density relative to water 2.35) was also tested [see figure 7.5(c)]. All phantoms were imaged with the centre of the phantom at the isocentre. 7.1.5 I M A G E R D O S E C A L I B R A T I O N Conversion of the gray-scale pixel values to dose was achieved using the methods described in [13, 30, 31, 39, 123, 132, 134] that were previously discussed in chapter 3. Briefly, a calibration curve to convert the pixel gray-scale values to dose at the central axis was measured for each field size and beam energy. This calibration curve is nonlinear [square root plus linear term, see equation (3.6)] for the liquid matrix portal imager and an example is given in figure 7.6. The dose at the imaging plane was varied by attenuating the photon beam with blocks of Solid Water in 1 cm increments. Average pixel values were calculated over a 5x5 pixel region of interest. The IC (ionization chamber) measurements for the pixel value to dose calibration curves were measured in a Solid Water phantom of the same water equivalent dimensions as the imager. To reduce the statistical noise in the IC data, three measurements were taken for each point. To reduce the statistical noise in the imager profiles, dose profiles were averaged over 5 pixels in the direction perpendicular to the profile. Imager dose profiles were corrected for the flat field calibration applied by the commercial image display software [31, 132, 134] (see figure 7.7). All measurements were carried out with the imager beneath the photon source using a source to detector distance of 185 cm. Chapter 7. Application - In vivo Dosimetry 144 I I i i i I i i I i I I i i i I I t i i I i i i i 1 0 5 10 15 20 25 Depth (cm) -6 -4 -2 0 2 4 6 Off-axis distance (cm) Figure 7.4. Comparison of the convolution calculation (•) and measured data (+) for a 10x10 cm? radiation beam,. From, the top: (a) percentage depth dose, 6 MV beam,; (b) depth dose, 10 MV and (c) profile at a depth of 10.5 cm, for a 10 MV beam,. Chapter 7. Application - In vivo Dosimetry 145 (a) t = 5,15, 25 A = 3, 10, 17 (b) (c) II 18 2.5 18 • Cork A = 5, 10, 17 I Aluminum A = 5, 10, 17 Figure 7.5. Schematic diagram, of the phantoms used for the experimental measure-ments. Sizes are in cm. (a) A homogeneous water equivalent, phantom,: the range of phantom, thicknesses t and beam areas A are indicated, (b) A cork slab phantom,, and (c) the aluminum, slab phantom,. 2500 0 50 100 150 200 250 300 350 400 Dose rate (cGy/min) Figure 7.6. An example of a calibration curve for the liquid matrix electronic portal imager. The error bars are too small to be seen for both, the pixel value and dose rate. Raw data (•), fitted curve (—). The equation for the fitted curve was W(D) = aVJj + bD where W was the pixel value, D the dose rate measured with the ionization chamber, and (a,b) the calibration constants. For this curve a=100.9±0.3 min1/2 cGy~x'2 and b=0.61±0.02 min, cGy~x. Chapter 7. Application - ln vivo Dosimetry '. 146 2 4 6 8 10 12 14 16 Off-axis distance (cm) Figure 7.7. Correction for the flat field calibration applied by the commercial im,age display software, (a) Comparison of the dose profile measured with the imager (—) to ionization chamber measurements (+) for a 10x10 cm?, 6 MV beam. The pixel value to dose conversion curve (see for example figure 7.6) was applied to calculate the dose profile. Off-axis doses measured by the imager (—) underestimate the ionization chamber measurements (+). This problem, occurs because the commercial software assumes that the flat field is uniform across the imager, (b) Off-axis correction to rectify the prob-lem, caused by the commercial software. Data shown for 10 MV (—) and 6 MV ( ) photon beam,s. This correction, is equal to the ratio of the ionization, chamber measure-ment to the uncorrected imager dose profile for a large field that completely irradiates the field, (c) Corrected imager dose profile (—) compared to the ionization chamber measure-ments (+). By multiplying the imager dose profile in part (a) by the off-axis correction in part, (b), the problem, caused by the commercial software is rectified. Chapter 7. Application - In vivo Dosimetry 147 7 . 1 . 6 I O N I Z A T I O N C H A M B E R M E A S U R E M E N T S Ionization chamber measurements were performed to determine the accuracy of: (i) the calibration of the imager for dosimetry, (see section 7.1.5), (ii) the total imager dose Dxifd) calculated using equation (7.6), (iii) the extracted dose DEX{?V) computed with equation (7.5), and (iv) the phantom transmission [Tc{fd), see equation (7.9)]. Mea-surements with a Farmer-type IC (PTW, New York) were taken at 1 cm increments along dose profiles at the depth of the midplane and exit plane within the phantom and at the imaging plane (see figure 7.1). The midplane of the phantom was located at the isocentre. The exit plane was located at a depth of (t — dmax) where t is the phantom thickness and dmax the depth of maximum dose. To reduce the statistical noise in the IC data, each point was the average of two measurements. 7 . 1 . 7 A N A L Y S I S Measurements taken with the Farmer IC were compared quantitatively to the follow-ing data sets: (i) portal dose profiles measured with the liquid matrix portal imager, Dpjifd); (ii) the total imager dose Dj-ifd) calculated using equation (7.6) , and (iii) the extracted exit and midplane doses DEX{^V) computed with equation (7.5). Each com-parison was carried out for the three test phantoms (see section 7.1.4). Measured imager dose profiles Dpiifd) were normalized to the isocentre dose measured by the ionization chamber. Extracted dose profiles Dpxifv) were also normalized to the isocentre dose measured by the ionization chamber. The phantom doses calculated with C S , Dcsi^v), and the computed total imager dose Dxifd) were normalized to the isocentre dose com-puted by C S . Doses measured by the ionization chamber were normalized to the IC isocentre dose. The accuracy was determined by calculating the mean and standard deviation of the Chapter 