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Study of wedged asymmetric photon beams Qiu, Yue 2006

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Study of Wedged Asymmetric Photon Beams by Yue Qiu B.Sc , Peking University, 2003 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF Master of Science in The Faculty of Graduate Studies (Physics) The University of British Columbia October 2006 © Yue Qiu, 2006 11 Abstract In radiation therapy, many recent advances have been made in the technology used for dose delivery. However, conventional physical wedges are still in clinical use. The combination of asymmetric field' collimation and physical wedge presents a challenge for accurate dose calculation. Algorithms for calculating monitor units (MUs) in wedged asymmetric photon beams as implemented in treatment planning systems have their.limitations. In this work, the dose calculations for rectangular wedged asymmetric fields by the Eclipse treatment planning system were tested by direct comparison to ion chamber measurements and up to 6.5% discrepancy was found. Monte Carlo simulation by BEAMnrc was used for independent dose calculations. Finally, a correction method was developed for accurate wedged asymmetric dose calculations. The difference in dose between a wedged asymmetric field and the corresponding wedged symmetric field is accounted for by a correction factor that is a function of field sizes, off axis distance and depth of measurement. For both 6MV and 18MV photon beams at dmax and 10cm, the correction factor is within 1% of the measurement in most cases and the maximum difference is 2%. The dose at the asymmetric field center, which is based on wedged symmetric profiles and the correction factor, is within 2% of the measured dose in most cases and the maximum difference is 4%. It can be concluded that our simple correction factor is able to calculate dose at the center of wedged asymmetric fields with acceptable accuracy. iii Contents Abstract ii Contents i ii List of Tables v List of Figures x Acknowledgements xiv 1 Introduction to Dose Calculation and Measurement Techniques . 1 1.1 Thesis Organization 1 1.2 Background Knowledge 2 1.2.1 Interactions of Radiation with Matter 2 1.2.2 Linear Accelerator 3 1.2.3 Treatment Planning System and Calculation Algorithm . . . . 4 1.2.4 Wedged Asymmetric Field 6 1.2.5 Measurement Techniques 8 1.2.6 Monte Carlo.Simulation 10 1.3 Radiation Absorbed Dose Quantities in External Beam Radiotherapy 11 1.3.1 The Depth of Maximum Dose (dmax) and the Percentage Depth Dose (PDD) 11 1.3.2 The monitor Unit (MU) and Dose Rate 12 1.3.3 Collimator Scatter Factor and Phantom Scatter Factor . . . . 13 1.3.4 The Tissue Maximum Ratio (TMR) 15 1.3.5 The Off Axis Ratio (OAR) 16 1.4 Review of Wedged Asymmetric Dose Calculations 17 1.4.1 Tolerances for the Accuracy of Photon Beam Dose Calculations 18 1.4.2 Review of Studies on Asymmetric Fields 19 1.4.3 Previous Studies on Wedged Asymmetric Fields 20 2 Materials and Methods 24 2.1 Calculation by Eclipse Treatment Planning System 24 2.2 Measurements by Ion Chamber 24 2.3 Verification by Monte Carlo Simulation 25 2.4 An Empirical Correction Method 28 2.4.1 Dose Calculation for Asymmetric Field 28 2.4.2 Extrafocal Radiation: An Analysis of Head Scatter 36 Contents iv 2.4.3 Extension to Wedged Asymmetric Fields: Correction for the Thin End . . . ' 37 2.4.4 Correction' for the Thick End 38 ' 3 Results and Discussion 39 3.1 Comparison of Measurements and Eclipse Results 39 3.2 Monte Carlo Results 57 3.3 Results of the Empirical Correction 64 3 .3! 6MV Photon Beam . 64 3.3.2 18MV Photon Beam ' . . . . 69 3.4 Discussion 74 4 Conclusion and Future Work 75 Bibliography 77 V List of Tables 3.1 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 60 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condi-tion of SAD=100cm, d=1.5cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 41 3.2 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 60 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under con-dition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed closes by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 42 3.3 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 45 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged, direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condi-tion of SAD=100cm, d=1.5cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 43 List of Tables vi 3.4 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 45 degree wedge. Y f and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under con-dition of SAD=f00cm, d=10cm, Xl=X2=f0cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 44 3.5 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 30 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condi-tion of SAD=f00cm, d=f.5cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 45 3.6 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 30 degree wedge. Y f and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under con-dition of SAD=f00cm, d=f0cm, Xf=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction axe shown 46 3.7 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 15 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condi-tion of SAD=d00cm, d=1.5cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 47 List of Tables vii 3.8 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 15 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under con-dition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 48 3.9 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 60 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condi-tion of SAD=100cm, d=3.2cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 49 3.10 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 60 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under con-dition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 50 3.11 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 45 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condi-tion of SAD=100cm, d=3.2cm, Xl=X2=10cm. Absorbed closes by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 51 List of Tables viii 3.12 Comparison of ion chamber reading. Eclipse calculation and empirical ' correction for 18MV 45 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under con-dition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 52 3.13 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 30 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condi-tion of SAD=100cm, d=3.2crn, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 53 3.14 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 30 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under con-dition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 54 3.15 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 15 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position .(OAP) indicates the measurement point. 200 M U is delivered under condi-tion of SAD=100cm, d=3.2cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 55 List of Tables ix 3:16 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 15 degree wedge. Y I and Y2 indicate the col-limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under con-dition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage' differences to measurement by Eclipse and empirical correction are shown 56 List of Figures 1.1 A medical linear accelerator (Varian CL21EX) is shown 4 1.2 Internal structure of a medical linear accelerator treatment head is shown 5 1.3 Sketched isodose curves for a wedge filter, normalized to Dmax. . . . 7 1.4 Wedged asymmetric field is used in breast therapy 9 1.5 Schematic diagram of a thimble ionization chamber is shown 10 1.6 The geometry used in the definition of the percentage depth close (PDD) at a fixed surface distance (SSD) is shown 12 1.7 A typical photon beam percentage depth dose (18MV) is shown. . . 13 1.8 The geometry used in the definition of the dose rate is shown. The absorbed dose at depth of maximum ionization (dmax) along the col-limator axis is obtained for a 10 x 10cm2 field and a W x L field. 14 1.9 Chamber with build-up cap in air to measure dose rate relative to a reference field to determine Sc versus field size 15 1.10 The geometry used in definition of tissue maximum ratio (TMR) at a fixed source to axis distance (SAD) 16 1.11 The geometry used in definition of off-axis ratio (OAR) at a fixed source to axis distance (SAD) 17 2.1 Schematic diagram of the Varian 21 E X treatment head with the asso-ciated component modules listed (not drawn to scale), as configured for BEAMnrc 26 2.2 . Schematic voxel setting for PDD (in the left) and O A R profile (in the right) in DOSXYZnrc. Not scaled for real voxel size 27 List of Figures xi 2.3 (a)Comparison of measured and calculated percentage depth dose (PDD)for 60 degree wedge with field size 10c?n x 10cm and SSD=100cm, nor-malized to dose at d m a x . (b) Comparison of measured and calculated cross profile in the wedged direction for 60 degree wedge with field size 15cm x 15cm, SSD=100cm and depth=5cm, normalized to the central axis dose 29 2.4 (a)Comparison of measured and calculated percentage depth dose (PDD)for 45 degree wedge with field size 10cm x 10cm and SSD=100cm, nor-malized to dose at d m a x . (b) Comparison of measured and calculated cross profile in the wedged direction for 45 degree wedge with field size 20cm x 20cm, SSD=100cm and depth=5cm, normalized to central axis dose 30 2.5 The equivalent field contributions used in dose calculation are illus-trated. In A, the absorbed dose to a point R in a symmetric field W x L is equivalent to the average of the two closes at the center of the two symmetric fields of (W + 2r) x L and (W - 2r) x L . In B, the absorbed dose at a point R in an asymmetric field AW x L is equiva-lent to the average of the two doses at the center of the two symmetric fields of (W + 2r) x L and (2AW - W - 2r) x L. fn C, the absorbed dose at a point P along the collimator axis in an asymmetric field is equivalent to the average of the two doses at the center of the two symmetric fields of W x L and (2AW — W) x L. (Reproduced with permission from Kwa et a/[14].) 31 2.6 The two component x-ray source model. The radiation beam is com-prised of x-ray produced at the focal spot and scattered x-rays, which from a broadly distributed extrafocal source, (a) and (b) are for non-wedged fields, (c) and (d) are for wedged fields 37 3 ! Percentage difference between measured and Monte Carlo calculated absorbed doses for asymmetric fields as a function of off axis distance N in the wedge direction for the 6MV beam with 60 degree wedge at dmax- Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups 58 List of Figures 3.2 Percentage difference between measured and Monte Carlo calculated absorbed doses for asymmetric fields as a function of off axis distance ' in the wedge direction for the.fjMV beam with 60 degree wedge at 10cm. Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups 59 3.3 Percentage difference between measured and Monte Carlo calculated absorbed doses for asymmetric fields as a function of off axis distance in the wedge direction for the 6MV beam with 45 degree wedge at dmax- Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups 60 3.4 Percentage difference between measured and Monte Carlo calculated absorbed closes for asymmetric fields as a function of off axis distance in the wedge direction for the 6MV beam with 45 degree wedge at 10cm. Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups 61 3.5 Ratios of the absorbed dose in the wedged asymmetric fields to those in the wedged symmetric fields are shown by ion chamber measurement, Eclipse treatment planning system and Monte Carlo simulation. . . . 