UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Study of wedged asymmetric photon beams Qiu, Yue 2006

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_2006-0622.pdf [ 5.04MB ]
Metadata
JSON: 831-1.0092737.json
JSON-LD: 831-1.0092737-ld.json
RDF/XML (Pretty): 831-1.0092737-rdf.xml
RDF/JSON: 831-1.0092737-rdf.json
Turtle: 831-1.0092737-turtle.txt
N-Triples: 831-1.0092737-rdf-ntriples.txt
Original Record: 831-1.0092737-source.json
Full Text
831-1.0092737-fulltext.txt
Citation
831-1.0092737.ris

Full Text

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 O F T H E REQUIREMENTS FOR 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 B E A M n r c 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 6 M V and 18MV photon beams at d 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. max  iii  Contents Abstract  ii  Contents  iii  List of Tables  v  List of Figures  x  Acknowledgements  xiv  1 Introduction to Dose Calculation and Measurement Techniques . 1.1 1.2  1.3  Thesis Organization Background Knowledge 1.2.1 Interactions of Radiation with Matter 1.2.2 Linear Accelerator 1.2.3 Treatment Planning System and Calculation Algorithm . . . . 1.2.4 Wedged Asymmetric Field 1.2.5 Measurement Techniques 1.2.6 Monte Carlo.Simulation Radiation Absorbed Dose Quantities in External Beam Radiotherapy 1.3.1 The Depth of Maximum Dose (d ) and the Percentage Depth Dose (PDD) 1.3.2 The monitor Unit (MU) and Dose Rate 1.3.3 Collimator Scatter Factor and Phantom Scatter Factor . . . . 1.3.4 The Tissue Maximum Ratio ( T M R ) 1.3.5 The Off Axis Ratio (OAR) Review of Wedged Asymmetric Dose Calculations 1.4.1 Tolerances for the Accuracy of Photon Beam Dose Calculations 1.4.2 Review of Studies on Asymmetric Fields 1.4.3 Previous Studies on Wedged Asymmetric Fields  1 1 2 2 3 4 6 8 10 11  max  1.4  2 Materials and Methods 2.1 2.2 2.3 2.4  Calculation by Eclipse Treatment Planning System Measurements by Ion Chamber Verification by Monte Carlo Simulation A n Empirical Correction Method 2.4.1 Dose Calculation for Asymmetric Field 2.4.2 Extrafocal Radiation: A n Analysis of Head Scatter  11 12 13 15 16 17 18 19 20  24 24 24 25 28 28 36  Contents  2.4.3 2.4.4 3  Extension to Wedged Asymmetric Fields: Correction for the Thin End . . . ' Correction' for the Thick End  37 38 '  Results and Discussion  39  3.1 3.2 3.3  39 57 64 64 69 74  3.4 4  iv  Comparison of Measurements and Eclipse Results Monte Carlo Results Results of the Empirical Correction 3 . 3 ! 6 M V Photon Beam 3.3.2 18MV Photon Beam Discussion  C o n c l u s i o n and F u t u r e W o r k  Bibliography  . ' . . . .  75 77  V  List of Tables 3.1  Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 60 degree wedge.  Y I and Y 2 indicate the col-  limator 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 3.2  41  Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 60 degree wedge.  Y I and Y 2 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 3.3  42  Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 45 degree wedge.  Y I and Y 2 indicate the col-  limator 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  43  List of Tables 3.4  vi  Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 45 degree wedge.  Y f and Y 2 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, X l = X 2 = f 0 c m . Absorbed doses by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown 3.5  44  Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 30 degree wedge.  Y I and Y 2 indicate the col-  limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition 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 3.6  45  Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 30 degree wedge.  Y f and Y 2 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 3.7  46  Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 15 degree wedge.  Y I and Y 2 indicate the col-  limator setting in the wedged direction, the off-axis position (OAP) indicates the measurement point. 200 M U is delivered under condition 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  vii  List of Tables 3.8  Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 15 degree wedge.  Y I and Y 2 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 3.9  48  Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 60 degree wedge. Y I and Y 2 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  49  3.10 Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 60 degree wedge. Y I and Y 2 indicate the collimator 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 Y 2 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 closes by measurement, Eclipse calculation and empirical correction are shown. The percentage differences to measurement by Eclipse and empirical correction are shown  51  List  viii  of Tables  3.12 Comparison of ion chamber reading. Eclipse calculation and empirical  '  correction for 18MV 45 degree wedge. Y I and Y 2 indicate the collimator 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 Y 2 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=3.2crn, 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 collimator 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 Y 2 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  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 Y 2 indicate the collimator 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 D .  