UNIVERSITY OF CALGARY. Monte Carlo model of the Brainlab Novalis Classic 6 MV linac using the GATE simulation. platform. Jared K.

Transcription

1 UNIVERSITY OF CALGARY Monte Carlo model of the Brainlab Novalis Classic 6 MV linac using the GATE simulation platform by Jared K. Wiebe A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF PHYSICS AND ASTRONOMY CALGARY, ALBERTA SEPTEMBER, 2014 Jared Wiebe 2014

2 Abstract Monte Carlo (MC) simulations are known to be the most accurate method to model radiation transport and absorbed dose. Geant4 application for tomographic emission (GATE) is a Monte Carlo simulation platform built and is relatively new at modeling radiotherapy systems. A MC model of the Brainlab Novalis Classic 6 MV was developed using GATE which will investigate GATE s capabilities in the application of a stereotactic radiosurgery (SRS) dedicated linear accelerator. Measured depth dose distributions and dose profiles using an ion chamber, diode detector, and radiochromic film are used as reference measurements for the model. The model shows agreement with the measured data with greater than 90% of points passing a 3%/1mm gamma comparison, with the exception of smaller field sizes in the penumbra region which still agree within 3%/3mm. This model demonstrates GATE ability to model linacs and can be used in the future for research and clinical comparisons. ii

3 Acknowledgements I would like to acknowledge the University of Calgary, Tom Baker Cancer Centre, and NSERC for funding and financial support. I would also like to thank my supervisor Dr. Nicolas Ploquin and co-supervisor Dr. Rao Khan for the opportunity to work on this project and their understanding and guidance throughout my Master s program. I would also like to thank Edward Pranoto, a summer student who created the CAD drawings seen in this thesis. iii

4 Table of Contents Abstract... ii Acknowledgements... iii Table of Contents... iv List of Tables... vi List of Figures and Illustrations... vii List of Symbols, Abbreviations and Nomenclature...x CHAPTER ONE: INTRODUCTION Radiation therapy...11 CHAPTER TWO: LINEAR ACCELERATORS X-ray production Linear accelerator design Radiological Measurements...23 CHAPTER THREE: MONTE CARLO SIMULATION Overview of method Particle simulation Photons Electrons General user parameters in a MC simulation Variance reduction techniques Phase space Statistics in MC simulation...44 CHAPTER FOUR: EXISTING MONTE CARLO CODES IN RADIATION THERAPY EGSnrc MCNP Geant Geant4 physics models and settings Geant4 validation in radiation therapy Geant4 Application for Tomographic Emission (GATE) Application of GATE to radiation therapy Motivation for using GATE as the MC package for this project...61 CHAPTER FIVE: MATERIALS AND METHODS Overview Varian Novalis linac Capabilities and Geometry Measured data Ion Chamber Radiochromic Film Diode measurements GATE simulations Physics settings...75 iv

5 5.4.2 Computer hardware Building the geometry GATE s actors Electron source Flattening Filter Energy spectrum Comparing the data Gamma index Uncertainty...86 CHAPTER SIX: RESULTS AND DISCUSSION Results Depth dose distributions Dose profiles Diagonal profile MLC evaluation Relative output factor X-ray spectrum Discussion CHAPTER SEVEN: CONCLUSION AND FUTURE WORK Summary Future Work Closing comments REFERENCES APPENDIX A: ACTORS IN GATE APPENDIX B: GATE MACRO v

6 List of Tables Table 4.1: Table summarizing the similarities and differences between EGSnrc, MNP, and Geant4 for modeling photon and electron transport. The table is adapted from Verhaegen and Seuntjens [38] Table 4.2: Summary of each parameter for the multiple scattering algorithm, ionisation, and production cuts. The user must specify each of these parameters in Geant Table 5.1: Table of the in-house measurements of the MLC on the Novalis. The table displays each leaf width type (as coloured in Figure 5.4) and shows the width and length of the sub-volume for each leaf corresponding to Figure 5.5. All measurements are in mm Table 5.2: Recommended physics settings in GATE for radiotherapy applications involving EM interactions. Table adapted from the OpenGATE collaboration website [51] Table 6.1: The columns display the results of the mean dose difference, mean gamma, and percentage of points passing gamma criteria of 3%/1mm and 3%/3mm. Results shown are for dose profiles and PDDs vi

7 List of Figures and Illustrations Figure 2.1: A plot of an x-ray spectrum produced from a kev electron beam. The unfiltered spectrum is shown by a straight line, reaching a maximum energy of the electrons used to produce the x-rays. The spectrum is filtered through the target causing the lower energy photons to be absorbed. Both axes are in arbitrary units and use a linear scale Figure 2.2: Diagram of the main linac components Figure 2.3: Diagram of the geometric penumbra due to the spot size. A narrower spot size will leave a smaller penumbra region, will a large spot size will cause a large penumbra.. 17 Figure 2.4: Diagram of the main linac components and a water phantom. The electron beam (red arrow) travels from the top to the bottom and produces photons (green lines) via Bremsstrahlung on the Tungsten and Copper target. The cone extending to the water phantom represents the edge of the x-ray beam Figure 2.5: A plot showing the angular distribution of x-ray production via bremsstrahlung. The measure of production is given in barns per steradian. The radial line indicates the number of barns per steradian at a particluar angle from the direction of the incident electrons. This trend continues when looking at higher electron energies. The plot isadapted from Attix, F. H. [2] Figure 2.6: Image shows an example of a Copper flattening filter (one specific to the Novalis linac was not available). The total conical shape is made up of smaller conical sections of varying heights and angles. The filter is designed to produce a flat dose profile at treatment depth. The filter will also harden the beam having a greater effect along the central axis Figure 2.7: Leaf end view of one bank of the micro MLC system on the Novalis. The width of the each leaf varies along its height to produce a tongue and groove. Each leaf can move separately from the other in and out of the field (in and out of the page). At this viewing angle the x-ray beam would be incident from the bottom. Looking at the vertical in the image, the leaves are at an angle to match the divergence of the incident radiation beam Figure 2.8: Plot of a percent depth dose curve for a 6 MV linac in a 98x98 mm 2 square field size. The measurement is performed in a water phantom with 100 cm SSD using a CC13 ion chamber. The plot is normalised to the maximum dose value. The curve characterizes the dose deposition with depth along the central axis Figure 3.1: A flowchart of the MC simulation of photon transport. The initial starting particle or primary is picked off the stack. If the particle is ever below a cuttoff threshold, it will be terminated and the energy deposited locally. The distance to interaction, type of interaction, and resulting properties of the particles due to the interaction all require random sampling. The resulting particle properties (of both primary and daughter vii

8 particles) are stored in the stack. The process is repeated until no more particles are in the stack. Adapted from D. W. O. Rogers and A. F. Bielajew [11] Figure 3.2: A diagram showing an incident electron passing by an atom. The impact parameter is the distance from the nucleus to the trajectory of the approaching electron and is the classical radius Figure 3.3: A sketch of the hypothetical paths of an electron using single scattering and a condensed history approach. The path for single scattering is not continuous as shown but is still made of discrete events. There are many interactions with single scattering and it would require a large amount of time. To approximate, the many small scattering events are grouped in large scattering events (the vertices) by using a multiple scattering theory for a condensed history. The large numbers of small interactions are elastic or semi-elastic and are approximated in the condensed history technique by a continuous energy loss along the electrons path; this energy is deposited locally about the track Figure 3.4: Diagram of a phase space. When the particle (green line) passes through the circular plane (blue), the energy, position in radius and angle, and direction given in angles and are recorded Figure 5.1: Novalis Classic 6 MV linac at the Tom Baker Cancer Centre Figure 5.2: Diagram of the MLC leaves on the Novalis. The outer leaves, in green, on both banks have a width of 5.5 mm at isocenter, the red leaves are thinner, with 4.5 mm width at isocenter, and the yellow leaves are 3 mm wide at isocenter. Each leaf can move in and out of the field (left-right in the diagram) Figure 5.3: Two banks of MLC s on the Novalis Classic 6 MV. The leaves are all in a closed position. The view is looking up towards the source Figure 5.4: Cross-sectional area of one of the MLC banks on the Novalis linac. The tongueand-groove design can be seen for each leaf. Red, green, and yellow indicate a projected leaf width of 5.5, 4.5, and 3 mm. The triangle of the same colour is a circle leaf flipped 180 (or vice versa) Figure 5.5: Image of one leaf end. The white lines section each part of the leaf according to width. Each of the leaf widths were measured and used in the MC model. The widths can be found in Table Figure 5.6: Image of one leaf on its side (the leaf would move in and out of the field horizontally). The leaf end in the radiation field is the left hand side. Note the leaf end has three different straight angles to mimic a curve. The yellow lines indicate the separation of these straight sections on the left hand side Figure 5.7: Welloffer Blue Phantom system. The tank is filled with water and the detector is placed on the black holder as indicated in the image. The position of the detector can be controlled remotely in and in predetermined paths viii

9 Figure 5.8: Left Diagram of the positions of the MLC for one the measured fields (from iplan commissioning report).three rectangular openings are made by closing two leaves in the upper middle portion and three leaves in the lower middle. Right Image of the same MLC positions rendered in GATE. The point of view is looking up the x-ray beam, into the linac Figure 5.9: - CAD model of the linac components modeled in GATE Figure 5.10: Components from the CAD model rendered in GATE. The green lines represent photons and the red lines electrons Figure 5.11: Diagram of the flattening filter used in the simulation. It consists of two conical sections to form an overall cone shape Figure 6.1: Plots of depth dose distributions for square field sizes of 98x98, 60x60, 30x30, 18x18, 6x6 mm 2. Plots display measured data (black line), MC data (blue dots), and the gamma at each point (green) with the gamma value boundary of 1 (red line). Dose is normalised to maximum. Some error bars are too small to be seen Figure 6.2: Plots of the dose profiles for square field sizes of 98x98, 60x60, 30x30, 18x18, and 6x6 mm 2 for depths of 15 mm and 100 mm, with the exception of the 98x98 mm 2 field size, which is at a depth of 16 mm instead of 15 mm and includes a depth of 200 mm. The plots display the measured data (black line), MC data (blue dots), and gamma comparison of each point (green) with the gamma boundary of one (red line). The gamma criteria is 3%/1mm. The dose is normalised to the central axis. Some error bars are too small to see in the plots Figure 6.3: Diagonal profiles at depths of 16 mm and 100 mm (top and bottom, respectively) at a field size of 98x98 mm 2. The blue dots are MC data and the black line are measured data. The green triangles are the gamma values for each point with a 3%/1mm criteria Figure 6.4: Plots comparing a dose profiles at a depth of 15 mm (top) and 100 mm (bottom), in the transverse irregular field shape. Blue dots are MC data, black line is measured data, and green is the gamma comparison (3%/1mm criteria) Figure 6.5: Comparison of relative output factors from MC and measured data. The MC dose decreases compared to the measured data with decreasing field size. The maximum discrepancy is seen at the 6x6 mm 2 field size by 17%. The measured data is taken from the CAX of the profile measurements Figure 6.6: - Plot of the MC calculated linac spectrum of the Novalis compared to a MC spectrum of the Elekta Precise [17].. The vertical axis is in arbitrary units and the curve is normalised ix

10 List of Symbols, Abbreviations and Nomenclature Symbol Definition AAPM American Association of Physicists in Medicine CAX Central axis CPE Charged particle equilibrium CSDA Continuous slowing down approximation DBS Directional bremsstrahlung splitting DD Dose difference DTA Distance-to-agreement EBRT External beam radiation therapy EGS Electron gamma shower EM Electromagnetic GATE Geant4 Application for Tomographic Emission Geant4 Geometry and Tracking 4 IMRT Intensity modulated radiation therapy Linac Linear accelerator MC Monte Carlo MCNP Monte Carlo N-particle MLC Multi-leaf collimator MS Multiple scattering MU Monitor unit NRC National Research Council PDD Percent depth dose RO Radiation Oncologist ROF Relative output factor SBRT Stereotactic body radiation therapy SRS Stereotactic radiosurgery SSD Source-to-surface distance VMAT Volumetric-modulated arc therapy VRT Variance reduction technique Z Atomic number x