62 3.6 The test fields are demonstrated, a) wedged symmetric field, b) wedged asymmetric field at thin end, c) wedged asymmetric field at thick end. 62 3.7 The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Com-parisons are made for 6MV photon beam with 60° wedge at dmax and 10cm 65 3.8 The correction factors, i.e., the ratios of the absorbed dosedn the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Com-parisons are made for 6MV photon beam with 45° wedge at dmax and 10cm .- 66 3.9 The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Com-parisons are made for 6MV photon beam with 30° wedge at 'dmax and 10cm 67 List of Figures xm 3.10 The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Com-parisons are made for 6MV photon beam with 15° wedge at dmax and 10cm 68 3.11 The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Com-parisons are made for 18MV photon beam with 60° wedge at dmax and 10cm 70 3.12 The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Com-parisons are made for 18MV photon beam with 45° wedge at dmax and 10cm 71 3.13 The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Com-parisons are made for 18MV photon beam with 30° wedge at dmax and 10cm 72 3.14 The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Com-parisons are made for 18MV photon beam with 15° wedge at dmax and . 10cm 73 xiv Acknowledgements I would like to thank my supervisors, Dr. William Kwa and Dr, Cheryl Duzenli, for their invaluable guidance and patience. My sincere gratitude goes to their dedica-tion throughout this research project . Without their continuous support and useful discussion, this work would not have been possible. Thanks to Alanah Bergman, Dr. Tony Popescu, Marco Stradiotto and Dr. Ermias Gete for helping me in Monte Carlo simulation. I also wish to thank Karl Bush for providing his massaged phase space. Many thanks to the staff of V C C , especially to Joseph Cortese, Vince LaPointe, Vince Strgar, Ayaz Rahim, John Paul Sweeney for assisting me solving linac-related problems. Last but not least, I would like to thank my parents and friends for their constant encouragement in the past two years. Words can not express how much I appreciate their unconditional love and emotional support. Chapter 1 i Introduction to Dose Calculation and Measurement Techniques 1.1 Thesis Organization The objectives of the thesis are: 1) rigorously assess the accuracy of M U calculations in the Eclipse treatment planning system for asymmetric, physical wedge fields; 2)ex-tend an existing empirical M U calculation method for non-wedged asymmetric fields to wedged asymmetric fields to improve on the Eclipse (Varian Medical System, Inc) TPS results; 3) perform Monte Carlo simulation of the dose deposition in the linac and phantom to provide a better understanding of the sources of error in the TPS algorithm and the empirical model. Chapter 1 is an introduction to radiation therapy physics covering basics of the accelerator, treatment planning systems, ion chamber measurements and Monte Carlo technique. In chapter 2, the experimental equipment and procedures used in this work are outlined. The setup of the measurement and the validation by Monte Carlo simulation are presented in this chapter. The results of ion chamber measurements, commercial treatment planning system and the new empirical method are compared in chapter 3. Chapter 4 gives conclusion and future work. Chapter 1. Introduction to Dose Calculation and Measurement Techniques 2 1.2 Background Knowledge 1.2.1 Interactions of Radiation with Matter Radiotherapy is a major treatment modality for cancer and external beam radiother-apy is the most common form of radiotherapy. Cancerous tissue is destroyed through damage caused by ionizing radiation. The photon beams transfer energy to tissue though particle interactions in the tissue. In the 0 to 25 MeV energy range produced by clinical linear accelerators, the main interactions are Rayleigh scattering, photo-electric effect, Compfcon effect and pair production. Rayleigh scattering is elastic and therefore no energy is deposited to matter. The photoelectric effect, Compton effect and pair production occur with the greatest probability in this energy range. In the photoelectric effect, there is a collision between a photon and an atom resulting in the ejection of a bound electron. The process is most likely to occur if the energy of the photon is just greater than the binding energy of the electron. The energy transferred to the electron E t r a n s is given by the difference between the incident photon energy hv and the binding energy of the electron B E , Etrans = hu - B E (1.1) Compton effect occurs when a photon interacts with a loosely bound or free electron. In this process the electron absorbs some of the photon energy and the remaining energy is retained by the scattered photon. The energy transferred to the electron is given by Etrans = hv - lw' (1.2) where hv and hu' are energy of the incident photon and energy of the scattered photon. Pair production occurs when a photon is stimulated by the electromagnetic field Chapter 1. Introduction to Dose Calculation and Measurement Techniques 3 of an atom and the incident photon is replaced by an electron-positron pair. Because the rest mass energy of the electron and positron, me, must be created in this process, the resulting energy transferred to the electron-positron pair is given Etrans = hv - 2?77,E ' (1.3) By a photoelectric, Compton or pair production process, one or more electrons are set into motion and these electrons carry away some of the energy of the photon. These electrons transfer their kinetic energy to the matter when they are slowing down and losing energy. Energy losses can be divided into two categories, ionizational and radiative. The former results in further ionization of electrons along the initial electron trajectory. Each one of these ejected electrons will also undergo their own ionizational and radiative losses until they come to rest. The latter occurs due to Bremsstrahlung processes that result in photon production and does not directly deposit energy in the matter. 1.2.2 Linear Accelerator The most common type of device in use for external beam therapy is the linear ac-celerator (linac) as shown in F i g . l ! and the internal structure of a linac is shown in Fig. 1.2. Electrons strike the target to produce photons. These photons are first col-limated by the primary collimator to form a cone of radiation and then pass through a flattening filter to produce a uniformly intense radiation field. Then they are col-limated by two pairs of movable collimators to produce any square or rectangular shaped field up to 40 x 40cm 2. The two pairs of collimators are perpendicular to each other and are referred to as the upper and lower jaws. By convention, the position of each collimator is defined as the projected dimension at the cross plane of the isocen-ter which is usually 100cm from the source. Linear accelerators have been designed to allow the independent movement of each pair of the upper and lower collimators. Chapter 1. Introduction to Dose Calculation and Measurement Techniques 4 This feature is called asymmetric collimation. For Varian Clinac linear accelerators (Varian Associates, Palo Alto, CA) , the upper pair of jaws are referred to as the Y\ and Y2 collimators and each can move up to 10cm over the central axis. The lower pair of jaws are referred to as the X\ and X2 collimators and each can move up to 2cm over the central axis. Figure 1.1: A medical linear accelerator (Varian CL21EX) is shown. 1.2.3 Treatment Planning System and Calculation Algori thm Treatment planning systems (TPS) are used in external beam radiotherapy to calcu-late dose distributions based on the patient's axial anatomy attained from C T (X-Ray Computed Tomography) imaging or MRI (Magnetic Resonance Imaging). The entire Chapter 1. Introduction to Dose Calculation and Measurement Techniques 5 Figure 1.2: Internal structure of a medical linear accelerator treatment head is shown. Chapter 1. Introduction to Dose Calculation and Measurement Techniques 6 treatment planning process involves several steps: patient data acquisition, treatment plan generation and evaluation, and final transfer of plan to treatment machine. Dose calculation algorithms are the most critical software component of a treat-ment planning system. The most frequently used model in commercial treatment planning system is based on a convolution or superposition principle. The incident beam is considered to be composed of very small pencil beams and the dose deposited, i.e. the pencil beam kernels, have been produced by Monte Carlo simulation or by deconvolving an experimentally measured beam profile. The beam kernels can also be split into more than one component with the primary kernel for dose deposited in the primary interactions and the scatter kernel for the dose deposited by scat-tered photons. If the dose kernels are spatially invariant, the superposition can be represented by a convolution. 1.2.4 Wedged Asymmetric Field Wedge and Wedge Factor A wedge is a wedge-shaped absorber made of a dense material to cause a progressive decrease in the intensity across the beam. Wedge angle is defined as "the angle through which an isodose curve is tilted at the central ray of a beam at a specific depth" [1]. In this definition, the wedge angle is the angle between the isodose curve and the normal to the central axis, as shown in F ig ! .3 . In addition, the specification of the depth is important because in general, the presence of scattered radiation causes the angle of isodose tilt to decrease with increasing depth in the phantom. The current recommendation is to use a single reference depth of 10 cm for wedge angle specification[f]. The presence of a wedge decreases the output of the machine due to attenuation of the photon beam. This effect is described by the wedge factor, which is defined as the ratio of doses with and without the wedge, at a point in phantom along the Chapter 1. Introduction to Dose Calculation and Measurement Techniques 7 Chapter 1. Introduction to Dose Calculation and Measurement Techniques 8 central axis of the beam. T i r , „ , T r r „ v Reference dose rate with luedge . WedqeFactor(WF) = n / - (1.4) Reference dose rate without wedge The wedge described above is known as a physical wedge. Physical wedges generally are manufactured to produce a range of wedge angles from 15° to 60°. A similar dose distribution can be created by sweeping the collimator from open to closed position while the beam is on. This type of wedging is referred to as dynamic wedging Asymmetr ic Fields Many modern linear accelerators are equipped with jaws that can move independently to allow asymmetric fields with field centers offset from the central axis of the beam. For example, one jaw can move to the central axis to block half the field to eliminate beam divergence along that edge. Applicat ion of Wedged Asymmetric Fields Even with the recent advances in treatment planning and delivery systems, such as dynamic wedges and intensity modulated radiation therapy, conventional wedges with asymmetric collimators are still used in clinical practice. Treatments of breast, head and neck and other sites are a few examples where wedged asymmetric fields are frequently encountered. F ig! .4 shows an application of wedged asymmetric fields in breast therapy. 