1.4  Wedged asymmetric field is used in breast therapy  1.5  Schematic diagram of a thimble ionization chamber is shown  1.6  The geometry used in the definition of the percentage depth close  max  . . .  9 10  (PDD) at a fixed surface distance (SSD) is shown  12  1.7  A typical photon beam percentage depth dose (18MV) is shown.  1.8  The geometry used in the definition of the dose rate is shown. The absorbed dose at depth of maximum ionization limator axis is obtained for a 10 x 10cm  2  7  (d ) max  . .  13  along the col-  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 S versus field size c  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) 2.1  17  Schematic diagram of the Varian 21 E X treatment head with the associated component modules listed (not drawn to scale), as configured for B E A M n r c  26  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  27  xi  List of Figures 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, normalized 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 2.4  29  (a)Comparison of measured and calculated percentage depth dose (PDD)for 45 degree wedge with field size 10cm x 10cm and SSD=100cm, normalized 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 2.5  30  The equivalent field contributions used in dose calculation are illustrated.  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 equivalent 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 K w a et a/[14].) 2.6  31  The two component x-ray source model. The radiation beam is comprised of x-ray produced at the focal spot and scattered x-rays, which from a broadly distributed extrafocal source, (a) and (b) are for nonwedged fields, (c) and (d) are for wedged  3!  fields  37  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 6 M V 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  3.3  59  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 6 M V beam with 45 degree wedge at d axm  Percentage difference between measured and Eclipse calculated  absorbed doses are shown under the same setups 3.4  60  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 6 M V beam with 45 degree wedge at 10cm. Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups  3.5  61  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. . . .  3.6  62  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 asymmetric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 6 M V photon beam with 60° wedge at  d  max  and  10cm 3.8  65  The correction factors, i.e., the ratios of the absorbed dosedn the asymmetric field to those in the symmetric field 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 10cm  3.9  d  max  and  .-  66  The correction factors, i.e., the ratios of the absorbed dose in the asymmetric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 6 M V photon beam with 30° wedge at 10cm  'd  max  and 67  List of Figures  xm  3.10 The correction factors, i.e., the ratios of the absorbed dose in the asymmetric field to those in the symmetric field are shown by ion chamber measurement, Eclipse planning system and empirical correction. Comparisons are made for 6 M V photon beam with 15° wedge at d  max  and  10cm  68  3.11 The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 60° wedge at d  max  and  10cm  70  3.12 The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 45° wedge at d  max  and  10cm  71  3.13 The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 30° wedge at d  max  and  10cm  72  3.14 The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 d  max  .  10cm  and 73  xiv  Acknowledgements I would like to thank my supervisors, Dr. William K w a and Dr, Cheryl Duzenli, for their invaluable guidance and patience. M y sincere gratitude goes to their dedication 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.  i  Chapter 1 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)extend 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) T P S 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 T P S 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  1.2  1. Introduction  to Dose Calculation  and Measurement  Techniques  2  Background Knowledge Interactions of Radiation with Matter  1.2.1  Radiotherapy is a major treatment modality for cancer and external beam radiotherapy 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, photoelectric 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, m , must be created in this process, e  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 accelerator (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 collimated 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 collimated by two pairs of movable collimators to produce any square or rectangular shaped field up to 40 x 40cm . The two pairs of collimators are perpendicular to each 2  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 isocenter 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, C A ) , the upper pair of jaws are referred to as the Y\ and Y collimators and each can move up to 10cm over the central axis. The lower 2  pair of jaws are referred to as the X\ and X collimators and each can move up to 2  2cm over the central axis.  