11 Chapter One: Introduction This research project will use the GATE Monte Carlo (MC) simulation platform to model the Novalis Classic 6 MV linear accelerator (linac). GATE is an acronym for Geant4 Application for Tomographic Emission. The GATE software is written from the Geant4 toolkit. Only a handful of linacs have been modeled with GATE since its release in This research will investigate GATE s capabilities for small field applications and provide a validated linac model to extend to multiple research projects. Also, the validated model will have the potential to provide an independent dose calculation for evaluating treatment plans. The first few chapters provide background material on radiation therapy, basic linac components and x-ray production, and commonly used MC codes with a focus on Geant4 and GATE. 1.1 Radiation therapy Ionizing radiation has the ability to damage cells in living tissue which can lead to cell death. This attribute is exploited in clinical treatments called radiation therapy or radiotherapy. The most common use is in radiation oncology where the objective is to use ionizing radiation to damage, and ultimately kill cancerous cells in the patient. Approximately 50% of all cases of cancer treatment should undergo radiation therapy [1]. One type of radiation therapy is called external beam radiation therapy (EBRT). In EBRT the radiation source is external to the patient and is most often created and delivered by a medical linac. In order to reach the intended treatment site in the patient, the radiation must pass through 11

12 and irradiate healthy normal tissues. In many situations EBRT planning seeks to maximize the dose to cancer cells while minimizing the dose to healthy normal tissue. For an EBRT treatment, the dose is usually divided into fractions. The amount of dose and the fractionation scheme are different depending on the patient, tumor size, site, and diagnosis. A Gray (Gy) is a unit of dose equal to energy (Joules) per unit mass (kilograms. An example of a radiation prescription would be 60 Gy over 30 fractions (that is 2 Gy per treatment and 30 treatments total) to a target volume defined by the RO, treating once a day. While it is always important to accurately deliver dose to the target, small errors in patient setup will affect the accuracy of the treatment. These setup errors are compensated for by added a margin around the target volume to ensure adequate dose coverage of the target. However, the wider margin will increase the dose to surrounding healthy normal tissue. Also, when the treatment is delivered over many fractions, these errors tend to average out from the variations in each setup. A special technique of radiation therapy is Stereotactic Radiosurgery (SRS): SRS is a high dose single fraction treatment to a small lesion, most commonly used for tumours in the brain. Given such a high dose in one fraction, accurate tumour localization and patient setup is absolutely required as there are smaller margins for random error. Another type of stereotactic treatment is stereotactic body radiation therapy (SBRT), typically this is a high dose in three to five fractions, delivered to other sites outside the central nervous system/brain Therapeutic radiation planning requires an accurate method to predict the dose delivered to the patient. One of the most accurate methods used is Monte Carlo simulations of radiation transport. This research used the GATE (Geant4 application for tomographic emission) 12

13 simulation platform to model the Novalis linac a dedicated SRS radiation treatment system. Background details on linear accelerators, MC simulation, and MC codes will be given followed by information on previous research in radiation therapy using GATE and the methods used for this work. 13

14 Chapter Two: Linear accelerators 2.1 X-ray production A linear accelerator (linac) is the most common way to produce x-rays for external beam radiation therapy. It produces x-rays through bremsstrahlung. Electrons are accelerated into a high atomic number target causing the electrons to collide with the atoms and as a result, produce photons. When the electrons undergo a high acceleration (or deceleration in this case), energy is radiated as light, more specifically x-rays for the accelerating energies utilised. The x- ray beam produced via bremsstrahlung is polyenergetic. An unfiltered spectrum in a vacuum would be a straight line with a negative slope from some maximum at zero (or near zero) to a minimum at the maximum energy of the incident electron (see Figure 2.1). The unfiltered spectrum would also contain characteristic x-rays from fluorescence of the target material. The photons produced cannot have an energy greater than the electrons that produce them. Practically, the spectrum is filtered through the target (self-attenuation). The bremsstrahlung photons created must traverse the remaining target material causing lower energy photons to be attenuated (the lower the energy of the photon, the higher probability of attenuation). This leads to a spectrum in the shape of a curve that is peaked at approximately 1/3 of the incident energy of the electron beam for kev electrons and peaked approximately at 1/6 of the incident energy for MeV electrons. Usually, the x-ray spectrum is never characterised directly, instead dosimetric measurements are used characterise the beam indirectly this is discussed in section

15 Figure 2.1: A plot of an x-ray spectrum produced from a kev electron beam. The unfiltered spectrum is shown by a straight line, reaching a maximum energy of the electrons used to produce the x-rays. The spectrum is filtered through the target causing the lower energy photons to be absorbed. Both axes are in arbitrary units and use a linear scale. 2.2 Linear accelerator design In a MC simulation of a linac, there are key components to be modeled in order to develop an accurate model. These key components will be discussed here. An electron gun is required to produce free electrons and then these electrons are accelerated into a waveguide, which as a whole is called the accelerating structure. The electrons are accelerated to energies ranging from 6 MeV to 20 MeV. Since the energy from the x-ray beam is a continuous spectrum and not mono-energetic, the energy is reported as 6 MV for a 6 MeV electron beam striking the target. 15

16 This nomenclature is adopted from kv x-rays where the beam is reported based on the potential used to accelerate the electrons. A magnetron is used to produce the microwaves in the waveguide. Modern linacs will use an RF driver and a klystron to amplify the EM waves produced by the RF driver in order to achieve a higher energy. A diagram of these main components of a linac is shown in Figure 2.2. For some linacs, a bending magnet is used to change the direction (usually through 270 o ) and focus the electron beam on the high Z target. Some linacs will house the entire electron gun and wave-guide vertically above the isocenter with no bending magnet. The entire gantry can rotate about the isocenter and the linac head, where the x-ray target is, can rotate as well. The area the electron beam strikes on the target is called the spot size. The electron spot size will affect the penumbra of the dose profile the most. The penumbra is broken into two parts, the geometric penumbra and the radiation penumbra. The geometric penumbra is due to the spot size as shown in Figure

17 Figure 2.2: Diagram of the main linac components. Figure 2.3: Diagram of the geometric penumbra due to the spot size. A narrower spot size will leave a smaller penumbra region, will a large spot size will cause a large penumbra 17

18 Figure 2.4: Diagram of the main linac components and a water phantom. The electron beam (red arrow) travels from the top to the bottom and produces photons (green lines) via Bremsstrahlung on the Tungsten and Copper target. The cone extending to the water phantom represents the edge of the x-ray beam. Figure 2.4 shows a cross-sectional diagram of the linac components. The components seen in this figure are critical to model correctly for our simulation: the target, primary collimator, flattening filter, monitor chamber, secondary collimators, and the multileaf collimator (MLC). The target usually consists of a combination of Tungsten and Copper. The Copper is included to dissipate heat from the target and to filter out low energy x-rays; in particular the characteristic x-rays from Tungsten due to fluorescence. The thicknesses of the Tungsten and Copper will depend on 18

19 the desired beam energy. After the target, the primary collimator shapes the beam into a cone, absorbing photons that will reach beyond the field size limits at treatment depth. The term collimator in this context refers to an absorbing material that will block the beam. The x-ray production via Bremsstrahlung at these energies is radially symmetric and forward directed. More photons are produced along where is the azimuthal angle from the axis along the direction of the incident electron beam. There is a sharp falloff in the number of photons as increases. Looking through a plane that is perpendicular to the direction of the beam, this forward peak creates a high fluence along the central axis that decreases radially outward. A plot of bremsstrahlung production from a few electron energies and their angular distributions are shown in Figure 2.5. This leads to some difficulty to create a treatment plan with an inhomogeneous energy fluence over the field area. For conventional 3D radiation therapy, it is more desirable to have a flat energy fluence across the whole field at the depth of the treatment target resulting in a flat dose profile. To produce such a beam, a flattening filter is introduced after the primary collimator. The flattening filter is an approximately conical piece of metal placed in the path of the beam and aligned with the central axis. Figure 2.6 shows an example fo a typical flattening filter the one in the Novalis linac being modeled was not available. The central axis will have a larger path of material to attenuate the beam, which decreases radially outward. More photons are attenuated along the central axis compared to the outer edges to produce a uniform energy fluence across the whole field. A side effect of the flattening filter is the beam hardening effect and decrease in the dose rate. This effect is the increase of the average energy of the beam due to preferential attenuation of low energy photons. A lower energy photon has a higher probability of being stopped in a specific length of a 19

20 material. The flattening filter geometry is important to have correctly modeled, however if the exact geometry is not known, a simple cone or combination of a few conical shapes can be used and fitted to match measurements, which will be shown in section 5.6. Electron beam direction Figure 2.5: A plot showing the angular distribution of x-ray production via bremsstrahlung. The measure of production is given in barns per steradian. The radial line indicates the number of barns per steradian at a particluar angle from the direction of the incident electrons. This trend continues when looking at higher electron energies. The plot isadapted from Attix, F. H. [2]. 20

21 Figure 2.6: Image shows an example of a Copper flattening filter (one specific to the Novalis linac was not available). The total conical shape is made up of smaller conical sections of varying heights and angles. The filter is designed to produce a flat dose profile at treatment depth. The filter will also harden the beam having a greater effect along the central axis. The output of the linac is monitored by two ionization chambers, one placed after the other, and are known as monitor chambers. The chambers are placed in the beam path after the flattening filter and are redundant to have a backup in case one fails. The composition and size of these chambers vary depending on the manufacturer. The attenuation from the monitor chambers is very small compared to the attenuation of the flattening filter. In order to improve conformality to the treatment target, photon beams are shaped to match the target. Jaws are pieces of Tungsten alloy, placed in the path of the beam to produce rectangular field sizes. The Novalis Classic linac modeled in this thesis has four jaws: two for each direction 21

22 labelled X1, X2, Y1, and Y2. These jaws are made of Tungsten alloy with 95% W, 3.5% Ni, and 1.5% Cu. To ensure there is uniform attenuation of the radiation beam outside the treatment field, the faces of the jaw are aligned to match the divergence of the radiation beam. This will create a sharper penumbra, which will improve dose conformality to the target. The upper jaws closest to the target are the Y jaws. The divergence is matched by moving the jaws along an arc. The X jaws move linearly in and out of the field and rotate to have the face match the divergence. With the X and Y jaws the beam can be collimated to any rectangular field size. In addition to the jaws, the MLC (seen in Figure 2.7) is used to collimate the beam further to be able to create a variety of shapes other than rectangles. It consists of many thin rectangular slabs of Tungsten alloy adjacent to one another. Each slab is called a leaf and can slide in and out of the field to an accuracy of 1 to 2 mm. Leaf width is typically given as the projected width at isocenter. For example, the Novalis linac has widths of 5.5, 4.5, and 3 mm for the MLC system. The leaf positioning accuracy for the MLC system on the Novalis linac is 0.5 mm instead of the standard 1 to 2 mm. A highly conformal radiation beam can be delivered to the target using many leaves. Leakage between leaves is reduced by a tongue-and-groove design to ensure there is some material between adjacent leaves. Each manufacturer has a different design for their MLC. 22

23 Direction of x-ray beam Figure 2.7: Leaf end view of one bank of the micro MLC system on the Novalis. The width of the each leaf varies along its height to produce a tongue and groove. Each leaf can move separately from the other in and out of the field (in and out of the page). At this viewing angle the x-ray beam would be incident from the bottom. Looking at the vertical in the image, the leaves are at an angle to match the divergence of the incident radiation beam. All of the main components mentioned in this section must be accurately modeled in a Monte Carlo simulation. Clinically, the most important information about a linac is the dosimetric behaviour of the radiation beam. Different types of measurements are used to characterise this behaviour and it is important to use this data to create a model that matches these measurements. 2.3 Radiological Measurements A variety of dosimeters are available to measure radiation dose. Two of the most common ones used to measure the output of linacs are ion chambers and diodes. Ion chambers measure the 23