1.2.5 Measurement Techniques The ionization chamber is the most widely used type of dosimeter for precise mea-surements of radiation dose. F ig! .5 shows a typical thimble ionization chamber. The inner surface of the thimble wall is coated by a special material to make it electrically conducting. This forms one electrode. The other electrode is a rod of low atomic Chapter 1. Introduction to Dose Calculation and Measurement Techniques 9 Figure 1.4: Wedged asymmetric field is used in breast therapy. number material held in the center of the thimble but electrically insulated from it. A suitable voltage is applied between the two electrodes to collect the ions produced in the air cavity. The absorbed dose in the cavity is proportional to the amount of charge collected. where Q is the amount of charge collected, V is the air volume, mair is the mass of air, W = 33.97CK is the average energy transferred from an electron to an air molecule to create an ion pair. In a well designed ion chamber, the thimble wall is air equivalent, which means the effective atomic number is the same as that of air and the thickness of the wall is enough to set up electronic equilibrium. The central electrode is insulated from the chamber wall and is attached to the electrometer. Measurements are usually obtained in tissue-equivalent materials (called phan-tom material). Water is the most commonly used phantom material because it is easily accessible and approximately equivalent to soft tissue and muscles. Solid water (Gammex RMI . Middleton. WI, USA) is also commonly used because it is easy to set up. For a material to be considered water equivalent, it should have an effective (1.5) Chapter 1. Introduction to Dose Calculation and Measurement Techniques 10 Insulator Central Electrode Figure 1.5: Schematic diagram of a thimble ionization chamber is shown. atomic number Zejf, an electron density pe and a mass density p close to that of water. The effective atomic number for solid water is 7.54 while it is 7.4 for water; the electron density for solid water is 3.41 x 1026e/kg and 3.34 x 1026e/kg for water. The mass density is 1.03 x 103kg/m3 and 1.0 x 1 0 3 % / m 3 for water. 1.2.6 Monte Carlo Simulation Monte Carlo simulation in radiotherapy is a numerical procedure in which one uses knowledge of the probability distributions governing the individual interactions of electrons and photons in materials to simulate the histories of individual particles. One keeps track of physical quantities of interest for a large number of such histories to get information about required quantities and distributions. Monte Carlo simulation is considered the most accurate approach to dose calculation in radiation therapy [2]. Due to the availability of fast computation, Monte Carlo is more and more widely used in radiotherapy physics. Chapter 1. Introduction to Dose Calculation and Measurement Techniques 11 1.3 Radiation Absorbed Dose Quantities in External Beam Radiotherapy 1.3.1 T h e D e p t h o f M a x i m u m D o s e (dmax) a n d t h e P e r c e n t a g e D e p t h D o s e ( P D D ) The depth of maximum dose is the depth in an irradiated medium at which the maximum dose is observed. The depth of maximum dose is energy dependent. For megavoltage photon beams, the dmax is 1.5cm for a 6MV photon beam and 3.2cm for an 18MV photon beam. The percentage depth dose is defined as the ratio of absorbed dose at a depth cl to the absorbed close at the depth of dose maximum along the central axis of the beam (as shown in Fig! .6) . For P D D the source to surface distance (SSD) remains fixed, typically at 100cm. As seen in Fig! .7 , the percentage depth dose decreases with depth beyond the depth of maximum close. However, there is a region between the surface and the point of maximum close, which is called dose build-up region. The physics of close build-up can be explained by the following: 1) as the photon beam enters the phantom, high-speed electrons are ejected from the surface and the subsequent layers primarily in the forward direction; 2) the electrons deposit their energy a significant distance away from their site of origin; 3)the electron fluence and hence the absorbed dose increase with depth until they reach a maximum, i.e., electronic equilibrium is set up. After that, the photon fluence as well as the production of electrons decreases with depth, due to photon attenuation in the material. PDD{d,W x L,SSD) = 100 x D{d,W x L, SSD)/D(dmax, W x L,SSD) (1.6) Chapter 1. Introduction to Dose Calculation and Measurement Techniques 12 D(d,WxL,SSD) Dfdmax.WxL .SSm Figure 1.6: The geometry used in the definition of the percentage depth dose (PDD) at a fixed surface distance (SSD) is shown. The percentage depth dose (an example of which is shown in Fig. 1.7) depends on photon energy, field size and source to surface distance. 1.3.2 The monitor Unit (MU) and Dose Rate A monitor unit (MU) corresponds to calibration of the linac beam monitor chamber to deliver an absorbed dose of 1 centigray under a reference dose condition. At the Vancouver Cancer Center the reference dose condition is at a depth of dmax for a field size of 10x10 cm for a source-to-axis distance (SAD) of 100 cm (as shown in Fig! .8) . Some linear accelerators are calibrated using source-to-skin distance (SSD) instead of SAD or at a different reference depth. The reference dose rate for a 10 x 10cm2 field is defined as £> r e / (10 x 10) = D(dmax, 10 x 10) /MU (1.7) Chapter 1. Introduction to Dose Calculation and Measurement Techniques 13 0 1 I ^ -I 4 Y dmax 10 20 30 40 depth(cm) Figure 1.7: A typical photon beam percentage depth dose (18MV) is shown. The close rate for a,W x L held size is defined as D(W x L) = Dref(10 x 10) x D(dmax, W x L)/D(dmax, 10 x 10) (1.8) in which D(dmax, W x L)/D(dmax, 10 x 10) is relative dose factor (RDF). 1.3.3 C o l l i m a t o r S c a t t e r F a c t o r a n d P h a n t o m S c a t t e r F a c t o r The dose to a point in a medium can be resolved to primary and scatter components. The primary dose is contributed by the original photons emitted from the source. The scattered dose can be separated into collimator scatter and phantom scatter. The collimator scatter factor Sc (also called head scatter factor) is defined as the ratio of the dose rate in air for a given field to that of a reference field (e.g., 10cm x 10cm). It includes photons scattered by all components of the machine head in the path of the beam. As shown in Fig. 1.9, Sc may be measured with an ion chamber with a build-up cap of a size large enough to provide maximum close build-Chapter 1. Introduction to Dose Calculation and Measurement Techniques 14 D(dmax,10x10) D(dmax.WxL) Figure 1.8: The geometry used in the definition of the dose rate is shown. The absorbed dose at depth of maximum ionization (dmax) along the collimator axis is obtained for a 10 x 10cm2 field and a W. x L field. up for the given energy. Problems arise in high energy beams due to the fact that the buildup cap becomes large and contributes scatter contaminating the measurement. The phantom scatter factor Sp accounts for the change in scatter radiation origi-nating in the phantom at a reference depth as the field size is changed. Sv is defined as the ratio of the dose rate for a given field at a reference depth (e.g., depth of the maximum dose) to the dose rate at the same depth for the reference field size (e.g., 10cm x 10cm), with the same collimator opening. It should be noted that Sp is related to the changes in the volume of the phantom irradiated for a fixed collimator opening. A practical method of measuring Sp is indirect determination from the following equation: where SCtP(r) is the total scatter factor (also called relative dose factor (RDF)) defined as the close rate at a reference depth for a given field size r divided by the dose rate at the same point and depth for the reference field size (10cm x 10cm). Sc<p(r) contains Chapter 1. Introduction to Dose Calculation and Measurement Techniques 15 S A D Figure 1.9: Chamber with build-up cap in air to measure dose rate relative to a reference field to determine Sc versus field size. both the collimator and phantom scatter so that SCtP(r) divided by Sc(r) yields Sp(r). Although Sp(r) and SCiP(r) are defined at the reference depth of dmax, actual measurements of these factors are made at a greater depth (e.g., 10cm) and the readings are converted to the reference depth dose of dmax by using percentage depth dose. The reason is to avoid the problems due to contaminant electrons incident on the phantom. . 1.3.4 The Tissue Maximum Ratio (TMR) The tissue maximum ratio is the ratio of the absorbed dose at a depth in a phantom to the absorbed dose at the same point at dmax in the phantom with the source to Chapter 1. Introduction to Dose Calculation and Measurement Techniques 16 point of measurement held constant. TMR(d, WxL) = D(d, W x L)/D(dmax, W x L) (1.10) D(d, W x L) and D(dmax, W x L) are shown in Fig. 1.10. D(d,WxL) D(dmax,WxL) Figure 1.10: The geometry used in definition of tissue maximum ratio (TMR) at a fixed source to axis distance (SAD). 1.3.5 The Off Axis Ratio (OAR) The off axis ratio describes the ratio of absorbed dose at a point a distance r away from the central axis to the absorbed dose at a point at the same depth along the collimator axis, which is OAR(r, d, W x L) = D(r,d,W x L)/D(0, d, W x L) (1.11) D(r, d,W x L) and D(0, d,W x L) are shown in F i g ! . 11. Chapter 1. Introduction to Dose Calculation and Measurement Techniques 17 D(r,d,WxL) D(0,d,WxL) Figure 1.11: The geometry used in definition of off-axis ratio (OAR) at a fixed source to axis distance (SAD). 1.4 Review of Wedged Asymmetr ic Dose Calculations In radiotherapy, accurate delivery of prescribed dose is of great importance. However, currently commercial treatment planning systems have their limitations in computing monitor units (MU) for complicated geometries. Wedged asymmetric fields are one sample of complex geometry and ha,ve been the subject of various studies. The challenges of modeling wedged asymmetric photon beams include the follow-ing: 1) The existence of the wedge causes a dose gradient in the wedge direction as well as altering the longitude profiles due to the scatter from the wedge; 2) The wedge preferentially absorbs the low energy photons of the bremsstrahlung component of the beam and causes beam hardening effect; 3) The wedge attenuates head scatter from the flattening filter and collimators and acts as source of scatter itself; 4) The wedge factor depends on depth and field size[5], which means many more beam data are required to accurately characterize the beams; 5) The combination of asymmetric collimator setting and wedge effect increases the difficulty and complexity of modeling Chapter 1. Introduction to Dose Calculation and Measurement Techniques 18 wedged asymmetric photon beams. Therefore, a simple and accurate dose calculation for wedged asymmetric beams is of great interest. 