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A Monte Carlo study to investigate the dosimetric accuracy in the small field regime Stradiotto, Marco 2007

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A Monte Carlo Study to Investigate the Dosimetric Accuracy in the Small Field Regime by Marco Stradiotto  B . S c , Laurentian University, 2004  A THESIS SUBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF Master of Science in i  The Faculty of Graduate Studies (Physics)  The University of British Columbia April 2007 © Marco Stradiotto, 2007  Abstract Stereotactic radiosurgery (SRS) is a technique where an external photon beam is used to deliver a high dose of ionizing radiation to a small, localized brain lesion. The treatment fields used in this technique can be of the order of 1 cm for a circular collimated field. Accurate dosimetry of small-field photon beams such as those used in stereotactic radiosurgery is difficult because of the presence of steep dose gradients and lateral electronic disequilibrium (LED). Conventional measurement devices and treatment planning systems (TPS) have difficulty in determining dose accurately for small treatment fields where L E D is present. Further, the pencil beam algorithm in certain TPS has been known to have certain limitations in regards to dose calculation in inhomogeneous media where L E D is present. The use of Monte Carlo simulations in radiotherapy has been established as an accurate way of assessing dose distributions in inhomogeneous media regardless of L E D , field size and for beam obliquity. In this work a Varian i X linear accelerator equipped with a micro-multileaf collimator was modeled using the Monte Carlo code BEAMnrc and dose calculations were performed with the Monte Carlo code DOSXYZnrc to accurately predict relative dose factors (RDF) and inhomogeneity correction factors (ICF) in inhomogeneous bone and air phantoms. The results were compared with ion chamber measurements and calculations with the TPS BrainSCAN (Brainlab, Germany). After benchmarking our BEAMnrc linear accelerator with measured data and obtaining good agreement, further calculations to determine RDF and ICF were performed with DOSXYZnrc. The R D F values obtained with Monte Carlo simulation agree to within 1% with their corresponding measured values and the ICF values obtained with Monte Carlo simulation agree to within 1% with their corresponding values obtained from BrainSCAN. Based on our observations and data we conclude that Monte Carlo is an effective tool for calculating RDFs for small radiation fields where L E D is a problem and for quantifying the possible limitations of a dose calculation algorithm in the region of L E D . In general, we also conclude that the TPS BrainSCAN inaccurately predicts dose in the presence of lower density inhomogeneities and this inaccuracy becomes worse for smaller field sizes.  n  Table of Contents Abstract  ii  List of Tables  v  List of Figures  •  Acknowledgements  vii •  xi  Chapter 1  ••••• 1  Introduction to stereotactic radiosurgery and small field dosimetry  1  1.1 THESIS ORGANIZATION  1  1.2 BACKGROUND KNOWLEDGE  1.2.1 1.2.2 1.2.3 1.2.4 1.2.5  ,  2  Introduction to radiotherapy and stereotactic radiosurgery 2 General principles of stereotactic radiosurgery 3 Interactions of radiation with matter 7. Linear Accelerator 9 Lateral electronic disequilibrium and the detector volume effect in small fields ;  12  1.3 ABSORBED DOSE QUANTITIES IN EXTERNAL BEAM RADIOTHERAPY..  1.3.1 1.3.2 1.3.3 1.3.4 1.3.5  16  The depth of maximum dose and percentage depth dose The off axis ratio Relative dose factor Absorbed Dose at an Interface The CT scanner and CT number  16 19 20 22 22  ;  1.4  THE BRAINLAB MICRO MULTILEAF COLLIMATOR  23  1.5  TREATMENT PLANNING SYSTEMS AND THEIR LIMITATIONS  24  Chapter 2.....  :  •••••26  Materials and Methods  26  . 2.1 REVIEW OF DOSIMETERS  26  2.1.1 Ion Chambers 2.1.2 Silicon diodes... 2.1.3 Silicon Diodes and their limitations  26 27 29  ,  2.2 MONTE CARLO SIMULATIONS IN RADIATION THERAPY  2.2.1 2.2.2 2.2.3 2.2.4 2.2.5  30  Monte Carlo - the ideal dosimeter Principles of a Monte Carlo simulation BEAMnrc simulation system DOSXYZnrc simulation system Monte Carlo Simulation with BEAMnrc/DOSXYZnrc  •  2.3 LINEAR ACCELERATOR TREATMENT HEAD MODEL  2.3.1 Validation of the treatment head model  34  ,  2.4 MICRO MULTI-LEAF COLLIMATOR MODEL  2.4.1 Validation of the linear accelerator with the u M L C component module  iii  30 31 31 32 33 35 38  39  2.5  V A L I D A T I O N OF T H E FINAL M O N T E C A R L O A C C E L E R A T O R M O D E L A N D  M E A S U R E M E N T OF DOSE DISTRIBUTIONS  40  2.5.1 Blue Phantom 2.5.2 6 M V Varian Clinac i X 2.5.3 Choice of dosimeters 2.5.4 Experimental Setup 2.6 E V A L U A T I N G T H E BRAINSCAN SRS T R E A T M E N T 2.7  PLANNING S Y S T E M  INHOMOGENEITY C O R R E C T I O N F A C T O R (ICF)  46  2.7.1 Phantom Design for Testing the BrianSCAN Inhomogeneity Correction Factors 2.7.2 Choice of dosimeters for ICFs 2.7.3 ICF Measurement using ion chamber 2.7.4 ICF calculation using BrainScan 2.7.5 ICF calculation with Monte Carlo 2.8  40 41 42 44 45  48 52 53 54 55  A N A L T E R N A T I V E D O S X Y Z N R C PROCEDURE  57  2.8.1 Creating a phantom using CTcreate  57  CHAPTER 3  58  R E S U L T S A N D DISCUSSION  58  3.1  V A L I D A T I O N OF T H E FINAL M O N T E C A R L O A C C E L E R A T O R  3.1.1 Measured Results 3.1.2 Verification with Monte Carlo 3.1.2.1 Off-axis Profiles 3.1.2.2 Depth Profiles.. 3.1.2.3 Relative Dose Factors 3.2 ICF INVESTIGATION - M E A S U R E M E N T , BRIANSCAN A N D M O N T E 3.2.1 Medium field investigation results 3.2.2 Small field investigation results 3.3  58  CARLO  A N A L Y Z I N G L A T E R A L ELECTRONIC DISEQUILIBRIUM WITH C T C R E A T E  CHAPTER 4 CONCLUSIONS  58 66 66 72 76 79 79 83 87  95 :  95  CHAPTER 5  97  FUTURE WORK  97  BIBLIOGRAPHY  98  IV  List of Tables Table 2.1 - The phantom designs for our medium field ICF investigation with the FC-65 ion chamber. BonePhantomA and BonePhantomB are modeled to simulate high density bone with varying adjacent water thicknesses and STYPhantoml was modeled to simulate a low density material such as air. The H 0 slabs are standard solid water and the bone is composed of a bone equivalent material. Extruded polystyrene styrofoam was used for the low density material in STYPhantoml. Below the last slab of each phantom, 15cm of solid water was added to minimize the effects of backscatter 49 2  Table 2.2 - The phantom designs for our small field ICF investigation with the CC-01 ion chamber. BonePhantomA and BonePhantomB are modeled to simulate a high density bone material with varying adjacent water thicknesses and STYPhantom2 was modeled to simulate a low density material such as air. The H2O slabs are standard solid water and the bone material is composed of a bone equivalent material. Extruded polystyrene styrofoam was used for the low density material in STYPhantom2. Below the last slab of each phantom, 15 cm of solid water was added to minimize the effects of backscatter 50 Table 2.3 - Voxel sizes used to score dose in calculating ICFs in DOSXYZnrc  56  Table 3.1- Measured relative dose factors for our three dosimeters. Each is field is specified by its jaw opening and u M L C collimator size  66  Table 3.2- A comparison of RDFs measured with the SFD and EFD diode and those simulated with Monte Carlo (including relative error). The Jaw and u M L C columns specify the collimator settings for these measurements and the RDFs in this table are calculated at 5 cm depth 79 Table 3.3 - The ICF values calculated for the medium field ICF investigation. The ICF is calculated via three different methods for each phantom in Table 2.1: measurement (FC-65 ion chamber), pencil beam algorithm (BrainSCAN) and Monte Carlo (DOSXYZnrc). The field sizes investigated are also listed. The ICFs were calculated for anterior beams (gantry 0 degrees) for all phantoms with the exception BonePhantomA, which was also examined with an oblique (gantry 45 degrees) beam. The relative error in the Monte Carlo ICF calculation is also listed 81 Table 3.4 - A comparison of differences between the Monte Carlo ICF calculation versus ion chamber measurement (MC- M E A S U R E D ) and the measured ICF calculation versus BrainSCAN (BrainSCAN- M E A S U R E D ) for the medium field phantoms. The differences are expressed in % 82  Table 3.5 - The ICF values calculated for the small field ICF investigation. The ICF is calculated via three different methods for each phantom: measurement (CC-01 compact chamber), pencil beam algorithm (BrainSCAN) and Monte Carlo (DOSXYZnrc). The field sizes investigated are also listed. The ICFs were calculated for anterior beams (gantry 0 degrees) for both phantoms and oblique beams of 45 degrees for BonePhantomC and 30 degrees for STYPhantom2. The relative error in the M C ICF calculation is also listed 85 Table 3.6 - A comparison of differences between the Monte Carlo ICF calculation versus ion chamber measurement (MC- M E A S U R E D ) and the measured ICF calculation versus BrainSCAN (BrainSCAN- M E A S U R E D ) for the small field phantoms. The differences are expressed in % 86  vi  List of Figures Figure 1.1-The stereotactic frame (a) is a device which is placed over the patient's head in order to immobilize the skull. At the four corners of the frame are clamps which are bolted into a patient's skull in order to immobilize it during the SRS procedure. The localization box (b), is used to define a stereotactic coordinate system on the CT images 4 Figure 1.2-The points created from the markers on an axial image slice are localized with the localization software where a coordinate system will be defined for the location of the isocenter 5 Figure 1.3- A standard patient setup for a SRS or SRT treatment. The patient is laid down on the treatment couch in a supine position with the head immobilized within the localizer box (a); (b) shows one out of the three target positioning printouts that is attached to a face of the box in (a) 6 :  Figure 1.4-Schematic representation of a linear accelerator illustrating all its functional components 10 Figure 1.5 - A view of the BrainLAB u M L C  12  Figure 1.6-Illustration depicting lateral electronic disequilibrium. For the larger beam on the left (a) the displacement of the electrons in the lateral direction, do not exceed half the field width and hence a further increase in field size would not cause an increase in the dose at the central axis. For the smaller beam (b) there is lateral electronic disequilibrium since the lateral electron range exceeds half the field width 14 Figure 1.7- The effect of lateral electronic disequilibrium on dose profile measurement. For the 1.0x1.0 cm field the sharp increase in dose along the central axis is due to electrons created near the edge of the beam having a lateral range that is greater than 0.5 cm 15 2  Figure 1.8- The geometric definition of the percentage depth dose (PDD) at a fixed surface distance (SSD). The dose is measured at depth d and divided by the dose measured at dmax  17  Figure 1.9 - A PDD curve for a 6 M V beam  19  Figure 1.10- The geometry which illustrates the definition of the O A R at a fixed SAD. The dose is measured a distance r away from the central axis of a beam and divided by the dose measured at a point at the same depth along the beam central axis 20  vii  Figure 2.1- Farmer type ionization chamber. Approximate dimensions are shown in millimeters  27  Figure 2.2 - Diagram of a semiconductor detector  29  Figure 2.3 - A diagram of the Varian i X treatment head with the component modules listed  35  Figure 2.4 - Comparison of measured and simulated 10x10 cm 6 M V depth dose profiles in water for a Varian i X linac. The error bars correspond to the Monte Carlo simulation data 37 Figure 2.5- Comparison of measured and simulated 10x10 cm 6 M V O A R profiles at 5 cm depth in water for a Varian C L i X 38 2  Figure 2.6-An illustration showing the u M L C C M which was incorporated into our linear accelerator model, a) shows the geometry of a leaf from the Brainlab u M L C and (b) shows as it was modeled from the V A R M L C C M . Although the angular tip is highly exaggerated in (b) it does show how the leaf ends of the V A R M L C C M were altered (d) to obtain a model for a u M L C leaf 39 Figure 2.7- The Scanditronix-Wellhofer Blue Phantom used for our relative dose measurements when benchmarking our Monte Carlo accelerator model  41  Figure 2.8 - A photograph of the Varian i X in the unit 2 vault at V C C ; used for taking all measurements in our work 42 Figure 2.9- A photograph showing the dosimeters used for the benchmarking studies of our Monte Carlo model. From left to right are the IC-10 ion chamber, electron field diode (EFD) and the stereotactic field diode (SFD) 44 Figure 2.10 - A 3D reconstruction of the head of a patient. In stereotactic radiosurgery, a combination of beams directed at different angles must penetrate the soft tissue surrounding the skull followed by the adjacent layer of bone (skull) to a target that is seated within the brain itself. This figure illustrates the motivation behind using oblique lateral beams in our ICF investigation 52 Figure 2.11 - A x i a l views of the phantoms constructed for the medium field investigation (not to scale) with dimensions shown in centimeters. The diagrams show the location of the slot where the ion chamber was inserted 49 Figure 2.12 - A x i a l views of the phantoms constructed for the small field investigation (not to scale) with dimensions shown in centimeters. The diagrams show the location of the slot where the ion chamber was inserted 50  Vlll  Figure 3.1- Depth profiles measured with SFD diode for 1.2 cm, 2.4 cm, 3.6 cm square field sizes at 100 cm SSD 59 Figure 3.2 - Off axis profiles measured with SFD and EFD diodes for an 8x8 cm field at 5 cm deep 60 2  Figure 3.3- Off axis profiles measured with the ion chamber, SFD and EFD diodes for a 4.2x4.2 cm field at 1.5 cm depth 61 2  Figure 3.4 - Off axis profiles measured with ion chamber, SFD and E F D diodes for a 1.8x1.8 cm field at 1.5 cm depth 2  62  Figure 3.5- Off axis profiles measured with the ion chamber, SFD and E F D diodes for a 1.2x1.2 cm field at 1.5 cm depth 64 2  Figure 3.6 - Off axis profiles measured with SFD and EFD diodes for an 0.6x0.6 cm field at 1.5 cm deep  65  Figure 3.7 - O A R profile for a 4.2x4.2 cm field at 1.5 cm depth. The ion chamber, SFD and EFD measurement is compared with the Monte Carlo result (with relative error) 68 2  Figure 3.8 - O A R profile for a 2.4x2.4 cm field at 1.5 cm depth. The ion chamber, SFD and E F D measurement is compared with the Monte Carlo result (with relative error) 69 2  Figure 3.9- O A R profile for a 1.2x1.2 cm field at 1.5 cm depth. The ion chamber, SFD and E F D measurement is compared with the Monte Carlo result (with relative error) 70 2  Figure 3.10 - O A R profile for a 1.8x1.8 cm field at 1.5 cm depth. The ion chamber, SFD and E F D measurement is compared with the Monte Carlo result (with relative error) 71 2  Figure 3.11 - O A R profile for a 0.6x0.6 cm field at 1.5 cm depth. The SFD and EFD measurement is compared with the Monte Carlo result (with relative error) 72 2  Figure 3.12 - Depth profile for a 2.4x2.4 cm field. The solid lines represent the measurements taken with the SFD diode. The circles represent the Monte Carlo results  73  Figure 3.13- Depth profiles for a 1.8x1.8 cm field. The solid lines represent the measurements taken with the SFD diode. The circles represent the Monte