Figure 1.1: A medical linear accelerator (Varian CL21EX) is shown.  1.2.3  Treatment Planning System and Calculation Algorithm  Treatment planning systems (TPS) are used in external beam radiotherapy to calculate dose distributions based on the patient's axial anatomy attained from C T (X-Ray Computed Tomography) imaging or M R I (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 treatment 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 scattered 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 i g ! . 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.  ,  „  ,  „v  WedqeFactor(WF) = T i r  T r r  Reference  dose rate with luedge  / Reference dose rate without wedge n  .  (1.4)  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  A s y m m e t r i c 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.  A p p l i c a t i o n of W e d g e d A s y m m e t r i c 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 i g ! . 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 measurements of radiation dose. F i g ! . 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.  (1.5) where Q is the amount of charge collected, V is the air volume, m  air  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 phantom 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 R M I . 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  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 Z jf, e  an electron density p and a mass density p close to that of e  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 10 e/kg 26  The mass density is 1.03 x 10 kg/m 3  1.2.6  3  and 3.34 x 10 e/kg 26  for water.  and 1.0 x 1 0 % / m for water. 3  3  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  1.3  1. Introduction  to Dose Calculation  and Measurement  Techniques  11  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 (d  )  max  Percentage D e p t h Dose  and the  (PDD)  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 d  max  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 F i g ! . 6 ) . For P D D the source to surface distance (SSD) remains fixed, typically at 100cm. As seen in F i g ! . 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 buildup 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  D(d,WxL,SSD)  and Measurement  Techniques  12  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 d  max  for a field  size of 10x10 cm for a source-to-axis distance (SAD) of 100 cm (as shown in F i g ! . 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 10cm field is defined as 2  £> (10 x 10) = D(dmax, 10 x 10)/MU re/  (1.7)  Chapter  1. Introduction  0  1  to Dose Calculation  I  dmax  and Measurement  ^  -I  4  10  20  30  Techniques  13  Y 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) = D (10 ref  x 10) x D(dmax,  in which D(dmax, W x L)/D(dmax,  1.3.3  W x L)/D(dmax,  10 x 10)  (1.8)  10 x 10) is relative dose factor (RDF).  Collimator Scatter Factor and P h a n t o m Scatter Factor  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 S  c  (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, S may be measured with an ion c  chamber with a build-up cap of a size large enough to provide maximum close build-  Chapter  1. Introduction  to Dose Calculation  and Measurement  D(dmax,10x10)  Techniques  14  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 (d ) along the collimator axis is obtained for a 10 x 10cm field and a W. x L field. max  2  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 S accounts for the change in scatter radiation origip  nating in the phantom at a reference depth as the field size is changed. S is defined v  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 S is p  related to the changes in the volume of the phantom irradiated for a fixed collimator opening. A practical method of measuring S is indirect determination from the following p  equation:  where S (r) is the total scatter factor (also called relative dose factor (RDF)) defined CtP  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). S (r) c<p  contains  Chapter  1. Introduction  to Dose Calculation  and Measurement  Techniques  15  SAD  Figure 1.9: Chamber with build-up cap in air to measure dose rate relative to a reference field to determine S versus field size. c  both the collimator and phantom scatter so that S (r) divided by S (r) yields S (r). CtP  Although S (r) and S (r) p  CiP  c  p  are defined at the reference depth of d , max  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 d  max  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 d  max  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 ( T M R ) 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)  D(r, d,W x L) and D(0, d,W x L) are shown in F i g ! . 