1.4.1 Tolerances for the Accuracy of Photon Beam Dose Calculations A tolerance of 2% in the dose value or 2mm in the position of an isodose line, whichever is smaller, was proposed for the overall required accuracy in dose cal-culations for use in radiation therapy[6]. In small dose gradient regions, criteria is preferably expressed as a percentage, while in large dose gradient regions it is prefer-ably expressed in a mm shift of the isodose line. A A P M Task Group 23 [7]and the Netherlands Commission on Radiation Dosime-try proposed test packages for evaluation of a treatment planning system. But such test packages have some limitations. New technical developments, such as asymmetric collimators are not induced in the test set. •Venselaar[3] proposed a set of tolerances for photon beam dose calculations. De-viations between results of calculations and measurements is defined as: 8% = 100% x (DCaic - Dmeas)/Dmeas (1.12) Equation 1.12 applies for i = 1,2, 3, where i refers to a region as described below: i = 1, (central beam axis data)high dose, small close gradient, 2% is acceptable for homogeneous, simple geometry; 3% is acceptable for complex beam geometry, such as wedges, inhomogeneities or asymmetry; 4% is acceptable for more complex geometry, i.e. the combinations of above. i = 2,(build-up region of central beam axis, penumbra region of the profiles) high dose, large dose gradient, the acceptable accuracy is 2mm or 10%, 3mm or 15%, 3mm or 15% respectively for increasing complexity as described above. i = 3,(outside cental beam axis region)high dose, small dose gradient, the accept-Chapter 1. Introduction to Dose Calculation and Measurement Techniques 19 able percentages are 3%,3%,4% respectively. For region 4, i = 4,(outside beam edges)low dose, small dose gradient,the accept-able percentages are 3%,4%,5% respectively. Here 5 is defined as: <54 = 100% x (Dcaic - Drneas)/Dmeas>cax (1.13) and DmeaS}Cax is the dose at a point at the same depth but on the central beam axis. 1.4.2 R e v i e w o f S t u d i e s o n A s y m m e t r i c F i e l d s Two documents have been published on monitor unit (MU) calculations in.high energy photon beams, an E S T R O booklet by an I A E A - E S T R O task group[8] and Report'12 of the Netherlands Commission on Radiation Dosimetry (NCS)[9]. Both of these documents support that the close rate at reference depth should be separated into the head and volume scatter components when calculating the number of mon-itor units necessary to deliver the prescribed dose. The head scatter factor can be measured by an ion chamber with a build-up cap of a size large enough to provide dose build-up. There are a large number of investigations on the dose rate (the dose per monitor unit) in asymmetric fields. Khan showed that beam data determined for symmetric fields (e.g.TMR, head scattering factor, off-axis ratio) can be used for calculations of asymmetric photon beams when off-axis softening is accounted for[10]. Chui and Mohan [11] improved Khan's method by separating the off-axis ratio into a boundary factor and a primary off-axis ratio. Tenhunen and Lahtinen separated the field into four quadrants and calculated the dose contribution of each quadrant using head scatter and volume scatter factors for symmetric fields [12]. Marinello and Dutreix separated the influence of each field-defining collimator when calculating the "output in air" of symmetric and asymmetric fields[13]. Kwa used Day's equivalent field size method by applying symmetric dose rates and T M R in asymmetric field [14]. Chapter 1. Introduction to Dose Calculation and Measurement Techniques 20 1.4.3 Previous Studies on Wedged A s y m m e t r i c Fie lds Venselaar and Welleweerd [4] recently showed for a number of commercial treatment planning systems, that the algorithms for calculating monitor units (MUs) in wedged asymmetric fields have their limitations. Deviations up to 13% between the calcu-lated and measured dose were observed at the thin and thick sides of the wedge. Compared with the criteria Venselaar proposed [3], improvements in M U calculation are required. Khan proposed an approach to calculate MUs for wedged asymmetric fields[15] in which close rates of asymmetric fields and off-axis ratios are used to relate the dose in the asymmetric field to the close under reference conditions. The number of monitor units for wedged asymmetric photon field can be calculated by: DreI x TPR(d,rd) x Sc(rc) x Sp(rd) x {SDcal/SPDf x OAR<w(x) xWFxTF (1.14) where DT is dose specified at point P in the center of an asymmetric field at depth d, M U is the number of monitor units, Dref is the dose per M U at a reference point at depth dcai, TPR,{d,r,i) is the tissue phantom ratio for open fields, is the equivalent field size at point P, Sc(rc) is the collimator scatter factor for open fields defined "in air" at depth dcai, Sp(rd) is the phantom scatter factor for open fields at depth dca[, SDcai is the distance from the source to the reference point, SPD is the distance from the source to point P, OARdiW(x) is the off axis ratio to account for wedged asymmetric fields with the field center at off-axis distance x, W F is the wedge factor determined along the central beam axis under full scatter conditions, T F is the transmission factor at point P accounting for beam attenuation. Georg published another model for determining monitor units in wedged asym-metric photon beams when the close prescription point is off axis along the wedged Chapter 1. Introduction to Dose Calculation and Measurement Techniques 21 direction [16]. The dose is given by D(c,x,z) = DRxUx OvJ-(c)x x S;e(c)x x kw(cR)0 x A%e(cR)x x Twe(c,z)x (1.15) where OQF'(C)X is the output ratio determined at 10cm depth in a mini-phantom in a wedged asymmetric field, Spe{c)x is the phantom scatter factor at 10cm depth obtained at the center of a wedged asymmetric field, kw(cR)0 is the wedge factor de-termined under reference conditions along the central beam axis in a water phantom, A^Q{CR)X is the off axis factor for off axis distance x determined in a mini-phantom along the wedge direction, Twe(c, z)x is the tissue-phantom ratio determined in a wedged asymmetric field. ' Smulders's method is similar to Georg's[17]. The dose at a point on the collimator rotation axis in a symmetric, wedged and blocked field is given by D(c, sb, z, w) = DRxUx00{C, W) XSp(sb, zR, w) x kw(cR) x k t ( c R ) x T ( s b , z, w) (1.16) where D(c, sb, z, w) is the dose at depth z in a large water phantom under isocentric conditions, c is the field size defined by the collimator, Sb is the field size defined by the shielding blocks at the point of interest, w indicates the presence of a wedge, D is the absorbed dose per monitor unit, under isocentric conditions determined in a large water phantom in reference conditions of depth (cR = 10cm) and field size {cR — 10cm) at a source to point of interest distance (fR = 100cm), U is the number of monitor units, Oo(c,w) is the output ratio in a wedged field determined at depth R in a mini-phantom for field size c, D0 is the dose determined in a mini-phantom, Sp(sb, zR,w) is the phantom scatter ratio in a wedged field, kw(cR) is the wedge factor determined under reference conditions in a full scatter phantom, T(sb,z,iu) is the tissue-phantom ratio at depth z for field size sb in a wedged field determined in Chapter 1. Introduction to Dose Calculation and Measurement Techniques 22 a full scatter phantom, kt(cR) is the transmission factor for the shadow tray carrying the shielding blocks, t indicates the presence of the shadow tray. The dose in a wedged asymmetric field with its field center at an off-axis point (x,y) can be described by DA(c, s6, x, y, z, w) = D(c, sb, z, w) x A(c, x, z, w) x A(c, y, z, w) (1.17) where . and A(c,x,z,W) = ^ f ^ (1.18) D(c,fR,z,w) A(c,y,^) = ^ f ^ (1.19) D(c,fR,z,w) Eighteen test fields were used by Smulders to test the accuracy of these empirical methods, including some fields of square and rectangular shapes with single and double asymmetric collimation, some fields shaped by M L C (Multi-leaf Collimator) or blocks. The analytical method of Khan showed errors up to 12.8%. The method by Georg shows differences up to 5.4% while only three of eighteen cases had errors larger than 2%. By Smulder's method, the maximum difference found was 6.5% and in 15 cases it was smaller than 2%. Mihailidis et al [18] used primary off axis ratios (POARws) to account for the changes in beam intensity across the field. The primary wedged off axis ratio (POARw) is defined as the ratio of primary dose at off axis point(x,y) to the central axis dose TOAB.O, y. i) = = g t ' i f " ! ('•») Dprim,w{0,0,d,) Dw(0,0,d,rd -> 0) The monitor unit can be calculated by MU = D A l / C F ) (121) kScir^S^r^TMR^r^SCD/SADyWF^r^POARuix^y^d) V ' ; Chapter 1. Introduction to Dose Calculation and Measurement Techniques 23 where Sc(rc) is the collimator scatter factor for collimator field size r c at C A , 5p(rd) is the phantom scatter factor for equivalent size rd at C A , TMR(d,rd) is the tissue-maximum ratio for the open field at C A , WF(d, rd) is the depth and field size depen-dent wedge factor at C A , POARw is the depth-dependent primary wedged off-axis ratio and C F is the additional correction factor such as block trays or compensators. The accuracy of this method was found dependent on the specific wedge used, off-axis distance and depth in the phantom. The accuracy was within 2% in most cases for both 6MV and 18MV photon bemas. 24 Chapter 2 Materials and Methods 2.1 Calculat ion by Eclipse Treatment Planning System The Eclipse treatment planning system in use at the Vancouver Cancer Center where this work is performed, is developed by Varian Medical Systems, Inc. The photon calculation algorithm in Eclipse is the Pencil Beam Convolution (PBC) algorithm. For configuration, the measurements required by the algorithm are PDDs and profiles at 5 depths for open and wedged fields, diagonal profiles for the largest field size at 5 depths for open fields, a longitudinal profile at 1 depth for each wedged field and dose rates for select field sizes. The effect of beam attenuation due to a fixed wedge is accounted for by using the wedged profiles and wedged central axis depth dose curves in the beam reconstruction model[19]. 2.2 Measurements by Ion Chamber The 6MV and 18MV photon beams in-this study were produced by a Varian CL21EX accelerator(Varian Oncology Systems, Palo Alto, C A ) . Physical wedges of 60°, 45°, 30°, 15° were used. There are two wedge configurations of this linac, the upper wedge configuration was investigated in this study. The material for 60° and 45° wedges is lead and the material for 30° and 15° wedges is steel. The maximum Chapter 2. Materials and Methods 25 opening in the non-wedged direction is 40cm for all the wedges and the maximum openings in wedge direction are 15cm, 20cm, 30cm, 30cm for 60°, 45°, 30°, 15° wedges respectively. The X-jaws can perform an over-axis travel of 2cm and the Y-jaws can perform an over-axis travel of 10cm. In this experiment, the Y direction is used as the wedge direction so that very asymmetric fields can be collimated. The source to axis distance is maintained at fOOcm. A l l measurements were made in a solid water phantom (Gammex RMI, Middleton, WI 53562, USA) dimension of 40cm x 40cm x 25cm with an ionization chamber having a sensitive volume of 0.6cm3 (Farmer type 30001 P T W , Freiburg, Germany). An electrometer (#530, Victoreen, Inc) was used. A l l measurements were performed twice and the average of the two measurements are used. 2.3 Verification by Monte Carlo Simulation The EGS4 Monte Carlo code, B E A M , developed by the National Research Council of Canada[20], is a powerful and flexible tool to simulate realistic clinical radiation beams and to obtain a detailed knowledge of the characteristics of therapy beams from accelerators. One of the design features of BEAMnrc is that each part of the accelerator is considered to be a single component module (CM) which takes up an horizontal slab portion of the accelerator. These component modules are re-usable and are all completely independent. Each C M can be used in a wide variety of applications although the name may not describe the full capacity of the module. For example, the JAWS C M is well suited to simulating a wedge[21]. Another feature is the ability to collect phase space files at various planes. The phase space file, which contains particle information such as charge, energy, direction and position, can be recorded at the end of any C M and is re-usable. A model of the Varian 21 E X linear accelerator treatment head was built using Chapter 2. Materials and Methods 26 BEAM-nrc. The model can be visualized in Figure2.1. Dimensions and positions of the component modules are chosen according to documentation provided by Varian. The values of the electron (ECUT) and photon (PCUT) transport cutoff energies are 0.7MeV and O.OlMeV respectively. The threshold energies for electron and photon creation, A E and A P are 0.7MeV and O.OlMeV respectively. The wedge is simulated by the component module JAWS. It has been demon-strated that the C M JAWS can handle simple wedges well[22]. Target(SLABS) Primary collimator(CONESTAK) Be vacuum window(SLABS) Flattening filter(SLABS) Monitor chamber(CHAMBER) Mirror(MIRROR) XYJaws(JAWS) Exit window(SLABS) Wedge(JAWS) Figure 2.1: Schematic diagram of the Varian 21EX treatment head with the asso-ciated component modules listed (not drawn to scale), as configured for BEAMnrc . Chapter 2. Materials and Methods 27 DOSXYZnrc is an EGSnrc-based Monte Carlo simulation program for calculating close distributions in a rectilinear phantom composed of volume elements (voxels) [23]. Density and material in every voxel may vary. A variety of beams may be incident on the phantom, including full phase-space hies from BEAMnrc . Fig.2.2 shows the schematic voxel setting in this work. Figure 2.2: Schematic voxel setting for P D D (in the left) and O A R profile (in the right) in DOSXYZnrc. Not scaled for real voxel size. In order to benchmark the Monte Carlo system, for both 60 degree and 45 degree wedges, the wedged percentage depth doses (SSD.