Carlo results  74  2  2  ix  Figure 3.14- Depth profiles for a 1.2x1.2 cm field. The solid lines represent the measurements taken with the SFD diode. The circles represent the Monte Carlo results  75  Figure 3.15- A comparison plot of RDFs for various square field sizes taken with the SFD and EFD diodes. The RDFs are taken at 5 cm  77  2  Figure 3.16-An isodose distribution for the heterogeneous STYPhantoml phantom as viewed with dosxyz_show. The distribution corresponds to a field size of 36x36 mm defined at d=12.8 cm in the transaxial plane . The buildup region apparent in the first slab is coincident with the 1.5 cm buildup range for a 6 M V photon beam. The wider spread of the isodose lines at the styrofoam is due to L E D 89  2  Figure 3.17-A PDD curve for the STYPhantoml heterogeneous and homogeneous phantoms as calculated in Monte Carlo from the CTcreate data. Plotted along the STYPhantoml PDD from Monte Carlo is the same result from BrainSCAN. Field size is 36x36 mm at d=12.8 cm. The effect from the styrofoam is clearly visible from the Monte Carlo simulation; producing a pronounced falloff in the profile while BrainSCAN overestimates the dose in this region 90 2  Figure 3.18- A PDD curve for the BonePhantomB heterogeneous and homogeneous phantoms as calculated in Monte Carlo from the CTcreate data. Plotted along the BonePhantomB PDD from Monte Carlo is the same result from BrainSCAN. Field size is 36x36 mm at d=12.8 cm. The effect from the bone is clearly visible from the Monte Carlo and BrainSCAN calculation; producing a pronounced drop in the dose 91 2  Figure 3.19- A PDD curve for the STYPhantoml heterogeneous phantom as calculated in Monte Carlo from the CTcreate data. Plotted along the STYPhantoml P D D from Monte Carlo is the same result from BrainSCAN. Field size is 12x12 mm at d=12.8 cm. The effect of L E D is more evident through the styrofoam gap for this field width producing a deeper dose fall off in the Monte Carlo data while BrainSCAN still overestimates the dose in this region to a large degree 93 2  X  Acknowledgements I would like to thank my supervisor Dr. Ermias Gete for his invaluable guidance and patience during the course of this thesis and his dedication to my success. Without his continuous support and useful discussions this work would not have been possible. I would also like to thank Dr. Cheryl Duzenli for her valuable opinions and suggestions for the content of this research work. Many thanks to Dr. Alanah Bergman for educating me in all aspects of the EGSnrc Monte Carlo Package Suite - BEAMnrc, DOSXYZnrc and CTcreate. Also her helpful advice in the subject of Matlab programming and Linux scripting proved to be very important in the progress of this work. Other acknowledgements go out to the staff of V C C , especially the Physics Assistants for assisting me in linac related problems. Last but not least, I would like to thank my family and friends for their continued support over the past two and a half years. Without them I would still be trapped in the city of Sudbury Ontario deciding what to do for the rest of my life.  XI  Chapter 1 Introduction to stereotactic radiosurgery and small field dosimetry 1.1 Thesis Organization The objectives in this thesis are to: 1) Assess the feasibility of using Monte Carlo simulation for determination of relative dose factors (RDF) in small field dosimetry ; 2) evaluate the accuracy of tissue inhomogeneity corrections in the BrainSCAN (BrainLAB, Germany) treatment planning system through high density and low density interfaces by comparing with measurement and Monte Carlo simulation as well to provide a better understanding of the error in the BrainSCAN dose calculation algorithm; 3)Investigate the accuracy with which BrainSCAN can predict dose in regions of lateral electronic disequilibrium by comparing with Monte Carlo simulation. This thesis is organized in the following way: Chapter 1 is an introduction to stereotactic radiosurgery (SRS) and small field dosimetry covering the basics of the SRS procedure; the physical problems associated with small field dosimetry and absorbed dose quantities used in this work. In chapter 2, the experimental equipment and procedures used in this work are outlined as well the rationale of using Monte Carlo simulations. The results and discussion of our measurements, tissue inhomogeneity correction calculations and validations by Monte Carlo are presented in chapter 3. Chapter 4 gives our conclusion and future work is discussed in chapter 5.  1  1.2 Background Knowledge 1.2.1 Introduction to radiotherapy and stereotactic radiosurgery Radiation has been used to treat cancer for more than one hundred years. The primary objective of radiation therapy is to deliver a prescribed dose of ionizing radiation to a pre-defined target volume in order to annihilate the cancerous cells by damaging their D N A molecules [1]. This thereby disables the cancer cells from reproducing and growing eventually leading to their demise. There are several techniques prescribed to deliver the radiation and they are generally categorized as either being either brachytherapy or external beam radiotherapy. In brachytherapy, radioactive seeds are inserted or deposited close to the tumor site. In external beam therapy, high-energy x-rays are delivered from a machine outside the body. One specialized technique of external beam radiotherapy is stereotactic radiosurgery. In this technique, an external photon beam is used to deliver a high dose of ionizing radiation to a small, localized brain lesion (typically less then 5 cm in diameter). Typical lesions treated include metastatic and benign tumors, vascular lesions and other selected conditions [2]. Since a very high dose is delivered to a highly localized tumor, accurate dosimetry of the delivered radiation is exceptionally important in stereotactic radiosurgery. The focus of this thesis is accurate dosimetry of small fields such as those delivered in stereotactic radiosurgery.  2  1.2.2 General principles of stereotactic radiosurgery In Stereotactic Radiosurgery (SRS) treatments can be prescribed to deliver the total dose of radiation in a single treatment or in a fractionated manner over the course of several weeks. The latter case is then commonly referred to as stereotactic radiotherapy (SRT). In SRS the prescribed dose usually ranges from 12-50 Gy all administered in a single fraction in order to achieve a more complete sterilization of the tumor. In SRT, treatments are generally given between 5 to 25 fractions and 200-600 cGy per fraction to take into account the sensitivity of normal surrounding tissues [3]. With such relatively high doses used in SRS, a very sharp dose fall off outside the treatment volume is required to spare the surrounding normal tissues such as the optic nerve, brain stem and optic chiasm. This is done by conforming the beam to the planning target volume with a high precision collimating device such as the BrainLab micro-multileaf collimator. Some additional requirements for SRS are a precise localization and positioning of the planned target volume and a precise and numerically accurate dose delivery [2]. In SRS a fixed coordinate system is defined outside the patient's skull within a stereotactic frame and localization box (Figure 1.1). This frame is also attached to the treatment couch in diagnostic and treatment procedures in order to immobilize the skull. Prior to treatment, the patient undergoes a computer tomography (CT) scan with the localization box placed around the patient's head, which is then attached to the frame (Figure 1.1(a)). Three faces of this box contain markers which are used to construct a stereotactic coordinate system. Axial images taken by the CT scanner will intersect each one of these markers. After the images are imported into the treatment planning system the user will localize the points from the markers (Figure 1.2). This will define a  3  coordinate system for the location of the isocenter, (the point where the prescription dose is set). In the treatment room the isocenter is the point where the collimator axis and the axis of the gantry rotation intersect. Once this is done, contours are drawn on the image data set by an oncologist to locate the position of the lesion. This contour surrounding the lesion is called the clinical target volume (CTV). The planning target volume (PTV) covers the visible extent of the tumor and includes margins accounting for any microscopic spread of the disease and spatial shifts caused by organ motion or breathing cycles. After the PTV is drawn, a 3D dose distribution is then calculated in and around the PTV with a treatment planning computer.  (a)  (b)  Figure 1.1 - The stereotactic frame (a) is a device which is placed over the patient's head in order to immobilize the skull. At the four corners of the frame are clamps which are bolted into a patient's skull in order to immobilize it during the SRS procedure. The localization box (b), is used to define a stereotactic coordinate system on the CT images.  4  Figure 1.2- The points created from the markers on an axial image slice are localized with the localization software where a coordinate system will be defined for the location of the isocenter.  Just before the treatment, the patient is setup on the treatment couch in a supine position and the stereotactic frame is fixed to the couch using an attachment device. Axial images of the patient's target volume are printed from the treatment planning software and attached to the three sides of the box. These printouts give the relative location of the isocenter on each side of the box. Once the target positioning printouts have been attached to the box it is ready to be placed around the patient's head. The couch is then  5  adjusted until the target isocenter is intersected by the room lasers (Figure 1.3). Under this system, a 1 mm accuracy in setup is achieved  (a) (b) Figure 1.3-A standard patient setup for a SRS or SRT treatment. The patient is laid down on the treatment couch in a supine position with the head immobilized within the localizer box (a); (b) shows one out of the three target positioning printouts that is attached to a face of the box in (a).  Accurate dosimetry in a SRS procedure is extremely important because it is essential that the position and dimensions of the treatment field be precisely matched and a precise dose delivered to the target volume. However, accurate dosimetry for small fields is difficult due to lateral electronic disequilibrium (LED) and the detector volume effect (DVE) [4-8]. The effect of L E D and D V E will be discussed in section 1.2.5. Throughout this work our main emphasis will be to explore the difficulties in small field dosimetry as it applies to SRS, namely the consequences associated with lateral  6  electronic disequilibrium as well as the difficulty in doing measurement due to the volume averaging effect.  1.2.3 Interactions of radiation with matter In the world of radiotherapy, the photon range produced by most linear accelerators can extend from 4 MeV up to 25 MeV. The photon beam transfers its energy in tissue through several different types of interactions. In the energy range stated above, the main interactions are photoelectric effect, Compton effect and pair production. Rayleigh scattering is another mode of interaction between photons and matter. However, it is an elastic collision and therefore no energy is imparted to matter. In the photoelectric effect, a photon will collide with an atom and eject a bound electron from the K, L , M or N shells. This interaction will only occur if the energy of an incoming photon is greater than the binding energy of the bound electron. The energy, E, then transferred to the photoelectron will be,  E =hv-E  b  (1.1)  Where hv is the energy of the incident photon and Eb is the binding energy of the electron in the atom. Shortly after the interaction the atom is left in an excited state and emits characteristic x-rays and Auger electrons as it returns to its ground state. The probability that a photoelectric effect will occur is approximately inversely proportional to the photon energy as 1/ (hv) and directly proportional to the atomic number as, Z , for the material of interaction. In the Compton effect, a photon will collide with a loosely bound electron in an atom. Some of the energy of the incident photon is transferred as kinetic energy to the  7  free electron and the remainder is scattered away. The energy, E, transferred to the free electron is given by,  E = hv - h v '  (1.2)  where hv is the energy of the incident photon and hv' is the energy of the scattered radiation. The Compton process is almost independent of atomic number and decreases with increase of photon energy. In soft tissue, the Compton process is much more important than either the photoelectric effect or pair production process for photons in the 100 keV to 10 M e V energy range. Pair production occurs when a photon, whose energy is greater than 1.02 M e V , 1  interacts with the electromagnetic field of an atom's nucleus. When a photon passes near the nucleus of the atom, it is subjected to the Coulomb field of the nucleus and may suddenly disappear and become a positron and electron pair. Since the rest mass energy of the electron and positron, 2moc , must be created in this process, the resulting energy 2  transferred to the electron-positron pair is,  E = hv - 2 m c 0  2  (1.3)  Where hv is the energy of the incident photon. The cross-section for the pair production process increases rapidly with energy above 1.02 MeV. Since the interaction occurs within the field of the nucleus; it also depends on the atomic number of the interacting material.  ' Triplet production is another type of interaction where a photon interacts with the Coulomb field of an electron, creating an electron and positron pair. The photon's energy is shared between the positronelectron pair and the interacting electron.  8  In either the photoelectric, Compton or pair process, electrons will acquire kinetic energy from the incident photons. As the electrons travel through a medium they undergo many interactions, loosing their energy through ionization and radiative processes. However, it is ionization that has a direct contribution to the dose deposited in a medium.  1.2.4 Linear Accelerator The linear accelerator or L I N A C is a machine that generates high energy x-rays or electrons for use in radiation therapy. In the L I N A C , electrons are accelerated to high speeds by powerful electric fields within an accelerating tube. These electrons then strike a target made of a material of high atomic number, Z which will produce photons or they may strike a scattering foil to spread the electrons. For the production of photons, when the electrons hit the target their energy is released as bremsstrahlung x-rays. These x-rays are then emitted in a forward direction away from the target at megavoltage energies. The traveling photons will first pass through a primary collimator as shown in Figure 1.4. When the beam emerges from the primary collimator, its intensity is the highest along its central axis and then begins to decrease sideways from the center. Generally in radiation therapy the beam intensity should be as uniform as possible. It is for this reason that the next component the beam will pass through is a flattening filter. The geometry of a flattening filter is such that its thickness is higher at the center than at its edge so that the higher intensity region of the beam will pass through the center, decreasing the intensity thus making the overall intensity as uniform as possible.  