11.  (1.11)  Chapter  1. Introduction  D(r,d,WxL)  to Dose Calculation  and Measurement  Techniques  17  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 A s y m m e t r i c 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 following: 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 calculations 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 preferably expressed in a mm shift of the isodose line. A A P M Task Group 23 [7]and the Netherlands Commission on Radiation Dosimetry 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. Deviations between results of calculations and measurements is defined as:  8 = 100% x %  (D aic C  - D )/D meas  meas  (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 acceptable percentages are 3%,4%,5% respectively. Here 5 is defined as:  <5 = 100% x (D 4  and D  - D )/D rneas  (1.13)  meas>cax  is the dose at a point at the same depth but on the central beam axis.  meaS}Cax  1.4.2  caic  Review of Studies on A s y m m e t r i c  Fields  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 monitor 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]. K w a 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  P r e v i o u s Studies o n W e d g e d A s y m m e t r i c F i e l d s  1.4.3  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 calculated 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:  D  x TPR(d,r )  reI  d  x S (r ) c  c  x S (r ) p  d  x {SD /SPDf cal  x OAR (x) <w  xWFxTF  (1.14) where D is dose specified at point P in the center of an asymmetric field at depth T  d, M U is the number of monitor units, D f  is the dose per M U at a reference  re  point at depth d i, TPR,{d,r,i) ca  is the tissue phantom ratio for open  equivalent field size at point P, S (r ) c  c  fields,  is the  is the collimator scatter factor for open fields  defined "in air" at depth d i, S (rd) is the phantom scatter factor for open fields ca  at depth d [, SD ca  cai  p  is the distance from the source to the reference point, SPD is  the distance from the source to point P, OAR (x) diW  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 asymmetric 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)  where  = D xUx  O J-(c)  OQ '(C) F  X  x S; (c)  v  R  e  x  x  x k (c ) w  R  x A% (c )  x T (c,z)  e  0  R  (1.15)  we  x  x  is the output ratio determined at 10cm depth in a mini-phantom in  a wedged asymmetric field, S {c)  is the phantom scatter factor at 10cm depth  e  p  x  obtained at the center of a wedged asymmetric field, k (c ) w  R  is the wedge factor de-  0  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, T (c, z)  is the tissue-phantom ratio determined in a  we  x  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, s , z, w) = D xUx0 {C, b  R  0  W) XS (s , p  b  z , w) x k (c ) R  w  R  x k ( c ) x T ( s , z, w) (1.16) t  R  b  where D(c, s , z, w) is the dose at depth z in a large water phantom under isocentric b  conditions, c is the field size defined by the collimator, S is the field size defined b  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 (c  R  {c — 10cm) at a source to point of interest distance (f R  R  of monitor units, Oo(c,w) R  = 10cm) and field size  = 100cm), U is the number  is the output ratio in a wedged field determined at depth  in a mini-phantom for field size c, D is the dose determined in a mini-phantom, 0  Sp(s , z ,w) b  R  is the phantom scatter ratio in a wedged field, k (c ) w  R  is the wedge  factor determined under reference conditions in a full scatter phantom, T(s ,z,iu) b  is  the tissue-phantom ratio at depth z for field size s in a wedged field determined in b  Chapter  1.  Introduction  to Dose Calculation  a full scatter phantom, k (c ) t  R  and Measurement  Techniques  22  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  D (c, s , x, y, z, w) = D(c, s , z, w) x A(c, x, z, w) x A(c, y, z, w) A  6  b  (1.17)  where . A(c,x,z, ) W  = ^ f ^ D(c,f ,z,w)  (1.18)  = ^ f ^  (1.19)  R  and A(c,y,^)  D(c,f ,z,w) R  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 " ! D , {0,0,d,)  D (0,0,d,r  prim w  w  d  ('•»)  -> 0)  The monitor unit can be calculated by  MU =  D  A  l  /  C  F  )  kScir^S^r^TMR^r^SCD/SADyWF^r^POARuix^y^d)  (121) V  '  ;  Chapter  1. Introduction  where S (r ) c  c  to Dose Calculation  and Measurement  Techniques  23  is the collimator scatter factor for collimator field size r at C A , 5 (rd) c  is the phantom scatter factor for equivalent size rd at C A , TMR(d,rd)  p  is the tissue-  maximum ratio for the open field at C A , WF(d, r ) is the depth and field size depend  dent wedge factor at C A , POAR  w  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 6 M V and 18MV photon bemas.  