=100cm, field size 10cm x 10cm, voxel size 1 x 1 x 1cm3) were calculated by Monte Carlo simulation and compared with measurements. (See Fig.2.3 and Fig.2.4) The statistic uncertainty in Monte Carlo is within 1% and the Monte Carlo results match the measurements very well (discrepancy < 1%). Cross profiles in the wedged direction were also calculated. For the 60 degree wedge, the maximum opening in the wedged direction is 15cm, so the 15 x 15cm field size was chosen. Again, SSD=100cm is used with depth=5cm. The comparison of measured and calculated cross profiles can be seen in Fig.2.3. The discrepancy is always within 2% and usually even better (< 1%). For the 45 degree wedge, the maximum opening in the wedged direction is 20cm, Chapter 2. Materials and Methods 28 so 20 x 20cm field size is chosen. Again, SSD=100cm is used with depth=5cm. The comparison of measured and calculated cross profiles can be seen in Fig.2.4. The discrepancy is always within 2% and usually even better (< 1%). The results show very good agreement (maximum difference< 2%, most within 1%) between the Monte Carlo calculated and the measured results. This indicates" that Monte Carlo simulation can be used to verify the measurements for wedged asymmetric fields by a Varian CL21EX linear accelerator. Furthermore, this bench-marked Monte Carlo system is reliable to investigate situations where measurements are difficult or impossible and useful for further exploration of the sources of. scatter. 2.4 A n Empirical Correction Method 2.4.1 D o s e C a l c u l a t i o n f o r A s y m m e t r i c F i e l d Kwa et al [14] proposed a dose computation method for asymmetric fields. This method is extended here to wedged asymmetric fields. The correction factor required to account for the reduced dose in an asymmetric field compared with a symmetric field is expressed by the geometric mean of the dose of several rectangular fields. The correction factor for an asymmetric field is given by x y/TMR(2AW - W - 2r) x L)/TMR({W - 2r) x L, where D is the dose rate for the specified field size and T M R is the tissue maximum ratio for the specified field size and depth. The derivation for this expression is as follows: For a,WxL field with the point R along the transverse principal plane being a distance r away from the collimator axis, the two rectangular fields providing contribution to the dose at R would be (W — 2r) x L and (W + 2r) x L as shown in Fig.2.5A. where r is some distance within the field edge. For an asymmetric field AW x L shown in Fig.2.5B, the two Chapter 2. Materials and Methods 29 PDD for 60 wedge — Measurement • Monte Carlo 0 5 10 15 20 25 30 Deptli(cm) (a) Profile for 60 Wedge — Measurement • Monte Carlo 15 | off-axis distance (cm) (b) Figure 2.3: (a)Comparison of measured and calculated percentage depth dose (PDD)for 60 degree wedge with field size 10cm x 10cm and SSD=100cm, normal-ized to dose at dmax. (b) Comparison of measured and calculated cross profile in the wedged direction for 60 degree wedge with field size 15cm x 15cm, SSD=100cm and depth=5cm, normalized to the central axis dose. Chapter 2. Materials and Methods 30 PDDfoi45Weclae 10 15 20 Deptli(cni) - Measurement Monte Carlo 30 (a). Profile for 45 Wedge 4-6--h+-• Measurement Monte Carlo -15 -10 -5 0 5 10 off axis distance (cm) 20 (b) Figure 2.4: (a)Comparison of measured and calculated percentage depth dose (PDD)for 45 degree wedge with field size 10cm x 10cm and SSD=100cm, normal-ized to dose at dmax. (b) Comparison of measured and calculated cross profile in the wedged direction for 45 degree wedge with field size 20cm x 20cm, SSD=100cm and depth=5cm, normalized to central axis dose. Chapter 2. Materials and Methods 31 Figure 2.5: The equivalent held contributions used in dose calculation are illustrated. In A , the absorbed close to a point R in a symmetric field W x L is equivalent to the average of the two doses at the center of the two symmetric fields of (W + 2r) x L and (W — 2r) x L. In B, the absorbed dose at a point R in an asymmetric field AW x L is equivalent to the average of the two doses at the center of the two symmetric fields of (W + 2?-) x L and (2AW - W - 2r) x L. In C, the absorbed dose at a point P along the collimator axis in an asymmetric field is equivalent to the average of the two doses at the center of the two symmetric fields of W x L and (2AW — W) x L. (Reproduced with permission from Kwa et al[14].) Chapter 2. Materials and Methods 32 rectangular fields centered at the point R a distance r from the central axis would be (W + 2r) x L and (2 AW - W - 2r) x L. In Fig.2.5C, the absorbed dose at a point P along the collimator axis in an symmetric held is equivalent to the average of the two doses at the center of the two symmetric fields of W x L and (2AW — W) x L. The dose rate along the collimator axis in an asymmetric field (r=0), DA(AW X L) is approximated by the arithmetic mean of D(W x L) and D((2AW — W) x L), which is DA(AW x L) = (D(W x L) + D{2AW - W) x L)/2 (2.1) The dose reduction in an asymmetric field AW x L as compared to the corresponding field W x L can be represented by a correction factor which is the ratio of the dose rate in an asymmetric field to the dose rate in the corresponding symmetric field. This correction factor (CF) at the collimator axis can be represented by CF^.AWXL) = y X f f D(W x L) (D(W x L) + D({2AW — W) x L))/2 D(W x L) (2-2) In order to simplify the calculation, the above C F (Eq.2.2) can be expressed as the geometric mean instead of the arithmetic mean of the dose rates, which is 'D(W x L) x D((2AW - W) x L) CF(dmax, AW x L) = 2L : V 7 D(W x L) V D{WxL) Then the dose rate along the collimator axis in an asymmetric field can be calcu-Chapter 2. Materials and Methods 33 lated from the correction factor, DA(AW x L) = D{W x L) x CF(dmax, AW x L) D { w x L) x W™" - ^ * L> = y ^ O ^ x L) x Z)((2Aiy - x L) (2.4) Similar to Eq.2.1, the dose rate at.a point an off-axis distance r from the collimator axis along the transverse plane in an asymmetric field can be written as ri / „ A D f J r r / r,D((2AW - W - 2r) x L) + D({W + 2r) x L) DA{r, AWxL) = OAR(dmax, r, WxL)-^ ^ '- '-(2.5) And the same off-axis point in a symmetric field is b(r, „ x L) = OARi^.r, W X + 2r) X L ) + D((W - 2r) X L) ^ So the correction factor is nr-iA u/ r\ DA(r,AWxL) CF(dmax,r, W x L) = ) D(r, W x L) (D((2AW - W - 2r) x L) + D((W + 2r) x L))/2 (D({W + 2r) xL) + D{{W - 2r) x L))/2 (2.7) Note that if the off axis point is towards the asymmetric collimator field edge, r is positive; if the off axis point is away from the asymmetric collimator edge, r is negative. Again, using geometric means, the calculation for C F is simplified. , „ „ rs D((2AW - W - 2r) x L) , s C F ( * ~ A W X L ) " V DdW^r^L) (2-8' Chapter 2. Materials and Methods 34 Then the asymmetric held close rate at dmax at any off axis point can be calculated from the correction factor: DA(r, AW x i ) = D(W x L) x OAR(r, dmax, W x L) x C7F(d m a x , r, A i V x L) . N ID((2AW - W - 2r) x i ) = £> W x L x 0>LR r . f l U * . ^ x L) x W U • ^ y Z?((W - 2r) x L) (2.9) The above development applies to dmax. To extend this to any depth d, we note that, for any depth along the transverse plane, the correction factor can be represented by the tissue maximum ratio (TMR). The absorbed dose D(d,W x L)) at point P along the collimator axis at depth cl of a symmetric field can be given as: D(d, W x L) = MU x D(W x V) x TMR(d, W x L) (2.10) For the same point P in an asymmetric field AW x L, the absorbed dose can be given from the two fields W x L and (2AW -W) x L, D(d, AW x L ) = MU x — ^ -TMR(d, W x L) + TMR(d, (2AW - W) x L) (2.11) Rewriting in terms of D(d, AW xL) = MU x A / D ( W X L) X D((2AW -W)XL) x y/TMR(d, W xL)x TMR(d, (2AW - W) x L) (2.12) The correction factor which is the ratio of the absorbed dose in the asymmetric field to that in the symmetric field at the same point P, can be described as Chapter 2. Materials and Methods 35 <D{{2AW - W) x L) x TMR(d, (2AW -W)xL) D{W x L) x TMR(d, W x L) (2.13) Similarly for an off-axis point R at an off-axis distance r, the correction fac-tor CF(r, d, AW x L) for an asymmetric field would be the ratio D(r, d, AW x L)/D(r,d,W x L), where D(r, d,W x L) = MU x JD((W - 2r) x L) x D((W + 2r) x L) x y/TMR(d, (W - 2r) x L) x TMR(d, (W + 2r) x L) x OAR{r, d, W x L) (2.14) D(r, d, AW x L) = MU x yj D((W + 2r) x L) x D((2AW - W -2r) x L) : y/TMR(d, (W + 2r) x L) x TMR(d, (2AW -W- 2r) x L) x OAR(r, d, W x L) (2.15) and D{r,d,AWxL) CF(r, d, AW x L) = D(r,d,W x L) ID'{{2AW - W - 2r) x L) TMR(d, (2AW - W - 2r) x L) D((W - 2r) x L) X TMR(d, (W - 2r) x L) (2.16) Now, the correction factor, which depends on the sizes of the asymmetric and Chapter 2. Materials and Methods 36 symmetric fields, beam energy, depth, off-axis ratio, distances with respect to the four field defining collimators, is represented by a function of dose rate and tissue maximum ratios (TMR). So the absorbed dose at point R in an asymmetric field can be calculated by D(r,d,W x L) M U = : L i _ 2 1 D(W x L) x TMR(d, M x L) x OAR(r, d, W x L) x CF(r, d, AW x L) (2.17) For a specific case, when R is at the center of the asymmetric field which is r a s y m away from the collimator axis, r = —rasym = (AW — W)/2, D(AW x L) TMR(d,AW x L) D({2W - AW) x L) X TMR(d, (2W - AW) x L) (2.18) 2.4.2 Extrafocal Radiation: An Analysis of Head Scatter A Monte Carlo study[24] on head scatter concluded that the collimator effect was determined primarily by the volume of the extended scatter source. The largest sources of head scatter were determined to be the flattening filter and the primary collimator. For a particular field, the magnitude of the head scatter contribution to dose is determined by the scattering source seen from the point of interest in phantom. An extrafocal source model is helpful to explain the dependence of head scatter on field size[25]. In this model, the x-ray source of a medical linear accelerator is described by two components: a small but intense focal component and a broadly distributed extrafocal component of low intensity. The extrafocal component is so broad that it can be shielded by the field defining collimators. The extrafocal com-ponent was found to account for 12% of the energy fluence on the central axis of the 6MV photon beam from a Varian Clinac 2100C accelerator[25]. As shown in Fig. 2.6 (a), the focal spot is located within the x-ray target, while the extra focal source is CF(rasym, d, AW x i ) = Chapter 2. Materials and Methods 37 located in a plane at the base of the field flattening filter. The energy fluence at a point of interest depends on field size because the extrafocal source can be shielded by the upper and lower jaws. The visible portion of the extrafocal source seen from the point of interest is determined by back projecting the field aperture onto the extrafocal plane. Compare Fig. 2.6 (a) and (b), two fields, which are the same field size but at different off axis distances, they correspond to different extrafocal sources. That is the reason that the head scatter factors are different for the two fields. In Fig. 2.6(c) and (d), the extrafocal radiation is reduced by the wedge. (a) (bl 1=1 <«) Figure 2.6: The two component x-ray source model. The radiation beam is com-prised of x-ray produced at the focal spot and scattered x-rays, which from a broadly distributed extrafocal source, (a) and (b) are for non-wedged fields, (c) and (d) are for wedged fields. 