7. Application - In vivo Dosimetry 148 ratio between the comparison data set and the IC data (both data sets were normalized). For example, the calculated imager dose profile £>r(Fd) could be the comparison data set. The ratio of the normalized dose for the comparison data set and the normalized IC data for each point along the profile was equal to: Dose(comparison data) . . R = B ^ i c ) • ( 7 ' 1 2 ) The mean ratio and standard deviation of the mean ratio were given by: R = ^ P (7.13) and W 5 6 ^ <-) respectively where N was equal to the number of IC measurements compared. All the data collected for one particular phantom and beam energy was analyzed as a single group. For example, all data measured for the homogeneous water equivalent phantoms irradiated with the 6 M V beam were analyzed together. In this case, N was equal to the sum of the number of IC data points measured for the 3x3 cm 2 , 10x10 cm 2 , and 17x17 cm 2 fields. Relative errors, expressed as percents, were equal to: 75 relative error = x 100%. (7.15) R 7 . 2 RESULTS In this chapter, a method was presented to extract the dose within the phantom DEx{rv) using a portal imager as a dosimeter. An example illustrating the total imager dose as well as the dose from primary and scatter at the imager was included (see fig-ure 7.3). The method to extract the dose DEX{TV) uses a pair of measured Dpi(rd) and calculated Dxifa) portal dose images. To test this idea, a liquid matrix portal imager Chapter 7. Application - In vivo Dosimetry 149 was calibrated for dosimetry and dose profiles Dpi(fd) were measured with this imager at a source to detector distance of 185 cm. Data were collected for three types of phan-toms (homogeneous Solid Water, cork and aluminum slab phantoms). The agreement was determined between calculated portal doses D^rd) and portal doses measured with (i) the imager Dpiifd) and (ii) an IC. Data were normalized to the isocentre dose in all cases. Further comparisons were made between the extracted doses DEX(^V) for the three phantoms and IC measurements. Typical results for this study are given in figures 7.8, 7.9, 7.10, and 7.11. These figures show the computed dose at the imaging plane Dri^d) calculated using equation (7.6), the extracted midplane dose Dpxifv) computed from equation (7.5), and the computed phantom transmission Tc(rd) given by equation (7.9). Table 7.1 presents the results from the quantitative analysis to determine the accuracy of the calculated and extracted doses (see subsection 7.1.7). Table 7.1. Number of measurements (N), mean ratio (R), and standard deviation of the mean ratio (Ra) between the Farmer ion chamber measurements and: (i) the total dose calculated at the imaging plane D^rd), (ii) the portal imager measurements Dpi(fd), (Hi) and the extracted dose DEX(fv) at the exit and midplane of the phantom,. Measurements were made using water equivalent plastic blocks (Solid Water, Gammex RMI, Middleton, WI) (SW) and two slab phantoms. Beam Calculation or Measurement Method Energy DT DPI _ DEx exit DEx midplane (MV) Phantom N R i i?<j R i Ro- R i Re R i Ra 6 SW 141 1.02±0.01 1.00±0.01 0 .99±0.02 0 .98±0.02 10 SW 141 1.00±0.02 1.00±0.02 1.00±0.03 1.00±0.03 6 Cork Slab 51 0 .99±0.01 1.00±0.01 1.02±0.01 1.01±0.01 10 Al Slab 51 0.99±0.01 1.01±0.01 1.03±0.01 1.02±0.01 Chapter 7. Application - In vivo Dosimetry 150 -10 -5 0 5 10 Off-axis distance (cm) 10 -5 0 5 10 Off-axis distance (cm) Figure 7.8. Comparison of the extracted and measured doses for a 25 cm thick solid water phantom, [see figure 7.5(a)] irradiated with a 6 MV, 10x10 cm2 photon beam. Description of symbols for all graphs: ionization chamber measurements (+); extracted dose (TJ) using portal im,ager measurements, analytical SPR approximation, and convolution/superposition calculation; portal imager measurements (—); and con-volution/superposition computations (•). Doses were normalized to the isocentre dose, and the location, of the isocentre is indicated in part (a). From, the top left: comparison of normalized doses at the (a) midplane, (b) imaging plane, and (c) exit, plane. For (d), the measured and calculated transmissions are graphed at the imaging plane. Chapter 7. Application - In vivo Dosimetry 151 I I i r • (a) Midplane J I i + • -10 -5 0 5 10 Off-axis distance (cm) 2 c 0.8 CD O O CO o 0.6 T3 CD N "I 0.4 o C ¥o .2 o Q 1 1 1 l I - t t -(c) Exit plane i i i i i + (d) Transmission j i i_ -10 -5 0 5 10 Off-axis distance (cm) Figure 7.9. Comparison of the extracted and measured doses for a 25 cm, thick solid water phantom, [see figure 7.5(a)] irradiated with, a 10 MV, 10x10 cm? photon beam. Description of symbols for all graphs: ionization chamber measurements (+); extracted dose (TJ) using portal imager measurements, analytical SPR approximation, and convolution/superposition calculation; portal im,ager measurements (—); and con-volution/superposition computations (•). Doses were normalized to the isocentre dose at midplane. From, the top left: comparison, of normalized doses at the (a) midplane, (b) imaging plane, and (c) exit, plane. For (d), the measured and calculated transmis-sions are graphed at the imaging plane. Chapter 7. Application - In vivo Dosimetry 152 a • + + T T £a) Midplane | I i CD 1 0.8 o o CO -I 2 0.6 T3 CD N | 0.4 i_ o ¥o .2 o Q }»frl»UW»M*t"*l*l*f»'Uli ^(c) Imaging plane H-0 + + + (c) Exit plane + -10 0 10 Figure 7.10. Comparison of the extracted and measured doses for the cork slab phantom [see figure 7.5(b)] irradiated with a 6 MV, 10x10 cm? photon beam.. Description of sym-bols for all graphs: ionization chamber measurements (+); extracted dose (O) using por-tal imager measurements, analytical SPR approximation, and convolution/superposition calculation; portal imager measurements (—); and convolution/superposition computa-tions (•). Doses were normalized to the isocentre dose at midplane. From, the top left: comparison of normalized doses at the (a) midplane, (b) imaging plane, and (c) exit plane. Chapter 7. Application - In vivo Dosimetry 153 0.2 h » 0.2 h u|«l»l»i»l«|»|»i»i»|«|» ,(b) Imaging plane 1 i i -10 0 10 Figure 7.11. Comparison of the extracted and measured doses for the aluminum, slab phantom, [see figure 7.5(c)] irradiated with a 10 MV, 10x10 cm2 photon beam,. Description of symbols for all graphs: ionization, chamber measurements (+); ex-tracted dose (TJ) using portal imager measurements, analytical SPR approximation, and convolution/superposition calculation; portal imager measurements (—); and convolu-tion/superposition, computations (•). Doses were normalized to the isocentre dose. From, the top left: comparison of normalized doses at the (a) midplane, (b) imaging plane, and (c) exit plane. Chapter 7. Application - In vivo Dosimetry 154 7 . 