24  Chapter 2 Materials and Methods 2.1  C a l c u l a t i o n by Eclipse Treatment P l a n n i n g 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 6 M V and 18MV photon beams in-this study were produced by a Varian C L 2 1 E X 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 R M I , Middleton, WI 53562, USA) dimension of 40cm x 40cm x 25cm with an ionization chamber having a sensitive volume of 0.6cm (Farmer type 30001 P T W , Freiburg, Germany). 3  A n 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 M o n t e C a r l o 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 B E A M n r c 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 demonstrated 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 associated component modules listed (not drawn to scale), as configured for B E A M n r c .  Chapter  2.  Materials  and  Methods  27  D O S X Y Z n r c 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 B E A M n r c . 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 1cm ) were calculated by Monte Carlo simulation and compared 3  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  28  Methods  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 C L 2 1 E X linear accelerator. Furthermore, this benchmarked 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 2.4.1  A n Empirical Correction Method Dose Calculation for A s y m m e t r i c  Field  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  29  Methods  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, normalized to dose at d . (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. max  2. Materials  Chapter  and  30  Methods  PDDfoi45Weclae  - Measurement Monte Carlo  10  15  20  30  Deptli(cni)  (a). Profile for 45 Wedge 4-6-h+-  • Measurement Monte Carlo  -15  -10  -5  0  5  10  20  off axis distance (cm)  (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, normalized to dose at d . (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. max  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 K w a et al[14].)  Chapter  2.  Materials  and  32  Methods  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 is approximated by the arithmetic mean of D(W x L) and D((2AW  X L)  — W) x L), which  is D (AW  x L) = (D(W  A  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  D(W (D(W  f  x L) x L) + D({2AW D(W  — W) x  L))/2  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  CF(d , max  V  AW  x L)  =  'D(W x L) x D((2AW - W) x L)  2L  7  V  :  D(W  x L)  D{WxL)  Then the dose rate along the collimator axis in an asymmetric field can be calcu-  Chapter  2.  Materials  and  33  Methods  lated from the correction factor,  D (AW  x L)  A  =  D{W  x L) x CF(d ,  AW  max  x L)  W™" - ^ * > L  D { w  =  x L)  x  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  /  D {r, A  AWxL)  „  A  rr/ ,D((2AW r, WxL)-^  = OAR(d , D  f  - W - 2r) x L) + D({W ^  r  J  max  + 2r) x L) ''-  (2.5) And the same off-axis point in a symmetric field is  b(r, „  W X  x L) = OARi^.r,  + 2r) X  L )  +  D((W  - 2r)  X  L)  ^  So the correction factor is  nr-iA  u/  CF(d ,r,  r\  W x L)  max  D (r,AWxL) A  =  ) D(r, W x L) (D((2AW  - W - 2r) x L) + D((W  (D({W  + 2r)  xL)  + D{{W  + 2r) x  - 2r)  x  L))/2  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. , C  F  (  * ~  „ „ A  W  s  D((2AW  r  X  L  )  " V  - W - 2r) x L)  DdW^r^L)  ,  s  -'  (2  8  Chapter  2. Materials  and Methods  Then the asymmetric held close rate at d  max  34  at any off axis point can be calculated  from the correction factor:  D (r, A  AW x i ) = D(W x L) x OAR(r,  d , W x L) x C 7 F ( d max  .  N  ID((2AW  = £> W x L x 0>LR r . f l U * . ^ x L) x W  U  y  max  , r, A i V x L )  - W - 2r) x i )  • Z?((W - 2r) x L)  ^ (2.9)  The above development applies to d . max  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 x y/TMR(d,  W xL)x  TMR(d,  -W)XL)  (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  <D{{2AW - W) x L) x TMR(d, x L) x TMR(d,  D{W  35  Methods  (2AW  -W)xL)  W x L)  (2.13)  Similarly for an off-axis point R at an off-axis distance r, the correction factor 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 y/TMR(d,  x L) = MU x JD((W  - 2r) x L) x D((W  (W + 2r) x L) x OAR{r,  (W - 2r) x L) x TMR(d,  + 2r) x L) d, W x L)  (2.14)  D(r, d, AW : y/TMR(d,  x L) = MU x yj D((W  (W + 2r) x L) x TMR(d,  + 2r) x L) x D((2AW  (2AW  -W-  - W -2r)  2r) x L) x OAR(r,  x L)  d, W x L)  (2.15)  and  CF(r,  d, AW  x L)  =  D{r,d,AWxL) D(r,d,W ID'{{2AW D((W  x L) - W - 2r) x L) - 2r) x L)  TMR(d, X  (2AW  TMR(d,  - W - 2r) x L)  (W - 2r) x L)  (2.16)  Now, the correction factor, which depends on the sizes of the asymmetric and  Chapter  2.  