24 ionizations created from radiation passing through a volume of gas. As ions are produced they are accelerated toward a cathode or anode due to a potential. The charge collected can be related to the number of ionizations and in turn to the dose. Diode detectors are semiconductors that detect charge carriers created from radiation that passes through the detector. The x-ray beam of a linac is never fully characterised. The output rate is too high for any direct measurement method used for spectroscopy, although some research has been done in the past to measure and/or reconstruct the spectrum of a linac [3,4,5,6]. Since these spectra measurements have proven to be difficult and clinically speaking only the dose deposition is important, the linac can instead be characterised by how the dose is deposited in a specific material. Water is chosen as a standard in radiological measurements because of its abundance/ease of access and its properties are close to most of the human body, specifically soft tissue. A clinical standard is a large rectangular tank filled with distilled water placed such that the surface of the water is 100 cm from the target or source. Such a setup is known as 100 cm source-to-surface distance or SSD. Two types of relative measurements are particularly important: how the dose changes with depth along the central axis and how the dose changes along a line, in a plane perpendicular to the central axis. These two measurements are called a depth dose curve, referred to as a percent depth dose curve (PDD), and a dose profile, respectively. The PDD is usually normalised to the maximum dose along the central axis (CAX). Figure 2.8 shows a plot of a PDD. The depth at which the maximum dose occurs is called.the dose profiles are broken into inline, crossline, or diagonal (a line along x or y or diagonally across the field) and are always reported 24

25 at a specific depth in the water phantom. The dose profile is usually normalised to the dose on the CAX. Since the dose profile varies with depth, measurements must be taken at various depths in the phantom. Measurements are performed at various depths because the energy spectrum changes with depth, becoming harder (average energy of the beam is increasing) and as a result, the relative dose profiles change shape with depth. The field size affects the amount of scattered radiation that contributes to dose, increasing with field size, and therefore causing surface dose to increase for PDDs. Both of these measurements vary depending on the field size used. PDD and dose profiles are the two types of measurements need to characterize the beam. These types of measurements are used in this work to ensure the MC model matches the linac. Another factor is the relative output factor (ROF). This is the ratio of the dose along the CAX, at a specific depth, for a given square field size, over the dose under the same conditions in a reference field size, normally taken to be 10x10 mm 2. The relative output factor gives a simple and qualitative method to compare the effects of field size on the dose output. The ROF changes with field size due to the scattering in the phantom and scattering within the linac head from the collimators and flattening filter. 25

26 Relative dose (%) Depth (mm) Figure 2.8: Plot of a percent depth dose curve for a 6 MV linac in a 98x98 mm 2 square field size. The measurement is performed in a water phantom with 100 cm SSD using a CC13 ion chamber. The plot is normalised to the maximum dose value. The curve characterizes the dose deposition with depth along the central axis. Finally, the dosimetric characteristics of the MLC need to be measured. The leaf transmission is a measure of how much of the radiation beam has travelled through a leaf. MLC systems should have <5% transmission through a leaf [7]. Despite the tongue and groove design, there is still less material in between leaves, allowing some radiation through; this is called the interleaf transmission. Another quantity of interest is the leaf end transmission, which is the radiation that leaks through the end where leaves of opposite banks are abutted against one another. These can be measured by looking at the dose deposited from a field shape created with the MLC. A 2D 26

27 dose map can provide all the information, although 1D profiles acquired along the 2D dose map are useful as well. All of these measurements are important to understand the behaviour of the x-ray beam. These measurements are used to plan treatments by extrapolating from the measured doses to patient specific circumstances. Monte Carlo simulation of particle transport is one method used to calculate dose using dosimetric measurements as a reference to ensure the MC simulation matches the real dose. 27

28 Chapter Three: Monte Carlo simulation 3.1 Overview of method Monte Carlo is known to be the most accurate method to predict dose deposition. MC calculation does not use corrections to existing measurement data but instead develop the dose deposition from knowledge and data of the principle interactions of particles, such as attenuation coefficients and cross-section data. Very few MC calculation engines are employed in a clinical setting because of the prohibitive calculation time. This was a greater issue in the past due to the processing power available on computers at the time. However, considering how rapidly computer technology has advanced and continues to, it is reasonable to predict that MC treatment planning would be the standard in clinical centres in the near future. The Monte Carlo method uses random sampling of probability distributions to solve problems. Two main components required to utilize the Monte Carlo method are: i) the ability to produce random numbers or pseudo-random numbers that pass sufficient randomness tests and ii) a stochastic model of the problem in question. The problem that must be solved can be inherently stochastic (such as particle transport) or if it is deterministic, a suitable stochastic model must be constructed. Problems are not always one or the other but can be both stochastic and deterministic. A complete simulation of a naturally occurring stochastic problem is known as an analog MC simulation. Analog simulations can be partly non-analog if desired, usually to reduce the computation time. 28

29 True random numbers can be produced through natural phenomenon such as radioactive decay and electronic noise but these methods are cumbersome and undesirable. It is useful to be able to reproduce the same results or sequence of events to be able to find any errors, which could be very difficult if the numbers were truly random. Instead the preferred method is pseudo-random numbers. These numbers are produced from an algorithm and are reproducible. The numbers pass randomness test sufficiently to act as random numbers. Extensive literature can be found on computer implemented random number generators. The Mersenne Twister is the random number generator used in the GATE MC software, which is used for this project [10]. The simplest MC case to look at is discrete probabilities. Let there exist probabilities where, such that, where each probability represents an event. If a random number where lies in, then the event occurs. The key is the cumulative probability. The method is more complicated for continuous probabilities. There exists a probability density function over a range [ ], where, which has the following properties: i) ii) d The cumulative probability distribution is then d. (4.1) 29

30 Note that and. Since where, random number can be used to sample values of, equating with. The value of interest though is what value of will give This is the fundamental concept behind MC methods. How to sample the probability function for a value of differs depending on the functions and. The most direct method is to invert the cumulative probability distribution so that. (4.2) If inverting the distribution is too complicated the rejection method can also be used to sample a distribution. If the probability distribution is finite over its range and has a global maximum, a new function is made by normalizing to the global maximum: where is the point where there is a maximum. The rejection method then requires two random numbers: the first is used to find an value with, the second will test this value found using by rejection: if then is accepted as the sampled value, otherwise reject it. The rejection method is not as efficient as the direct inversion method because two random numbers are required for one sample. However if direct inversion is too complicated it may be faster to use the rejection method. Both direct inversion, either through analytical or numerical methods, and the rejection method can be used together by factoring the probability distribution; assuming it equals the product of two distributions. With this technique, the more complicated characteristics of the function can be factored out to apply the rejection method to this component and use the direct inversion method for the other function. 30

31 3.2 Particle simulation The stochastic nature of particle interactions makes them ideal to model with Monte Carlo methods. The random numbers generated are used to sample data points from probability distributions, such as cross sections and differential cross sections that are derived from measured particle data, which have been collected over the years from many experiments. A key component in particle simulation not seen in other applications of MC methods is a system to track geometries and particle position. This is also referred to as ray tracing Photons For a MC simulation of a photon there are four main steps where random sampling occurs. i) The first step is to determine the step size or the length of the path travelled by a photon of a given starting energy and direction. This is to determine how far the photon travels before an interaction occurs. ii) Once a step size is determined, the particle is moved to the new position (the step size in a straight line from the photon s original direction) and then the type of interaction that occurs is determined. For a photon, the competing interactions are Rayleigh scattering, photoelectric effect, Compton scattering, and pair production (both triplet and double). Rayleigh scattering is an elastic scattering of photons interacting with molecules or atoms. Rayleigh scattering is not an important process in the operating energy range of a 6 MV linac and is dominated by the other processes. The photoelectric effect is an interaction with the electrons in molecules or atoms. All of the photons energy is given to an electron that is liberated from the atom. The energy of the photon must be greater than the binding energy of the electron in the atom, allowing the electron to escape the atom. The electrons in the K-shell have a higher probability of being liberated. This will cause a hole left in the electronic structure of the atom 31

32 and electrons from higher energy levels will fill the hole (the point of lowest energy). This cascade is called atomic relaxation and can result in multiple photons being emitted, known as x- ray fluorescence, or electrons to be emitted, known as Auger electrons. Compton scattering is a process where the incident photon gives a significant amount of energy to an electron in the atom causing both the photon to be scattered, leaving with a different energy, and an electron to be emitted from the atom. Pair production is a process where a high energy photon, greater than MeV, interacts with the electric field of the nucleus of an atom to produce an electron and positron (or interact with the electric field of an electron, ejecting the electron and producing the positron and electron pair). The electron and positron share the energy of the photon with 511 kev needed for each particle (the rest energy) and the remaining energy used as kinetic energy. A cross section can be interpreted as a probability of interaction and is given in units of area. It can be thought of as the effective target area for the incident particle; the bigger the target, the more likely the interaction is to occur. The cross section for each type of interaction depends on the energy of the photon and material where the interaction occurs. The cross sections are weighted by the total cross section (which is the sum of cross sections from all possible interactions) giving each a statistical likelihood compared to one another. iii) After a type of interaction is determined, the energy and angle of deflection of the original photon and every daughter particle must be determined. iv) The original particle is in this manner until it loses all of its energy or leaves the volume of interest and then the daughter particles are modeled in the same fashion. Once the parent and daughter particles are all finished another starting photon is modeled. This process is repeated for millions of starting or primary particles, also called histories. Figure 3.1 shows a simple flowchart for a MC simulation of photon transport. 32

33 Figure 3.1: A flowchart of the MC simulation of photon transport. The initial starting particle or primary is picked off the stack. If the particle is ever below a cuttoff threshold, it will be terminated and the energy deposited locally. The distance to interaction, type of interaction, and resulting properties of the particles due to the interaction all require random sampling. The resulting particle properties (of both primary and daughter particles) are stored in the stack. The process is repeated until no more particles are in the stack. Adapted from D. W. O. Rogers and A. F. Bielajew [11]. To determine the step size of an interaction data about the linear attenuation coefficient is used. The attenuation of photons in a given material, with a given energy will be, (4.3) 33

34 where is the number of particles after travelling a distance and is the number of particles before attenuation. µ is the linear attenuation coefficient which is in units of inverse distance. The equation can be rearranged to ( ). (4.4) Note that the ratio will always be between 0 and 1. The quantity is known as the mean free path. The mean free path is the average distance a photon travels in a material between interactions. Once the photon has been moved by the determined step size to the interaction site, the type of interaction that occurs must be determined. The total cross section of a photon interaction in a specific material with a given energy is, (4.5) where,,, and are the Rayleigh, Compton, photoelectric effect, and pair production cross sections, respectively. The probabilities of each interaction can be found by dividing the total cross section by itself:, (4.6) 34

35 where,,, and are the Rayleigh, Compton, photoelectric effect, and pair production probabilities, respectively. If these probabilities are arranged into different intervals between 0 and 1 we get [ ] [ ] [ ] [ ]. (4.7) Whichever interval a random number [ ] lies in, that interaction is chosen to occur. Once the type of interaction is chosen, the probability distributions for resulting energy and scattering angle are sampled to determine the primary particle and any daughter particles and their properties. Sampling methods are from equations from first principles (Klein-Nishina) or from evaluated data sets, or a mix of both. The data used is either parameterised or can be used directly with interpolation schemes. In most codes the particles will repeat the whole process until their energy becomes lower than a predefined cutoff energy, resulting in the remaining energy deposited locally as dose. Some codes will follow particles down to zero range (or zero energy) Electrons MC simulations of electrons interactions are more complicated than photons. A charged particle is far more likely to interact in a material when compared to a neutral particle due to their 35