9  Target  Primary collimator  Flattening filter Monitor ion chamber  Mirror  jj—  HI  Y Jm  ^jj^jjj^  \  x  Jaw  m  Figure 1.4-Schematic representation of a linear accelerator illustrating the essential components ( M L C not included).  Just below the flattening filter is a monitor ion chamber, which measures the beam's dose, flatness as well as symmetry. Following the monitor chamber is a mirror,  10  which reflects a light source inside the L I N A C head onto the same plane irradiated by the x-ray beam. The primary function of this light field with an embedded cross-hair is to provide visual information on the size and position of the radiation beam. On Varian linacs a secondary collimator is then placed below the mirror. It consists of two sets of blocks which are known as the jaws. The upper set of blocks is known as the Y jaw and lower block set is known as the X jaw. These two sets of jaws are capable of defining a rectangular field of the radiation beam. A tertiary collimator known as a multi-leaf collimator (MLC) is located below the secondary collimator. It consists of a series of leaf pairs usually made of a high Z material. These leaf pairs are used to define a field shape that conforms to the PTV. The L I N A C gantry can rotate 360 degrees in either direction (± 180 degrees) around the isocenter, with the distance from the source to the isocenter remaining the same. For SRS applications, and in particular, at the Vancouver Cancer Center (VCC), a third collimator is used, known as a micro-multi-leaf collimator  (LIMLC  Germany). The leaves of the fixed M L C are fully retracted and the below the fixed M L C . A view of the  LIMLC  -BrainLAB,  LIMLC  is shown in Figure 1.5. The  is attached  LIMLC  allows  the definition of much smaller radiation fields not possible with a standard M L C such as those used in SRS.  11  Figure 1.5 - A view of the BrainLAB u M L C  1.2.5 Lateral electronic disequilibrium and the detector volume effect in small fields Accurate dosimetry of small-field photon beams used in SRS is difficult because of the presence of steep dose gradients and of a physical phenomenon known as lateral electronic disequilibrium (LED). For a rectangular field, L E D occurs when the mean lateral range of a secondary electron created is greater than the equivalent radius of the field. In Figure 1.6 (a), secondary electrons created near the edge of the beam do not reach the central axis. This is because the beam is wide enough and any further increase in the field width will not result in an increase in primary dose at the central axis. In (b), however, secondary electrons created near the edge of the beam have a lateral range that is greater than half the field width and hence any further decrease in the field width  12  would result in an increase of primary dose on the central axis. L E D is said to exist on the central axis for narrower photon beams because electrons that are created and displaced laterally from the central axis are not replaced by an equal number of electrons from elsewhere [9]. This can be observed in Figure 1.6 (b) since electrons that would be created from the central axis are able to travel further than the beam edge, in a region where no electrons are created.  13  I (a)  I I I (b)  Figure 1.6-Illustration depicting lateral electronic disequilibrium. For the larger beam on the left (a) the displacement of the electrons in the lateral direction, do not exceed half the field width and hence a further increase in field size would not cause an increase in the dose at the central axis. For the smaller beam (b) there is lateral electronic disequilibrium since the lateral electron range exceeds half the field width.  14  Figure 1.7- The effect of lateral electronic disequilibrium on dose profile measurement. For the 1.0x1.0 cm field the sharp increase in dose along the central axis is due to electrons created near the edge of the beam having a lateral range that is greater than 0.5 cm. 2  Figure 1.7 illustrates the effect L E D has on dose profile measurements. The Figure contains a lateral axis dose profile for a 10x10 cm field and a 1.0x1.0 cm field was simulated with a Monte Carlo technique. The 1.0x1.0 cm field has a sharp peak in 2  the dose along its central axis which is due to electrons created near the edge of the beam having a lateral range that is greater than 0.5 cm. The accuracy of measurement of such narrow photon beams is extremely dependent on the sensitive volume of the detector being used. For a point of measurement, if the entire sensitive volume of the detector is not contained within a region where dose is uniform, the detector will give an inaccurate  15  reading. For example, in Figure 1.7, if the size of the detector's sensitive volume is not smaller than the width of the dose peak at central axis, then a measurement of the dose in the center of the field may also be averaging dose outside the point of measurement. This will result in a reading lower than what it actually should be. This consequence is known as the detector-volume effect (DVE) and its presence has always been an issue in the dosimetry of small fields [10-13]. In section 3.1.2, the D V E will be discussed further with respect to beam penumbra. L E D is one of the biggest tribulations facing small field dosimetry. It creates uncertainties in dose profile measurement [4,10-12,14-16], relative dose factor (section 1.3.3) measurement [17-18] and it is difficult to model for some treatment planning systems [19-20]. The influence of L E D on our measurements presented in this work will be discussed thoroughly in chapter 3.  1.3 Absorbed Dose Quantities in External Beam Radiotherapy 1.3.1 The depth of maximum dose and percentage depth dose The depth of maximum dose, d  maXt  is the depth in an irradiated medium, along the  beam's central axis, where the maximum dose is observed. It is characterized by the energy of a photon beam and generally increases with increasing photon energy. For the 6 M V megavoltage photon beam used in this work, the d , is 1.5 cm [19]. max  One way of characterizing the dose distribution along the central axis of a beam is to normalize the dose at depth with respect to the dose at d . The quantity used to max  characterize this in radiotherapy is known as the percentage depth dose or simply PDD.  16  PDD is defined as the ratio of absorbed dose at a depth d to the absorbed dose at d, along the central axis of the beam (see Figure 1.8).  S S D  | dmax  Figure 1.8- The geometric definition of the percentage depth dose (PDD) at a fixed surface distance (SSD). The dose is measured at depth d and divided by the dose measured at d m a x  For the PDD, the distance from the beam source (target) to the surface of the irradiated medium (SSD) remains fixed, typically at 100 cm. The factors that affect a PDD are the energy of the photon beam being used, field size and SSD. Mathematically, PDD can be defined as,  PDD(d,A,SSD)=  mM§B  D(d „,A,SSD)  xl00  (1.4)  m  where A , is the field size of the photon beam. Figure 1.9 is a typical PDD curve for a 6 M V megavoltage photon beam. The PDD decreases with depth beyond d , however there is a region between the surface max  and d  max  which is known as the dose build-up region. The physical explanation behind  17  this build-up region, which is common for all megavoltage PDDs, may be explained by the high speed electrons that are ejected from the top layer of the irradiated medium as the photon beam enters the medium. More electrons are then ejected in the subsequent layers primarily in the forward direction and these electrons then deposit their energy at a significant distance away from their site of origin. The electron fluence and thus the dose will increase with depth until they reach a maximum point. At this point and at further depths, the number of charged particles entering a volume, V , are balanced by the same number leaving it. This is the condition for electronic equilibrium. After this maximum point, ionization and hence the production of electrons will decrease with depth because of the photon attenuation in the material medium.  18  10  5  10  15 20 Depth (cm)  25  ~30  35  Figure 1.9 - A PDD curve for a 6 M V beam  1.3.2 The off axis ratio The off axis ratio (OAR) is expressed as the ratio of absorbed dose, at a point a distance r away from the central axis of a beam, to the absorbed dose at a point at the same depth on the central axis of the beam. Mathematically, O A R can be defined as,  OAR(r,d,A)=  (1.5)  D(r,d,A)  D(0,d,A)  19  where A is the field size being measured. Figure 1.10 illustrates the definition of the O A R at a fixed source to axis distance (SAD).  Figure 1.10-The geometry which illustrates the definition of the O A R at a fixed SAD. The dose is measured a distance r away from the central axis of a beam and divided by the dose measured at a point at the same depth along the beam central axis.  Equation 1.5 is the method by which O A R profiles are calculated in this work.  1.3.3 Relative dose factor One of several ways to describe the field size dependence of the dose from a radiotherapy unit is through a quantity called its relative dose factor. The relative dose factor (RDF) of a beam describes the photon scatter induced by all components in the head of the linac as well as the scatter induced as the beam propagates through the medium. Since the amount of photon scatter depends on the beam energy, field size and distance from the source, such quantities will directly affect the relative dose factor of a beam. Mathematically it is defined as  20  RDF(d,A) -  at d for a field size A Dose at d for the reference field size  ( 1  6 )  where A is the area of the field size (in cm) for which the relative dose factor needs to be determined and the reference field size is usually taken to be 10x10 cm . To measure 2  relative dose factors, a dosimeter is placed at a depth d in water. A reference field (usually 10x10 cm ) is set with the beam collimator at depth d and the reading from a 2  detector such as an ion chamber, is recorded. The field size is then altered and the ratio of the readings is taken to calculate the RDF for a standard field size [19]. In order to avoid the possible influence of contaminant electrons [19] incident on the phantom, we chose to make our RDF measurements at a depth of 5 cm. Accurate RDF measurement for small fields depends on the size of the sensitive volume for the detector being used. Since RDFs are typically measured at central axis, L E D and hence the D V E will play an important role. In measuring these RDFs for small fields, we wish to find a dosimeter that isn't greatly affected by the D V E from L E D .  21  1.3.4 Absorbed Dose at an Interface If a fluence,  of charged particles passes through an interface between two  different media mi and ni2, then the absorbed dose in either medium can be written as  (1.7)  where  is the mass collision stopping power of the charged particles at the point of  interest in the medium. The value of the mass collision stopping power is directly proportional to the  ratio, where Z is effective atomic number of the medium and A  its atomic weight. Assuming that the fluence of the charged particles is continuous at the interface, one can write the ratio of absorbed doses in the two media adjacent to their boundary as,  D.  AM  (1.8)  (S/P):  Equation (1.8) then states that the absorbed dose in m relative to mi is just the ratio of 2  their mass collision stopping powers.  1.3.5 The C T scanner and CT number A computed tomography (CT) scanner is a device that uses x-rays to reconstruct images of an object in the plane under examination. The CT scanner will scan an object in millimeter increments and each increment is labeled as a CT image slice. A l l image slices obtained for the phantom are then compiled together in what is known as the CT image  22  set. In the current generation of C T scanners, a narrow beam o f x-rays rotates around a patient in synchrony with radiation detectors located on the opposite side o f a patient. If a sufficient number o f transmission measurements are taken at different angles around the patient, a distribution of attenuation coefficients within the plane scanned can be determined. B y assigning a grayscale to different attenuation coefficients, an image can be reconstructed that represents various structures with different attenuation properties. The image reconstruction algorithm generates what are known as C T numbers, which are related to attenuation coefficients and are expressed in a formalism called Hounsfield units. The C T numbers range from -1000 for air to +1000 for bone, with water set at 0. The C T numbers are normalized as,  C  T  =  M tissue ~ M  waler  \000  (1.9)  X  water where p is the linear attenuation coefficient. Thus a C T number represents a change o f 0.1% in the attenuation coefficient relative to water.  1.4 The Brainlab Micro Multileaf Collimator The Brainlab u M L C is a high resolution collimator for radiosurgery/radiotherapy that can shape the treatment beam to conform to a tumor's shape. It consists o f 26 leaf pairs made o f a tungsten alloy with 95% tungsten. The width of the 26 leaf pairs projected to the isocenter varies from the inner to outermost pairs as follows: 14 inner pairs at 3mm wide, 6 middle pairs at 4.5 m m wide and 6 outer pairs o f 5.5 mm. The widths include an inter-leaf air gap that allow the leaves to move with minimal friction.  23  One of the distinct characteristics of the  LIMLC,  as compared to a M L C , is that its  effective penumbra is smaller. The effective penumbra of both an M L C and u M L C is strongly influenced by the leaf edge angle. The penumbra will become smaller as the edge angle decreases [44]. Since the leaf edge angles on a u M L C are smaller than those on a M L C , its effective penumbra is also smaller. Thus the dose can be tailored exactly to the shape of a lesion while sparing normal tissue as much as possible.  1.5 Treatment planning systems and their limitations In section 2.1 it will be emphasized that one of the factors that contributes to accurate dose delivery is accurate dose measurement. It will also be discussed that detectors with large sensitive volumes are inadequate for SRS dosimetry for the reason of the detector volume effect (DVE) and the presence of electronic disequilibrium across the treatment field. However, another factor that will contribute to accurate dose delivery is the accuracy of the dose calculation algorithm used in the treatment planning system. Early treatment planning systems (TPS) were based on empirical functions that used ray line geometries, assuming a broad beam dose distribution. Dose corrections for inhomogeneities were incorporated into these TPS by using a simple path length correction and by using transmission data measured from these inhomogeneities.  Major limitations of these empirical methods are their lack of ability to predict dose distributions of small fields, sudden changes in surface contours, oblique beam incidence and small inhomogeneities [5,19,21-22]. There have been improvements to these methods in recent years, including the use of Gaussian pencil beam distributions  24  that can be placed along a surface contour to predict the effects of small fields and surface irregularity [23] but better accuracy to calculate inhomogeneity correction is still limited and these limits have been well documented in lung tissue and for treatments involving the head and neck region [24-25]. The reason may be traced back to L E D . Electrons can have a larger lateral range in a lower density material, so we should expect L E D to be greater in an air interface than in water equivalent tissue. Kornelson and Young [26] have discussed the problem of loss of L E D when a high energy beam traverses the lung. Because of the lower density of lung, an increasing number of electrons can travel outside the geometrical limits of the beam causing a reduction in dose along the central axis of the beam.  