Materials and  36  Methods  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 ( T M R ) . So the absorbed dose at point R in an asymmetric field can be calculated by  M  U  D(r,d,W x L) Li_2 1 M x L) x OAR(r, d, W x L) x CF(r, d, AW x L) :  =  D(W  x L) x TMR(d,  (2.17) For a specific case, when R is at the center of the asymmetric field which is r away from the collimator axis, r = —r  asym  CF(r , asym  d, AW x i )  =  D(AW D({2W  a s y m  = (AW — W)/2,  x L)  - AW)  TMR(d,AW x L)  X  TMR(d,  x L)  (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. A n 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 component was found to account for 12% of the energy fluence on the central axis of the 6 M V 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  Chapter  2.  Materials  and  37  Methods  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 comprised 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 T h i n E n d  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  38  and Methods  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  D ((2W  - AW)  W  2.4.4 For  x L)  TMR (d,  (2W - A W )  w  x L) (2.19)  Correction for the Thick E n d  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. A t d , max  n T ?  ^J-"w,thick  —  D w j F S = asymm) —• —  [Z.ZU)  . D ( F S = sym) w  where D ( F S = asymm) and D ( F S = sym) are the on-axis wedged dose rates. W  The  W  correction factor at any depth d can be written as D (asym,d)  D (asym,dmax)  .D (sym,d)  D (sym,dmax)  w  w,tinck  w  w  _  w  D (asym)  TMR (asym,,d,)  w  D {sym) w  w  X  TMR (sym,d)  All the data are central axis beam data.  w  x TMR (asym, w  x  d)  TMR (sym,d) w  39  Chapter 3 Results and Discussion 3.1  C o m p a r i s o n 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 planning system calculations when 200MU is delivered. The comparisons are made for both 6 M V and 18MV photon beams at depths of d  max  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 6 M V 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  41  Discussion  Table 3.1: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 60 degree wedge. Y I and Y 2 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. Y2  OAP  Measure  Eclipse  Eclipse  (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  .  Empirical  Empirical  YI  Chapter  3.  Results and  42  Discussion  Table 3.2: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 60 degree wedge. Y I and Y 2 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. YI  Y2  OAP  Measure  Eclipse  Eclipse  (cm)  (cm)  (cm)  (cGy)  (cGy)  %diff  -7.5  7.5  -5  100.3  103.1  -7.5  7.5  -3.75  90.8  -7.5  7.5  -2.5  -7.5  7.5  -7.5  Empirical  Empirical  (cGy)  %diff  2.8  N/A  N/A  92.7  2.1  N/A  N/A  82.5  84.6  2.5  N/A  N/A  0  69.4  69.9  0.7  N/A  N/A  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  43  Discussion  Table 3.3: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 45 degree wedge. Y I and Y 2 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. YI  Y2  OAP  Measure  Eclipse  Eclipse  (cm)  (cm)  (cm)  (cGy)  (cGy)  %diff  -10  10  -7.5  147.9  148.3  -10  10  -5  130.0  -10  10  -2.5  -10  10  -10  Empirical  Empirical  (cGy)  %diff  0.2  N/A  • N/A  129.8  -0.2  N/A  N/A  114.9  115.0  0.2  N/A  N/A  0  103.2  103.5  0.3  N/A  N/A  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  76!  76.9  1.0  N/A  N/A  -10  -5  -7.5  139.5  135.2  -3!  138.7  -0.6  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  70.5  1.8  69.9  0.8  -10.  •  1  Chapter  3.  Results and  44  Discussion  Table 3.4: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 45 degree wedge. Y I and Y 2 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. . YI  Y2  OAP  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  45  Discussion  Table 3.5: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 30 degree wedge. Y I and Y 2 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. YI  Y2  OAP  Measure  Eclipse  Eclipse  (cm)  (cm)  (cm)  (cGy)  (cGy)  %diff  -15  15  -12.5  185.6  -15  15  -10  -15  15  -15  Empirical , Empirical •  (cGy)  %diff  181.6  -2.1  N/A  N/A  168.7  169.5  0.5  N/A  N/A  -7.5  ' 153.3  152.6  -0.5  N/A  N/A  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  46  Discussion  Table 3.6: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 30 degree wedge. Y I and Y 2 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. YI  Y2  OAP  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  47  Discussion  Table 3.7: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 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. YI  Y2  OAP  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  48  Discussion  Table 3.8: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 6 M V 15 degree wedge. Y I and Y 2 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. YI  Y2  OAP  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  49  Discussion  Table 3.9: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 60 degree wedge. Y I and Y 2 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. YI  Y2  OAP  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  61!  4.3  59.8  2!  •  Chapter  3.  