36 electromagnetic field. A charged particle undergoes near constant interactions because of Coulomb interactions from atoms. Additionally, electrons have little mass causing them to scatter more frequently at larger angles. Another issue is the approximate continuous energy loss of electrons; although interactions are stochastic, electrons interact frequently and can be approximated by a continuous interaction, with the exception of large or catastrophic events. Electron interactions can be broken into three categories: soft collisions, hard collisions (or knock-on), and nuclear Coulomb field interactions. Approximately 50% of an electron s energy loss is due to soft collisions. Soft collisions happen when the electron passes near an atom but not close with respect to the size of the atom. Consider the approximate radius of the atom is (the classical radius with the origin at the nucleus) and an incoming charged particle that passes at a distance (known as the impact parameter) from the nucleus (see Figure 3.2). If, then the collision is considered soft. Soft collisions are the most probable interactions to occur. 36

37 Figure 3.2: A diagram showing an incident electron passing by an atom. The impact parameter is the distance from the nucleus to the trajectory of the approaching electron and is the classical radius. Hard or knock-on collisions occur when. Hard collisions are considered to interact with an individual electron in the atom, which can liberate an electron from the atom, the secondary electron is sometimes referred to as a delta ray. The secondary electron travels through the matter in the same fashion as the primary. Although soft collisions are capable of ionizing atoms, only the outer electrons can be ejected. For hard collisions, the inner shell electrons typically get ejected from the atom. The atom is left in an excited state and will relax into a lower energy state. The lower energy state is achieved by electrons in the outer shells falling into the hole left by the liberated electron. When the atom relaxes, energy is released via two competing processes: x-ray fluorescence (energy released as photons) or the Auger effect where an electron is released from the atom instead of a photon. 37

38 Lastly, when, the electron interacts with the nucleus field. The impinging electron is either elastically scattered approximately 98% of the time or undergoes inelastic scattering for the remaining two percent. The inelastic scattering process radiates energy via x-rays and is known as Bremsstrahlung. The most accurate way to model electron transport in a Monte Carlo simulation is by modeling each electron scattering event individually, no matter how small. This is time consuming and most small events do not have a large effect on the electrons trajectory. To speed up the calculation, most MC codes used a condensed history approach, treating many small interactions as one larger event. Berger [12] in 1963 developed a classification scheme for how a condensed history is implemented; these are class I and class II. Class I algorithms will treat all types of electron collisions the same and transport the electron along a predetermined energy-loss grid. The secondary particles produced are accounted for after. This allows the calculation of the probability distributions for each grid point to be done before simulating the electron. In class II algorithms, the distribution is calculated during the electron simulation process. The soft collisions are grouped together like the Class I scheme but the hard collisions are simulated explicitly. In other cases, during a grouped phase where the electron is transported to the next interaction point, the energy loss from soft collisions are accounted for using the continuous slowing down approximation (CSDA). The CSDA assumes that, since electrons interact frequently over even a small range, the energy loss can be modeled as a deterministic quantity 38

39 rather than a stochastic one. Figure 3.3 illustrates the difference between a single scattering and the condensed history technique. The code uses a multiple scattering theory for electrons in the condensed history technique. The theory used differs depending on the model. There are three commonly used multiple-scattering theories for electrons developed: Molière [13], Goudsmit- Saunderson [14], and Lewis [15]. Some implementations in software will combine aspects from each or add small corrections as well. Each of the three, or variants of them, can be found in use today for MC simulations. Most of the inaccuracies in MC simulations are a result of the approximations made in the MS approach. 39

40 Figure 3.3: A sketch of the hypothetical paths of an electron using single scattering and a condensed history approach. The path for single scattering is not continuous as shown but is still made of discrete events. There are many interactions with single scattering and it would require a large amount of time. To approximate, the many small scattering events are grouped in large scattering events (the vertices) by using a multiple scattering theory for a condensed history. The large numbers of small interactions are elastic or semi-elastic and are approximated in the condensed history technique by a continuous energy loss along the electrons path; this energy is deposited locally about the track General user parameters in a MC simulation Most MC calculations will allow the user to set some general parameters. There are some that are common to all codes, including the one used in this thesis. The first is a production threshold: the user can set an energy for a primary particle that will prohibit secondary particles from being 40

41 produced if the primary particle is below this energy. For example, a 100 kev production threshold set for photons will prohibit any secondary electrons produced once the photon s energy is below 100 kev. Instead of producing a secondary particle, the energy that would be lost is deposited locally. These thresholds are set for each type of particle and typically allow the user to set different energies in different regions, for example in the target and in the water phantom. More details can be found in sections for Geant4 and for the settings used in GATE for this work. Another parameter is an energy cutoff for the life of the particle. This is set for a type of particle and the region it is in. Once a particle s energy is reduced to this cut-off, the particle is terminated and all the energy is deposited locally. This is sometimes referred to as a range cutoff as well. The user may also specify the maximum distance a particle is allowed to travel without interacting. This would be useful for looking at electron dose in a very small region relative to the range of the electron. Geant4, and therefore GATE, track all particles down to zero energy. Details can be found in sections and Variance reduction techniques Variance reduction techniques (VRT) are methods to lower the overall variance of the simulation, usually with the goal of reducing the simulation time while still achieving the same results, without biasing the results of the simulation. Some VRTs used in MC simulations of photon/electron radiation therapy will be discussed here. 41

42 Particle splitting is the technique of artificially creating multiple secondary particles from an interaction where typically only one would be produced. An example is Bremsstrahlung splitting. For a single bremsstrahlung interaction from an electron striking a target, a single photon is produced. This photon would have a statistical weight of. If the splitting technique is applied with a splitting value of, number of photons are produced instead of one, but are sampled from the same distribution. The statistical weight of each new photon will be equally. Another technique is called Russian roulette. In Russian roulette, a survival probability is assigned to a particle type (photons, electrons, etc.) and if a particle of this type is created during the simulation, a random number is generated to determine if the particle survives, < or if it is killed. The surviving particles statistical weight is adjusted to not bias the simulation by. The user may want to eliminate particles that will not reach the region of interest or contribute to the simulation rather than simulate them all. The Russian roulette technique is usually combined with particle splitting. Directional Bremsstrahlung splitting (DBS) is a combination of the splitting technique and Russian roulette. DBS uses a constant splitting factor of applied to Bremsstrahlung photons. If the photons are directed towards the region of interest, than they are transported as normal. If they are not, Russian roulette is applied to the particles with a survival probability of. The photons directed towards the region of interest will have a weight of and photons directed away will have a weight of. Other VRTs exist as well, such as 42

43 range rejection, cross-section enhancement, interaction forcing, woodcock tracking, correlated sampling, and more [16]. GATE allows users to use the DBS VRT and it has been shown to shorten calculation time without biasing results [17] Phase space A phase space is a method to record particle properties in a simulation. A phase space is a user defined plane or volume in the simulation which records the properties of all particles that pass through the plane or volume. Some codes will allow the user to specify the type of particle to be recorded as well as a range of energies.. Typically a plane is chosen where the normal aligns with the beam direction along the CAX. When a particle crosses this plane, the particle type, energy, position, and direction (usually given as two angles) are stored. Figure 3.4 is a diagram depicting a particle s properties as it travels through a phase space. A phase space can be used as a particle source in a simulation. The target, flattening filter, primary collimator, and monitor chambers are independent of patient treatments and a phase space placed below these structures, but above the jaws can save time for future simulations.. A phase space file was not used for this work and would be the next step taken to shorten the simulation time and increase the efficiency. Once the parameters are adjusted to ensure the MC data matches measurements, a phase space file can be created for subsequent simulations. 43

44 Figure 3.4: Diagram of a phase space. When the particle (green line) passes through the circular plane (blue), the energy, position in radius and angle, and direction given in angles and are recorded Statistics in MC simulation A MC simulation follows each primary particle individually until the primary particle and its daughter particles deposit all of their energy (the primary particle can be referred to as the parent particle in this context). One event alone will not be representative of reality but only one of the possible outcomes for a single particle. To produce results that are consistent with reality, a large amount of primary particles are needed. Monte Carlo methods use the law of large numbers to produce results that converge to the real expected value. In the limit where, where is the number of particles simulated, then the result calculated will converge to the expected value. It is not necessary to simulate an infinite amount; a sufficiently large amount will approach the expected value. Regarding dose calculation in a medium, the MC simulation will cumulate the 44

45 dose deposited from the many particles simulated, but only a fraction of the total number of particles simulated may actual reach the target. 45

46 Chapter Four: Existing Monte Carlo codes in radiation therapy 4.1 EGSnrc The EGSnrc code developed by Kawrakow, I. at the National Research Council of Canada (NRC) [18] is an improved version of the EGS4 code EGS is an acronym for electron gamma shower and was designed to simulate electron and photon interactions. All EGS codes have been written in FORTRAN and/or FORTRAN based languages. The development of the EGS code started in 1974 by Ford et al [19]. Version three, EGS3, was publically released in 1978 and received wide spread use in physics research [19]. EGS3 was designed for simulating 1 kev to 100 GeV photons and 1.5 MeV to 100 GeV for charged particles. A notable change in EGS4 from EGS3 was the lower limit in particle energy: charged particles down to 10 kev were allowed. Two extensions of EGSnrc are BEAMnrc and DOSXYZnrc [20]. The BEAMnrc is a user-code based on EGSnrc designed to model the linac head in radiation therapy. BEAMnrc comes with prebuilt geometries common to a linac such as the target, primary collimator, flattening filter, secondary collimators (jaws), and MLC. DOSXYZnrc is included in BEAMnrc to score dose in voxelized geometries, such as a voxelized CT image from a patient. EGSnrc has been tested and used extensively in radiation therapy research. It is often considered the gold standard in Monte Carlo simulations of radiation therapy systems. Details and history on the EGS code extensively discusses in the EGS4 [21] and EGSnrc [22] documents. 46

47 4.2 MCNP The Monte Carlo N-Particle (MCNP) code has gone through a number of iterations. MCNP can be traced directly to the original development of MC methods in neutron transport done by Von Neumann and Ulam during the Manhattan Project [23]. The code was developed at the Los Alamos National Laboratory to be able to model radiation transport in nuclear reactors. Despite the original focus on nuclear reactors, it is a general-purpose code. MCNP has been applied to many problems including MCNP5 deals solely with nuclear processes modeling neutrons, photons, and electrons whereas MCNPX (where the X stands for extended) is capable of dealing with more types of particles and interactions beyond nuclear processes. MCNP6 is the latest software and is a merger of MCNP5 and MCNPX. MCNP5 was shown to have some differences up to 20% when modeling electron dose transport, in a comparative study with EGS and measurement [24]. MCNP is known to be computational intensive compared to the EGS code. 4.3 Geant4 Geant4 (GEometry ANd Tracking) is an open source C++ toolkit developed by CERN [25]. The purpose was to develop a general purpose Monte Carlo code that is continuously supported by the research community. While the code is general purpose, the focus was on high energy particle physics rather than medical physics applications. Currently it has been applied to high energy physics, nuclear and accelerator physics, space science, and medical physics. Many years of research and validation of Geant4 s physics models make it a very robust toolkit for particle modeling. A notable project, the Large Hadron Collider, takes advantage of Geant4 to design detectors for experiments [26]. The original release of Geant4 was in 2003 and there have been 47

48 many updates since then [27]. The most current version is Geant as of June 13, 2014, but the release relevant to this research is 9.5 (released in December 2011) [28]. Geant4 has some advantages over other Monte Carlo codes previously discussed in sections 5.1 and 5.2. It has the ability to model all types of particles in a wide range of energies, down to ev range and up to TeV. Extensive research has shown Geant4 to be well validated for a wide range of particles and particle energies [29,30,31,32,33]. Geant4 has the most advanced geometry modeling allowing complex geometries to be used in the simulation and is written with the object-oriented C++, whereas most other codes are written in FORTRAN. The Geant4 user manual and guides provide more details about Geant4 s capabilities [28]. More details on Geant4 s physics models are discussed next Geant4 physics models and settings Geant4 is considered a Class II algorithm under Berger s classification scheme (section 3.2.2) and it employs a variant of the Lewis MS theory, the Urban95 model [34], for multiple scattering of all charged particles with all of the EM physics models. The electromagnetic processes are of particular interest for the scope of this research. Geant4 contains three main options for EM physics models: i) Standard, ii) Low Energy, and iii) Penelope. The Standard is said to be applicable from 10 kev up to 1 TeV, the Low Energy and Penelope options extend the range down to 250 ev. Details of the physics models used for each process can be found in the Gean4 physics reference manual [35]. The similarities and differences between EGSnrc, MCNP, and Geant4for photon and electron transport are summarized briefly in Table