For SRS treatments, the TPS must apply inhomogeneity corrections for tissues close to air cavities and the skull. A significant overdosing would be expected in areas beyond an air interface while the opposite occurring in areas beyond a high density bone interface [25,27]. Therefore, the TPS will need to consider these effects for treatments near the nasal cavity or nasopharynx region as well as intra-cranial lesions. The accuracy at which the TPS is able account for these tissue inhomogeneities is something we wish to investigate.  25  Chapter 2 Materials and Methods 2.1 Review of Dosimeters 2.1.1 Ion Chambers Ion chambers for use in radiation therapy may be divided into two main types: cylindrical (thimble) and plane parallel chambers. In our work we will only be using thimble ion chambers and will focus on describing these. Thimble chambers are the most frequently used ion chambers in medical radiation physics at present. They have a cylindrical geometry and are irradiated through the cylindrical mantle. Regardless of the type of ion chamber used, they all measure ionization in an air volume.  When ionizing radiation ,such as x-rays, pass through the air volume, collisions with the air molecules produce ion pairs, typically charged molecules and free electrons. A voltage is applied to a central electrode within the cylinder which in turn creates an electric field that will sweep any ions created towards the respective oppositely charged electrodes where their charge is accumulated and read out on an electrometer. Figure 2.1 shows a schematic of a commonly used thimble chamber known as a farmer chamber and is typically used for absolute dose measurements. Its inner electrode is made of aluminum and its chamber walls typically made of graphite with a low atomic number of 6 as compared to tissue (7.5). Most modern farmer chambers have a nominal volume of about 0.6 cm and a cavity length of approximately 2.0 cm [9]. 3  26  aluminum electrode  7  21.4 36.8 Figure 2.1- Farmer type ionization chamber. Approximate dimensions are shown in millimeters  The volume of an air filled ion chamber depends on its application. For our applications, ideally, we wish to find an ion chamber with a minimal volume to achieve the best spatial resolution. Another limitation that can be expected from the ionization chamber, due to its cylindrical design, is that the dose response will vary with angle of beam incidence [9]. In section 3.1.1, we will illustrate that the ion chamber is not a suitable dosimeter when measuring small field dose quantities like relative dose factors (RDF). The effects of L E D and the D V E cause inaccuracies in their charge output readings.  2.1.2 Silicon diodes A silicon diode is a semiconductor radiation detector. Although silicon itself is a poor conductor, it can be doped with electron donor atoms to produce n-type semiconductors or electron acceptor atoms to produce p-type semiconductors. The diode  27  itself is then formed by a thin layer of a p-type semiconductor over the substrate of an ntype semiconductor as shown in Figure 2.2. The region between these two types is referred to as a p-n junction. It is a region that acts as a barrier for current flow. When the diode is irradiated with ionizing radiation, charged particles such as electrons and electron holes are set free in this barrier, allowing a signal current to flow. The electric field that exists in a semiconductor junction causes these electrons to be swept toward the n-type material and any holes swept to the p-type material. Their motion causes a current to flow and the resulting charge is monitored by an electrometer. For radiation dosimetry applications requiring extremely good spatial resolution and small field dosimetry being no exception, the silicon diode has many advantages. The solid medium of the junction is approximately one thousand times more dense than the air medium of an ionization chamber and the mean energy required to produce a charge carrier is very small (~ 3eV) compared to air (-34 eV). This implies that the detector volume can be extremely small and yet still produce enough ion pairs for an electric current to flow [28]. In conclusion this makes diodes the detector of choice where steep dose gradients such as those produced in depth dose curves or beam penumbras from narrow photon beams are present.  28  Ionizing radiation  p-type Si (high doping)  hole  electron  Depletion layer.  • Signal current  n-type Si (low doping) Figure 2.2 - Diagram of a semiconductor detector.  2.1.3 Silicon Diodes and their limitations Although the silicon diode seems to be a promising dosimeter for small field measurements, it is not in any way a perfect dosimeter. It does come with limitations and the exactness or accuracy of this dosimeter is also something we want to investigate in this paper. Generally semiconductor detectors have several limitations concerning their use. They display a dose rate dependence of their reading which can be a concern for pulsed radiation beams like those produced from a medical linear accelerator. They show a temperature dependence and any temperature dis-equilibrium between the diode and its surroundings should thoroughly be checked for in vivo dosimetry [29]. The direction of a radiation beam incident on a diode can also affect its response. This has to do with the particular geometry of the p-n junction and its orientation relative to the incident beam [28]. A problem with this detector is the rather high atomic number in the active region. The depletion region in Figure 2.2 contains silicon which has an atomic number, Z=14  29  compared to air (Z= 7.78) [28]. This causes a greater photoelectric response but usually is only significant at lower energies [9]. Although higher energy (megavoltage) beams do have low energy components in their spectrum, they are usually not significant enough to affect the diode's response by more than 2% for typical energies in the clinical range (1.5 to 15 M V effective energy) [9].  2.2 Monte Carlo Simulations in Radiation Therapy 2.2.1 Monte Carlo - the ideal dosimeter Despite the limitations associated with ionization chambers and silicon diodes in addition to the difficulties related to L E D and D V E , there is one method used in radiation medical physics that has all the advantages of an ideal dosimeter and yet is not hampered by the above difficulties nor does it require a source of ionizing radiation. This method is known as the Monte Carlo method. The Monte Carlo method is a simulation that is capable of calculating dose distributions from photon beams in inhomogeneous volumes. With Monte Carlo simulation, doses can be calculated accurately in regions where there is L E D . This is because Monte Carlo is able to model interactions of radiation with matter including energy losses, scatter, bremsstrahlung and delta rays. Over the past years many research groups have incorporated Monte Carlo methods as a means of data verification in small field dosimetry [14-16,30]. As part of this investigation we will be using Monte Carlo techniques to accurately predict dose parameters for small photon fields from a 6 M V linear accelerator. We will make comparisons with these results together with ionization chamber and diode measurements.  30  2.2.2 Principles of a Monte Carlo simulation Any Monte Carlo simulation system used in radiotherapy must be capable of following a basic physical principle. The simulation must be able to transport a particle through a medium by simulating all the physical interactions that the particle will encounter. These interactions occur according to known probabilty functions, which are sampled using random numbers generated by computer routines. The transporting medium will usually have an intricate geometry such as the head of a linac or a patient's anatomy. When simulating an external photon beam, photons and a small number of particles are transported out of the linac head and until they encounter a volume of interest. This volume is normally divided into small voxels of a rectangular shape where a physical quantity such as the dose, is scored.  2.2.3 BEAMnrc simulation system The development of B E A M by the O M E G A (Ottawa Madison Electron Gamma Algorithum) project was designed to simulate radiation beams from medical linear accelerators. It is based on a code system known as EGSnrc and is capable of accurately modeling the geometry of a linear accelerator. The EGS (Electron Gamma Shower) code is a powerful tool for Monte Carlo simulation which has been widely used for medical physics. Its initial development originated from collaboration between Stanford Linear Accelerator Center and High Energy Physics Laboratory at Stanford University. To perform a simulation, the first step is to build the treatment head of the L I N A C by assembling different component modules (CMs). A C M is a simple geometric shape that is perpendicular to the beam axis. It can vary from a simple slab to a complicated  31  structure such as a multi leaf collimator. These different CMs are assembled in the exact order as it is engineered in the L I N A C . The dimensions and materials of each C M is specified in the input file along with the other simulation parameters such as the number of histories, source characteristics, cutoff energies and transport algorithm used. A data file, also known as a PEGS file, contains information about the radiological properties of the materials used (i. e. scatter cross-sections, restricted stopping power, densities and atomic numbers etc). Once all the CMs and the PEGS file is loaded, BEAMnrc will simulate the transport of incident particles (i.e. electrons) through its treatment head, passing through and interacting with all the CMs, and produces as its output, a phase space file. It is essentially a scoring plane defined by the user within the accelerator model, which contains the position, energy, charge, direction and a complete history of the interactions of all the particles crossing this scoring plane. The phase space file is typically positioned near the bottom of the head so that it may be used as a source for other simulations in patient related geometries.  2.2.4 DOSXYZnrc simulation system DOSXYZnrc is used to read phase-space files from BEAMnrc and to score dose in patient related geometries. The patient is modeled as a phantom with rectangular voxels to score the dose. The voxels are made of a certain material, usually water. A l l information about the phantom, its size, voxel material and other simulation parameters is contained in an input file similar to BEAMnrc.  32  2.2.5 Monte Carlo Simulation with B E A M n r c / D O S X Y Z n r c When a photon enters a medium it can undergo several types of interactions including: Rayleigh scattering, photoelectric effect, Compton effect, pair or triplet production. The probability of each interaction occurring depends on the energy of the incident photon and the material it interacts with. Photons are initially placed on a "stack" which stores information about a photon's energy, position and direction [9,31]. After the photon travels a certain distance in the medium, the probability of an interaction can be described in terms of an exponential attenuation function. Once the type of interaction is determined by a random number, the particle's final energy, position and direction can be calculated by sampling these quantities from certain distribution functions. At any point in the simulation when the energy of the photon falls below an energy cut off (PCUT) specified by the user, or when the particle leaves the region of interest, the photon's history is terminated. The above procedure will repeat itself until all the photons in the stack have been simulated.' Unlike photons, electrons can undergo many more interactions in a medium because of scattering events. In a real life application, it is possible for an electron to go through millions of these scattering events when it is traveling through a medium [9]. Since it is unfeasible to simulate these many scattering events for each particle, BEAMnrc and DOSXYZnrc employ a condensed history technique for the transport of electrons. This technique condenses a large number of interactions into a single step and will be divided into two categories denoted as Class I or Class II [9,31]. In the Class I category, particles will move according to a step size and all interactions that occur for each step are grouped together. The creation of secondary particles in each step is  33  simulated by sampling from certain probability distribution functions. In the Class II category, collisions are modeled explicitly i f any energy losses from particles are above certain threshold energy. These threshold energies are defined as A E (for electrons) and A P (for photons) in EGS terminology. In a Class II collision, energy losses can be modeled using a mixed procedure; i f any of these losses are below the A E or A P thresholds, then they would be grouped such that the energy is considered to be deposited evenly or continuously. This is known as the continuous energy loss or continuous slowing down approximation (CSDA). The consequence in using the C S D A means that much of the randomness in particle transport would be lost. For instance, all electrons with initially the same energy will travel the same distance before stopping. For those energy losses above these thresholds, they are treated on an individual basis. In both Class I and Class II categories, the condensed history method will determine the energy loss due to inelastic scattering and the change in position and direction due to elastic scattering. During the transport of a particle, its total energy energy (mc + T ) is constantly being compared to a cut off energy, ECUT. The particle 2  e  will be discarded if its energy is lower than E C U T and would not continue in the simulation.  2.3 Linear accelerator treatment head model A model of a Varian i X linear accelerator treatment head was assembled using BEAMnrc for our use in this work. A schematic of the basic model can be seen in Figure 2.3. The positioning and dimensions for each C M were designed according to the technical documentation provided by the manufacturer. The electron beam hitting the  34  target was simply specified by its energy and radial intensity distribution. The values chosen for the electron and photon cutoff energies were 700 keV and 10 keV respectively while the same values were chosen for A E and AP threshold energies.  Target (SLABS)  0 cm'  Primary CoDimator(CONS3R)  Beryllium Exit Window (SLABS) Flattening Filter (FLATFILT) Monitor Chamber (SLABS) Mirror (MIRROR) Y Jaws (JAWS) X Jaws (JAWS) Exit Window (SLABS)  59 cm 65 cm 100 cm  Phantom  Figure 2.3 - A diagram of the Varian i X treatment head assembled with BEAMnrc with the component modules listed.  