Results and  50  Discussion  Table 3.10: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 60 degree wedge. Y I and Y 2 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. YI  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  51  Discussion  Table 3.11: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 45 degree wedge. Y I and Y 2 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. Empirical  Empirical  (cGy)  %diff  -0.6  N/A  N/A  140.1  -1!  N/A  N/A  125.9  125.8  -0!  N/A  N/A  0  112.6  112.9  0.2  N/A  N/A  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  Eclipse  YI  Y2  OAP  Measure  Eclipse  (cm)  (cm)  (cm)  (cGy)  (cGy)  %diff •  -10  10  .-7.5  158.0  157.1  -10  10  -5  141.6  -10  10  -2.5  -10  10  -10  Chapter  3.  Results and  52  Discussion  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. YI  Y2  OAP  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  53  Discussion  Table 3.13: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18A4V 30 degree wedge. Y I and Y 2 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. YI  Y2  OAP  Measure  Eclipse  Eclipse  (cm)  (cm)  (cm)  (cGy)  (cGy)  %diff  -15  15  -12.5  196.0  191.0  -15  15  -10  184.2  -15  15  -7.5  -15  15  -15  Empirical  Empirical  (cGy)  %diff  -2.6  N/A  N/A  178.9  -2.9  N/A  N/A  172.1  167.9  -2.4  N/A  N/A  0  142.4  141.5  -0.6  N/A  N/A  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  54  Discussion  Table 3.14: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 30 degree wedge. Y I and Y 2 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. YI  Y2  OAP  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  55  Discussion  Table 3.15: Comparison of ion chamber reading, Eclipse calculation and empirical correction for 18MV 15 degree wedge. Y I and Y 2 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. YI  Y2  OAP  Measure  Eclipse  Eclipse  Empirical  Empirical  (cm)  (cm)  (cm)  (cGy)  (cGy)  %diff  (cGy)  %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  56  Discussion  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. YI  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  3.2  3.  Results and  Discussion  57  M o n t e 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  58  Discussion  2 •  •  1 a  a) $  1  0  1  -6  -4  Q.  -2 •  a  • Moiife Carlo  0  ()  2 •  4  6  -i  • Eclipse  -2  B  -3  off axis distaiice (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 6 M V beam with 60 degree wedge at d . Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups. max  Chapter  3.  Results  and  59  Discussion  5  •  4 B  3 .  O  S  •  2  5  °'"  • Monte Carlo  •  1 ,  -6  ,  *  •  *  -4  "  -2  • Eclipse  •  r  i  0  I  )  2 •  i 4  i  6  B  •  -2 -3  off axis distance (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 6 M V 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  60  Discussion  3 •  2 1  QJ 1—1  1>  i—<  /!>  4=1 Q  •  1  i  -10  1  i a  »  -5 •  ?  ^ 6-  B  (  )  •  • Moiite Carlo 10  5  1  -  r  " Eclipse  •  a  -3 -4  off axis clis 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 6 M V beam with 45 degree wedge at d . Percentage difference between measured and Eclipse calculated absorbed doses are shown under the same setups. max  61  Chapter 3. Results and Discussion  CD  • Monte Carlo -10  -5 •  -1  10  • Eclipse  -2 -3 -4  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 6 M V 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  62  Discussion  Ratio for 60° Wedge at 10 a n 1. 1  1  no u. J 1  6  • Eclipse  U.V.'  •••• *  -  - • - Measurement  • ;>-'  » _ ~-  1  1  1  4  \  —8TS5-  -  2  • Monte Carlo  N .  S.  i  0  2  i  4  i  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  3.3 3.3.1  3.  B,esults and  Discussion  64  Results of the Empirical Correction 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.  65  Chapter 3. Results and Discussion  Correction Factor for 60° Wedae 6 M V at dmax  fe  • Measurement I  O  • Eclipse « Empirical 1  1  -6  -4  1  6T9-  -2  0  2  off axis distance(cm) Correction Factor for 60° Wedse 6 M V at 10cm  • Measurement!  fe o  a Eclipse * Empirical  -6:9-  1  6r$5-  -2  0  -  2  off axis distance(cni)  Figure 3.7: The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 60° wedge at d and 10cm. max  Chapter  3.  Results and  66  Discussion  Correction Factor for 45° Wedse 6 M V at dmax  o o fe  • Measurement • Eclipse « Empirical  10  0  -10  off axis distance(cm) Correction Factor for 45° Wedse 6 M V at 10cm  • Measurement • Eclipse  -fb95-  • Empirical O  -10  1  -5  0r«50  5  10  off axis distance(cm)  Figure 3.8: The correction factors, i.e., the ratios Of the absorbed dose in the asymmetric 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 d and 10cm. max  67  Chapter 3. Results and Discussion  Correction Factor for 30° Wedge 6MV at dmax ±705-h  Measiireinentl Eclipse  -0T95-  Empirical o U -  -15  -10  1  0TS5  -5  0  5  10  15  off axis distance(cm) Correction Factor for 30° Wedge 6MV at 10cm -h05• Measmenientl  -0T95-  B  6T9~  Eclipse  * Empirical  -0TS51  -15  1  -10  1  -5  0T8-  0  ' 5  10  15  off axis distance(cm)  Figure 3.9: The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 d and 10cm. max  Chapter  3.  