3 DISCUSSION Throughout this chapter, quantitative comparison was made to IC measurements to investigate the accuracy of each part of the study. This analysis was carried out at 1 cm increments along a single beam profile. Doses were normalized first to the isocentre dose to have a common reference point before the accuracy was calculated as described in section 7.1.7. The total imager dose Drifd) given by equation (7.6) agreed with the IC measure-ments to within ^3% (see fourth column of Table 7.1). Several reasons may be given for differences between the calculated imager dose Drifd) and the IC measurements. The energy of the electron beam before it hits the target is likely different for our linear ac-celerator and for that used in the Monte Carlo simulation by Liu et al. [62] to derive the photon source models. Discrepancies also arise because of the limits of the kernel tilting and beam hardening algorithms within the convolution code. To assess the impact of the electron energy differences and the limits of the beam hardening and kernel tilting algo-rithms, CS calculated Dcsifv) and measured doses were compared for a water phantom: these doses were found to agree within « l - 2 % (see section 7.1.2). Differences between the calculated and measured imager doses [DT(fd) and DPI(fd) respectively] were also caused by each approximation within the analytical SPR method. For the cases studied here, the mean and maximum differences between measured and analyticalally calculated SPRs on the central axis were better than 0.01 and 0.02, respectively [90]. The system-atic errors contributed by the differing electron energies, the limits of the kernel tilting and beam hardening algorithms, and the analytical SPR method fully explain the small disagreement between the calculated imager dose and that measured with the IC. Total portal dose images measured with the liquid matrix portal imager Dpj(fd) agreed with IC measurements to within « l - 2 % . This finding was consistent with previous Chapter 7. Application - In vivo Dosimetry 155 studies [30, 31, 132, 134]. The method for calculating the extracted dose DEX(?V) was presented in section 7.1.2. These doses were computed from the measured portal image, the CS algorithm, and the SPR method. Extracted doses DEx(fv) agreed with those measured using the IC to within « 3 % . The reasons for systematic errors in the extracted doses include the different electron beam energies for the photon source model and the linear accelerator, each approximation in the SPR and convolution/superposition algorithms, and the imager dose calibration. Since the liquid matrix portal imager only measured dose rate images, rather than integrated dose for the entire time the beam was on (100 monitor units), the current work was limited to investigating the extracted dose rates within the phantom. The advantage of the current method to calculate portal dose images compared to semi-empirical approaches is that the dose images, normalized to the isocentre, were calculated without a database of measured scatter dose data. This reduces the time to implement the algorithm and may be potentially beneficial to other institutions who wish to calculate portal dose images. The relative error of the current approach for in vivo dosimetry («3%) is comparable to the relative error for in vivo measurements with thermoluminescent dosimeters (~3%). The accuracy of the extracted doses, DEX^V), as compared to IC measurements was within « 3 % . This accuracy is comparable to similar techniques. McNutt et al. [73, 74, 75, 76] and Hansen et al. [42] also applied the CS algorithm for in vivo dosimetry. McNutt et al. [73, 75] compared planned doses to in vivo doses and found a mean difference of « l - 2 % with a standard deviation of « 1 % (dose differences were expressed as a percentage of the isocentre dose). Hansen et al. [42] compared measurements to in vivo doses and found a maximum difference of 3% (differences were also expressed as a percentage of the isocentre dose). The advantage of the current method for computing the extracted doses DEX^V), Chapter 7. Application - In vivo Dosimetry 156 compared to previous approaches for in vivo dosimetry that apply the CS algorithm, is that the current technique is faster. An approximate estimate of the order O of our algorithm, and several previous methods, is presented here to illustrate this point. The number of computations for the current in vivo method was proportional to where Np is the number of fields for the treatment and ND the number of points within the phantom at which the in vivo dose is to be calculated. Methods that convolve the primary photon energy fluence with the dose deposition kernels (for example, Hansen et al. [42] or McNutt et al. [75]) are (very roughly) proportional to where Ny is the number of voxels within the irradiated part of the phantom. The additional factor Nv in equation (7.17) compared to equation (7.16) occurs because of the convolution. The value of Ny for a typical treatment (20 cm thick patient, 10x 10 cm 2 field area, 0.5x0.5x0.5 cm 3 voxel volume) would be AV=16000. 