49 The user has number of parameters to specify for the simulation. A production threshold for secondary particles is specified by the user in terms of an energy; if a secondary particle is produced below this threshold energy, the energy that would be used for the transport of a secondary particle is deposited locally instead of modeling the transport of the secondary particle. This cutoff is specified as a range and Geant4 converts this value to an energy depending on the material. This allows one parameter to be given for all geometries. The user can also set a cut for the maximum step size allowed in a given region for a given particle type. There are two notable parameters in Geant4 related to electron ionization: droverrange and finalrange. The droverrange parameter is the fractional range; it is the maximum fraction of the electron s stopping power range it can travel in one step. The droverrange ensures the electron s step size s will be calculated such that, where R is the remaining range of the electron of a given starting energy, in a given medium. The electron will travel until the remaining range reaches below the finalrange parameter, at which point the last step is reached and the electrons remaining energy is deposited locally. Another restriction on electron ionization is the linear loss limit - the user specifies a maximum fraction of energy the particle is allowed to lose in a given step. The user can specify some parameters relating to the multiple scattering algorithm used for the condensed history technique. The range factor limits the step size in a region so that it never exceeds a fraction (the range factor) of the larger of the particles remaining range or mean free path. The geometric factor also limits the step size ensuring a minimum number of steps occur 49

50 within a given volume so that a particle cannot traverse a volume without having a step in the volume. The skin is a setting that determines the thickness around a volume boundary where, once the charged particle enters, a single scattering model is used instead of a multiple scattering algorithm. The setting choices and a brief description are summarized in Table

51 Process/Algorithm EGSnrc MCNP Geant4 Rayleigh scattering Atomic form factors from Hubbell and Øverbø [36] Atomic form factors from Hubbell and Øverbø [36] Atomic form factors from Hubbell and Øverbø [36] Compton scattering Klein-Nishina with relaxation Klein-Nishina Klein-Nishina with Hubbell functions Photoelectric effect Single element interactions, shell selection, angular distribution sampling, atomic relaxation X-ray fluorescence and Auger electrons X-ray Fluorescence, auger electrons, angular distribution sampling Gamma Conversion Both pair and triplet Pair, not triplet Both pair and triplet e-/e+ scattering Møller and Bhabha scattering Møller, e-/e+ treated as e-/e- Møller and Bhabha scattering Bremsstrahlung Multiple Scattering Theory Bethe-Heitler cross section with correction [37] Moliere theory [13] with modifications: spin,effect, single scattering for short step sizes Bethe-Heitler cross section with correction [37] Goudsmit- Saunderson theory [14], Landau theory, Bethe-Heitler cross section with correction [37] Lewis theory [15], Goudsmit- Saunderson theory [14], single scattering for short step sizes Condensed History Class Class II Class II Class I down to I kev Table 4.1: Table summarizing the similarities and differences between EGSnrc, MNP, and Geant4 for modeling photon and electron transport. The table is adapted from Verhaegen and Seuntjens [38]. 51

52 Setting Category Setting Name Range factor Description Limits step size to a fraction of the larger of range or mean free path Multiple Scattering Algorithm Geometric factor Limits step size to ensure a minimum number of steps occurs in a volume Skin Parameter that determines when single scattering occurs at the boundary droverrange Step size cannot be such that step/range > droverrange Electron Ionisation finalrange Final range at which point the last step is the remaining range of the particle Linear Loss Limit Particle cannot lose more than a specified fraction of initial energy in a given step Cuts Production threshold Step limitation Sets a minimum energy for the parent particle to produce secondary particles Sets a maximum step size allowed in a region for a particle type Table 4.2: Summary of each parameter for the multiple scattering algorithm, ionisation, and production cuts. The user must specify each of these parameters in Geant4. 52

53 4.3.2 Geant4 validation in radiation therapy Validation of Geant4 for electromagnetic processes has been investigated. A study in 2005 by Poon et al [39] showed there were some deficiencies with the electron transport with respect to calculating dose in clinically significant conditions. Since then, there have been updates to Geant4 to address these issues in the electron lateral displacement to improve electron transport [35]. Geant4 has been used for radiation therapy applications. In 2003, Rodrigues et al [40] used Geant4 to calculate the dose in anthropomorphic phantoms and achieved an agreement within 2.4% of for PDDs and within 2.6% for dose profiles in comparison to measured doses using ion chambers and TLDs. The study used a phase space file of a 6 MV photon beam from a Siemens Mevatron KD2 linac provided by Chaves et al [41]. The next year in 2004, Carrier et al [42] looked at the validation of Geant4 for medical physics by looking at the dose from electron and photon beams in homogeneous phantoms and multi-slab phantoms of different materials and compared to MCNP, EGS4, EGSnrc, and experimental data. For monoenergetic photon beams the dose difference in a multi-slab heterogeneous phantom was approximately 5% between MC codes and for simulated linac x-ray beams the dose difference was 2.5%. The study concluded that Geant4 produced comparable results to MCNP, EGSnrc, and EGS4. Foppiano et al [43] in 2004 modeled an IMRT prostate treatment with Geant4 and compared to ion chamber and film measurements. A full linac model was developed and validated compared with ion chamber measurements of PDDs and dose profiles for various field sizes. The study used a Kolmogorov- Smirnov test for the comparisons and found the two distributions to be equal within statistical uncertainties. Prostate IMRT fields were modeled and qualitatively compared to radiographic 53

54 film measurements. In 2005, Poon and Verhaegen [36] investigated the three Geant4 (version 4.6.1) EM models (Standard, Low Energy, and Penelope) in the application of radiotherapy. The study looked at the cross sections and sampling algorithms and compared them to EGSnrc and the XCOM [44], ICRU 37 [45], and PEGS4 data [21]. The comparisons of incident photon beams, both monenergetic and clinical beams, showed an agreement within 2% of EGSnrc and the databases for all three models. When looking at an incident electron beam, the study found some issues with the electron transport algorithms and concluded that a more thorough investigation was required. Again in 2005, a Fano cavity study was conducted with Geant by Poon et al [46] to investigate the electron transport algorithms. By adjusting the maximum step size, the step function (for imposing a fractional range with parameters droverrange and finalrange), and the function (determines the step length after an electron is transported away from a boundary) they demonstrated that there were some dependencies on the step function and, which can lead to erroneous results. These two studies demonstrated issues with the electron transport in Geant4, however the clinical photon beams were modeled accurately within 2%. In 2005, Amako et al [47] compared the newer Geant4 s (version 6.2) electromagnetic models to the National Institute of Standards and Technologies (NIST) reference data using a goodness-offit test. Geant4 was found to be equivalent to NIST reference data within a 0.05 confidence level. Faddegon et al [48] modeled a Siemens Primus linac with Geant4 9.0 and investigated dose in water phantom for electron beams with energies from 6 to 21 MeV, for a 40x40 cm 2 field size. MC calculated PDDs and profiles were compared to measured data, using diodes and ion chambers, and were found to be within 2% for most areas with some exception in the build-up 54

55 region. No significant differences were found between the Standard and Low Energy EM physics models. In 2011, Cornelius et al [49] modeled a 6 MV photon beam on the Varian ix Clinac using Geant4. The linac model was validated against PDD and profile measurements in a water phantom, as well as radiochromic film measurements for the modeled MLC. Good agreement was seen with experimental data where 98% of points passed a 3%/3mm dose difference/distance-to-agreement criteria. The same year, Constantin et al [50] used Geant4 to model the Varian Truebeam linac. The 6 MV beam was modeled using dose profiles and PDDs at field sizes ranging from 4x4 to 40x40 cm 2 and at depths ranging from 2.5 to 30 cm. The model agreed with experimental measurements having 98% of points within 2% of experimental data. In all cases, Geant4 was shown to be a capable and accurate tool. Geant4 does have limitations for electron dose deposition on a small scale, 5-90 micrometers. A cubic voxel used to score dose in the MC simulation tends to range from 1 to 5 mm for each side and on these scales Geant4 is capable of accurate dose calculation. Geant4 has been shown to accurately model clinical photon beams. Geant4 is robust toolkit that has shown big improvements over the past decade. It is continuously being validated against measurements and improved with frequent releases to address any issues and discrepancies. 4.4 Geant4 Application for Tomographic Emission (GATE) Geant4 Application for Tomographic Emission or GATE is a macro-structured software built from the Geant4 toolkit by the OpenGATE collaboration [51]. The software is a community 55

56 effort from researchers around the world and is open-source where users are encouraged to offer suggestions and edit source-code to expand GATE s utility. The software was initially designed for nuclear medicine and PET and SPECT imaging and has been validated for these applications [49,50,51], but has also been extended to dosimetry. The goal was to develop a MC tool for researchers in medicine that was as robust as Geant4 but easier to learn and use. Geant4 is a toolkit in C++ where the user must write the application using the toolkit whereas GATE is macro structured software with predefined commands. Users skilled in C++ can add new commands and libraries or modify existing libraries of GATE or Geant4. The first release of GATE was in 2003 accompanied by a paper from Santin et al [55] and Strul et al [56]. The next year in 2004 another publication by Jan et al [57] introduces GATE. Many studies have applied GATE to SPECT and PET imaging but this review will focus on the publications regarding dosimetry and radiation therapy. The software comes with many different examples for common medical research scenarios that help new users learn GATE and can be reworked to fit the user s needs. The software inherits the robust capabilities of Geant4, notably well-validated physics models, geometry modeling tools, and visualization and three-dimensional rendering. An important feature of GATE is the ability to model time-dependent events. Time-dependence is incorporated into all steps, including dynamic sources, source decays, and geometry motion. The program uses a synchronised virtual clock to keep track of all time dependent events coherently. A recent update to GATE, GATE V6, facilitates modeling of CT and radiotherapy systems [58]. The version of GATE used for this research is v6.2. This version was released in September of 2012 and is validated for use with Geant4 9.5p01. The new version brought some extra key features: 56

57 new options to speed up simulations, components to use for dose calculation, and optical physics models for modeling detector response Application of GATE to radiation therapy Most of the work done with GATE was with respect to PET and SPECT imaging until version 6 was released in Before version 6 a study by Visvikis et al [59] in 2006 investigates the use of GATE for dosimetry applications. They compared GATE to MCNPX2 and EGSnrc in two depth dose curves, from an 18 MV x-ray and 20 MeV electron beam incident on a slab of different thicknesses of water, aluminum, lung, and water. They found the GATE results were in good agreement (approximately 2.3%) with EGSnrc. The GATE calculations had a slower computational time and had some deficiencies in the boundary crossing models and multiple scattering algorithms used in Geant4. It is worth noting that since this study, the Geant4 version of GATE used as been updated to address the electron transport issues and GATE has been updated to include more variance reduction techniques to improve the efficiency. In 2008 Thiam et al [60] published their results on evaluating the low-energy photon dose calculated by GATE v They looked at doses from brachytherapy sources of 125 I from Best, Symmetra, and Amersham and compared to the TG-43 formulism. Looking at the radial dose function, anisotropy function, and dose rate constants, all were approximately 1 3.5% with the exception of the radial dose function from the Amersham source which had a difference of ~15%. Grevillot et al [61] in 2010 investigated the free parameters in Geant4 through GATE for the purpose of modeling proton therapy. All of the work done using GATE in radiotherapy has been done with versions before 6. In version 6, new features were added specifically for radiotherapy. 57