2.4.3 Extension to Wedged Asymmetric Fields: Correction for the Thin End For wedged asymmetric fields at the thin end of the wedge, it is expected that the reduction of the extrafocal radiation by the wedge may be negligible. If this is indeed the case, the correction method for asymmetric open beams by Kwa can be easily Chapter 2. Materials and Methods 38 extended to the thin end of the wedge. The dose rate is replaced by wedged dose rate for the specific wedge and T M R is replaced by wedged T M R for the specific wedge. Eq.2.18 can be rewritten as DW((2W - A W ) x L ) TMRw(d, (2W - A W ) x L ) (2.19) 2.4.4 Correction for the Thick End For the thick end of the wedge, it is anticipated that the wedge reduces the extrafocal radiation to a negligible level. It is expected that the head scatter contribution is almost independent on the off-axis distance, therefore central axis beam data may be used for asymmetric fields at the thick end of the wedge. At dmax, n T ? D w j F S = asymm) ^J-"w,thick — —• — [Z.ZU) . D w ( F S = sym) where D W ( F S = asymm) and D W ( F S = sym) are the on-axis wedged dose rates. The correction factor at any depth d can be written as Dw(asym,d) Dw(asym,dmax) x TMRw(asym, d) w,tinck .Dw(sym,d) Dw(sym,dmax) x TMRw(sym,d) _ Dw(asym) TMRw(asym,,d,) Dw{sym) X TMRw(sym,d) A l l the data are central axis beam data. 39 Chapter 3 Results and Discussion 3.1 Comparison of Measurements and Eclipse Results Table3.1-Table3.16 show the comparisons of measured absorbed closes for wedged asymmetric fields and corresponding symmetric fields with Eclipse treatment plan-ning system calculations when 200MU is delivered. The comparisons are made for both 6MV and 18MV photon beams at depths of dmax and 10cm with SAD=100cm. A l l the symmetric helds are rectangular and 20cm in the X direction (non wedged direction). The maximum openings in the Y direction are 15cm, 20cm, 30cm, 30cm respectively for 60°, 45°, 30°, 15° wedges. The asymmetric helds are 20cm in the X direction and 5 to 15cm in the Y direction. A negative sign indicates the thin end of the wedge. A l l the measurements for wedged asymmetric helds are made at the centers of the helds. The uncertainty of measurement is about 1% due to the fluctuation of the machine output and uncertainty in ion chamber positioning. For the symmetric fields, most Eclipse results match the measurements within 2%, usually within 1%. Only for some cases, when the measured points are close to the edge of the wedged fields, the percentage differences are larger than 2% but still within 3%. Since the criteria of dose calculation for wedged photon beam is within 2% by Venselaar, the Eclipse treatment planning system performs well for such geometries. For the wedged asymmetric fields, the criteria is within 4%. Most of the calculated Chapter 3. Results and Discussion 40 doses are within 4% with respect to the measurements. Up to 6.5% differences are observed for the 30° wedge for both 6MV and 18MV photon beams. Both cases are at the thin end of the wedge with off-axis distance 12.5cm and 5cm field width in the wedged direction. Generally, the more asymmetric the field is, the greater the difference between the Eclipse calculation and the measurement. The doses at the thin end of the wedges are usually underestimated while the doses at the thick end of the wedges are usually overestimated. Chapter 3. Results and Discussion 41 Table 3.1: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 60 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=1.5cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) • %diff (cGy) %diff -7.5 7.5 -5 126.30 . 128.34 1.6 N / A N / A -7.5 7.5 -3.75 112.6 112.6 0.0 N / A N / A -7.5 7.5 -2.5 100.9 101.2 0.3 N / A N / A -7.5 7.5 0 83.0 83.2 0.2 N / A N / A -7.5 7.5 2.5 69.4 69.5 0.2 N / A N / A -7.5 7.5 3.75 64.0 64.3 0.5 N / A N / A -7.5 7.5 5 59.1 59.6 0.9 N / A N / A -7.5 -2.5 -5 120.3 117.2 -2.6 119.3 -0.8 -7.5 0 -3.75 108.7 106.3 -2.2 108.3 -0.4 -7.5 2.5 -2.5 98.6 97.5 -1.1 98.5 -0.1 -2.5 7.5 2.5 67.1 67.0 -0.1 67.4 0.5 0 7.5 3.75 60.3 60.6 0.5 60.7 0.7 2.5 7.5 5 54.2 54.8 1.3 54.6 0.7 Chapter 3. Results and Discussion 42 Table 3.2: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 60 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 MC is delivered under condition of SAD=f00cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -7.5 7.5 -5 100.3 103.1 2.8 N / A N / A -7.5 7.5 -3.75 90.8 92.7 2.1 N / A N / A -7.5 7.5 -2.5 82.5 84.6 2.5 N / A N / A -7.5 7.5 0 69.4 69.9 0.7 N / A N / A -7.5 7.5 2.5 58.0 59.0 1.7 N / A N / A -7.5 7.5 3.75 52.9 54.2 2.5 N / A N / A -7.5 7.5 5 48.7 50.0 2.7 N / A N / A -7.5 -2.5 -5 93.7 92.4 -1.4 92.2 -1.6 -7.5 0 -3.75 86.8 86.2 -0.7 85.9 -1.0 -7.5 2.5 -2.5 80.2 80.5 0.4 80.8 0.7 -2.5 7.5 2.5 55.0 56.2 2.2 55.4 0.8 0 7.5 3.75 48.5 50.6 4.3 48.9 0.8 2.5 7.5 5 42.7 45.1 5.6 43.0 0.6 Chapter 3. Results and Discussion 43 Table 3.3: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 45 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=1.5cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -10 10 -7.5 147.9 148.3 0.2 N / A • N / A -10 10 -5 130.0 129.8 -0.2 N / A N / A -10 10 -2.5 114.9 115.0 0.2 N / A N / A -10 10 0 103.2 103.5 0.3 N / A N / A -10 10 2.5 94.3 94.3 0.0 N / A N / A -10 10 5 85.3 86.2 1.0 N / A N / A -10 10 7.5 7 6 ! 76.9 1.0 N / A N / A -10 -5 -7.5 139.5 135.2 - 3 ! 138.7 -0.6 -10. • 0 -5 125.7 123.4 -1.9 125.3 -0.3 -10 5 -2.5 113! 112.7 -0.3 113.0 - 0 ! -5 10 2.5 92.5 92.2 -0.3 92.7 0.2 0 10 5 81.4 81.6 0.2 81.6 0.2 5 10 7.5 69.3 1 70.5 1.8 69.9 0.8 Chapter 3. Results and Discussion 44 Table 3.4: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 45 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. . Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -10 10 -7.5 115.7 116.1 0.4 N / A N / A -10 10 -5 105.3 105.1 -0.3 N / A N / A -10 10 -2.5 94.9 94.9 -0.1 N / A N / A -10 10 0 85.9 85.9 0.0 N / A N / A -10 10 2.5 • 78.8 78.5 -0.5 N / A N / A -10 10 5 70.8 70.9 0.2 N / A N / A -10 10 7.5 62.0 62.5 0.8 - N / A N / A -10 -5 -7.5 ' 106.6 103.3 -3.0 105.1 , -1.4 -10 0 -5 101.1 99.8 -1.3 100.1 -1.0 -10 5 -2.5 93.2 92.6 -0.6 92.8 -0.4 -5 10 2.5 76.2 76.5 0.4 76.9 0.9 0 10 5 66.2 67.4 1.8 66.4 0.3 5 10 7.5 54.2 56.1 3.6 53.9 -0.5 Chapter 3. Results and Discussion 45 Table 3.5: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 30 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=1.5cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical , Empirical (cm) (cm) (cm) (cGy) (cGy) %diff • (cGy) %diff -15 15 -12.5 185.6 . 181.6 -2.1 N / A N / A -15 15 -10 168.7 169.5 0.5 N / A N / A -15 15 -7.5 ' 153.3 152.6 -0.5 N / A N / A -15 15 0 121.4 123.1 1.4 • N / A N / A . -15 15 7.5 100.2 102.1 1.9 N / A N / A -15 15 10 93.4 95.1 1.8 N / A N / A -15 15 12.5 89.3 91.1 2.0 N / A N / A -15 -10 -12.5 170.4 159.3 -6.5 171.1 0.4 -15 -5 -10 159.5 153.9 -3.5 160.0 0.3 -15 0 -7.5 147.5 145.6 -1.3 147.9 0.3 0 15 7.5 95.6 96.9 1.4 95.7 0.1 5 15 10 86.1 88.0 2.2 86.4 0.3 10 15 12.5 78.2 80.2 2.5 78.4 0.3 Chapter 3. Results and Discussion 46 Table 3.6: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 30 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -15 15 -12.5 142.3 141.6 -0.5 N / A N / A -15 15 -10 134.6 132.4 -1.7 N / A N / A -15 15 -7.5 125.3 124.4 -0.7 N / A N / A -15 15 0 101.2 101.6 0.4 N / A N / A -15 15 7.5 82.5 83.4 1.1 N / A N / A -15 15 10 76.3 76.7 0.5 N / A N / A -15 15 12.5 71.6 72.3 1.0 N / A N / A -15 -10 -12.5 126.6 121.6 -3.9 126.6 0 -15 -5 -10 126.1 122.4 -2.9 125.5 -0.5 -15 0 -7.5 120.1 118.2 -1.6 119.7 -0.3 0 15 7.5 77.8 79.6 2.3 77.5 -0.4 5 15 10 69.1 71.4 3.4 68.6 -0.7 10 15 12.5 60.1 63.0 4.8 59.6 -0.9 Chapter 3. Results and Discussion 47 Table 3.7: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 15 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, cl=1.5cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -15 15 -12.5 186.5 185.4 -0.6 N / A N / A -15 15 -10 178.9 177.3 -0.9 N / A N / A -15 15 -7.5 173.6 172.8 -0.5 N / A N / A -15 15 0 155.5 155.7 0 ! N / A N / A -15 15 7.5 140.9 143.2 1.6 N / A N / A -15 15 10 137.4 138.4 0.7 N / A N / A -15 15 12.5 135.7 136.8 0.8 N / A N / A -15 -10 -12.5 172.6 166.8 -3.4 173.3 0.4 -15 -5 -10 169.8 166.3 - 2 ! 170.5 0.4 -15 0 -7.5 168.0 166.8 -0.7 168.0 0 0 15 7.5 136! 137.6 1!. 135.7 -0.3 5 15 10 129.4 130.0 0.5 128.9 -0.4 10 15 12.5 122.7 123.3 0.5 121.8 -0.7 Chapter 3. Results and Discussion 48 Table 3.8: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6MV 15 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical. (cm) (cm) (cm) (cGy) (cGy) %cliff (cGy) %diff -15 15 -12.5 144.8. 144.8 0.0 N / A N / A -15 15 -10 142.7 141.0 -1.2 N / A N / A -15 15 -7.5 140.6 139.6 -0.7 N / A N / A -15 15 0 127.2 127.9 0.6 N / A N / A -15 15 7.5 115.2 116.0 0.7 N / A N / A -15 15 10 110.7 111.0 0.3 N / A N / A -15 15 12.5 107.1 107.9 0.7 N / A N / A -15 -10 -12.5 129.1 126.5 -2.0 129.9 0.6 -15 -5 -10 133.9 132.2 -1.3 133.8 -0.1 -15 0 -7.5 135.1 134.3 -0.6 134.8 -0.2 0 15 7.5 110.2 111.7 1.4 109.2 -0.9 5 15 10 102.5 104.5 2.0 101.1 -1.4 10 15 12.5 92.8 95.0 2.4 90.5 -2.5 Chapter 3. Results and Discussion 49 Table 3.9: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 60 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=3.2cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -7.5 7.5 -5 136.6 138.0 1.0 N / A N / A -7.5 7.5 -3.75 123.4 123.2 -0.2 N / A N / A -7.5 7.5 -2.5 110.6 111.0 0.4 N / A N / A -7.5 7.5. 0 91.3 92.0 0.8 N / A • N / A -7.5 7.5 2.5 76.8 77.4 • 0.8 N / A N / A -7.5 7.5 3.75 71.6 72.5 1.3 N / A N / A -7.5 7.5 5 65.9 67.0 1.7 N / A N / A -7.5 -2.5 -5 128.0 125.9 -1.7 127.4 -0.5 -7.5 0 -3.75 118! 116.4 -1.4 ll'6.9 -1.0 -7.5 2.5 -2.5 107.7 107.0 -0.6 107.4 -0.3 -2.5 7.5 2.5 73.2 74.4 L6 74.2 1.3 0 7.5 3.75 66.3 68.1 2.7 67.6 1.9 2.5 7.5 5 58.6 6 1 ! 4.3 59.8 2 ! Chapter 3. Results and Discussion 50 Table 3.10: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 60 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 OAP Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff • -7.5 7.5 -5 122.4 124.6 1.8 N / A N / A -7.5 • 7.5 -3.75 111.5 111.1 -0.3 N / A N / A -7.5 7.5 -2.5 99.9 100.5 0.6 N / A N / A -7.5 7.5 0 82.3 82.4 0.1 N / A N / A -7.5 7.5 2.5 68.8 69.2 0.6 N / A N / A -7.5 7.5 3.75 64.0 64.7 1.1 N / A N / A -7,5 7.5. 