7.4 SUMMARY This chapter described a method to calculate portal dose images without the use of a database of measured scatter dose data. With the current increases in treatment complexity, such as intensity modulated radiation therapy, the ability to independently verify the dose delivery across the whole radiation field would be advantageous. The cur-rent technique for in vivo dosimetry uses generic Monte Carlo calculated photon spectra and dose deposition kernels, as well as an analytical method to estimate the central axis scatter to primary dose ratio. Portal dose images were calculated and normalized to the O oc NFND (7.16) O oc NFNDNV (7.17) Chapter 7. Application - In vivo Dosimetry 157 phantom isocentre dose computed with the convolution/superposition algorithm. Exam-ples were presented of the use of this method to extract the phantom dose and to calculate the phantom transmission. The method was tested by comparing calculated profiles to data measured with an ionization chamber as well as with a calibrated commercial por-tal imager. Measurements were carried out for two beam energies (6 and 10 MV) , three phantoms (homogeneous water equivalent, cork slab, and aluminum slab), and three field sizes for each phantom. Calculated portal dose profiles agreed with ionization chamber measurements to within ~3%. The reasons for differences between the calculated profiles and those measured with the ionization chamber were discussed. Extracted doses at the midplane and exit plane agreed with ionization chamber measurements to within « 3 % . The current method for extracting the in vivo dose is faster than previous methods that also applied the convolution/superposition algorithm. In summary, the method presented here to calculate portal dose images is an attractive alternative for in vivo dosimetry. C H A P T E R 8 C O N C L U S I O N S In this thesis, an analytical method was validated for estimating the portal scatter to primary dose ratio on the central axis for heterogeneous phantoms. The first section of this chapter summarizes the accomplishments reported in this thesis. Future areas that could be explored to continue the development of the work here are discussed next. Finally, a summary is given of the major conclusions drawn from this research. 8 . 1 SUMMARY OF W O R K Chapter 2 presented a literature review of current methods for calculating the portal imager dose from scatter radiation. This review revealed that the uniform scatter dose approximation was a powerful simplification for dosimetry with portal imagers. Portal imagers have been applied for the design of customized breast compensators at the Royal Marsden Hospital (RMH) [36, 95, 117] and in vivo dosimetry at the Netherlands Cancer Institute [11, 12, 30, 31] and at the R M H [36]. At the R M H , the central axis scatter to primary dose ratio at the imaging plane was calculated using a simple model based on the probability of first and second order Compton scatter [117]. At the Netherlands Cancer Institute, the ratio of the total to primary dose at the imaging plane was estimated using a look-up table of this ratio measured for homogeneous water equivalent phantoms [14]. Both the SPR model and the look-up table approach were limited to large air gaps (defined in [12] as greater than 50 cm). The SPR model was also limited to homogeneous or nearly homogeneous scattering objects [43]. 158 Chapter 8. Conclusions 159 Chapter 2 also discussed a problem with semi-empirical scatter estimation techniques, such as the method based on empirical slab derived scatter kernels [97]. Scatter estima-tion methods that use measured data have the drawback of requiring, in some cases, substantial time for measurement of the data for the scatter dose calculation algorithm. Chapter 3 presented a review of the literature for calibration of the liquid matrix portal imager for dosimetry. This calibration converts the pixel gray-scale image to a dose image. The dose in this case is the dose as measured by an ionization chamber within a rectangular block of Solid Water. The Solid Water is placed at the same source to detector distance as the portal imager. Buildup material is added to both the portal imager and the ionization chamber for this calibration procedure. In chapter 4 an analytical method for estimating the central axis SPR at the imaging plane for heterogeneous scattering objects was presented. The analytical expression for the SPR from first-order Compton scatter, which was given the symbol S P R £ , was dis-cussed and several examples of the use of this expression were given. This technique uses generic data for the photon source models. SPR$ was limited to large air gaps, approxi-mates the portal scatter dose by a uniform distribution, and neglects multiply scattered particles. One of the advantages of this method is that it could be used elsewhere without measuring a database of scatter doses. A Monte Carlo validation of the analytical method for SPR^ was described in chap-ter 5. For this validation, the EGS4 code DOSXYZ was modified to calculate the contri-bution to the SPR from each scatter mode. The resulting code, SDOSXYZ, computes the SPR from first-order Compton scatter, multiple photon scatter, and patient-generated electrons, as well as the uncertainties for each scatter mode. Comparison of the doses calculated with SDOSXYZ to published data was presented. A total of 576 SPRs were calculated for homogeneous water phantoms: these SPRs were computed for a point photon source and the SPRs are included in appendix B. The total SPRs are new since Chapter 8. Conclusions 160 they included the contribution from patient-generated electrons. A statistical analysis of the agreement between SPR$ and the Monte Carlo calculated SPRs for three anthropo-morphic phantoms (representing the neck, thorax, and pelvis) found that the accuracy of the analytical SPR method was comparable to similar analyticalal approaches that are limited to homogeneous phantoms. Chapter 6 discussed an experimental validation of SPR$. SPRs were measured using an ionization chamber for Varian linear accelerators with beam energies from 4 