2.3.1 Validation of the treatment head model  In order to proceed with the implementation of the last phase of our Monte Carlo accelerator model which was to incorporate a custom made micro-multi leaf collimator C M , we needed to be sure that the linear accelerator treatment head model was an accurate representation of the real Varian i X linac. In order to test its validity several  35  BEAMnrc simulations of PDDs and off-axis ratio (OAR) profile measurements were performed for selected fields defined by the Jaws. These results were compared with measured data. The dosimeter used for this measured data was a Wellhofer ion chamber IC-10 (0.10 cm effective volume) model. Figures 2.4-5 show the preliminary results 3  using this model as our template. Figure 2.4 is a comparison of a simulated and measured PDD profile for a 10x10 cm field defined at 100 cm SSD. It can be seen that there is 2  very good agreement between the measured and Monte Carlo data in Figure 2.4. The measured data is well within the region of the error bars plotted with the Monte Carlo data. Figure 2.5 is a comparison of a simulated and measured O A R profile for the same 10x10 cm field at 1.5 cm depth. The voxel resolution across the width of the field was 2  0.5 cm and again we can observe a very good agreement between the measured and Monte Carlo data. The PDD profile is indicative that our accelerator model does in fact model a 6 M V linear accelerator pretty well. The electron energy chosen for this model was 6.0 M e V and the F W H M of the electron radial intensity distribution was 1.2 mm. Several published studies indicate that for a Varian i X linear accelerator, the electron mean energy varies from 5.7 M e V to 6.5 M e V and the F W H M of the electron radial intensity distribution varies from 1.2 mm to 4 mm [30,32-33]. The good agreement obtained with these results shows that the Monte Carlo model of our linear accelerator head compares very well with the actual Varian i X linac. Our next course of action was to implement a C M for a micro-multileaf collimator (uMLC).  36  MC Wellhoffer 10X10 Comparison  1001-  0  ^  5  10  15 cm  20  25  30  Figure 2.4 -Comparison of measured and simulated 10x10 cm 6 M V depth dose profiles in water for a Varian i X linac. The error bars correspond to the Monte Carlo simulation data.  37  MC Wellhoffer 10X10 Comparison, d=1.5cm measured data  100  Monte Carlo  90 80 70 60 CD to  g  50 40 30 20 10 0  -10  10 cm  Figure 2.5- Comparison of measured and simulated 10x10 cm 6 M V O A R profiles at 1.5 cm depth in water for a Varian i X linac.  2.4 Micro multi-leaf collimator model In BEAMnrc, the user may select either a M L C or V A R M L C C M for modeling M L C ' s . However, neither of these is suitable for modeling the geometry of a u M L C . Thus, a model is required and must be designed or obtained from another research group. A dedicated u M L C model was obtained for this work from a Monte Carlo research group at Mcgill University (Montreal). We like to acknowledge the author, Jason Belec [34], for allowing us to utilize his custom designed u M L C C M in our research efforts. The u M L C C M was based on the V A R M L C C M . Although the V A R M L C C M alone does not allow angled leaf ends and since one of the distinct features of the BrainLAB  38  |LlMLC is its angled leaf ends, the V A R M L C C M was modified in this way. The u M L C C M itself essentially consists of three of these modified C M ' s stacked one on top of the other to obtain a segmented leaf end with three edges. Figure 2.6 is a schematic of the modified V A R M L C leaf end and leaf sides and how it was stacked together to obtain a leaf in the u M L C C M .  (a)  (c)  (b)  (d)  Figure 2.6- A n illustration showing the u M L C C M which was incorporated into our linear accelerator model, a) shows the geometry of a leaf from the Brainlab u M L C and (b) shows as it was modeled from the V A R M L C C M . Although the angular tip is highly exaggerated in (b) it does show how the leaf ends of the V A R M L C C M were altered (d) to obtain a model for a u M L C leaf.  2.4.1  Validation of the linear accelerator with the u M L C component module Since the p M L C C M was written in the BEAMnrc user code it was very feasible  to insert it into the BEAMnrc input file for our linear accelerator. Once compilation issues had been resolved in getting the u M L C C M to be accepted in the input file, we were ready to validate our final linear accelerator model equipped with a u M L C . Initial tests for benchmarking of the new input file showed promising results for large field sizes (10x10 cm ) but since the application of our work is in the realm of small fields (< 2x2 2  cm ), at this point we needed to perform a series of dosimetric measurements with a focus 2  on small fields. To do this we would need the very best dosimeters in terms of spatial  39  resolution and ones suitable for small field dosimetry (i.e. small detector volumes). In the following section we present the validation of our final linear accelerator model through PDDs, O A R profiles and relative dose factors. The results presented include those from Monte Carlo and measurement.  2.5 Validation of the final Monte Carlo accelerator model and measurement of dose distributions 2.5.1 Blue Phantom The Scanditronix-Wellhofer Blue Phantom 3D beam analyzing system (Scanditronix-Wellhofer™, Sweden) consists of a water filled plastic tank with a scanning volume of 48x48x41 cm. The tank is equipped with an automated arm where a dosimeter can be mounted (Figure 2.7). The dosimeter is placed in a small housing that can be calibrated with a position indicator for detector position accuracy. The arm may be translated in the x, y or z directions with a manual controller connected to the tank or through a computer interface. The tank is connected to a microprocessor control unit that has a built in electrometer, which is also controlled by the computer interface. The computer interface, which is responsible for the data acquisition (PDDs, off axis profiles, relative dose factors) is run by the software program, OmniPro-Accept (Scanditronix-Wellhofer) (OPA). OPA is advanced software for data acquisition and analysis in dosimetry. It supports all specifications of the L I N A C and has a convenient selection of pre-defined equipment such as the dosimeters used in our data acquisition.  40  Figure 2.7- The Scanditronix-Wellhofer Blue Phantom used for our relative dose measurements when benchmarking our Monte Carlo accelerator model.  2.5.2 6 M V Varian Clinac i X A l l measurements in this work were carried out with a 6 M V photon beam from the Varian i X Clinac (S/N: 291018) in the unit 2 vault at the V C C . This linac has a 120 M L C capable of delivering photon energies of 6 and 10 M V . Figure 2.8 is a photograph of the linac in the V C C unit 2 vault. For our measurements the Varian M L C was retracted completely so the u M L C could be attached to the linac head.  41  Figure 2.8 - A photograph of the Varian i X in the unit 2 vault at V C C ; used for taking all measurements in our work.  2.5.3 Choice of dosimeters Three different dosimeters were used in this work to obtain relative dose measurements such as PDDs, off-axis profiles and RDFs that were used to verify our Monte Carlo model. Two waterproof p-type silicon diodes from the Scanditronix silicon diode series: the electron field diode (EFD) and the stereotactic field diode (SFD). The third dosimeter used was the IC-10 cylindrical ionization chamber (Wellhofer Dosimetric). The advantage of using the diodes was due to their small sensitive volume, high uniform spatial resolution and very rapid response while the IC-10 was used for  42  comparative purposes and to illustrate its consequences regarding D V E . The advantage of using detectors with smaller sensitive volumes, such as diodes, was well-suited for the validation of our Monte Carlo model when it came time to determine dose properties of smaller sized fields (< 2.0x2.0 cm ). 2  Figure 2.9 is a photograph of the two diodes and the IC-10 ion chamber used for our benchmarking studies. The EFD diode has an active volume with a 2 mm diameter and a thickness of 0.06 mm. The sensitivity is approximately 190 nC/Gy. The SFD diode has an active volume with a 0.6 mm diameter with a 0.06 mm thickness. Since its active volume is smaller than the E F D diode its sensitivity is lower and is approximately 6 nC/Gy. Our third dosimeter, the IC-10 ionization chamber, has a cylindrical volume with a 3.1 mm cavity radius and an 8.8 mm cavity length. The wall of the chamber and central electrode are made from air equivalent plastic Shonka C552.  43  Figure 2.9- A photograph showing the dosimeters used for the benchmarking studies of our Monte Carlo model. From left to right are the IC-10 ion chamber, electron field diode (EFD) and the stereotactic field diode (SFD).  2.5.4 Experimental Setup In order to properly align the blue phantom water tank with the room lasers, the tank walls and bottom have engraved cross-hairs that are used for initial positioning of the isocenter. Once this is done the tank is filled with water and the dosimeter is mounted to the automated arm. The arm is then adjusted appropriately to the desired SSD (100 cm in our case) with the remote controller. At this stage any uncertainty in isocenter position may be corrected by doing a central axis check via Omni-Pro Accept (OPA). For all of our measurements, the gantry was set to zero degree and the U.MLC was set to 90  44  degrees. From this point all PDD, off-axis and RDF measurements were performed via OPA and the L I N A C console.  2.6 Evaluating the BrainSCAN SRS treatment planning system BrainSCAN is a commercial treatment planning system developed by the makers of the u M L C (BrainLAB, Germany). BrainSCAN models the u M L C and is able to conform a beam(s) to the shape of a lesion in a patient treatment plan. This is important since it is an essential requirement for SRS treatments to reduce radiation exposure to nearby critical structures.  BrainSCAN is based on the pencil beam dose algorithm where each treatment beam is divided into several small pencil beams. For each pencil beam an individual pathlength correction is performed which takes into account very small-structured tissue inhomogeneities as well as surface curvature. The pencil beam path length correction becomes especially important for lesions close to bone (ie. skull) or nearby air structures (ie. nasal cavity) and where the beam passes through other inhomogeneous media. The accuracy of this path length correction used in BrainSCAN, is what we wish to investigate with our Monte Carlo model. The use of Monte Carlo techniques to test the accuracy of pencil beam calculations has also been well documented in recent years [3537]. One of the primary reasons is that Monte Carlo techniques in radiotherapy can model L E D quite well whether for small treatment fields, surface irregularities or lower density structures.  45  We define a parameter which is intended to quantify the deviations in the absorbed dose level through three independent methods: BrainSCAN, Monte Carlo and ion chamber measurements. It has been proven that Monte Carlo methods accurately account for the effects of tissue heterogeneities [20,24,37] so we will use it as our reference in this investigation where systematic errors occur with our measured data such as regions where there is a loss of electronic equilibrium.  In section 3.1.2 the accuracy of our Monte Carlo model was verified with measurement with good agreement and as a result we expect our Monte Carlo model to maintain the same accuracy when making comparisons with BrainSCAN calculations and ion chamber measurements.  2.7 Inhomogeneity Correction Factor (ICF) In most TPS systems, for heterogeneous tissues, the dose is first calculated assuming the tissues are homogeneous and water equivalent. Then the dose in water is multiplied by an inhomogeneity correction factor (ICF) defined as:  ICF =  DOSE IN HETEROGENEOUS PHANTOM DOSE AT SAME POINT IN HOMOGENEOUS PHANTOM  (2.1)  or equivalently,  ICF =  D HETEROGENEOUS  (2.2)  D HOMOGENEOUS  46  Equation 2.2 can be appropriate when calculating an ICF from measurement such as that from an ion chamber or from Monte Carlo dose data. Our Monte Carlo model will output relative dose values and hence this will not pose a problem for us i f we use these values in conjunction with 2.2. Similarly with ion chamber measurements we can use the readings from the electrometer since these readings are directly proportional to the dose in the surrounding medium. In BrainSCAN, however, dose is not measured but defined as a prescription dose to an isocenter before the start of the plan. The number of monitor units (MU) required to achieve the prescription dose to the isocenter is what BrainSCAN will calculate for a clinical treatment. As a result, 2.2 will need to be rewritten so we can use it for our BrainSCAN verifications. Equation 2.2 can also be expressed by taking the ratio of the dose rates in both phantoms,  ^•^HETEROGENEOUS/  ICF = —  ^  (2.3)  HOMOGENEOUS /  /dt  To achieve the same dose, D, at isocenter in both phantoms we can express 2.3 as,  D/ jQp  _ / Ml) HETEROGENEOUS  ^  4)  HOMOGENEOUS  where MU  hetero  and MU  homo  are the monitor units required to achieve the same dose at  isocenter in the heterogeneous and homogeneous phantoms. Rearranging 2.4 gives,  47  JQP  —  ry §\  HOMOGENEOUS  ~ MU,HETEROGENEOUS Equation 2.5 is a more appropriate way to calculate the ICF via BrainSCAN. We will use 2.5 for all our BrainSCAN ICF calculations.  2.7.1 Phantom Design for Testing the BrianSCAN Inhomogeneity Correction Factors  The heterogeneous and homogeneous phantoms were constructed from a variety of solid water slabs. A slab of a bone equivalent material (Gammex RMI™) (p= 1.829 g/cm , Zerf=14.017) was used to mimic skull and a slab of extruded polystyrene 3  styrofoam (STYROFOAM™ - © The Dow Chemical Company) (p=0.045 g/cm ) was 3  used to simulate a low density material similar to air. Table 2.1 and Table 2.2 are a plan of the different phantom configurations that we used in this investigation, which was divided into two parts: medium field (> 4.2x4.2 cm ) and small field (< 2.4x2.4 cm ). We 2  2  thought that comparing the ICF among the three methods as a function of field size would also be an interesting study. There was a slot centered at the midpoint of slab 4 for each phantom in Table 2.1 and Figure 2.11 and the midpoint of slab 3 for each phantom in Table 2.2 and Figure 2.12. This slot was the location where our isocenter and ion chamber would be placed. Below the last slab of each phantom, 15 cm of solid water was added to provide for adequate backscatter.  48  Phantom Configuration  BonePhantomA  Bone^PhantomB  STYPhantoml  Slabl Slab2  0.5 cm H 0 1.0 cm bone (p= 1.829 g/cm )  4.0 cm H 0 1.0 cm bone (p= 1.829 g/cm )  4.0 cm H 0 3.8 cm styrofoam (p=0.045 g/cm ) 4.0 cm H 0 2.0 cm H 0  2  2  3  3  2  3  Slab3 Slab 4  0.5 cm H 0 2.0 cm H 0  4.0 cm H 0 2.0 cm H 0  2  2  2  2  2  2  Table 2.1 - The phantom designs for our medium field ICF investigation with the FC-65 ion chamber. BonePhantomA and BonePhantomB are modeled to simulate high density bone with varying adjacent water thicknesses and STYPhantoml was modeled to simulate a low density material such as air. The H 0 slabs are standard solid water and the bone is composed of a bone equivalent material. Extruded polystyrene styrofoam was used for the low density material in STYPhantoml. Below the last slab of each phantom, 15cm of solid water was added to minimize the effects of backscatter 2  BonePhantomA  BonePhantomB  STYPhantoml  Figure 2 . 1 1 - Axial views of the phantoms constructed for the medium field investigation (not to scale) with dimensions shown in centimeters. The diagrams show the location of the slot where the ion chamber was inserted.  