58 Version 6 of GATE was released in 2011, which included updates to facilitate modeling radiotherapy systems. The first linac modeled with GATE v6 was a 6 MV Elekta Precise by Grevillot et al [17] in Dose profiles and depth dose curves were measured and compared to MC calculated values from the 6 MV beam delivered to a water phantom for field sizes from 5x5 to 30x30 cm 2. Good agreement was achieved with 90% of all points passing a 3%/3mm gamma comparison. The next couple of studies calculate electron and photon dose kernels using GATE. In 2011, Maigne et al [62] compared electron dose calculations from GATE with results from EGSnrc and MCNP for energies between 15 kev and 20 MeV. The comparison used the Standard EM option for the physics models to calculate dose point kernels and pencil beam kernels. The dose point kernels were calculated at energies from 15 kev to 4 MeV. Energies from 50 kev to 4 MeV had less than 3% difference between GATE and EGSnrc while 15 kev was greater than 8%, perhaps indicating the Standard EM physics models were no longer appropriate. The pencil beam kernels were calculated from 15 kev to 20 MeV and the results showed that GATE and EGSnrc differed by less than 4%. The authors concluded that GATE is well suited for calculating electron dose distributions for energies greater than 50 kev. In 2012 Papadimitroulas et al [63] developed a dose point kernel database for nuclear medicine applications using GATE. Dose point kernels were calculated with monoenergetic electron beams and various radioisotopes. GATE calculated values were compared to previously published results. Electron dose point kernels had a difference of less than 5% for energies greater than 50 kev and approximately 6% for less than 50 kev. Beta radionuclides had a mean difference of 4% and photon values 2%. These studies have shown that GATE is adequate for 58

59 photon dose calculations. Electron dose calculations using GATE are feasible at energies greater than 50 kev. The studies discussed next are in clinical settings. A clinical IMRT (intensity modulated radiation therapy) treatment planning system was evaluated using GATE by Benhalouche et al [64] in They modeled the Siemens Oncor 6 MV linac with a 160 MLC. The model was validated with measurements of profiles, at 15 mm depth, and depth dose curves for field sizes of 4x4, 5x5 10x10, 15x15, 20x20, 25x25, 30x30, and 40x40 cm 2. The MC PDD and profile data were within 1.472% ± 0.3% and 4.827% ± 1.3% of measured data, respectively. Seven IMRT head-and-neck plans were reproduced with the MC model and compared to the treatment planning system and phantom measurements. A 2D gamma comparison was used to compare measurements. For seven different plans, 90.8% of all points passed a 5%/4mm dose difference/distance-to-agreement gamma criteria. Later in 2013, Sadoughi et al [65] compared GATE with MCNPX applied to a linac. A model of the Elekta Compact 6 MV linac was developed for both GATE 6.1 and MCNPX 2.6. GATE results agreed with MCNPX calculations having 100% of points passing a 2%/2mm dose difference/distanceto-agreement gamma criteria. The author concluded that the Standard and Low Energy EM physics models are appropriate for modeling a 6 MV linac, but not the Penelope EM model. A Monte Carlo model of the Elekta Synergy 6 MV linac was developed by Tayalati et al [66] in 2013 using GATE v6.2. Depth dose curves and dose profiles for square field sizes of 5x5, 10x10, 20x20, and 30x30 cm 2 were calculated and compared to measured values. Greater than 98% of points passed a 3%/3mm gamma comparison for the depth dose curves and 100% of points passed for the dose profiles. All of the studies up until now only dealt with static treatment or at 59

60 most dynamic leaf motion for IMRT. In the following study, GATE was applied to a treatment with dynamic geometry. GATE has also been used to model more complex treatment techniques such as Volumetricmodulated arc therapy (VMAT). VMAT is a technique where the gantry continuously rotates around the patient while the beam is delivered. Throughout the rotation, gantry rotation speed, MLC s, and dose rate are modulated. A study by Boylan et al [67] used GATE to model an Elekta Synergy 6 MV linac performing VMAT treatments in The model was intended as a quality assurance tool for patient plans. The static model (no rotation or MLC motion) was matched against depth dose curves and dose profiles with field sizes from 4x4 cm 2 to 30x30 cm 2. All field sizes had over 95% of points pass a 2%/2mm dose difference/distance-to-agreement gamma comparison. Two VMAT plans were looked at: a prostate plan and a head & neck plan. The MC calculated distributions were compared to film measurements. The MC calculated values had 99.8% of points pass a 3%/3mm gamma comparison for the prostate plan and 98.4% of passed a 4%/4mm gamma comparison for the head & neck plan. This study demonstrates GATE s time-dependent geometry capabilities applied to complex radiotherapy techniques. Lastly, a review paper on GATE s capabilities, regarding radiotherapy and dosimetry, was published in 2014 by Sarrut et al [68]. The paper highlights GATE s capabilities demonstrated by previous research and provides insights to the future of GATE for modeling radiotherapy systems and dosimetry studies. While there is still room for improvement in GATE s features and accuracy, previous research has demonstrated that it is capable of accurately modeling radiotherapy dosimetry. 60

61 4.5 Motivation for using GATE as the MC package for this project While GATE is closely connected with Geant4, other MC particle simulation software differs in their calculation methods. Most often these differences arise in the method used to model electron transport. Many of the studies previously mentioned compare multiple MC codes with one another and often the EGSnrc code is considered a gold standard due to its wide spread use and validation in the medical physics field. Within statistical uncertainty and parameters of the experiments, these codes are found to be in agreement for linac modeling. A major advantage of GATE over the other codes is its robust geometry capabilities (built on Geant4), object-oriented language, and well-validated physics models for all particle types. A key difference from Geant4 is GATE s time-dependent modeling capabilities. GATE allows users to specify motion of any and all geometries in one simulation, synchronising all motion together. Another advantage is GATE s user-friendly macro structure makes it a more attractive simulation package to use. This research project will use GATE to model the Novalis Classic 6 MV linac. The Novalis Classic linac has not been modeled by GATE, or by any other MC software. This research will investigate GATE s capabilities for small field applications and provide a validated linac model to extend to multiple research projects. Also, the validated model will have the potential to provide an independent dose calculation for evaluating treatment plans. 61

62 Chapter Five: Materials and Methods 5.1 Overview This chapter will outline the materials and methods used for the development and validation of the Monte Carlo model of the Novalis Classic linac. First, an overview of the linac and its capabilities, then the reference data used, followed by the GATE simulation settings and methods to analyze the data. The strategy used for modeling the linac is as follows: first appropriate computational power needs to be assessed and acquired, whether a local machine or cluster, or grid computing. The software package needs to be installed, tested, and benchmarked using the existing tests and examples provided in the installation. Next, the specifications of the key components of the linac geometry need to be acquired from the manufacturer s documentation and/or measurements of components. These data on dimensions and materials of each component are place in the MC model. Measured data must be obtained from the linac in order to adjust model parameters to create an accurate model. These measurements are done under controlled conditions in a water phantom (large tank of water). The measurement setup and conditions must be reproduced in the MC model. The model begins with the simulation of the electron beam striking the target. The electron beam has a number of user specified parameters that must be adjusted. Simulations are then run and the results are compared to the measurements and manual optimization is performed, assessing how each parameter should be adjusted to achieve a good match. This is done iteratively with new parameters until the results are in good agreement with the measured 62

63 data. Simulations are then run for other field sizes and compared to measurement to ensure a good agreement is achieved under different conditions. The MLC geometry is then tested using an irregular field size produced by the leaves. The following section will go into more detail. 5.2 Varian Novalis linac The Varian Novalis 6 MV Classic was developed by partnership of Varian and Brainlab (headquartered in Munich, Germany) [69]. The Novalis Classic was released in 1997 as a dedicated radiosurgery treatment platform. A picture of the linac is shown in Figure 5.1. The Novalis is a modified 6 MV linac from Varian s 600 C series that includes a Brainlab MLC system integrated into the linac head. The MLC system replaces Varian s Millennium MLC. The MLC system is placed after the Y and X jaws in the beam path. 63

64 Figure 5.1: Novalis Classic 6 MV linac at the Tom Baker Cancer Centre Capabilities and Geometry The Novalis has operational capabilities that differ from most linacs. The maximum field size allowed on Novalis is 98 x 98 mm². Since the linac is primarily designed for SRS treatments (section 1.1), this field size is sufficient for most lesions. The beam is collimated further with the MLC or with cone attachments that collimate the beam with very small circular openings. The 64

65 MLC design is different from Varian s standard MLC options on their linacs. Since the Novalis is designed for treating small lesions, the MLC has a smaller leaf width than most other MLC s, providing better resolution at isocenter. The widths of the leaves projected at isocenter are 3, 4.5, and 5.5 mm, with the smaller widths in the centre and moving to a wider width towards the edge of the field. Figure 5.2 is a diagram of the MLC system. There are 26 leaves per bank (52 total and mirrored), 14 having a 3 mm projected width and 6 for each of 4.5 and 5.5 mm widths. Each full leaf bank can be seen in Figure 5.3. The exact specifications of the MLC were not known and Brainlab did not provide the information. Each of the 6 different leaf types, 3 different widths and 2 for each (adjacent leafs are different design), had to be measured using high precision calipers. Figure 5.4 is an image of the leaf end view of one bank of leaves and indicates the 6 different types of leaves. Each individual leaf is broken into 15 sub-volumes with different widths to achieve the tongue-and-groove pattern. The 15 different widths can be seen in Figure 5.5. Also, the leaf end is curved as shown in Figure 5.6 to ensure consistent attenuation in at the edge of the field for any field size. The curve is approximated by three straight edges. These measurements were then used for the MC model and are listed in Table 5.1 for each leaf. 65

66 Figure 5.2: Diagram of the MLC leaves on the Novalis. The outer leaves, in green, on both banks have a width of 5.5 mm at isocenter, the red leaves are thinner, with 4.5 mm width at isocenter, and the yellow leaves are 3 mm wide at isocenter. Each leaf can move in and out of the field (left-right in the diagram). 66

67 Figure 5.3: Two banks of MLC s on the Novalis Classic 6 MV. The leaves are all in a closed position. The view is looking up towards the source. 67

68 Figure 5.4: Cross-sectional area of one of the MLC banks on the Novalis linac. The tongueand-groove design can be seen for each leaf. Red, green, and yellow indicate a projected leaf width of 5.5, 4.5, and 3 mm. The triangle of the same colour is a circle leaf flipped 180 (or vice versa). 68

69 Figure 5.5: Image of one leaf end. The white lines section each part of the leaf according to width. Each of the leaf widths were measured and used in the MC model. The widths can be found in Table

70 Figure 5.6: Image of one leaf on its side (the leaf would move in and out of the field horizontally). The leaf end in the radiation field is the left hand side. Note the leaf end has three different straight angles to mimic a curve. The yellow lines indicate the separation of these straight sections on the left hand side. 70

71 Sub- Volume Leaf Type RED GREEN YELLOW Width Length Width Length Width Length (mm) (mm) (mm) (mm) (mm) (mm)

72 Table 5.1: Table of the in-house measurements of the MLC on the Novalis. The table displays each leaf width type (as coloured in Figure 5.4) and shows the width and length of the sub-volume for each leaf corresponding to Figure 5.5. All measurements are in mm. The geometry of each component of the linac and their materials were created with the GATE software using Varian s Monte Carlo Data package, provided by Varian [70]. The information for the 6 MV beam from the low-energy package was used. The data package gives technical specifications on the target, primary collimator, flattening filter, monitor chamber, X and Y jaws and Varian s MLC s. The in-house measurements for the MLC were used in the model. 5.3 Measured data Ion Chamber All depth dose distribution measurements were performed with the Wellhofer Blue Phantom system (Figure 5.7) and accompanying OmniPro software using a CC13 ion chamber from IBA Dosimetry [71]. The Wellhofer system is a large tank with a remote position system. The tank is filled with water and a detector is attached to the position system allowing the detector to move in full 3D motion through the water. The measurements were taken as part of the annual quality control program at the TBCC in Field sizes used for each type of measurement were 6x6, 18x18, 30x30, 60x60, and 98x98 mm 2. In addition to the PDDs, the 98x98 mm 2 field size dose profile was measured with the Wellhofer system.. The dose profile was measured at depths of and 100 mm, and 200 mm in a 100 cm SSD setup. 72