to 18 M V . The experimental uncertainty in the SPRs was estimated and the data for homogeneous water-equivalent phantoms was included in appendix C: this data is new. SPRs were also measured for heterogeneous phantoms representing the neck, thorax, and pelvis. In chapter 6, SPR^ was computed on the central beam axis using generic isotropic point photon source models for these linear accelerators. A quantitative comparison of SPR$ and measured SPRs for the three anthropomorphic phantoms showed that the accuracy of the analytical SPR method was comparable to similar techniques. Finally, chapter 7 illustrated how SPR^. can be applied for calculation of portal dose images and extraction of the dose within the phantom using a measured portal image. The method described in chapter 7 for calculation of the portal dose image used only published data for the photon source model. Thus, an advantage of this approach is that implementation of the method elsewhere could be possible without using a database of measured scatter dose data. Calculated portal dose images were compared to measure-ments taken with a calibrated commercial portal imager as well as with an ionization chamber. Extracted doses within the phantom were compared to doses measured using an ionization chamber. Measured and extracted doses agreed to within ~3% (one stan-dard deviation). The method described here to extract the phantom dose is faster than previous methods for in vivo dosimetry that also apply the convolution/superposition algorithm. Chapter 8. Conclusions 8 . 2 F U T U R E RESEARCH 161 The experimental validation in this thesis was limited to Varian linear accelerators. The database of experimental SPRs could be expanded to include measured SPRs for: (i) source to detector distances less than 185 cm for the homogeneous phantoms, and (ii) linear accelerators manufactured by Elekta (Crawley, UK) and Siemens (Concord, CA). SPRs for different brands of accelerators could be inter-compared. A statistical analysis of the agreement between the analytical SPR method and the experimental SPRs could also be carried out when the air gap is equal to 50 cm or larger (for SPRs other than those reported in appendix C). The application of the analytical SPR method was restricted to the Varian liquid matrix portal imager. Other imagers can also be calibrated to convert the pixel values to dose. Portal dose images could be measured using an amorphous silicon flat-panel array [4, 5, 6, 29, 82] and then compared to calculated images. Clinical application of the portal dose image calculation and dose extraction meth-ods could be achieved by modifying commercial software written to apply the convo-lution/superposition algorithm for dose calculation within the patient. Specifically, the code could be modified to calculate the dose from primary photons [see equation (7.7)] and the analytical SPR method [see equation (4.18)]. Suitable commercial software in-cludes the codes marketed by MDS Nordion (Kanata, Canada; code marketed under the name Helax) and Philips (Amsterdam, Netherlands). An interface could also be written to allow C T data to be used with the current codes. The methods described in this thesis could then be applied for quality assurance of patient treatments in several ways. A pair of calculated and measured portal dose images can be compared. As well, the extracted and intended patient doses can be analyzed statistically. Newer treatment modalities, called intensity modulated radiation therapy or IMRT, Chapter 8. Conclusions 162 control the field area and dose rate dynamically during the treatment. Rapid and accurate evaluation of the two-dimensional dose data from IMRT fields is a current challenge in radiotherapy. Due to the complexity of the resulting dose delivery, it is of interest to be able to calculate IMRT portal dose images and extract the patient dose using a portal image for quality assurance during IMRT. Application of the analytical SPR method for quality assurance of IMRT would likely be the most significant potential application for future research. 8.3 SUMMARY The goal of this thesis, which was successfully achieved, was to extract the phan-tom dose using a measured portal image. New Monte Carlo calculated SPRs and new measured SPRs were reported, as well as the uncertainties on these quantities. An an-alytical method for calculating the SPR on the central axis for heterogeneous cases was quantitatively validated for a wide range of clinically relevant phantoms. The method for calculating the portal dose images presented here relies only on previously calculated photon source models and dose kernels, and not on measured scatter dose databases as in some semi-empirical portal dose calculation algorithms. In the future, this approach could be applied for in vivo dosimetry for verification of the radiation dose to patients. This chapter presented several avenues for future research in this direction. A P P E N D I X A S D O S X Y Z Following are the important modifications of the subroutines within DOSXYZ. The programming language is M O R T R A N . Some parts of the original D O S X Y Z code are included so that the code makes sense. Within the A U S G A B subroutine: "Turn on flags for keeping track of particle interactions" iausfl(8)=l; "Bremsstrahlung" iausfl(14)=l; iausf1(15)=1; "Annihilation" iausfl(19)=l; "Compton" iausfl(21)=l; "Photoelectric" iausf1(17)=1; "Pair production" IF ( ( (ir(np) > 1) & (edep~=0.0) ) & (iarg < 5) ) [ "Score dose" IF ( LATCH(np)=3 ) "score the primary dose" [ edoseis(ir(np)-l,is) = edoseis(ir(np)-l,is) + edep*wt(np); ] ELSEIF ( LATCH(np)=5 ) "score the dose from f i r s t Compton scatter" [ sdoseis(ir(np)-l,is) = sdoseis(ir(np)-l,is) + edep*wt(np); ] ELSEIF ( LATCH(np)=4 ) "score the dose from multiple photon scatter" [ mdoseis(ir(np)-l,is) = mdoseis(ir(np)-l,is) + edep*wt(np); ] ] ELSEIF ( ((iarg=18) & (Z(np) < botob)) & ( (E(np)+E(np-l)=etotin+RM) ) ) [ "First order Compton has occurred" IF (iq(np) = 0) [ ipoint=np; ] ELSE [ ipoint=np-l; ] LATCH(ipoint)=5; "Tag the photon" IF (iq(np) = 0) "Tag the electron" 163 Appendix A. SDOSXYZ 164 [ LATCH(np-l)=3; ] ELSE [ LATCH(np)=3; ] ] ELSEIF ( ((iarg=18) & (Z(np) < botob)) & ( (E(np)+E(np-1)~=etotin+RM) ) ) [ "Higher order Compton has occured, tag the photon and electron" IF (iq(np) = 0) [ ipoint=np; ] ELSE [ ipoint=np-l; ] IF ( LATCH(ipoint)=5 ) [ " Second scatter " "photon is part of multiple scatter, electron i s f i r s t scatter" LATCH(ipoint)=4; IF (iq(np) = 0) [ LATCH(np-l)=5; ] ELSE [ LATCH(np)=5; ] ] ELSE [ "Third or higher scatter" "Both particles are now part of the multiple scatter dose" LATCH(ipoint)=4; IF (iq(np) = 0) [ LATCH(np-l)=4; ] ELSE [ LATCH(np)=4; ] 3 ] ELSEIF ( (iarg=16) & ( Z(np)<botob ) ) [ "Pair production has occured, tag the positron and electron" IF (LATCH(np-l)=0) [ LATCH(np)=3; LATCH(np-l)=3;] IF (LATCH(np-l)=5) [ LATCH(np)=5;] IF (LATCH(np-l)=4) [ LATCH(np)=4;] ] ELSEIF ( (iarg=20) & ( Z(np)<botob ) & (LATCH(np)=0) ) "Photoelectric event, tag electron" [ LATCH(np)=3; 3 ELSEIF ( (iarg=20) & ( Z(np)<botob ) & (LATCH(np)~=0) ) "Photoelectric event from scattered photon, tag electron" [ LATCH(np)=4; ] ELSEIF ( (iarg=7) & ( Z(np)<botob ) ) "Bremsstrahlung" Appendix A. SDOSXYZ 165 IF (iq(np) = 0) [ LATCH(np)=4; ] ELSE [ LATCH(np-l)=4; ] ] ELSEIF ( ( (iarg=13) I (iarg=14) ) & ( Z(np)<botob ) ) "Annihilation" [ LATCH(np)=4; LATCH(np-l)=4; ] In subroutine HOWFAR, discard primary photons at the bottom of the scattering object. IF ((E(np).EQ.etotin).AND.(iq(np).EQ.0).AND.(Z(np).GE.botob)) [ IDISC=1; RETURN; ] A P P E N D I X B M O N T E C A R L O C A L C U L A T E D S P R S Table B . l . Portal scatter to primary dose ratios (SPRs) calculated using SDOSXYZ for a 6 MV photon beam. The source to detector distance (SDD) is the distance to the top of the detector: the dose scoring voxel is at a distance of (SDD+dmax) from the photon source. SPRMC is the total SPR at the imaging plane. SPRpC is the SPR from photons that Com.pton scatter once within the scattering object. SPR^s *s the SPR from photons that scatter m.ore than once with the scatter object, and includes the dose from bremsstrahlung and annihilation photons. SPR^p is the SPR from patient-generated electrons. Phantom Field thickness length SDD (cm) (cm) (cm) S P R M C S P R £ f c qt3t) MC orixcp 10 3 150 0.002±0.001 0.002±0.001 0.000±0.001 0 .000±0.001 10 8 150 0.018±0.001 0.013±0.001 0 .001±0.000 0 .003±0.001 10 14 150 0.047±0.003 0.035±0.002 0 .002±0.000 0 .007±0.001 10 20 150 0.078±0.003 0.061±0.002 0 .006±0.000 0 .009±0.001 10 3 160 0.002±0.001 0.002±0.001 0.000±0.001 O.OOOiO.001 10 8 160 0.016±0.001 0.011±0.001 0 .000±0.000 0 .003±0.001 10 14 160 0.041±0.001 0.033±0.001 0 .001±0.000 0 .004±0.001 10 20 160 0.069±0.003 0.054±0.002 0 .004±0.000 0 .009±0.001 10 3 170 0.002±0.001 0.002±0.001 0 .000±0.001 0 .000±0.001 10 8 170 0.013±0.001 0.008±0.001 0 .001±0.000 0 .003±0.001 10 14 170 0.034±0.002 0.025±0.002 O.OOliO.000 0 .004±0.001 10 20 170 0.060±0.002 0.046±0.002 0 .004±0.000 0 .009±0.001 10 3 185 0.000±0.001 0.000±0.001 O.OOOiO.001 O.OOOiO.001 10 8 185 0.010±0.001 0.010±0.001 O.OOOiO.OOl 0 .000±0.001 10 14 185 0.028±0.001 0.021±0.001 0 .001±0.000 0 .004±0.001 10 20 185 0.051±0.002 0.040±0.002 0 .003±0.000 0 .006±0.001 166 Appendix B. SPRs from Monte Carlo Simulation 167 Phantom Field thickness length SDD (cm) (cm) (cm) S P R M C S P R ^ C C D D M C z>rixMS Q D D M C DriXQp 10 3 200 O.OOOiO.OOl O.OOOiO.OOl O.OOOiO.OOl O.OOOiO.001 10 8 200 0.009i0.001 0.006±0.001 O.OOOiO.OOO O.OOliO.OOO 10 14 200 0.023±0.001 0.019i0.001 O.OOliO.OOO 0.002±0.001 10 20 200 0.044±0.002 0.035±0.001 0 .003±0.000 0 .004±0.001 10 3 230 O.OOOiO.OOl O.OOOiO.OOl O.OOOiO.OOl 0 .000±0.001 10 8 230 0.006i0.001 0.004±0.000 O.OOOiO.OOO 0.001±0.000 10 14 230 0.017±0.001 0.013±0.001 O.OOliO.OOO 0.001±0.001 10 20 230 0.035±0.002 0.028±0.002 O.OOliO.OOO 0.004±0.001 20 3 150 0.007±0.003 0.007±0.003 O.OOOiO.OOl O.OOOiO.OOl 20 8 150 0.024±0.001 0.018±0.001 0 .002±0.000 0 .003±0.001 20 14 150 0.096±0.004 0.076±0.003 0 .010±0.001 0 .009±0.001 20 20 150 0.161±0.007 0.126±0.004 0.021±0.001 0 .014±0.002 20 3 160 0.003±0.002 0.003±0.002 0.000±0.001 0 .000±0.001 20 8 160 0.032±0.003 0.024±0.002 0.003±0.001 0 .005±0.001 20 14 160 0.077±0.005 0.062±0.003 0 .008±0.001 0.007_t0.001 20 20 160 0.141±0.007 0 .112±0.004 0.017±0.001 0 .012±0.002 20 3 170 O.OOliO.OOl O.OOliO.OOl 0 .000±0.001 0 .000±0.001 20 8 170 0.024±0.002 0.018±0.001 0 .002±0.001 0 .003±0.001 20 14 170 0.070±0.003 0.055±0.002 0.009±0.001 0 .006±0.001 20 20 170 0.122±0.007 0.097±0.005 0 .015±0.001 O.OlOiO.OOl 20 3 185 0.004±0.001 0.002±0.001 O.OOOiO.OOO O.OOOiO.OOO 20 8 185 0.020±0.003 0.015±0.001 0 .002±0.001 0.003i0.001 20 14 185 0.051±0.005 0.038±0.005 0.005±0.001 0.002i0.002 20 20 185 0.096±0.004 0.076±0.003 0.009±0.001 0.008i0.001 20 3 200 O.OOOiO.OOl O.OOOiO.OOl O.OOOiO.OOl O.OOOiO.OOl 20 8 200 0.016±0.002 0.012±0.001 0.002±0.001 O.OOliO.OOl 20 14 200 0.048±0.004 0.038±0.003 0.006±0.001 0.004i0.001 20 20 200 0.091±0.004 0.073±0.002 O.OlOiO.OOl 0.008i0.001 20 3 230 0.002±0.001 0.002±0.001 O.OOOiO.001 O.OOOiO.OOl 20 8 230 0.015±0.001 O.OlliO.001' 0 .001±0.000 O.OOliO.OOl 20 14 230 0.036i0.001 0.029±0.001 0 .003±0.000 0.002i0.000 20 20 230 0.065±0.003 0.052±0.002 0.007±0.001 0.005i0.001 Appendix B. SPRs from. Monte Carlo Simulation 168 Phantom Field thickness (cm) length (cm) SDD (cm) S P R M C SPRfc 30 3 150 0 .008±0.004 0.007±0.003 0.001±0.001 0 .000±0.001 30 8 150 0 .061±0.004 0.043±0.003 0.005±0.001 0 .007±0.002 30 14 150 0.150±0.004 0.114±0.002 0.023±0.001 0 .013±0.001 30 20 150 0.248±0.006 0 .190±0.004 0.042±0.001 0 .015±0.001 30 3 160 0.006±0.002 0.006±0.002 0.000±0.001 0 .000±0.001 30 8 160 0.049±0.002 0.037±0.002 0 .005±0.000 0 .006±0.001 30 14 160 0.122±0.002 0.092±0.002 0 .017±0.001 0 .012±0.001 30 20 160 0.211±0.004 0.161±0.003 0 .033±0.001 0 .014±0.001 30 3 170 0.010±0.004 0.010±0.004 0 .000±0.001 0 .000±0.001 30 8 170 0.038±0.001 0.029±0.001 0.005±0.001 0 .004±0.001 30 