Results  and  68  Discussion  Correction Factor for 15° Wedge 6 M V at dmax •i r\ r l.UJ  i nn  i  I Xiv  '  A fl  •  •  r  o o  u.yu  n  1  -15  -10 L  1  • Eclipse  •  u.y.j  »  Hi  • Measurement I  t  • O  • Empirical  •  0r85-  -5  0  i  i  5  10  15  off axis distance(cm) Correction Factor for 15° Wedse 6 M V at 10cm  Measurement | Eclipse  -ft9d-  Empirical  -OTS^1  1  -15  -10  ;  6TS6-  1  -5  0  5  10  15  off axis distance(cm)  Figure 3.10: The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 15° wedge at d and 10cm. max  Chapter  3.3.2  3.  Results and  Discussion  69  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 d , the Eclipse results match the measurements max  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%.  70  Chapter 3. Results and Discussion  Correction Factor for 60° Wedge 1 8 M V at dmax  — >  -j  1  1  Measurement |  1  I  I  A O " A  A  u.y  © 1  1  • •  Eclipse  • •  Empirical  -—6r$5-  l  -2  0  ]  off axis distance(aii)  Correction Factor for 60° Wedge 18MV at 10cm EOf-  d-  Measurement | Eclipse Empirical  &TS5-  !  -6  2  o  :  off axis distance(cm)  Figure 3.11: The correction factors, i.e., the ratios of the absorbed close in the asymmetric 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 d and 10cm. max  Chapter  3. Results  and  71  Discussion  Correction Factor for 45° Wedge 1SMV at dmax 1 1  A T  1  1  1'  $  t  u.y.)  •a  U 1  Measurement! Eclipse  •  Empirical  u.y i  ft*?—  1  10  0  -10  off axis distance(cin)  Correction Factor for  45°  Wedge  ISMV  at  10cm  h&r-  i  o  Measurement I  -0T95-  Eclipse Empirical  -6T9-  o  ©785-  10  ,10 off axis distance(cni)  Figure 3.12: The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 d and 10cm. max  Chapter 3. Results and Discussion  72  Correction Factor for 30° Wedse 18MV at dmax  o o  • Measurement!  3 t3  • Eclipse » Empirical &^5-  1  -15  -10  5  0  5  10  15  off axis distnnce(cin)  Correction Factor for 30° Wedge 1SMV at 10cm  -ir  • Measurement!  UH  o  B  -6^5-  -8r9' 0.85  1  -15  -10  Eclipse  * Empirical  5  0  5  10  15  off axis clistance(cm)  Figure 3.13: The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 d and 10cm. max  Chapter  3. Results and  73  Discussion  Correction Factor for 15° Wedge 18MV at dmax  1.000  fc  Measurement I  a  0.950  O  Eclipse Empirical  0.900 0.350 -15  -10  5  0  5  10  15  off axis distance(cm) Correction Factor for 15° Wedge 1 8 M V at 1 0cm h#541.000  fc  • Measurement!  0.950  o Eclipse « Empirical  0.900 u  0.850 -15  -10  10  15  off axis distance(cm)  Figure 3.14: The correction factors, i.e., the ratios of the absorbed dose in the asymmetric 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 d and 10cm. max  Chapter  3.4  3.  Results and  Discussion  74  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 K w a for non-wedged helds can be extended to wedged helds with the correction of these two sources of scatter. A t 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 6 M V and 18MV photon beams, the correction method brings the correction 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 prohie 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 measurement 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 6 M V 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 6 M V and 18MV wedged asymmetric photon beams, the maximum difference 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 B E A M n r c and the water phantom 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. Determination of absorbed dose in a patient irradiated by beams of x or gamma rays in radiotherapy procedures. Report No.24. Washington, D C : National Bureau of Standards, 1976 [2] C. M . M a , 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 intercomparison 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 dependence 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. I C R U Report 42. Baltimore, M D : I C R U , 1987  78  Bibliography  [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 Commission  on Radiation  Dosimetry(NCS)  Netherlands  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 megavoltage 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 27581 (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 asymmetric 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] B E A M n r c :  A Monte Carlo Simulation System for Modelling Radiotherapy  Sources, Ioinzation Radiation Standards Group, Institue for National Measurement Standards, National Research Council Canada [21] B E A M n r c Users Manual,. D. W. O Rogers, C - M M a , 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] D O Z X Y Z n r c Users Manual, B . Walters, I. Kawrakow and D. W . O . Rogers, Ionizing 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).  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0092737/manifest

Comment

Related Items