73 Detector placement Figure 5.7: Welloffer Blue Phantom system. The tank is filled with water and the detector is placed on the black holder as indicated in the image. The position of the detector can be controlled remotely in and in predetermined paths Radiochromic Film The measurement with film used Gafchromic EBT3 radiochromic film [72] placed in solid water at 100 cm SSD. The films were scanned using the Epson Expression XL scanner [73] and analyzed with DoseLab Pro [74] software from Mobius Medical Systems. The film was calibrated with doses ranging from 0 to 800 cgy using a 10x10cm 2 field and a 6 MV x-ray beam. To correct for possible film heterogeneities, the films are scanned before and after irradiation in 73

74 the same position on the scanning bed and the difference in optical density is used to calculate the dose. The scanner is known to have a variation in response over the scanning area, with a lower response towards the edges of the scanner. A bowing correction is used to correct for the varying response. Uniformly developed films were used to create a bowing curve to correct the scanned films. The precision of the scanner is (0.22 ± 0.26) % and the scanner is capable of detecting a variation of 1 cgy with the exception of low dose regions and high dose regions where the uncertainty can increase to 11% and 4%, respectively. The dose profiles at field sizes of 60x60, 30x30, 18x18, and 6x6 mm 2 were measured with EBT3 film. Due to the limitations of solid water available the profiles were measured at depths of 15 and 100 mm Diode measurements In order to validate the MC modeled MLC system, an irregular field shape created with the MLC is measured and compared to calculated data. Irregular field shapes will investigate characteristics of the MLC fields, namely the leaf transmission, interleaf transmission, leaf end transmission, and penumbral effects. The field can be seen in Figure 5.8 made with three rectangular openings. The field shape was measured using the Wellhofer apparatus, the same setup mentioned previously for the PDD and 98x98 mm 2 field size profile. The measurements were performed with an EDGE diode detector from Sun Nuclear [75]. This field shape is used to compare to the profiles calculated from the MC model of the MLC, to measured profiles at depths of 16 mm and 100 mm. 74

75 Figure 5.8: Left Diagram of the positions of the MLC for one the measured fields (from iplan commissioning report).three rectangular openings are made by closing two leaves in the upper middle portion and three leaves in the lower middle. Right Image of the same MLC positions rendered in GATE. The point of view is looking up the x-ray beam, into the linac. 5.4 GATE simulations Physics settings The simulation uses the recommended physics settings for radiotherapy given on GATE s main website [51]. These settings are based off previous research with GATE in radiation therapy and dosimetry, as well as research with Geant4. The GATE settings are based off the Standard Physics list option 3 settings in Geant4. Table 6.1 shows a summary of the options chosen - these are provided from GATE s website. These settings are implemented by using the StandardModel option when selecting the physics model for photoelectric, Compton scattering, pair production, bremsstrahlung, and electron ionization interactions. For electron/positron scattering, GATE uses the Urban95 [34] multiple scattering model in Geant4, which is a modified Lewis theory [15] 75

76 (section 4.3.1). The secondary production thresholds are set to a range of 1 mm in the world, the initial starting geometry where all other volumes are produced (all the daughters of the world volume inherit the cuts set in the world if none are specifically given), and 0.5 mm in the phantom or patient voxels with a maximum step size set at 0.02 mm for the phantom or patient. The world volume is the initial structure that must be created in the software (a big box to place everything in); all subsequent volumes are created as daughters of the world (or daughters of daughters of the world, etc.). Parameters specific to the electron (and positron) multiple scattering algorithm are shown in Table 5.2. The step function parameters for electron ionization are set to 0.2 mm and 0.1 mm for droverrange and finalrange, respectively. There are three types of step limitation for the multiple scattering algorithm: minimal, UseSafety, and UseDistanceToBoundary. The UseDistanceToBoundary selection uses the range factor, geometric factor, and skin together. The direction bremsstrahlung splitting technique is used to improve photon production. Splitting was performed in a forward directed cone of 20 degrees with photons being split 100 times. All of the physics settings were chosen based off recommendations by the OpenGATE collaboration for modeling radiotherapy systems. These recommendations have been chosen based on results from Maigne et al [62]. 76

77 Particle Process Parameters (if applicable) G4PhotoElectric Gamma G4ComptonScattering G4GammaConversion G4RayleighScattering MSC Model Urban95 G4eMultipleScattering Step Limit fusedistancetoboundary Type Range Factor 0.04 Geom Factor 2.5 e-/e+ Skin 1 drr 0.2 G4eIonisation fr 0.1 Linear Loss 0.01 Limit G4eBremsstrahlung e+ G4eplusAnnihilation Table 5.2: Recommended physics settings in GATE for radiotherapy applications involving EM interactions. Table adapted from the OpenGATE collaboration website [51]. 77

78 5.4.2 Computer hardware Simulations were performed on the European Grid Infrastructure (EGI) [76] via GateLab [77]. GateLab allows GATE collaboration members to upload macros to be submitted to the EGI. Tasks can be performed with different versions or modifications of GATE to meet the user s needs. The exact hardware used for any given simulation is unknown since the resources are allocated dynamically and the computer grid is heterogeneous. A local computer is used to initially write the macros and to perform tests before submitting the job to GateLab. The local computer is an Intel Xeon 3.2 GHz CPU Building the geometry Geometry is built in GATE by first creating the world volume. GATE can produce volumes in a number of predefined shapes, such as boxes, cylinders, cones, trapezoids, etc., with some user parameters that depend on the shape. The material is set for a volume using a one-line command that specifies a name, corresponding to a defined material and its properties in a GATE material file. The GATE material file contains information on the elements, and some common compounds. Users can create their own material in the materials file by specifying the density and the elements of the material by stoichiometric composition or by percentage by weight. If the user is rendering the geometry, they can specify the volume to be transparent, solid fill, or wire frame, and is able to specify the colour of the volume. The geometry is placed in its mother volume in reference to their origins, placed in the middle of volume (or with the case of a wedge, close to the middle). The simulation geometry was built using the data from Varian s MC data package. The geometry was built using the local computer for visualization and test runs. CAD images and images in GATE of the linac components can be seen in Figure 5.9 and Figure

79 The visualization was used to verify the correct shape, orientation, and positioning of the volumes. Target Primary Collimator Flattening Filter Jaws MLC Figure 5.9: - CAD model of the linac components modeled in GATE. 79

80 Target Flattening Filter Jaws Monitor chamber MLC Water Phantom Figure 5.10: Components from the CAD model rendered in GATE. The green lines represent photons and the red lines electrons GATE s actors GATE uses the concept of an actor to store information from a simulation. An actor is similar to the concept of a sensitive detector in Geant4, but has some extended capabilities. In Geant4, a sensitive detector is a class that represents a detector to score hits from the steps of a particle track. The GATE actor extends the sensitive detector to allow scoring to be done along each track, event, and run in addition to a step. In Geant4 terminology, from top down, a run is the 80

81 simulation as a whole, with all of the histories; an event is the simulation of a single particle history; each history simulates the tracks of the primary and all secondary particles; and a step is the smallest increment that moves a particle in a linear distance to the next point of interaction. An actor is assigned to a volume and that volume s daughters inherit the actor as well. A few examples of actors are the Dose, Kill, and Phasespace actors. The Dose actor will measure the energy deposited in a volume, the Kill actor will stop tracking particles that enter into the volume, and the Phasespace actor will create a phase space from the particles that enter or leave the volume. In addition, the GATE user can apply a filter to any of the actors. The filter allows users to enable an actor when certain parameters are met, such as energy range, type of particle, direction, etc. The spectrum of a beam can be filtered to only record the gamma spectrum, for example. Of particular interest is the Dose actor. The dose actor scores the energy deposited per voxel in a voxelised volume in the simulation. This energy is converted into dose depending on the material properties. The dose actor has the option to include the energy deposited, energy deposited squared, dose, dose squared, number of hits in a voxel, the uncertainty for both the dose and energy deposited, and to normalise the dose. The units are MeV and Gy for energy deposited and dose, respectively. The information from the dose actor can be stored in a number of file formats. The dose can be outputted as an ASCII file (.txt), root file (.root), Analyze (.hdr/.img) and MetaImage (.mhd/.raw). The root file can only output 1D and 2D information. Root is a C++ framework developed by CERN for analyzing data [78]. An example of the implementation of a dose actor is given in appendix A. The main macro used for the simulation is also given in appendix B. 81

82 5.5 Electron source Following the suggestion from Verhaegen and Seuntjens [79], the electron source was first modeled as a monoenergetic pencil beam to match to reference PDD measurements. An energy of 5.7 MeV was found to be appropriate. Then a Gaussian spread in the energy was added with a FWHM of 3% of the mean energy based on findings from Grevillot et al [17]. An electron spot size of 2 mm in the X and Y direction was used.. All simulation runs were with 10 9 electron primaries or histories to fit the correct parameters. 5.6 Flattening Filter The flattening filter specified by Varian did not produce a match to the measurements dose profiles. The filter could not be removed from the Novalis linac and there were no extra flattening filters available to measure. To solve this problem, a custom flattening filter was designed as seen in Figure This filter was made of two conical sections, forming an overall cone shape resembling a flattening filter. The dimensions of the two-piece filter were adjusted to match dose profile measurements. The electron settings had to be re-adjusted to match the measured depth dose distribution. 82

83 Figure 5.11: Diagram of the flattening filter used in the simulation. It consists of two conical sections to form an overall cone shape. 5.7 Energy spectrum The energy spectrum of a MV x-ray beam is typically not measured due to the limitations of current spectroscopy detectors. Any device that has sufficient energy resolution is incapable of measuring the high fluence rates of linacs the radiation beam induces too much dead time in the detector. The dead time is a time after an event is measured for which the detector is unable to measure another event. The output rate of the linac is too high relative to the dead time of the detectors available, saturating the detector. Any information on linac spectra is obtained through MC simulation. GATE possesses an actor capable of storing the energy spectrum at a user- 83

84 defined plane. The spectrum measured in GATE is a histogram tallying the number of particles for a particular energy bin that cross the plane it is the total spectrum of the radiation field. 5.8 Comparing the data Gamma index All quantities calculated are relative measurements. PDDs are normalised to the maximum dose and dose profiles are normalised to the midpoint, along the CAX. When a large number of photons are simulated, both in MC simulation and in reality, only the relative measurements are needed to characterise the beam, with only a scaling factor needed to change to absolute dose. Absolute measurements are important in the clinic to ensure the linac is calibrated properly to deliver the prescribed dose to the patient. The reference data used and the MC calculated quantities are all relative measurements. There exist methods to calibrate the MC model of the linac to produce absolute dose measurements. The two data are compared using the percent dose difference (DD) and distance-to-agreement (DTA). The dose difference is a straightforward point-to-point comparison of the doses from the calculated and measured distributions. While the dose difference is useful for relatively homogeneous dose regions, it can lead to erroneous comparisons in high dose gradient region. If the calculated dose distribution is off by a small shift, it can lead to a large dose differences in the penumbra region when comparing dose profiles. The concept of DTA was developed to compare distributions in high dose gradient regions. The DTA compares the reference data to the calculated data by looking at physical distance from the reference dose point to the nearest calculated dose point of agreement. The - index looks at the deviation of the DD and DTA on a point-to-point basis from desired criteria [79]. The generalised gamma function is 84