49  Phantom Configuration  BonePhantomC  STYPhantom2  Slabl Slab2  1.0cmH 0 1.0 cm bone (p=1.829 g/cm )  4.0 cm H 0 3.8 cm styrofoam (p=0.045 g/cm ) 6.0 cm H 0 2  2  3  3  Slab3  6.0 cm H 0 2  2  Table 2.2 - The phantom designs for our small field ICF investigation with the CC-01 ion chamber. BonePhantomA and BonePhantomB are modeled to simulate a high density bone material with varying adjacent water thicknesses and STYPhantom2 was modeled to simulate a low density material such as air. The H 0 slabs are standard solid water and the bone material is composed of a bone equivalent material. Extruded polystyrene styrofoam was used for the low density material in STYPhantom2. Below the last slab of each phantom, 15 cm of solid water was added to minimize the effects of backscatter. 2  BonePhantomC  STYPhantom2  Figure 2.12 - Axial views of the phantoms constructed for the small field investigation (not to scale) with dimensions shown in centimeters. The diagrams show the location of the slot where the ion chamber was inserted.  50  In SRS procedure, a combination of beams directed at different angles penetrate the soft tissue of the head surrounding the skull followed by the adjacent layer of bone (skull) to a target that is seated within the brain itself. Figure 2.10 is a model of the head of a patient undergoing SRS with a combination of different beam angles. These oblique beams will need to penetrate more bone in the skull in contrast to an anterior or posterior beam. As a result, these photon beams streaming through the skull will suffer a greater attenuation loss. As a result of this greater attenuation, the ICF will be larger for the oblique beam. It is for this reason and the fact that a typical SRS procedure employs a number of oblique beams like in Figure 2.10, that we use oblique beams in our study.  So in summary the main premise behind the design of BonePhantomA and BonePhantomC was too mimic the head of a human as close as possible. The top slab of water would represent the soft tissue surrounding the skull while the 1.0 cm bone slab was added in to model the human skull. For BonePhantomB, a deeper seated bone slab was added in to investigate how well BrainSCAN could model the attenuation of a photon beam at greater depths when crossing inhomogeneities such as bone. The design of STYPhantoml and STYPhantom2, was intended for investigating how well BrainSCAN could model dose in a region where there is a loss of electronic equilibrium and what effects this has at calculating dose at depths beyond the L E D region.  51  Figure 2.10 - A 3D reconstruction of the head of a patient. In stereotactic radiosurgery, a combination of beams directed at different angles must penetrate the soft tissue surrounding the skull followed by the adjacent layer of bone (skull) to a target that is seated within the brain itself. This figure illustrates the motivation behind using oblique lateral beams in our ICF investigation.  2.7.2 Choice of dosimeters for ICFs  In our medium field ICF study we integrated the use of the FC-65 (Scandatronix Wellhofer) farmer ion chamber. It has a medium sized cavity volume, 0.65 cm , with a cavity diameter of 6.2mm and length, 23.1mm. In the small field study we incorporated the CC-01 (Scandatronix -Wellhofer) compact ion chamber. This dosimeter has a much  smaller cavity volume, which is more appropriate for accurate dosimetry of smaller fields. It has a cavity volume of 0.01 cm , with a cavity diameter of 2.0mm and length, 3  3.6mm. Both dosimeters are known to have high reproducibility in air, in solid or in water phantoms, which make them an appropriate dosimeter for our relative ICF measurements.  2.7.3 I C F Measurement using ion chamber  The measurements for our ICF investigation were taken using the Varian i X linac with a 6 M V photon beam selected. The slabs were stacked one on top of each other as shown in Tables 2.1 and 2.2, on top the treatment couch. With the chamber slot facing the superior direction the FC-65 or CC-01 ion chamber would then be inserted and the isocenter was aligned with the room lasers at the midpoint of the fourth slab for phantoms in Table 2.1 and third slab for phantoms in Table 2.2. This experimental method was therefore an SAD setup with SAD-100 cm. Two hundred monitor units were delivered for each run and the reading was measured with a Keithley Model 530 electrometer. For the medium field investigation three fields were considered: 42x42 mm , 2  36x36 mm and 60x60 mm , defined by the u M L C collimator. Each phantom was 2  2  irradiated with an anterior beam (gantry 0 degrees) with the exception of BonePhantomA, which was also irradiated with an oblique lateral beam (gantry 45 degrees). For the small field investigation four fields were considered: 24x24 mm , 18x18 mm and 2  2  12x12 mm and 6x6 mm defined by the u M L C collimator. Both phantoms in this section 2  2  were irradiated with an anterior beam (gantry 0 degrees) and an oblique beam. BonePhantomC was also irradiated with the gantry set at 45 degrees and STYPhantom2  53  with a gantry angle of 30 degrees. In all cases, the electrometer readings were then used in conjunction to calculate the ICF from the heterogenous and homogeneous phantoms. The results are summarized in Table 3.3 for various medium field sizes and gantry angles and Table 3.6 for various small field sizes and gantry angles.  2.7.4 I C F calculation using BrainScan  The homogeneous and heterogeneous phantoms from Figure 2.11 and Figure 2.12 were CT scanned with the Picker PQ 5000 CT scanner at the V C C with a slice thickness of 2 mm. These scans were then transferred to the BrainSCAN treatment planning computer. In BrainSCAN, the isocenter was located at the position of the ion chamber. A prescription dose to the isocenter was specified for a single anterior beam (gantry 0 degrees, collimator 90 degrees). This dose was completely arbitrary since the ICF is based on a relative dosimetry calculation. The jaw and u M L C leaf positions were then set to match the same field parameters as ion chamber measurements. With the isocenter defined and an arbitrary prescription dose, the number of M U required for the plan could then be calculated. In BrainSCAN, the user has the option of turning the inhomogeneity path length correction on or disabling it when calculating dose distributions. B y disabling it all CT numbers for all image slices are set to their default value of zero being water. Choosing this option would enable us to simulate a homogeneous phantom. The ICFs were then calculated by taking the number of M U with the inhomogeneity correction off and dividing it by the number of M U required with the inhomogeneity correction on. The results are again summarized in Tables 3.3 and 3.6.  54  2.7.5 ICF calculation with Monte Carlo  Calculating the ICFs through Monte Carlo methods was a straightforward task. A rectangular voxel phantom was created in DOSXYZnrc using the dimensions of the materials and their densities as specified in Tables 2.1 and 2.2. In choosing a voxel size to score dose in for each field, we started with a voxel of 0.5x0.5x0.5 cm for the 60x60 2  3  2  mm field and progressively decreased this to 0.2x0.2x0.2 cm for the 6x6 mm field. Table 2.3 shows the voxel size used to score dose in at the isocenter for each field size investigated. Deciding an exact voxel size to choose was a trial and error process because we were looking for the ideal voxel dimension that would provide adequate spatial resolution for the field and at the same time still keep the statistical uncertainty in the ICF calculation to a minimum (by scoring more particles in the voxel). Nevertheless it produced very good results for the ICF calculation as can be seen in Table 3.3 and Table 3.6.  55  Field Size 60x60  42x42  36x36  24x24  18x18  12x12  6x6  5x5x5  5x5x5  5x5x5  3x3x3  3x3x3  2x2x2  2x2x2  (mm) Voxel Dimension (mm) (X,Y,Z) Table 2.3 - Voxel sizes used to score dose in calculating ICFs in DOSXYZnrc  The heterogeneous voxel phantoms were constructed in DOSXYZnrc using the information from Tables 2.1 and 2.2. The H O700ICRU material was used for all H 0 2  2  layers with the default density. For the bone equivalent material, BONE700ICRU was used with the default density overwritten to 1.829 g/cm . For the styrofoam, 3  AIR700ICRU was used with the default density overwritten to 0.045 g/cm to 3  accommodate the density of the styrofoam. The homogeneous phantoms were created in DOSXYZnrc simply by setting the bone and styrofoam slabs to H O700ICRU in the 2  heterogeneous phantoms.  The ICF was calculated by taking the relative dose scored in the scoring voxel, at isocenter, for the heterogeneous phantom and dividing it by the relative dose scored in the scoring voxel, at isocenter, for the homogeneous phantom. The statistical uncertainties for this calculation are summarized in Tables 3.3 and 3.6.  56  2.8 An Alternative DOSXYZnrc procedure In DOSXYZnrc the user is given two options on how they wish to score dose in a phantom. The most common method is to construct a rectangular voxel phantom and assign certain physical properties to these voxels so that they resemble some sort of material. The other option is to use CT image data from an object scanned in a CT scanner. The CT image set is then transferred to a file directory where it can be used by a program that will assemble the image slices into a virtual phantom. This virtual phantom can then be imported into DOSXYZnrc to calculate isodose distributions within the virtual phantom and the result can be viewed with a separate phantom image viewer. The program responsible for assembling the image slices into a virtual phantom is called CTcreate.  2.8.1 Creating a phantom using CTcreate In DOSXYZnrc, the user is given the option to calculate dose distributions with data derived from CT image sets. This allows simulations in realistic anthropomorphic phantoms. It is currently supported in three formats: the A D A C Pinnacle format, the C A D P L A N format and D I C O M format. The D I C O M format is the one that is currently used at the V C C . CTcreate is a program that imports a CT image slice set of an object (ie. phantom) and assemble these image slices into a virtual object. The virtual phantom itself, along with the isodose distribution, can be viewed with an image viewer called dosxyz_show.  57  Chapter 3 Results and Discussion 3.1 Validation of the final Monte Carlo accelerator model 3.1.1 Measured Results  Figure 3.1 is a comparison of PDDs for three field sizes, 1.2x1.2 cm , 2.4x2.4 cm 2  and 3.6x3.6 cm as measured with the SFD diode. As can be seen from this figure, the 2  contrasts in percent depth dose, after d , between the different field sizes is natural due max  to an increase in scatter from larger field sizes at deeper depths. The nominal depth of maximum dose for a 6 M V linear accelerator photon beam measuring a 10x10 cm field 2  at 100 cm S A D is known to be 1.5 cm. However in Figure 3.1, the approximate value for d , seems to be slightly higher than this nominal depth. The reason for this is because mnx  for sufficiently smaller field sizes, the contribution of scattered photons to the depth dose at shallower depths is negligibly small and the dose deposition is mainly due to primary photons.  58  2  SFD, 12x12mm, 24x24mm, 36x36mm  2D h 1D -  Q I  I  I  0  2  .  4  I  i  6  8  I  10  I  12  1  1  1  14  16  18  20  depth (cm)  Figure 3.1- Depth profiles measured with SFD diode for 1.2 cm, 2.4 cm, 3.6 cm square field sizes at 100 cm SSD.  Figures 3.2-6 show a comparison of off axis dose profiles for varying field sizes with the different dosimeters used. Figure 3.2 shows measured profiles of an 8x8 cm field at 100 cm SSD as measured with both diodes at a depth of 5 cm. In this figure there is no noticeable difference in the response of either diode.  59  EFD, SFD BxBcm, d=5cm — EFD — - SFD  1  0.9  0.8  0.7  S 0.6 o Q  CD CP CD  CE  D.4  0.3 0.2  0.1  _i_ 0  cm  Figure 3.2 - Off axis profiles measured with SFD and EFD diodes for an 8x8 cm field at 5 cm depth.  Figure 3.3 shows measured profiles of a 4.2x4.2 cm field at 100 cm SSD, 1.5 cm depth, as measured with both diodes as well as the IC-10 chamber. In this figure it is interesting to see that the chamber profile has a wider 20-80% penumbra than the two diodes. This is due to the detector volume effect, since the sensitive volume of the E F D is  60  approximately three hundred times smaller than the IC-10 and the SFD is approximately ten times smaller than the EFD [14,32-33].  EFD, SFD vs chamber, 42x42mm T  I  I  I  I  I  I  I  T  ] I  I  I  I  I  I  I  I  I  I  I  -5  -4  -3  -2  -1  1  2  3  4  5  0 (cm)  Figure 3.3- Off axis profiles measured with the ion chamber, SFD and EFD diodes for a 4.2x4.2 cm field at 1.5 cm depth. 2  Figure 3.4 shows measured profiles of a 1.8x1.8 cm field at 100 cm SSD 2  respectively, as measured with both diodes again as well as the IC-10 chamber.  61  EFD, SFD vs chamber, 1Bx18mm  -3  -  2  -  1  0  1  2  3  (cm)  Figure 3.4 - Off axis profiles measured with ion chamber, SFD and EFD diodes for a 1.8x1.8 cm field at 1.5 cm depth. 2  Figure 3.5 illustrates the limitations of the IC-10 chamber in a smaller field zone (1.2x1.2 cm ). The chamber is limited by its spatial resolution, which is why we see a 2  pronounced rounding in the profile. This rounding effect that is seen with the ion chamber detector in Figures 3.4 and 3.5 has been reported with several groups [38-41].  62  This effect is known as the detector volume effect (DVE) which we first presented in section 1.2.5. When measuring dose near the edge of the field or in the penumbra with ion chambers of a finite diameter, the measurement produces a pronounced rounding in the profile shape. At the 50% dose line of Figures 3.4 and 3.5, we see an under response in the signal reading of the chamber relative to the two diodes and then a slight over response below the 50% line. Since the penumbra gets slightly larger as we get closer to the edge of the field, more dose is gradually being averaged within the chamber volume as it moves down the edge of the field. This rounding effect becomes less pronounced as the collection volume of the detector becomes smaller, as can be observed with both diodes in Figures 3.4 and 3.5. Hence the diode measurement is expected to give a more accurate reading in the profile measurement. Some groups [39,41] have developed correction methods to deal with the detector volume effect i f a smaller sized detector such as a diode is not available. In conclusion, this is why smaller diameter detectors such as silicon diodes are the preferred dosimeter for small field dosimetry measurements. One can also observe a rounding beginning to take form in the diode profiles around the central axis. Secondary electrons created near the edge of the field have a lateral range that is greater than half the field width and are depositing their energy close to the central axis (LED). This rounding is more prominent in Figure 3.6.  63  EFD, SFD vs chamber, 12x12mm  ce  -2  -1.5  -1  -D.5  D  0.5  1  1.5  2  (cm)  Figure 3.5- Off axis profiles measured with the ion chamber, SFD and EFD diodes for an 1.2x1.2 cm field at 1.5 cm depth. 2  2  For the smallest field obtained, Figure 3.6, we have profiles taken at 0.6x0.6 cm with both diodes only. It was anticipated that the IC-10 chamber would have a very poor resolution at this field size and hence the effect of electronic disequilibrium, i.e. a steep dose gradient wouldn't be noticeable. The sharp dose fall off is quite apparent with both diode profiles though.  