14 170 0.100±0.006 0.076±0.004 0 .013±0.001 0 .010±0.001 30 20 170 0.171±0.006 0.133±0.003 0 .027±0.002 0 .011±0.001 30 3 185 0.002±0.001 0.000±0.001 0.000±0.001 0 .000±0.001 30 8 185 0.027±0.008 0.024±0.007 0.002±0.001 0 .000±0.001 30 14 185 0.084±0.010 0.062±0.005 0.010±0.002 0 .012±0.004 30 20 185 0.148±0.005 0 .113±0.004 0.024±0.001 0 .009±0.002 30 3 200 0.001±0.000 0 .000±0.000 O.OOOiO.OOO 0.000±0.000 30 8 200 0.027±0.005 0.020±0.003 0.003±0.001 0 .004±0.001 30 14 200 0.076±0.005 0.062±0.004 0 .009±0.001 0 .005±0.001 30 20 200 0.137±0.007 0.105±0.005 0.021±0.001 0 .011±0.001 30 3 230 0.000±0.001 0.000±0.001 0.000±0.001 0 .000±0.001 30 8 230 0.020±0.001 0.013±0.001 0 .001±0.000 0 .001±0.001 30 14 230 0 .052±0.003 0.039±0.003 0 .007±0.001 0 .003±0.001 30 20 230 0.103±0.009 0.081±0.006 0.016±0.001 0 .006±0.001 Appendix B. SPRs from Monte Carlo Simulation 169 Table B.2. Scatter to primary dose ratios calculated using SDOSXYZ for an 18 MV photon beam,. The source to detector distance (SDD) is the distance to the top of the detector: the dose scoring voxel is at, a distance of (SDD+dmax) from, the photon source. Phantom Field thickness length SDD (cm) (cm) (cm) g p R M C S P R ^ C C D D M C 10 3 150 0.004±0.001 0.002i0.000 O.OOOiO.OOO 0.003i0.000 10 8 150 0.023±0.001 O.OlOiO.OOl O.OOliO.OOO O.OlliO.001 10 14 150 0.047±0.002 0.025±0.001 0.002i0.000 0.019i0.001 10 20 150 0.068±0.004 0.043±0.002 0.005i0.000 0.021i0.001 10 3 160 0.004±0.001 O.OOliO.OOO O.OOOiO.OOO 0.002i0.001 10 8 160 0.020±0.002 0.009±0.001 O.OOOiO.OOO 0.009i0.001 10 14 160 0.050±0.002 0.026±0.001 0.002i0.001 0.020i0.002 10 20 160 0.060±0.003 0.035±0.002 0.003i0.000 0.021i0.001 10 3 170 0.004i0.001 O.OOliO.OOl O.OOliO.OOO 0.002i0.001 10 8 170 0.018i0.001 0.008±0.001 O.OOliO.OOO 0.007i0.001 10 14 170 0.042±0.002 0.021i0.002 O.OOliO.OOO 0.018i0.002 10 20 170 0.062i0.002 0.038±0.001 0.002i0.000 0.020i0.002 10 3 185 0.003±0.000 O.OOliO.OOO O.OOOiO.OOO O.OOliO.OOO 10 8 185 0.013±0.001 0.007±0.001 O.OOliO.OOO 0.004i0.001 10 14 185 0.033±0.002 0.016±0.002 O.OOliO.OOO 0.014i0.001 10 20 185 0.052±0.002 0.031±0.002 0.002i0.000 0.017i0.001 10 3 200 0.003±0.001 O.OOliO.OOO O.OOOiO.OOO 0.002i0.001 10 8 200 0.013±0.001 0.005±0.001 O.OOOiO.OOO 0.006i0.001 10 14 200 0.028±0.002 0.016±0.001 O.OOliO.OOO 0.010i0.001 10 20 200 0.049±0.003 0.028±0.001 0.002i0.000 0.018i0.001 10 3 230 0.003±0.001 O.OOliO.OOO O.OOOiO.OOO 0.002i0.001 10 8 230 0.013±0.001 0.005i0.001 O.OOOiO.OOO 0.007i0.001 10 14 230 0.028±0.001 0.014i0.001 O.OOliO.OOO 0.012i0.001 10 20 230 0.042±0.003 0.023i0.002 0.002i0.000 0.015i0.002 Appendix B. SPRs from Monte Carlo Simulation 170 Phantom Field thickness (cm) length (cm) SDD (cm) S P R M C S P R ^ C Q T J T ) MC S P R ^ 7 20 3 150 0.009±0.002 0.006±0.002 0 .000±0.000 0 .003±0.001 20 8 150 0.040±0.002 0.024±0.001 0 .002±0.000 0 .013±0.001 20 14 150 0.092±0.003 0.063±0.003 0 .008±0.000 0 .021±0.002 20 20 150 0.120±0.002 0.081±0.002 0 .013±0.001 0 .025±0.001 20 3 160 0.006±0.002 0.002±0.001 0 .000±0.000 0 .004±0.001 20 8 160 0.033±0.002 0.018±0.001 0 .002±0.000 O.OlliO.001 20 14 160 0.086±0.003 0.052±0.002 0.007±0.001 0 .026±0.002 20 20 160 0 .110±0.003 0.077±0.002 0.010±0.001 0 .022±0.001 20 3 170 0.004±0.001 0.002±0.001 0 .000±0.000 0 .002±0.001 20 8 170 0.031±0.002 0.018±0.001 0 .002±0.000 0 .009±0.001 20 14 170 0.068±0.005 0.043±0.003 0 .005±0.001 0 .020±0.002 20 20 170 0 .099±0.004 0.070±0.002 0 .009±0.001 0 .020±0.001 20 3 185 0.004±0.001 0.002±0.001 O.OOOiO.OOO 0.002±0.000 20 8 185 0 .028±0.003 0.017±0.002 O.OOliO.OOO 0,008±0.002 20 14 185 0.060±0.004 0.038±0.002 0 .004±0.001 0 .017±0.001 20 20 185 0.089±0.005 0.061±0.003 0 .008±0.001 0 .020±0.001 20 3 200 0.002±0.001 0.002±0.001 0 .000±0.000 0 .000±0.000 20 8 200 0.022±0.002 0.012±0.001 0 .000±0.000 0 .008±0.001 20 14 200 0.050±0.002 0.032±0.001 0 .003±0.000 0 .014±0.001 20 20 200 0 .078±0.003 0.052±0.002 0 .007±0.000 0 .019±0.001 20 3 230 O.OOliO.OOO 0.001±0.000 0 .000±0.000 0 .000±0.000 20 8 230 0.017±0.001 0.009±0.001 0 .000±0.000 0 .006±0.001 20 14 230 0.043±0.001 0.025±0.002 0.003±0.001 0 .013±0.001 20 20 230 0.069±0.001 0.046±0.001 0 .006±0.000 0 .017±0.001 Appendix B. SPRs from Monte Carlo Simulation 111 Phantom Field thickness length SDD (cm) (cm) (cm) S P R M C S P R ^ C S P R ^ g GOT} MC orsXQp 30 3 150 0.014±0.003 0.008±0.002 O.OOOiO.OOO 0.006i0.001 30 8 150 0.061±0.003 0.037±0.003 0.005±0.001 0.017i0.001 30 14 150 0.122±0.004 0.084±0.002 0.013±0.001 0.025i0.001 30 20 150 0.170±0.004 0.110±0.003 0.021±0.001 0.029i0.001 30 3 160 0.005i0.002 O.OOOiO.OOO O.OOOiO.OOO 0.005i0.002 30 8 160 0.051±0.002 0.030i0.002 0.003±0.001 0.016i0.002 30 14 160 0.105±0.006 0.073±0.003 O.OlOiO.OOl 0.022i0.002 30 20 160 0.152±0.006 0.108±0.004 0.018i0.001 0.026i0.002 30 3 170 O.OOliO.OOO O.OOOiO.OOO O.OOOiO.OOO O.OOOiO.OOl 30 8 170 0.043±0.003 0.027±0.002 O.OOliO.OOl 0.009i0.002 30 14 170 0.092±0.003 0.063±0.003 0.008i0.001 0.019i0.001 30 20 170 0.141i0.006 0.101i0.003 0.016i0.001 0.024i0.002 30 3 185 0.004±0.002 0.002i0.001 O.OOOiO.OOO O.OOliO.OOl 30 8 185 0.032±0.002 0.018±0.002 0.003i0.000 O.OlOiO.OOl 30 14 185 0.081i0.003 0.054±0.002 0.007i0.001 0.019i0.001 30 20 185 0.122±0.003 0.085±0.002 0.013i0.001 0.023i0.001 30 3 200 0.004±0.001 0.004±0.001 O.OOOiO.OOO O.OOOiO.OOO 30 8 200 0.026±0.003 0.015±0.002 O.OOliO.OOl 0.006i0.001 30 14 200 0.073±0.002 0.049±0.002 0.006i0.001 0.017i0.001 30 20 200 0.114±0.003 0.080±0.002 O.OlliO.000 0.022i0.001 30 3 230 0.004±0.001 0.004i0.001 O.OOOiO.OOO O.OOOiO.OOO 30 8 230 0.021±0.002 O.OlOiO.OOl O.OOliO.OOl 0.005i0.001 30 14 230 0.063i0.003 0.039i0.002 0.006i0.001 0.016i0.001 30 20 230 0.093±0.005 0.061±0.003 0.009i0.001 0.020i0.002 A P P E N D I X C M E A S U R E D SCATTER TO PRIMARY DOSE RATIOS Table C . l . Scatter to primary dose ratios measured for a 4 MV photon beam,. The ab-solute uncertainty for all cases was 0.006. The source to detector distance is the distance to the mid-point of the ionization chamber within the solid water. Source to Field detector length Phantom thickness (cm) distance (cm) (cm) 10 20 30 185 5 0.004 0.008 0.011 7 0.006 0.013 0.023 10 0.013 0.029 0.042 14 0.026 0.054 0.088 17 0.035 0.078 0.122 20 0.049 0.103 0.161 28 0.086 0.172 0.274 200 5 0.003 0.006 0.012 7 0.00.5 0.012 0.017 10 0.009 0.022 0.036 14 0.019 0.044 0.074 20 0.041 0.088 0.141 28 0.075 0.149 0.240 172 Appendix C. Measured SPRs 173 Table C . 