5 58.3 59.3 1.7 N / A N / A -7.5 -2.5 -5 115.2 112.0 -2.8 114.6 -0.5 -7.5 0 -3.75 107.2 104.7 -2.3 106.1 -1.0 -7.5 2.5 -2.5 97.4 97.0 -0.4 97.1 -0.3 -2.5 7.5 2.5 66.1 67.1 1.5 66.8 1.0 0 7.5 3.75 59.7 61.2 2.5 60.7 1.7 2.5 7.5 5 52.2 54.4 4.2 53.0 1.5 Chapter 3. Results and Discussion 51 Table 3.11: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 45 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=3.2cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff • (cGy) %diff -10 10 .-7.5 158.0 157.1 -0.6 N / A N / A -10 10 -5 141.6 140.1 - 1 ! N / A N / A -10 10 -2.5 125.9 125.8 - 0 ! N / A N / A -10 10 0 112.6 112.9 0.2 N / A N / A -10 10 2.5 . 103.2 103.6 0.4 N / A N / A -10 10 5 94.4 95.5 1 ! N / A N / A -10 10 7.5 84.7 86.4 1.9 N / A N / A -10 -5 -7.5 146.0 140.6 -3.8 146.0 0 -10 0 -5 135.9 ' 133.2 -2.0 135.9 0 -10 5 -2.5 123.4 122.9 -0.4 122.8 -0.5 -5 10 2.5 100.5 101.3 0.7 101.5 1.0 0 10 5 88.6 90.6 2.2 90.1 1.7 5 10 7.5 74.9 76.9 2.7 75.9 1.4 Chapter 3. Results and Discussion 52 Table 3.12: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 45 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 MU-is delivered under condition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed closes by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -10 10 -7.5 141.3 142.7 0.9 N / A N / A -10 10 -5 127.1 126.8 -0.2 N / A N / A -10 10 -2.5 113.3 113.6 0.2 N / A N / A -10 10 0 101.4 101.4 0 N / A N / A -10 10 2.5 92.5 93.3 0.8 N / A N / A -10 10 5 84.1 85.4 1.5 N / A N / A -10 10 7.5 74.8 76.8 2.7 N / A N / A -10 -5 -7.5 131.2 126.5 -3.5 131.2 0 -10 0 -5 122.4 120.6 -1.5 122.4 0 -10 5 -2.5 111.4 111.4 0 110.7 -0.6 -5 10 2.5 90.7 91.6 1.0 91.2 0.5 0 10 5 79.8 81.5 2.2 80.4 0.7 5 10 7.5 67.0 ' 68.8 2.8 67.1 0.2 Chapter 3. Results and Discussion 53 Table 3.13: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18A4V 30 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=3.2cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -15 15 -12.5 196.0 191.0 -2.6 N / A N / A -15 15 -10 184.2 178.9 -2.9 N / A N / A -15 15 -7.5 172.1 167.9 -2.4 N / A N / A -15 15 0 142.4 141.5 -0.6 N / A N / A -15 15 7.5 123! 123.8 0.6 N / A N / A -15 15 10 116.8 118.0 1.0 N / A N / A -15 15 12.5 111.9 113.2 1.2 N / A N / A -15 -10 -12.5 177.5 165.8 -6.6 179.5 1 ! -15 -5 -10 173! 166.0 - 4 ! 174.5 0.8 -15 0 -7.5 165.3 161.2 -2.5 166.3 0.6 0 15 7.5 117.3 117.9 0.5 118.0 0.6 5 15 10 107.8 108.4 0.6 108.2 0.4 10 15 12.5 98.0 97.5 -0.5 97.3 -0.7 Chapter 3. Results and Discussion 54 Table 3.14: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 30 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 O A P Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -15 15 -12.5 173.7 172.4 -0.7 N / A N / A -15 15 -10 165.4 162.5 -1.8 N / A N / A -15 15 -7.5 154.4 152.2 -1.4 N / A N / A -15 15 0 127.9 127.6 -0.2 N / A N / A -15 . 15 7.5 110.5 111! 0.5 N / A N / A -15 15 10 105.2 106.8 1.5 N / A N / A -15 15 12.5 100! 101.7 1,6 N / A N / A -15 -10 -12.5 158.4 150.6 -4.9 160.3 1.2 -15 -5 -10 157.0 152.7 -2.7 157.8 0.5 -15 0 -7.5 149.5 147.0 -1.7 149.9 0.3 0 15 7.5 106.5 107.2 0.7 106.7 0.2 5 15 10 98.6 99.7 1 ! 98.7 0 ! 10 15 12.5 88.9 89.8 1.0 88.0 -1.0 Chapter 3. Results and Discussion 55 Table 3.15: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 15 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=3.2cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I (cm) Y2 (cm) O A P (cm) Measure (cGy) Eclipse (cGy) Eclipse %diff Empirical (cGy) Empirical %diff -15 15 -12.5 198.0 192.7 -2.7 N / A N / A -15 15 -10 192.0 187.4 -2.4 N / A N / A -15 15 -7.5 187.9 184.2 -2.0 N / A N / A -15 15 0 170.1 169.4 -0.4 N / A N / A -15 15 7.5 159.6 161.0 0.9 N / A N / A -15 . 15 10 156.7 157.4 0.4 N / A N / A -15 15 12.5 1 5 4 . 1 155.6 1.0 N / A N / A -15 -10 -12.5 179.6 170.1 -5.3 183.4 2.1 -15 -5 -10 181.0 175.1 -3.3 183.4 1.3 -15 0 -7.5 181.3 177.0 -2.4 182.0 0.4 0 15 7.5 153.6 154.3 0.5 154.1 0.3 5 15 10 146.7 146.7 0 147.4 0.5 10 15 12.5 137.9 136.4 -1.1 138.7 0.6 Chapter 3. Results and Discussion 56 Table 3.16: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 15 degree wedge. Y I and Y2 indicate the collimator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition of SAD=100cm, d=10cm, Xl=X2=10cm. Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown. Y I Y2 OAP Measure Eclipse Eclipse Empirical Empirical (cm) (cm) (cm) (cGy) (cGy) %diff (cGy) %diff -15 15 -12.5 175.0 174.2 -0.5 N / A N / A -15 15 -10 172.0 170.1 - 1 ! N / A N / A -15 15 -7.5 168.5 166.4 -1.3 N / A N / A -15 15 0 152.7 152.8 0 ! N / A N / A -15 15 7.5 143.4 144.2 0.6 N / A N / A -15 15 10 140.4 142.7 1.6 . N / A N / A -15 15 12.5 136.9 139.4 1.8 N / A N / A -15 -10 -12.5 159.7 154.6 -3.2 162.7 1.9 -15 -5 -10 163.8 161.0 -1.7 164.9 0.7 -15 0 -7.5 163.7 161.2 -1.5 163.7 0 0 15 7.5 139.1 139.9 0.6 139.0 -0.1 5 15 10 133.5 134.2 0.5 133.0 -0.4 10 . 15 12.5 124.5 124.4 -0.1 122.4 -1.7 Chapter 3. Results and Discussion 57 3.2 Monte Carlo Results Fig.3!-Fig.3.4 show the Monte Carlo simulation results. For 60° and 45° wedges, all the measured absorbed doses for wedged asymmetric fields were also calculated by Monte Carlo simulation. Very good agreement with measurement is shown for both thin end.and thick end. The maximum percentage difference is 2%. This can be caused by a measurement error of up to 1% and Monte Carlo uncertainty of f %. It takes about one hour of computation time to get one simulation in dosxyz. 30° and 15° wedges can be simulated with the same method. The Monte Carlo simulation can verify the ion chamber measurements and provide an accurate method to calculate dose distributions in wedged asymmetric fields. As shown in Fig. 3.5, the Eclipse planning system only accounts for the reduction of the field size without distinguishing whether the smaller asymmetric field is at the thin end or the thick end of the wedge. Although the algorithm in the treatment planning system is not explicitly described, from the calculation of ratio of dose rates, one can see that the Eclipse planning system calculates the dose at the thin end and thick end by using the dose rate D for symmetric fields. However, both the ion chamber measurements and Monte Carlo simulation support that the ratios of the absorbed dose in the wedged asymmetric field to those in the wedged symmetric field are different at the two ends. In order to better understand head scatter and phantom scatter, we ran the Monte Carlo simulation was performed for asymmetric fields defined by block placed under the wedge instead of by linac jaws. This kept the head scatter component constant and varied only the phantom scatter component of dose. A 45 degree- wedge is used with symmetric field size 20 x 20 and asymmetric field size 5 x 20, 7.5cm from the central axis. The setup is shown in Fig.3.6. In Fig.3.6 a, doses at the thick end and the thin end are calculated for wedged symmetric fields. In Fig.3.6 b and c, doses in asymmetric fields as defined by block are calculated for both the thin end Chapter 3. Results and Discussion 58 2 • 1 • a a) 1 1 0 $ -6 -4 -2 ( Q . • - i -2 a B -3 off axis dis 0 • Moiife Carlo ) 2 • 4 6 • Eclipse taiice (cm) Figure 3.1: Percentage difference between measured and Monte Carlo calculated absorbed doses for asymmetric fields as a function of off axis distance in the wedge direction for the 6MV beam with 60 degree wedge at dmax. Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups. Chapter 3. Results and Discussion 59 5 4 3 . O S 2 1 5 , , • r • B • • • i i i • Monte Carlo • Eclipse * 0 °'" -6 * -4 " -2 I B -2 • -3 off axis dis ) 2 • 4 6 tance (cm) Figure 3.2: Percentage difference between measured and Monte Carlo calculated absorbed doses for asymmetric fields as a function of off axis distance in the wedge direction for the 6MV beam with 60 degree wedge at 10cm. Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups. Chapter 3. Results and Discussion 60 3 2 QJ 1 1—1 1> i i ^ • • ? i—< 1 1 6-/!> a 4=1 -10 » -5 ( Q • - 1 a -3 -4 off axis clis B • • Moiite Carlo ) 5 10 - r " Eclipse • tance (cm) Figure 3.3: Percentage difference between measured and Monte Carlo calculated absorbed doses for. asymmetric fields as a function of off axis distance in the wedge direction for the 6MV beam with 45 degree wedge at dmax. Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups. Chapter 3. Results and Discussion 61 CD -10 - 5 • -1 -2 -3 -4 10 • Monte Carlo • Eclipse off axis distance (cm) Figure 3.4: Percentage difference between measured and Monte Carlo calculated absorbed doses for asymmetric fields as a function of off axis distance in the wedge direction for the 6MV beam with 45 degree wedge at 10cm. Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups. Chapter 3. Results and Discussion 62 Ratio for 60° Wedge at 10 a n 1. 1 1 1 • ;>-' - • - Measurement • Eclipse • Monte Carlo » _ ~- U.V.' •••• n o S . N . * u. J 1 1 1—8TS5-\ i i i - 6 4 - 2 0 2 4 6 off axis distance (an) Figure 3.5: Ratios of the absorbed dose in the wedged asymmetric fields to those in the wedged symmetric fields are shown by ion chamber measurement, Eclipse treatment planning system and Monte Carlo simulation. a) Figure 3.6: The test fields are demonstrated, a) wedged symmetric field, b) wedged asymmetric field at thin end, c) wedged asymmetric field at thick end. Chapter 3. Results and Discussion 63 and the thick ends. The ratios between the dose for asymmetric blocked field and corresponding symmetric field are 0.980 at the thick end and 0.982 at the thin end of the wedge. Within the 1% uncertainty of Monte Carlo simulation, these two values can be considered identical. This ratio is accounted for by the phantom scatter only. This indicates that the discrepancy in correction factor between the thick and the thin ends of the wedge is due to the head scatter effect. Chapter 3. B,esults and Discussion 64 3.3 Results of the Empirical Correction 3.3.1 6MV Photon Beam Fig.3.7-Fig.3.10 show the correction factors, i.e., the ratios of absorbed doses of wedged asymmetric helds to the closes of corresponding wedged symmetric helds. The Eclipse planning system calculated the ratio well in thick end with a maximum difference of 2% but at the thin end up to 6.5% difference is found. Our correction method reduced the maximum difference at the thin end from 6.5% to 2%, and at the thick end from 2% to 1% in most cases. Chapter 3. Results and Discussion 65 Correction Factor for 60° Wedae 6 M V at dmax fe O 1 1 1 6T9--6 -4 -2 0 2 off axis distance(cm) • Measurement I • Eclipse « Empirical fe o Correction Factor for 60° Wedse 6 M V at 10cm -6:9--1 6r$5--2 0 - 2 off axis distance(cni) • Measurement! a Eclipse * Empirical Figure 3.7: The correction factors, i.e., the ratios of the absorbed dose in the asym-metric held to those in the symmetric held are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 6MV photon beam with 60° wedge at dmax and 10cm. Chapter 3. Results and Discussion 66 o o fe -10 Correction Factor for 45° Wedse 6 M V at dmax • Measurement • Eclipse « Empirical 0 off axis distance(cm) 10 O -10 Correction Factor for 45° Wedse 6 M V at 10cm -fb95-• Measurement • Eclipse • Empirical - 1 0r«5--5 0 5 off axis distance(cm) 10 Figure 3.8: The correction factors, i.e., the ratios Of the absorbed dose in the asym-metric held to those in the symmetric held are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 6 M V photon beam with 45° wedge at dmax and 10cm. Chapter 3. Results and Discussion 67 Correction Factor for 30° Wedge 6MV at dmax ±705-o U -h - 0 T 9 5 -Measiireinentl Eclipse Empirical -15 -10 - 1 0TS5 -5 0 5 off axis distance(cm) 10 15 Correction Factor for 30° Wedge 6MV at 10cm -h05--0T95-6T9~ -0TS5-• Measmenientl B Eclipse * Empirical 1 1 1 0T8--15 -10 -5 0 ' 5 off axis distance(cm) 10 15 Figure 3.9: The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 6MV photon beam with 30° wedge at dmax and 10cm. Chapter 3. Results and Discussion 68 O Hi o o