64  EFD, SFD vs chamber, 6x6mm  (cm)  2  Figure 3.6 - Off axis profiles measured with SFD and EFD diodes for a 0.6x0.6 cm field at 1.5 cm depth.  Table 3.1 shows a comparison of the measured relative dose factors (RDF) for a few selected field sizes as measured at 100 cm SSD, depth of 5 cm and collimator at 90 degree. Each field is defined by its jaw opening and u M L C collimator size. One can notice a correlation between the detector volume and magnitude of the RDF. We observe for larger detector volumes, the magnitude of the RDF increases. The reason for this  65  relationship can be traced back again to the detector volume effect. A larger volume placed near the central axis of the field may have a portion of its volume in a region where no dose is present. This will yield an underestimate in the output. Since the SFD has the smallest active volume we will assume the measurement it provides is the most accurate. Also the magnitude of the output decreases as field size decreases which can be explained by the smaller contribution of scatter to the absorbed dose in smaller field sizes.  Measured Relative Dose Factors Jaw Size (cm) u M L C (cm)  SFD  EFD  8 8 4.2 1.8  8 6 4.2 1.8  0.967 0.946 0.885 0.809  0.971 0.952 0.894 0.816  1.2  1.2  0.766  0.773  0.6  0.6  0.642  0.637  Table 3.1- Measured relative dose factors for our three dosimeters. Each is field is specified by its jaw opening and u M L C collimator size  3.1.2 Verification with Monte Carlo 3.1.2.1 Off-axis Profiles The phantom setup in DOSXYZnrc used to generate off-axis profiles was a simple rectangular phantom consisting of water (H2O52IICRU) contained voxels. Figures 3.7-3.11 are off-axis profiles generated using our Monte Carlo model and compared against our measured data from both silicon diodes and ion chamber. A 3D smoothing filter based on the Savitzky-Golay formalism [43], was used to denoise the  66  Monte Carlo data. The addition of a denoising filter reduced the statistical uncertainty of the data to a usable level. The voxel size chosen for the length and width of the phantom was related to the field size in question. As field size decreases, voxel size would need to be decreased and particle events increased to maintain good statistics. Figure 3.7 is a O A R profile at 1.5 cm depth for a 4.2x4.2 cm field defined by the u M L C with a 6x6 cm jaw setting. The solid 2  2  lines represent the diode measurement and the circle points represent the Monte Carlo simulation. The voxel resolution used in the simulation for this field was a modest 0.4 cm across the entire length of the field. Good agreement is obtained well within 2% and the average statistical uncertainty for the twenty highest doses is 0.8%. Figure 3.8 is a O A R profile at 1.5 cm depth for a 2.4x2.4 cm field defined by the p M L C with a 4.2x4.2 cm 2  2  jaw setting. The voxel resolution used in the simulation for this field was 0.2 cm across the entire length of the field and we report the average statistical uncertainty for the twenty highest doses was 1.3%. Figure 3.9 is an O A R profile at 1.5 cm depth for a 1.2x1.2 cm field defined by the p M L C with a 1.8x1.8 cm jaw setting. The voxel 2  2  resolution used in the simulation for this field was 0.1 cm across the entire length of the field and we report the average statistical uncertainty for the twenty highest doses in this Monte Carlo simulated profile to be 2.3%. Figure 3.10 is a O A R profile at 1.5 cm depth for a 1.8x1.8 cm field defined by 2  the u M L C with a 4.2x4.2 cm jaw setting. The voxel resolution used in the simulation for 2  this field was 0.15 cm across the entire length of the field. In this figure, the Monte Carlo data appears much smoother across the region of the field. Our last O A R profile, Figure 3.11 is that of a 0.6x0.6 cm field, at 1.5 cm depth, defined by the u M L C with a 1.8x1.8 2  67  cm jaw setting. We chose a voxel resolution of 0.05 cm across the field length for our 2  Monte Carlo simulations and note the average statistical uncertainty for the twenty highest doses in this Monte Carlo simulated profile to be 3.6%.  MC42X42mm,d=1.5cm  cm  Figure 3.7 - O A R profile for a 4.2x4.2 cm field at 1.5 cm depth. The ion chamber, SFD and E F D measurement is compared with the Monte Carlo result (with relative error). 2  68  MC24X24mm,d=1.5cm i  1  1  1  r EFD  1 0.9  —SFD  — IC-10 o MC  0.8 0.7 0.6  $0.5 0.4 0.3 0.2 0.1 0 III) -4  IS Ul l^j  0 cm  4  Figure 3.8 - O A R profile for a 2.4x2.4 cm field at 1.5 cm depth. The ion chamber, SFD and E F D measurement is compared with the Monte Carlo result (with relative error)..  69  MC12X12mm, d=1,5cm  cm  Figure 3.9- O A R profile for a 1.2x1.2 cm field at 1.5 cm depth. The ion chamber, SFD and E F D measurement is compared with the Monte Carlo result (with relative error). 2  70  MC 18X18mm, d=1.5cm  -2  -1.5  -1  -0.5  0 cm  0.5  1  1.5  2  Figure 3.10 - O A R profile for a 1.8x1.8 cm field at 1.5 cm depth. The ion chamber, SFD and E F D measurement is compared with the Monte Carloresult (with relative error). 2  71  MC6X6mm, d=1.5cm  cm  Figure 3.11 - O A R profile for a 0.6x0.6 cm field at 1.5 cm depth. The SFD and E F D measurement is compared with the Monte Carlo result (with relative error). 2  3.1.2.2 Depth Profiles  The phantom setup in DOSXYZnrc used to generate depth profiles was a simple rectangular phantom consisting of voxels containing water (H 0521ICRU). The voxel 2  settings along the central axis where chosen to be 0.5 cm in the build-up region and 1.0 cm where the dose begins to fall very smoothly. Figures 3.12-14 are plots of three P D D  72  2  2  profiles for three different fields sizes defined at 100 cm SSD, 2.4x2.4 cm , 1.8x1.8 cm and 1.2x1.2 cm . A l l three PDDs were measured with the SFD. The Monte Carlo 2  simulation data is compared with the measured profiles. Agreement with the Monte Carlo simulation is reported to be very good for these profiles (within the statistical uncertainty).  MC vs SFD  0-2 o  i  i  2  4  i  .  6  i  i  i  i  i  r  8  10  12  14  16  18  20  cm  Figure 3.12 - Depth profile for a 2.4x2.4 cm field. The solid lines represent the measurements taken with the SFD diode. The circles represent the Monte Carlo results. 2  73  MC vs SFD  cm  Figure 3.13- Depth profiles for a 1.8x1.8 cm field. The solid lines represent the measurements taken with the SFD diode. The circles represent the Monte Carlo results. 2  74  MC vs SFD  75  3.1.2.3 Relative Dose Factors Verifying RDF measurements via Monte Carlo is nothing new in radiotherapy. In fact, several groups have explored this subject [14,17-18,42]. Nevertheless, RDF verification via Monte Carlo for small fields (< 2x2 cm ) is not as common. 2  To calculate the RDFs for a selected number of field sizes, the detector was placed at 5 cm in the water tank to acquire a dose reading at that depth. Although RDFs were measured with each detector, we were primarily interested in the small field domain and in this region it is more reasonable to examine our results for the SFD and EFD diodes. Figure 3.15 is a comparison plot of RDFs measured, for various square field sizes defined by the u M L C and measured at a depth of 5 cm. From the plot it appears that for field sizes l x l cm or greater the performance of both diodes differ by <1%. However for fields below l x l cm the difference may be as high as 4% (as in the 0.6x0.6 cm OF measurement) or higher for even smaller fields. The most obvious reason is that around the l x l c m area the sharp dose gradient, which is a consequence of electronic disequilibrium, becomes more pronounced across the length of the field and since the diameter of the EFD's scoring volume is 2 mm and the SFD's is 0.6 mm, one can assume that the SFD RDF measurement is a more accurate one. Now with this in consideration, it will prove to be interesting how an RDF, simulated and calculated by Monte Carlo, will compare to the SFD result and hence enable us to understand the effective performance of the SFD diode when measuring small fields.  76  EFD RDF versus SFD RDF at d=5cm 1.2r-  0.8  §0.6  • EFD • SFD  Q  0.4  0.2  4  5  6  square field size (cm)  Figure 3.15- A comparison plot of RDFs for various square field sizes taken with the SFD and EFD diodes. The RDFs are taken at 5 cm.  For the Monte Carlo simulations, a simulation for a 10x10 cm field was executed to an SAD of 100 cm and the dose was scored at 5 cm depth in a cubic voxel with dimensions 3.0x3.0x3.0 cm . A large voxel size was chosen to improve statistics and to 3  reduce uncertainty in the calculated dose. It also offered the benefit of a shorter simulation time. Now, it was discovered that choosing the appropriate voxel size to score the dose at 5 cm, for whichever field size we wanted to calculate an RDF for, had a direct impact on the RDF value we obtained. In other words, it was discovered that decreasing  77  the scoring voxel size, as the field size was decreased, at 5 cm achieved a better result. The RDF values obtained with Monte Carlo were initially compared to a measured table of RDFs for the linac being used. Table 3.2 is a summary of RDFs calculated via Monte Carlo and these are cross listed with matching RDFs measured with the SFD and EFD at 5 cm depth. The Jaw and u M L C columns denote the collimator settings for the secondary and u M L C collimators, respectively. In deciding the size of voxel to be chosen for scoring dose at a 5 cm depth, we followed a basic principle of proportionality. Since we used 3.0x3.0x3.0 cm for our reference 10x10 cm field, simply taking the field 3  2  dimension and dividing it by 3.0 gave us an approximate voxel dimension which was used to score the dose and hence calculate our RDFs. Table 3.2 contains a column designating the voxel dimension chosen. In order to replicate the delivery of an equal number of monitor units for one field and that of the 10x10 cm reference field, we simulated an equal number of histories for the field in question and the 10x10 cm field. Of course the number of events simulated increased dramatically for the smaller field RDFs to stay in the limit of good statistical accuracy. The SFD agreement with the Monte Carlo simulation is to within 1 % for all field sizes and this limit is well within the statistical uncertainty from the Monte Carlo. The EFD disagreement with Monte Carlo is larger than 2 % for some fields (0.6x0.6 cm ) however the disagreement is again within 2  the statistical error from the Monte Carlo. The good agreement obtained between the Monte Carlo and the measured RDFs shows a very promising outcome that Monte Carlo may be extremely useful for determining relative dose factors for small fields.  78  RelativeDoseFactors(RDF)d=5cm Jaw (cm)  4.2 1.8 1.8 1.2 0.6 6.0 1.8  measured (EFD)  uMLC (cm) 4.2 1.8 0.6 1.2 0.6 4.2 1.2  0.885 0.809 0.669 0.766 0.642 0.904 0.776  0.895 0.814 0.646 0.765 0.602 0.915 0.778  M C (±%)  0.898 0.823 0.675 0.768 0.640 0.913 0.778  (0.5) (1.2) (2.6) (1.6) (2.6) (0.5) (1.6)  Voxel Dimension (X,Y,Z) cm 1.3x1.3x1.3 0.5x0.5x0.5 0.2x0.2x0.2 0.4x0.4x0.4 0.2x0.2x0.2 1.3x1.3x1.3 0.4x0.4x0.4  Table 3.2- A comparison of RDFs measured with the SFD and EFD diode and those simulated with Monte Carlo (including relative error). The Jaw and p M L C columns specify the collimator settings for these measurements and the RDFs in this table are calculated at 5 cm depth.  3.2  ICF Investigation - Measurement, BrianSCAN and Monte Carlo  3.2.1 Medium field investigation results  Table 3.3 contains a summary of the ICF values for the medium field investigation as determined from the ion chamber (FC-65), BrainSCAN and Monte Carlo (DOSXYZnrc) results. It may be observed that the ICFs are greater than unity for the styrofoam phantom (STYPhantoml) and less than unity for the high density bone phantoms (BonePhantomA, BonePhantomB). This is due to a lower attenuation coefficient of the styrofoam slab relative to water and a higher attenuation coefficient of bone relative to water. Since there is a lower attenuation through the styrofoam slab, the photon fluence passing through the measurement point (ie. ion chamber) is larger than it would be if the styrofoam slab was replaced with solid water. This higher photon fluence would then increase the number of interactions creating the production of more secondary  79  electrons (i.e. ionization). Another interesting observation is how the measured and Monte Carlo ICFs agree to within 1% and the values for both BonePhantomA and BonePhantomB are also in agreement. The BrainSCAN calculation however, for these two phantoms differs by more than 2%. This may indicate a limitation on the path length correction in BrainSCAN for deeper bone structures or higher density materials that are deep seated.  Table 3.4 is a ICF comparison between Monte Carlo versus measurement and BrainSCAN versus measurement. For all phantoms and all fields, the M C - M E A S U R E D values are within the statistical error from Table 3.3.  The BrainSCAN - M E A S U R E D values for the 42x42 mm and 36x36 mm 2  2  fields from BonePhantomB anterior beam, differ by approximately 3.0 %.from the corresponding M C - M E A S U R E D values. This error again may indicate a limitation on the path length correction in BrainSCAN for deep bone structures. The values we arrive at between M C - M E A S U R E D and BrainSCAN - M E A S U R E D for BonePhantomA, are comparable for the anterior beams (with the exception of the 36x36 mm measurement) but approach noticeable differences for the oblique beams. For the oblique measurements, all fields present a difference >1.1% and the latter two fields at nearly 2%. We suspect this may be due to an uncertainty in the alignment of the center of the ion chamber's sensitive volume relative to the central axis of the photon beam. If the measured fields were smaller, then the alignment of the center of the ion chamber at the center of the radiation field must be as precise as possible because of the sharp falloff caused by L E D . As L E D becomes more pronounced in smaller field measurements, the  80  uncertainty will become greater as well. In general though the Monte Carlo ICF calculations are within the statistical uncertainty for all cases and the BrainSCAN M E A S U R E D values differ by up to 3%.  Gantry Angle: 0 BonePhantomA, d=3cm  FC-65  BrainSCAN  Monte Carlo  Monte Carlo (± %)  42x42mm 36x36mm 60x60mm  0.979 0.979 0.980  0.968 0.968 0.973  0.971 0.979 0.982  1.26 1.24 1.32  0.972 0.972 0.973  0.942 0.941 0.954  0.971 0.971 0.976  1.27 1.25 1.31  1.170 1.176  1.162 1.165  1.164 1.173  1.28 1.27  0.968 0.965 0.985  0.946 0.945 0.953  0.957 0.963 0.971  1.27 1.25 1.30  BonePhantomB,d=1 Ocm 42x42mm 36x36mm 60x60mm STYPhantoml, d=12.8cm 42x42mm 36x36mm  Gantry Angle: 45 BonePhantomA, d=3cm 42x42mm 36x36mm 60x60mm  Table 3.3 - The ICF values calculated for the medium field ICF investigation. The ICF is calculated via three different methods for each phantom in Table 2.1: measurement (FC65 ion chamber), pencil beam algorithm (BrainSCAN) and Monte Carlo (DOSXYZnrc). The field sizes investigated are also listed. The ICFs were calculated for anterior beams (gantry 0 degrees) for all phantoms with the exception BonePhantomA, which was also examined with an oblique (gantry 45 degrees) beam. The relative error in the Monte Carlo ICF calculation is also listed .  