85 ( ) ( ), (6.1) where is the vector position of the evaluated point, is the vector position of the reference point, is the DTA criteria, and are the evaluated and reference doses at positions and, respectively. For a given reference point, is calculated for every evaluated point. The -index is then { } { }; (6.2) the minimum value of all computed gamma values with respect to a reference point. If the gamma index is < 1, then the point is said to pass, and if it is > 1 it fails. The gamma index is able to test both the DD and DTA simultaneously. The DD is more useful for the PDD and homogeneous regions of dose profiles, whereas the DTA is useful for the penumbra region of the dose profiles. A dose profile can be broken into three regions: the high dose region, the penumbra, and the low dose tails. The gamma value tool has been shown to appropriately default to the dose difference in flat regions, the high dose middle region and low dose tails, and to the DTA in the penumbra. A gamma comparison criteria of 3%/1mm DD/DTA was chosen for this work. The choice of 3% is based off previous work when comparing calculated and measured distributions. The 1 mm criterion was chosen instead of a more standard 3 mm to compare small radiation fields where spatial inaccuracies are exaggerated. Also, 1 mm was chosen due to the 85

86 tight margins required for SRS treatments knowing that this model has the potential to be used for independent dose calculations Uncertainty All of the MC data have some statistical uncertainty and a systematic uncertainty. The systematic uncertainty is inherited from the data used in the MC code and the methods used to model interactions, most prominently electron multiple scattering. The statistical uncertainty can be calculated for each voxel. GATE s dose actors are capable of giving information on dose, dosesquared, uncertainty in dose, energy deposited, energy deposited-squared, uncertainty in energy deposited, and the number of hits for each voxel. The uncertainty given is a relative uncertainty using the history-by-history method for the standard deviation: ( ( ) ), (6.2) where is the standard deviation for the i th voxel, is the number of histories or primaries, and is the dose deposited in the i th voxel by the j th event. Events that deliver zero dose are not tallied. The uncertainty is carried through to all subsequent calculations. To estimate the overall uncertainty in the simulation, the method suggested by Rogers and Mohan [80] is used. The overall uncertainty is 86

87 ( ), (6.3) where is the number of voxels receiving >50% of the maximum dose, is the uncertainty calculated in the i th voxel using equation (6.2), and is the calculated dose in the i th voxel. This gives the overall uncertainty for the regions where the dose is greater than 50% of the maximum which represents the radiation field size. The efficiency of the MC simulation can be calculated, using the simulation time and the square of the uncertainty, by. The uncertainty used is the overall uncertainty calculated in (6.3). All MC calculated PDDs and profiles are compared to measurements. The spectrum is shown to be characteristic for a linac photon beam. As previously mentioned in section 6.5, spectrum measurements are nonexistent and the only other data to compare to is published spectra on 6 MV beams from MC simulations of other linacs. A qualitative comparison is done, but since there is no published MC spectrum on the Novalis Classic 6 MV, a direct comparison with measurement cannot be done. The next chapter will present the results of these comparisons and discusses them. 87

88 Chapter Six: Results and Discussion 6.1 Results Table 6.1 summarises all of the results for the PDDs and dose profiles, displaying the mean dose difference and gamma index for each field size. A separate simulation is run for each field size. The percentage of MC data points that pass the gamma evaluation criteria is given for each measurement. Two different criteria are looked at: 3%/1mm and 3%/3mm. The 3%/3mm criteria are commonly seen for comparison of MC and calculated dose distributions. 88

89 Field size (mm 2 ) Depth (mm) Profiles PDD % of % of % of % of passing passing passing passing (%) (3%/1 points points (%) (3%/1 points points mm) (3%/1m (3%/3m mm) (3%/1m (3%/3m m) m) m) m) 6x x x x x

90 Table 6.1: The columns display the results of the mean dose difference, mean gamma, and percentage of points passing gamma criteria of 3%/1mm and 3%/3mm. Results shown are for dose profiles and PDDs Depth dose distributions The depth dose distributions were compared using the dose difference metric as well as a gamma comparison. Good agreement was observed between measured and MC data with a passing criterion of 3% between measured and calculated data. A few points in some the PDDs were greater than 3%, particularly in the buildup region or near the end of the tail. The buildup region is the initial dose buildup to a maximum from a depth of zero to. This phenomenon is due to the finite range of the electrons created which initially pile up, increasing the dose. Looking at the gamma comparison, 100% of points passed the 3%/1mm criteria for the 98x98 mm 2 field size with progressively lower percentage for smaller field sizes. The lowest percentage of points is seen for the 6x6 mm 2 field size with 87.5%. Figure 6.1 displays a plot for each field size comparing the PDD of the calculated and measured data. The lower points indicate the gamma of each measured point with depth, for each field size. A dose difference greater than 3% was observed in the buildup region for some field sizes. This is due to loss of charged particle equilibrium (CPE) in the region leading to large uncertainties in the measurements with the ion chamber. The mean dose difference ranged from 1.28% to 1.98% for the largest and smallest field size, respectively. Also, the mean gamma value ranged from to for the largest and smallest field sizes, respectively. 90

91 Relative dose (%) Gamma value Relative dose (%) Gamma value x98 mm Depth (mm) x60 mm Depth (mm) 91

92 Relative dose (%) Gamma value Relative dose (%) Gamma value Relative dose (%) Gamma value x30 mm Depth (mm) x18 mm Depth (mm) x6 mm Depth (mm) 92

93 Figure 6.1: Plots of depth dose distributions for square field sizes of 98x98, 60x60, 30x30, 18x18, 6x6 mm 2. Plots display measured data (black line), MC data (blue dots), and the gamma at each point (green) with the gamma value boundary of 1 (red line). Dose is normalised to maximum. Some error bars are too small to be seen Dose profiles Dose profile measurements were compared using the gamma evaluation tool. The 98x98 mm 2 field sizes passed at all depths with 97.5% of points passing at a depth of 16 mm and the least at 200 mm depth with 92.5% of points passing. Figure 6.2 shows the plots for each field size, with the two depths on each plot (three for 98x98 mm 2 ). The gamma is plotted at each point, for each position in the dose profile. Agreement is worst at larger depths and smaller field sizes with 6x6 mm 2 at depth of 100 mm having 83.3% of the points pass a 3%/1mm gamma comparison. The highest uncertainty is seen for smaller field sizes with 9.2% in the dose-scoring region defined by the 50% isodose line. Most uncertainties for the dose scoring regions are below 2% in the other fields. 93

94 Relative dose (%) Gamma value Relative dose (%) Gamma value x98 mm 2 d=16 mm Position (mm) x98 mm 2 d=100 mm Position(mm)

95 Relative dose (%) Gamma value Relative dose (%) Gamma value x98 mm 2 d=200 mm Position (mm) x60 mm 2 d=15 mm Position (mm)

96 Relative dose (%) Gamma value Relative dose (%) Gamma value x60 mm 2 d=100 mm Position (mm) x30 mm 2 d=15 mm Position (mm) 0 96

97 Relative dose (%) Gamma value Relative dose (%) Gamma value x30 mm 2 d=100 mm Position (mm) x18 mm 2 d=15 mm Position (mm)

98 Relative dose (%) Gamma value Relative dose (%) Gamma value x18 mm 2 d=100 mm Position (mm) x6 mm 2 d=15 mm Position (mm) 0 98

99 Relative dose (%) Gamma value 120 6x6 mm 2 d=100 mm Position (mm) 0 Figure 6.2: Plots of the dose profiles for square field sizes of 98x98, 60x60, 30x30, 18x18, and 6x6 mm 2 for depths of 15 mm and 100 mm, with the exception of the 98x98 mm 2 field size, which is at a depth of 16 mm instead of 15 mm and includes a depth of 200 mm. The plots display the measured data (black line), MC data (blue dots), and gamma comparison of each point (green) with the gamma boundary of one (red line). The gamma criteria is 3%/1mm. The dose is normalised to the central axis. Some error bars are too small to see in the plots Diagonal profile Diagonal profiles at a field size of 98x98 mm 2, at depths of 16 mm and 100 mm are shown in Figure 6.3. The percentage of points passing a 3%/1mm gamma criteria are 76.3% for both depths and for passing a 3%/3mm gamma criteria are 78.9% and 76.3% for a depth of 16 mm and 100 mm, respectively. Large discrepancies can be seen in the penumbra region with the MC 99

100 Relative dose (%) Gamma value field being a smaller width than the measured data. The differences in field size, as defined by the 50% dose line are, 18.9 mm and 16.9 mm for a depth of 16 mm and 100 mm, respectively. 120 Diagonal profile 98x98 mm 2 d=16 mm Position (mm)

101 Relative dose (%) Gamma value 120 Diagonal profile 98x98 mm 2 d=100 mm Position (mm) Figure 6.3: Diagonal profiles at depths of 16 mm and 100 mm (top and bottom, respectively) at a field size of 98x98 mm 2. The blue dots are MC data and the black line are measured data. The green triangles are the gamma values for each point with a 3%/1mm criteria MLC evaluation A dose profile taken at a depth of 15 mm and 100 mm in a water phantom was used to investigate the irregular field size. Figure 6.4 shows the plots of the profiles and the gamma comparisons. For the depth of 15 mm, an agreement of 88.6% of points passed the 3%/1mm gamma criteria. When the gamma criteria are changed from 3%/1mm to 3%/3mm, 98.6% of points in the dose profile pass. For the 100 mm depth, the passing percentages are 83.6% and 95.7% for 3%/1mm and 3%/3mm gamma criteria, respectively. Some discrepancies are seen in the low dose regions where the leaves cover the field and in the two peaks in the outer regions. 101

102 The low dose region covered by the MLC indicates an issue with leaf transmission where the MC model is allowing too much through. The doses in the peaks need to be higher than the central part of the beam which could be an indication of a lack of scattered dose reaching those regions. It could also be an indication of the leaf angle not matching the divergence, causing some attenuation of the beam. 102

103 Relative dose (%) Gamma value Relative dose (%) Gamma value d=15 mm Position (mm) d=100 mm Position (mm)

104 Figure 6.4: Plots comparing a dose profiles at a depth of 15 mm (top) and 100 mm (bottom), in the transverse irregular field shape. Blue dots are MC data, black line is measured data, and green is the gamma comparison (3%/1mm criteria) Relative output factor The comparison of ROF s between MC and measured data is shown in Figure 6.5. The measured values are derived from the profile measurements. When using GateLab the simulation can be terminated prematurely before the desired primaries are reached (due to the way resources are allocated). To correct for the variation of output the MC dose values where normalised to the number of primaries. The data is at 1000 mm SSD at a depth of 100 mm. The values agree for field sizes of 98x98 mm 2 and 60x60 mm 2 but begin to diverge for smaller field sizes, reaching a maximum difference of 17% at 6x6 mm

105 Figure 6.5: Comparison of relative output factors from MC and measured data. The MC dose decreases compared to the measured data with decreasing field size. The maximum discrepancy is seen at the 6x6 mm 2 field size by 17%. The measured data is taken from the CAX of the profile measurements X-ray spectrum The energy spectrum of the x-ray beam across the whole radiation field was calculated using the energy spectrum actor in GATE. Since there are no direct measurements of linac spectra to compare the MC spectrum to, a qualitative comparison is shown with the results of the GATE model of the Elekta Precise from Grevillot et al [17]. The spectra shown in Figure 6.6 is typical for a 6 MV beam. Some variations exist between the two spectra but the energy spectrum of linacs can vary while still producing desirable dosimetric distributions. 105

106 Figure 6.6: - Plot of the MC calculated linac spectrum of the Novalis compared to a MC spectrum of the Elekta Precise [17].. The vertical axis is in arbitrary units and the curve is normalised. 6.2 Discussion The comparison between our Monte Carlo calculated data and measurements used the gamma evaluation criteria by looking at the percentage of points passing a 3%/1mm dose difference/distance-to-agreement. A summary of the percentage of points meeting these criteria for all PDDs and profiles is shown in Table 6.1. A criteria of 3%/3 mm is also in Table 6.1. A 1 mm DTA criterion is tight when compared to the more standard 3 mm used in the literature [17, 64]. The best agreement was seen with larger field sizes, with 100% of the points passing for the depth dose distribution and greater than 97.5% for the profiles at different depths. The smaller field sizes showed some discrepancies in the buildup region and tail region of the PDD. The buildup region (the region from zero depth to ) of a PDD is problematic to measure due to 106