Correction Factor for 15° Wedge 6 M V at dmax •i r\ r l . U J i nn i I Xiv ' • • A fl r t • u.y.j » • n u.yu 1 L - 1 0r85-• i i • Measurement I • Eclipse • Empirical -15 -10 -5 0 5 off axis distance(cm) 10 15 Correction Factor for 15° Wedse 6 M V at 10cm -ft9d--OTS^-1 1 ; 1 6TS6--15 -10 -5 0 5 off axis distance(cm) Measurement | Eclipse Empirical 10 15 Figure 3.10: The correction factors, i.e., the ratios of the absorbed dose in the asym-metric held to those in the symmetric held are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 6MV photon beam with 15° wedge at dmax and 10cm. Chapter 3. Results and Discussion 69 3.3.2 18MV Photon Beam Fig.3!1-Fig.3.14 show the correction factors, i.e., the ratios of absorbed doses of wedged asymmetric fields to the doses of corresponding wedged symmetric fields. The performance of the Eclipse planning system for 18MV is very similar to that for 6MV. For the thick end of the wedge, Eclipse treatment planning system performs well with a maximum difference of 2%. At dmax, the Eclipse results match the measurements even better. For the thin end of the wedge, the Eclipse calculation leads to differences up to 6.5%. Again, the correction method reduced the maximum difference in both thin end and thick end to about 2%, in most cases within 1%. Chapter 3. Results and Discussion 70 —> © Correction Factor for 60° Wedge 18MV at dmax -j 1 1 1 I A O " I A A • • • u.y 1 1 l - — 6 r $ 5 -• -2 0 ] off axis distance(aii) Measurement | Eclipse Empirical -6 Correction Factor for 60° Wedge 18MV at 10cm EOf-d-! &TS5 -2 o : off axis distance(cm) Measurement | Eclipse Empirical Figure 3.11: The correction factors, i.e., the ratios of the absorbed close in the asym-metric held to those in the symmetric held are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 18MV photon beam with 60° wedge at dmax and 10cm. Chapter 3. Results and Discussion 71 U Correction Factor for 45° Wedge 1SMV at dmax 1 A T 1 1 1 1 ' $ t u.y.) • • a u.y 1 1 ft*?— i -10 0 off axis distance(cin) Measurement! Eclipse Empirical 10 o o ,10 Correction Factor for 45° Wedge ISMV at 10cm h&r-i -0T95--6T9-©785-off axis distance(cni) Measurement I Eclipse Empirical 10 Figure 3.12: The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 18MV photon beam with 4 5 ° wedge at dmax and 10cm. Chapter 3. Results and Discussion 72 Correction Factor for 30° Wedse 18MV at dmax o o 3 t3 • Measurement! • Eclipse » Empirical -15 -10 1 &^5-5 0 5 off axis distnnce(cin) 10 15 UH o Correction Factor for 30° Wedge 1SMV at 10cm -ir -6^5--8r9-• Measurement! B Eclipse * Empirical -15 -10 1 ' 0.85 5 0 5 off axis clistance(cm) 10 15 Figure 3.13: The correction factors, i.e., the ratios of the absorbed dose in the asym-metric held to those in the symmetric held are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 18MV photon beam with 30° wedge at dmax and 10cm. Chapter 3. Results and Discussion 73 fc O -15 Correction Factor for 15° Wedge 18MV at dmax 1.000 0.950 0.900 0.350 -10 a 5 0 5 off axis distance(cm) 10 Measurement I Eclipse Empirical 15 fc u -15 Correction Factor for 15° Wedge 18MV at 1 0cm h#54-1.000 0.950 0.900 -10 • Measurement! o Eclipse « Empirical 0.850 off axis distance(cm) 10 15 Figure 3.14: The correction factors, i.e., the ratios of the absorbed dose in the asym-metric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 18MV photon beam with 15° wedge at dmax and 10cm. Chapter 3. Results and Discussion 74 3.4 Discussion For asymmetric field defined by collimators, the dose rate depends on both the head scatter and phantom scatter. At the thin end of the wedge, the method of Kwa for non-wedged helds can be extended to wedged helds with the correction of these two sources of scatter. At the thick end, the head scatter variance with off-axis distance is eliminated by the attenuation of the wedge so the central axis beam data match the off axis results well. For both 6MV and 18MV photon beams, the correction method brings the correc-tion factor to within 2% of measurement and in most cases the difference is within 1%. The absorbed dose for wedged asymmetric helds is calculated by using the symmetric held wedged profile and the correction factor. The Eclipse calculated symmetric pro-hie is accurate within 2%, usually within 1%. So the hnal dose result will be always accurate to within 4%, usually within 1-2%, which satisfies the criteria of Venselaar. Further improvement in the accuracy will depend on more accurate modeling or mea-surement of symmetric prohles. Table3.1-Table3.16 shows the empirical results based on accurate wedged symmetric prohles. Compared with Khan, Smulder and Georg's methods, this empirical correction method developed here is simple and effective. The maximum difference between dose calculation using this method and measurement is about 4% while the analytical method of Khan shows a maximum difference of 12.8% and Georg and Smulder's methods show maximum differences of 5.4% and 6.5% respectively. There are, however, some limitations in the method. In Smulder's method, helds shaped with M L C and blocks are also considered while this method, which is based on Day's equivalent field size is only applicable to rectangular helds. 75 Chapter 4 Conclusion and Future Work The performance of the Eclipse treatment planning system for wedged asymmetric helds is tested by direct comparison of ion chamber measurements and calculations. Both 6MV and 18MV photon beams with 60°, 45°, 30°, 15° wedges are tested. The rectangular helds range from half collimation to extreme asymmetric situations. For both 6MV and 18MV wedged asymmetric photon beams, the maximum dif-ference between ion chamber measurements and Eclipse calculations ranges from 4% to 5% when the held moves to a very asymmetric situation. Up to 6.5% difference is observed for 30° wedge with held center 12.5cm from the axis. Wedges have been simulated by Monte Carlo code BEAMnrc and the water phan-tom was simulated by DOSxyz. Good agreement between Monte Carlo simulation and ion chamber measurement was obtained with maximum discrepancy 2%. On one hand, the simulation verified the ion chamber measurements. On the other hand, the simulation provided an accurate way to calculate dose distributions by wedged asymmetric helds and may be very useful for further exploration of sources of scatter. A computation method was proposed by using a correction factor which is the ratio of the dose rate in an asymmetric held to the dose rate in the corresponding symmetric held. At the thick end of the wedges, the Eclipse planning system can be accurate to about 2% for the dose ratios. The correction method can further reduce this deference to within 1%. At the thin end of the wedges, the correction method can reduce the error of the dose ratios from 6.5% by Eclipse to 2%. The accuracy of the wedged symmetric profile is always within 2% and usually within 1%. The hnal dose result is thus always within 4% and usually within 2% when using this empirical Chapter 4. Conclusion and Future Work 76 correction method. This satisfies the criteria that the dose calculation for complex fields, e.g., combinations of wedge and asymmetric collimators should be within 4%. For further understanding of the wedge effect at both the thick end and the thin end, more Monte Carlo study is required to separate the dose from head scatter, phantom scatter and primary components by tagging the particles during simulation. 77 Bibliography [1] International Commission on Radiation Units and Measurements. Determina-tion of absorbed dose in a patient irradiated by beams of x or gamma rays in radiotherapy procedures. Report No.24. Washington, DC: National Bureau of Standards, 1976 [2] C. M . Ma, E . Mok, A. Kapur, T. Pawlicki, D. Findley, S. Brain, F.Forster and A. L. Boyer, "Clinical implementation of a Monte Carlo treatment planning system", Med. Phys. 26, 2133-2143(1999). [3] Jack Venselaar, Hans Welleweerd, Ben Mijnheer Tolerances for the accuracy of photon beam dose, calculations of treatment planning systems Radiother. Oncol. 60 191-201 (2001). [4] Venselaar J L M and Welleweerd J Application of a test pakage in an inter-comparison of the performance of treatment planning systems used in a clinical setting Radiother. Oncol. 60 203-13 (2001). [5] Niroomand-Rad A, Haleem M , Rodgers J, Obcemea C, Wedge factor depen-dence on depth and field size for various beam energies using symmetric and asymmetric jaw setting Med. Phys. 19 (6) 1445-50 (1992). [6] International Commission on Radiation Units and Measurements (ICRU). Use of computers in external beam radiotherapy procedures with high-energy photons and electrons. ICRU Report 42. Baltimore, M D : ICRU, 1987 Bibliography 78 [7] American Association of Physicists in Medicine. Radiation treatment planning dosimetry verification. A A P M Report 55 of Task Group 23 of the Radiation Therapy Committee. Woodbury, N Y : American Institute of Physics, 1995 [8] Dutreix A , Bridier A, Svensson H, Shaw J and Bjarngard B E, Monitor unit calcualtion for high energy photon beams ESTRO Booklet no 3 (1997). [9] Van Gasteren J J M , Heukelom S, Jager H N , Mijnheer B J, van der Laarse R, van Kleffens, Venselaar J L M and Westermann C F 1998b Determination and use of scatter correction factors of megavoltage photon beams Netherlands Commission on Radiation Dosimetry(NCS) Report 12 [10] Khan F M , Gerbi B J and Deibel F C, Dosimetry of asymmetric x-ray collimators Med. Phys. 20 1447-51 (1986). [11] Chui C and Mohan R, Off-center ratio for three-dementional dose calcualtions Med. Phys. 13 409-12 (1986). [12] Tenhumen M , and Lahtinen T, Relative output factors of asymmetric megavolt-age beams Radiother. Oncol 32 226-31 (1994). [13] Marinello G and Dutreix A, A general method to perform dose calculations along the axis of symmetric and asymmetric photon beams Med. Phys. 19 275-81 (1992). [14] Kwa W, Kornelson R O, Harrison R W and El-Khatib, Dosimetry for asymmetric x-ray helds Med.Phys. 21(10) 1599-1604 (1994). [15] Khan F M , Dosimetry of wedged helds with asymmetric collimation Med. Phys. 20 1447-51 (1993). [16] Georg D, Monitor unit calcualtion on the beam axis of open and wedged asym-metric high-energy photon beams Phys. Med. Biol. 44 2987-3007 (1999). Bibliography 79 [17] Bob Smulders, Iain A D Bruinvis and Ben J Mijnheer Monitor unit calculations for wedged asymmetric photon beams Phys. Med. Biol. 47 2013-2030 (2002). [18] Dimitris N Mihailidis, Pelagia D Tomaral and John P Gibbons, Measurements of primary off-axis ratios in wedged asymmetric photon fields: a formalism for dose and monitor unit calculations Phys. Med. Biol. 50 2003-2014 (2005). [19] Calculation Algorithm, Varian Associates Inc., Oncology Systems [20] BEAMnrc : A Monte Carlo Simulation System for Modelling Radiotherapy Sources, Ioinzation Radiation Standards Group, Institue for National Measure-ment Standards, National Research Council Canada [21] BEAMnrc Users Manual,. D. W. O Rogers, C - M Ma, B W alters, G. X . Ding, D. Sheikh-Bagheri and G. Zhang Ionizing Radiation Standards, National Research Council of Canada [22] W. van der Zee and J. Welleweerd, Internal Wedges using B E A M Med. Phys. 29(5) 876-885 (2002). [23] DOZXYZnrc Users Manual, B. Walters, I. Kawrakow and D. W.O. Rogers, Ion-izing Radiation Standards, National Research Council of Canada [24] E. L. Chaney T. J. Cullip and T. A . Gabriel, A Monte Carlo study of accelerator head scatter Med. Phys. 21 (9) 1383-1390 (1994). [25] M . B. Sharpe, D. A . Jaffray, J. J. Battista and P. Munro, Extrafocal radiation: A unified approach to the prediction of beam penumbra and output factors for megavoltage x-ray beams Med. Phys. 22 (12) 2065-2074 (1995). 

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