81  MC - M E A S U R E D (%)  BrainSCAN -  M E A S U R E D (%)  Monte Carlo (± %)  Gantry Angle: 0 BonePhantomA, d=3cm 42x42mm 36x36mm 60x60mm  0.7 0.0 -0.2  -1.0 -1.1 -0.6  1.26 1.24 1.32  0.1 0.1 -0.2  -3.0 -3.0 -1.9  1.27 1.25 1.31  0.6 0.3  -0.8 -1.1  1.28 1.27  1.0 0.2 1.3  -2.1 -2.1 -3.1  1.27 1.25 1.3  BonePhantomB,d=1 Ocm 42x42mm 36x36mm 60x60mm STYPhantoml, d=12.8cm 42x42mm 36x36mm Gantry Angle: 45 BonePhantomA, d=3cm 42x42mm 36x36mm 60x60mm  Table 3 . 4 - A comparison of differences between the Monte Carlo I C F calculation versus ion chamber measurement ( M C - M E A S U R E D ) and the measured I C F calculation versus B r a i n S C A N ( B r a i n S C A N - M E A S U R E D ) for the medium field phantoms. The differences are expressed in %.  82  3.2.2 Small field investigation results Table 3.5 is a summary of the ICF values for the small field investigation. As with Table 3.3, they contain the ICF values calculated via three methods: compact chamber (CC-01), BrainSCAN and Monte Carlo (DOSXYZnrc). As in Table 3.3, the styrofoam phantom has higher ICF values than that of the bone phantom. The reason can be traced back again to the lower attenuation of photons in the styrofoam and hence more energy deposition in the scoring slab, as discussed in the previous section. If we had replaced the styrofoam slab with an air gap we would expect the ICF values to be even higher.  Table 3.6 is an ICF,comparison between Monte Carlo versus measurement and BrainSCAN versus measurement. For all phantoms and all fields, the M C - M E A S U R E D values are within the statistical error from Table 3.5. For BonePhantomC, the comparisons between M C - M E A S U R E D and BrainSCAN - M E A S U R E D seems to show random variations but in all cases are <1% from each other. For STYPhantom2, this is not the case. Here, all values are between 1-2% of each other. We can suggest a few possible reasons for this. The first consideration is that BrianSCAN may have problems in modeling the L E D present in the styrofoam slab. Since the BrainSCAN M E A S U R E D values are positive, it may indicate that BrainSCAN estimates a higher electron fluence near the measurement point, implying it either underestimates the effects of L E D or doesn't take it into account at all in the styrofoam slab. It is not certain how this would have an effect in the dose scored in the neighboring slab, but this it is certainly something to consider and will be investigated further.  83  It can also be observed in Table 3.6 that this discrepancy gets smaller for the 12x12 mm and 6x6 mm fields. This may suggest that BrainSCAN is better at predicting 2  2  the effects of photon scatter for smaller fields since as field size deceases there is less photon scatter in the field boundary.  84  Gantry Angle: 0 BonePhantomC, d=5cm  CC-01  BrainSCAN  Monte Carlo  Monte Carlo (± %)  24x24mm 18x18mm 12x12mm 6x6 mm  0.972 0.970 0.968 0.967  0.970 0.968 0.960 0.965  0.974 0.968 0.968 0.961  1.6 1.7 2.1 2.5  1.179 1.187 1.196 1.186  1.204 1.208 1.207 1.203  1.185 1.185 1.198 1.203  1.7 1.7 2.3 2.6  0.959 0.954 0.947  0.949 0.947 0.940 0.939  0.960 0.953 0.954 0.947  1.7 1.7 2.2 2.5  1.213 1.222 1.233 1.222  1.233 1.236 1.241 1.244  1.209 1.222 1.224 1.239  1.7 1.7 2.2 2.6  STYPhantom2, d=10.8cm 24x24mm 18x18mm 12x12mm 6x6mm Gantry Angle: 45 BonePhantomC, d=5cm 24x24mm 18x18mm 12x12mm 6x6mm Gantry Angle: 30 STYPhantom2, d=10.8cm 24x24mm 18x18mm 12x12mm 6x6 mm  Table 3.5- The ICF values calculated for the small field ICF investigation. The ICF is calculated via three different methods for each phantom: measurement (CC-01 compact chamber), pencil beam algorithm (BrainSCAN) and Monte Carlo (DOSXYZnrc). The field sizes investigated are also listed. The ICFs were calculated for anterior beams (gantry 0 degrees) for both phantoms and oblique beams of 45 degrees for BonePhantomC and 30 degrees for STYPhantom2. The relative error in the M C ICF calculation is also listed.  85  MC - M E A S U R E D (%)  Gantry Angle: 0  BrainSCAN - M E A S U R E D (%) Monte Carlo (±%)  BonePhantomC, d=5cm 24x24mm 18x18mm 12x12mm 6x6 mm  0.3 -0.3 0.0 -0.7  0.3 -0.3 0.0 -0.7  1.6 1.7 2.1 2.5  0.7 -0.2 0.2 1.7  2.6 2.1 1.1 1.7  1.7 1.7 2.3 2.6  0.1 -0.2 0.8  -1.0 -0.7 -0.7  1.7 1.7 2.2  -0.4 -0.1 -0.9 1.7  2.1 1.3 0.7 2.3  .1.7 .1.7 2.2 2.6  STYPhantom2, d=10.8cm 24x24mm 18x18mm 12x12mm 6x6mm Gantry Angle: 45 BonePhantomC, d=5cm 24x24mm 18x18mm 12x12mm Gantry Angle: 30 STYPhantom2, d=10.8cm 24x24mm 18x18mm 12x12mm 6x6mm  Table 3.6- A comparison of differences between the Monte Carlo ICF calculation versus ion chamber measurement (MC- M E A S U R E D ) and the measured ICF calculation versus BrainSCAN (BrainSCAN- M E A S U R E D ) for the small field phantoms. The differences are expressed in %.  86  3.3 Analyzing Lateral Electronic Disequilibrium with CTcreate Figure 3.16 is an isodose distribution overlay in the transaxial plane for the heterogeneous STYPhantoml phantom, which is seen through dosxyz_show. A 36x36 mm field was simulated at isocenter (d=12.8 cm). The majority of the dose 2  deposited can be seen near the top of the first slab. This coincides with the dose buildup properties of the 6 M V photon beam where the buildup occurs within 1.5 cm from the surface. One can also observe a wider spread of the isodose lines in the styrofoam. This is primarily due to L E D . In a lower density medium (<  p ter) wa  the mean lateral range of  secondary electrons will increase, thus enhancing the L E D effect. The premise behind this was discussed in section 3.2.2. A noise-like effect in the isodose lines as they progress toward the bottom of the phantom is also noticeable. This effect is the result of the beam being attenuated as it moves through the lower slabs, hence increasing the statistical uncertainty.  Figure 3.17 is the PDD curve in the z direction for the STYPhantoml phantom. There are two PDD curves calculated from Monte Carlo: One representing the heterogeneous phantom (styrofoam included) and one representing the homogeneous phantom. The third PDD curve is the BrainSCAN calculation through the heterogeneous phantom. The effect of the styrofoam is clearly visible from the Monte Carlo simulation; producing a pronounced falloff in the dose. The reason is because L E D is more prominent in this region. The lateral range of secondary electrons is greater in the styrofoam and more electrons deposit their energy far away from the central axis of the beam. What is startling is the overestimation in dose from the BrainSCAN dose  87  calculation. It would seem that BrainSCAN is underestimating the effects of L E D in the styrofoam, meaning the predicted lateral range of secondary electrons is shorter than what we may normally expect. We suspect that the pencil beam algorithm does not have a good way of handling L E D . This underestimated range can certainly raise the dose deposited around the central axis of the beam, which is why we see the dose overestimation in the styrofoam. In regards to photon attenuation, the BrainSCAN dose calculation algorithum seems to be modeling this correctly in that after the styrofoam, the dose with Monte Carlo seems to agree quite well. Both of these effects were observed by Haraldsson et al [20]. They discovered that their TPS (CadPlan 6.2.7) overestimated the absorbed dose in an air interface from a custom designed phantom.  88  150  %  J40  %  1150  %  _J  J 1*0 _J i i < ?  3.0  •%  2.5 %  i<?5 % %  r  2.0  95 % %  #5  %  OT* <•—  75  %  70  %  1,3  n 60 so  % %  r J»6 Slice-  <"  uutJter  JO % 20  %  10  %  5  %  Figure 3.16- A n isodose distribution for the heterogeneous STYPhantoml phantom as viewed with dosxyzshow. The distribution corresponds to a field size of 36x36 mm defined at d= 12.8 cm in the transaxial plane . The buildup region apparent in the first slab is coincident with the 1.5 cm buildup range for a 6 M V photon beam. The wider spread of the isodose lines at the styrofoam is due to L E D . 2  89  36x36mm  Figure 3.17- A PDD curve for the STYPhantoml heterogeneous and homogeneous phantoms as calculated in Monte Carlo from the CTcreate data. Plotted along the STYPhantoml PDD from Monte Carlo is the same result from BrainSCAN. Field size is 36x36 mm at d=12.8 cm. The effect from the styrofoam is clearly visible from the Monte Carlo simulation; producing a pronounced falloff in the profile while BrainSCAN overestimates the dose in this region. 2  90  36x38mm  Figure 3.18- A PDD curve for the BonePhantomB heterogeneous and homogeneous phantoms as calculated in Monte Carlo from the CTcreate data. Plotted along the BonePhantomB PDD from Monte Carlo is the same result from BrainSCAN. Field size is 36x36 mm at d^^.S cm. The effect from the bone is clearly visible from the Monte Carlo and BrainSCAN calculation; producing a pronounced drop in the dose. 2  Figure 3.18 is the PDD curve in the z direction for the BonePhantomB heterogeneous and homogeneous phantoms as calculated in Monte Carlo from the CTcreate data. Plotted along with the BonePhantomB PDD from Monte Carlo is the same result from BrainSCAN. The effect from the bone is only slightly visible here and the agreement between BrainSCAN and Monte Carlo seems quite good. The first consideration for this better agreement is that here we are in an improved condition for  91  electronic equilibrium. The BrainSCAN and Monte Carlo doses are lower after the region of the bone than the dose for the homogeneous phantom. In section 1.3.4 we discussed that when we have two media, such as bone and water, separated by a thin interface, then the ratio  D bone  can be expressed as the ratio of their mass collision stopping powers. In  ^ water  this case the absorbed dose at a point in bone relative to absorbed dose at the same point in the homogeneous phantom (i.e. water) is:  D bone  A.  / — \ bone  (3.1)  or\ \ PJ \  / water  We also said that the mass collision stopping power explicitly depended on the ratio of a medium. Since this is the case, it can be shown that  f—  \col  ' s^ V^  <  ' S ^  (3.2)  J  J bone  Based on this formalism, the dose to bone would be less than that in water. It is important to realize that this approach could not be used to explain the lower dose from the styrofoam in Figure 3.17 since equation (3.1) is based under the conditions of electronic equilibrium.  92  . 1Zx12mm MC BrainSCAN  i  0.8 0.7  il it  Relative Dcse  0.5  « i  0.4 i 0.3 0.2 0.1  styrofoam 10 cm  12  16  Figure 3.19- A PDD curve for the STYPhantoml heterogeneous phantom as calculated in Monte Carlo from the CTcreate data. Plotted along the STYPhantoml PDD from monte carlo is the same result from BrainSCAN. Field size is 12x12 mm at d=12.8 cm. The effect of L E D is more evident through the styrofoam gap for this field width producing a deeper dose fall off in the Monte Carlo data while BrainSCAN still overestimates the dose in this region to a large degree. 2  Figure 3.19 is the PDD curve for the STYPhantoml heterogeneous phantom as calculated in Monte Carlo from the CT data for a 12x12mm field size. Plotted along the 2  STYPhantoml PDD from Monte Carlo is the same result from BrainSCAN. For this field size, the effect from the styrofoam is clearly more pronounced than that in Figure 2  3.17. The lowest dose is approximately 20% lower than that of the 3 6x3 6mm field,  93  20  which can be explained from the discussion in section 1.2.5. It was discussed that as field size decreases, L E D has a greater effect since secondary electrons can travel further outside the geometrical limits of the field width itself. While BrainSCAN still overestimates the dose in this region to a large degree, it still is able to model the photon attenuation quite well with the close agreement observed after the styrofoam.  94  Chapter 4 Conclusions Based on the data presented in this thesis we conclude that Monte Carlo can be an effective means for calculating RDFs for small radiation fields where L E D may be a problem. The RDF values obtained with our Monte Carlo model agree to within 1% with the values obtained via measurement with the SFD. Based on this result and the good agreement obtained in Figures 3.7-14 we can also conclude that a SFD silicon diode can be a useful dosimeter when measuring RDFs for radiation fields smaller than l x l cm or 2  when the highest accuracy in relative dosimetry is required. The result of Figure 3.5 goes to illustrate that the sensitive volume of an ion chamber is inadequate for accurate relative dosimetry of small fields. The physical phenomena of L E D and the D V E should reserve its use for large (> 5x5 cm ) field dosimetry i f absolutely necessary. 2  Monte Carlo can also be useful tool when quantifying the possible limitations of a dose calculation algorithm in regions where L E D is present. Although our results for the ICFs calculated from BrainSCAN agree to within 1.5% for most cases with Monte Carlo in the small field investigation, we may have discovered other limitations with the BrainSCAN dose calculation. In Table 3.4 we observed that the BrainSCAN - M E A S U R E D values for the 42x42 mm and 36x36 mm fields from BonePhantomB anterior beam, differ by 2  2  approximately 3.0 % from the corresponding M C - M E A S U R E D values. Even taking the statistical error into account from the Monte Carlo, there is still a more than 1.5 % difference that is unaccounted for. We can conclude from this that BrainSCAN might have some limitation on its path length correction for deeper bone structures or higher  95  density materials that are deep seated. If time permitted this is something that would have been investigated further. In closing we would like to say that CTcreate can be an effective method for calculating accurate dose distributions in an experimental phantom or a patient CT phantom where inhomogeneities are present. Using this program we have shown that the pencil beam algorithm is unable to model the effects of L E D in inhomogeneities such as air. Its lack of ability to predict L E D in low density media is a concern and warrants further study in order to quantify the extent of this underestimation for a variety of cases. Combined with DOSXYZnrc, CTcreate makes an excellent potential verification tool when confirming dose distributions from a TPS.  96  Chapter 5 Future Work The work initiated in this thesis has great potential to be extended through further investigations. We have shown that CTcreate can be an accurate tool for calculating dose distributions in a CT phantom. One could take this a step further and use it to generate isodoses from actual patient CT data. Using our Monte Carlo model in conjunction with CTcreate and patient CT data and then comparing results with BrainSCAN would have been the ideal study to investigate since it would be most applicable to the real life condition. In doing so one could also test this using a variety of irregular shaped fields; another feature that wasn't explored. Further, it was observed in Figures 3.17 and 3.19 that BrainSCAN overestimates the dose in lower density structures. It would have been ideal to place an ion chamber in our styrofoam slab and hence measure the ICFs in our inhomogeneities. This alone would present a good case that BrainSCAN has severe limitations when calculating dose through these inhomogeneities.  Another potential application of our Monte Carlo model would be to modify the u M L C C M into a dynamic leaf motion sequence then potential IMRT applications might be explored and the ability of BrainSCAN to predict doses for deeper seated high density structures like in BonePhantomB is also something we believe could be analyzed further.  97  Bibliography [I] H Johns, J Cunningham, The Physics of Radiology, 4th edition, Charles C Thomas Publishing, Springfield, IL, 1983. 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