2 . Scatter to primary dose ratios measured for a 6 MV photon beam,. The ab-solute uncertainty for all cases was 0.006. The source to detector distance is the distance to the m,id-poi,n,t of the ionization chamber within the solid water. Source to Field detector length Phantom thickness (cm) distance (cm) (cm) 10 20 30 185 5 0.001 0.006 0.009 7 0.005 0.012 0.017 10 0.018 0.030 0.039 14 0.025 0.047 0.071 17 0.035 0.072 0.102 20 0.043 0.096 0.134 28 0.077 0.156 0.226 200 5 0.005 0.007 0.009 7 0.004 0.008 0.018 10 0.007 0.015 0.030 14 0.015 0.036 0.062 20 0.039 0.072 0.122 28 0.067 0.130 0.200 Appendix C. Measured SPRs 174 Table C.3. Scatter to primary dose ratios measured for a 10 MV photon beam. The ab-solute uncertainty for all cases was 0.006. The source to detector distance is the distance to the mid-point of the ionization chamber within the solid water. Source to Field detector length Phantom thickness (cm) distance (cm) (cm) 10 20 30 40 185 5 0.002 0.006 0.009 0.013 7 0.005 0.010 0.016 0.017 10 0.008 0.018 0.029 0.040 14 0.019 0.039 0.061 0.080 17 0.027 0.055 0.086 0.135 20 0.036 0.073 0.113 0.149 28 0.063 0.122 0.181 0.245 200 5 0.003 0.005 0.009 0.008 7 0.004 0.009 0.013 0.013 10 0.007 0.016 0.025 0.030 14 0.016 0.032 0.050 0.058 20 0.033 0.065 0.098 0.122 28 0.053 0.107 0.159 0.245 Appendix C. Measured SPRs 175 Table C.4. Scatter to primary dose ratios measured for an 18 MV photon beam. The ab-solute uncertainty for all cases was 0.006. The source to detector distance is the distance to the m,i,d-point of the ionization chamber within the solid water. 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I N D E X bremsstrahlung yield 17 buildup cap 43 compensator 34 Compton detector 34 computed tomography 9 C T 9 cutoff energy 26 depth of maximum dose 21 detector response 34 EHP 44 equivalent homogeneous polystyrene phan-tom 44 G y 5 isocenter 22 K E R M A 62 monitor unit 111 M V 6 off-axis softening 106, 109 phantom 11 photon counter 26, 34 photopeak detector 34 pixel 9, 53 portal scatter calculation, Boellaard 40 Bogaerts 46 Descalle 39 Hansen 35, 36 McCurdy 29, 38 McNutt 29 Pasma 43 Spies 35 Swindell and Evans 32 Wong 27 Ying 27 primary 3 radiological thickness 36 radiosurgical field 36 record and verify system 132 scatter fraction of dose 84 scatter to primary dose ratio 26 SDD 65 SPR 26 SSD 65 stopping power 12 T E R M A 29 treatment planning system 27 voxel 9, 64 watertank 12, 46 187
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Portal scatter to primary dose ratio of 4 to 18 MV photon spectra incident on heterogeneous phantoms Ozard, Siobhan R. 2001
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Title | Portal scatter to primary dose ratio of 4 to 18 MV photon spectra incident on heterogeneous phantoms |
Creator |
Ozard, Siobhan R. |
Date Issued | 2001 |
Description | Electronic portal imagers designed and used to verify the positioning of a cancer patient undergoing radiation treatment can also be employed to measure the in vivo dose received by the patient. This thesis investigates the ratio of the dose from patient-scattered particles to the dose from primary (unscattered) photons at the imaging plane, called the scatter to primary dose ratio (SPR). The composition of the SPR according to the origin of scatter is analyzed more thoroughly than in previous studies. A new analytical method for calculating the SPR is developed and experimentally verified for heterogeneous phantoms. A novel technique that applies the analytical SPR method for in vivo dosimetry with a portal imager is evaluated. Monte Carlo simulation was used to determine the imager dose from patient-generated electrons and photons that scatter one or more times within the object. The database of SPRs reported from this investigation is new since the contribution from patientgenerated electrons was neglected by previous Monte Carlo studies. The SPR from patient-generated electrons was found here to be as large as 0.03. The analytical SPR method relies on the established result that the scatter dose is uniform for an air gap between the patient and the imager that is greater than 50 cm. This method also applies the hypothesis that first-order Compton scatter only, is sufficient for scatter estimation. A comparison of analytical and measured SPRs for neck, thorax, and pelvis phantoms showed that the maximum difference was within ±0.03, and the mean difference was less than ±0.01 for most cases. This accuracy was comparable to similar analytical approaches that are limited to homogeneous phantoms. The analytical SPR method could replace lookup tables of measured scatter doses that can require significant time to measure. In vivo doses were calculated by combining our analytical SPR method and the convolution/ superposition algorithm. Our calculated in vivo doses agreed within ± 3% with the doses measured in the phantom. The present in vivo method was faster compared to other techniques that use convolution/superposition. Our method is a feasible and satisfactory approach that contributes to on-line patient dose monitoring. |
Extent | 9278101 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
FileFormat | application/pdf |
Language | eng |
Date Available | 2009-10-08 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0085704 |
URI | http://hdl.handle.net/2429/13779 |
Degree |
Doctor of Philosophy - PhD |
Program |
Physics |
Affiliation |
Science, Faculty of Physics and Astronomy, Department of |
Degree Grantor | University of British Columbia |
GraduationDate | 2001-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
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