Monte Carlo simulation of cylindrical ionization chamber ... · tally study the ionization chamber response to high-energy photon beams with aryingv eld sizes and shapes (quadratic

Monte Carlo simulation of cylindrical

ionization chamber response to high-energy

photon beams in external radiotherapy

M.Sc. thesis in medical physicsPeter Andersson

[email protected]

Supervisors:

Roumiana Chakarova

John Swanpalmer

Department of Radiation physics

University of Gothenburg, Sweden

June 2014

Abstract

The use of Monte Carlo methods in medical physics is becoming an in-creasingly common practice. This is especially true for applications in doseprediction models. Such prediction models can later be used for patienttreatment planning. This report presents results of Monte Carlo simulationsand experimental measurements using high-energy photon beams.

The aim of the present investigation is to theoretically and experimen-tally study the ionization chamber response to high-energy photon beamswith varying �eld sizes and shapes (quadratic and rectangular). In partic-ular, to determine a total correction factor fw,air to convert the measuredcharge using an air-�lled cylindrical ionization chamber under non-referenceconditions for determination of absorbed dose to water.

Monte Carlo simulations are employed using the EGSnrc package withthe egs_chamber user code. Four photon beam geometries are simulated,the reference �eld 10x10 cm2, 2x2 cm2, 20x20 cm2 and a rectangular �eld2x10 cm2. The dependence of the correction factor fw,air on the positionof the ionization chamber in the radiation beam is examined. Experimentalmeasurements are also performed in a water phantom.

Throughout the present work the compact chamber CC13 is utilized.The results show that the correction factor for non-reference conditions,

where lack of e− equilibrium is present, is di�erent from that of the referenceconditions, i.e. 10x10 cm2 at 10 cm depth for a certain beam energy andSSD. A di�erence of up to 10.6 % was observed. The four largest devia-tions from the ratio for reference conditions were obtained in the penumbraregion for the 6 MV beam at SSD 90 cm in �eld size 10x10 cm2 (d=1.5cm, deviation=9.6%) and at SSD 100 cm in �eld sizes of 10x10 cm2 (d=1.5cm, deviation=10.6%), 2x2 cm2 (d=1.5, deviation=9.1% cm and d=10 cm,deviation=9.3%). Finally the results also show that the simulation resultsand experimentally determined data were in agreement within 2.2% in thecentral axis of the beam and within 9.9% in the penumbra region.

Acknowledgements

For all the wise words and wonderful explanations to questions regardingboth medical physics in general and external beam radiotherapy in particu-lar. To Dr. Swanpalmer for your patience and sharing of great knowledgein radiation dosimetry. To Dr. Chakarova for your critical thinking, atten-tion to detail and continued encouragement. To the teams working on EGS,EGSnrc and egs_chamber, fundamentally enabling this thesis. And �nallyto my family for being who you are.

I am in debt to you all.

i

Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 fw,air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Monte Carlo method . . . . . . . . . . . . . . . . . . . . . . . 3

1.3.1 Variance reduction techniques . . . . . . . . . . . . . . 4

1.3.1.1 Photon Splitting (PS) . . . . . . . . . . . . . 4

1.3.1.2 Range Rejection (RR) . . . . . . . . . . . . . 4

1.3.1.3 Correlated Sampling (CS) and IntermediatePhase-Space Scoring (IPSS) . . . . . . . . . . 5

1.3.1.4 Photon Cross-Section Enhancement (XCSE) 5

1.3.2 Simulation of radiation source . . . . . . . . . . . . . . 5

1.3.3 EGSnrc . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.4 The egs_chamber user code . . . . . . . . . . . . . . . 6

2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . 72.1 Monte Carlo simulations . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 EGSnrc and BEAMnrc . . . . . . . . . . . . . . . . . . 7

2.1.2 Modeling the CC13 chamber . . . . . . . . . . . . . . 8

2.1.3 Implementation of the irradiation geometries . . . . . 8

2.1.4 Input �le development . . . . . . . . . . . . . . . . . . 8

2.1.5 Cavity dose and Per Incident Particle . . . . . . . . . 10

2.1.6 Calculation of fw,air . . . . . . . . . . . . . . . . . . . 10

2.1.7 Error propagation . . . . . . . . . . . . . . . . . . . . 10

2.1.8 Validation of egs_chamber dose calculations . . . . . . 11

2.2 Experimental measurements . . . . . . . . . . . . . . . . . . . 11

2.2.1 CC13 chamber . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2 Blue Phantom . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Evaluation I . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.2 Evaluation II . . . . . . . . . . . . . . . . . . . . . . . 12

ii

CONTENTS Monte Carlo simulation of...

2.3.3 Evaluation III . . . . . . . . . . . . . . . . . . . . . . . 132.3.4 Evaluation IV . . . . . . . . . . . . . . . . . . . . . . . 13

3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.1 CC13 model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 Validation of the method . . . . . . . . . . . . . . . . . . . . . 15

3.2.1 Monte Carlo simulations . . . . . . . . . . . . . . . . . 153.2.1.1 Cavity dose simulations . . . . . . . . . . . . 15

3.3 fw,air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 Experimental measurements . . . . . . . . . . . . . . . . . . . 203.5 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.5.1 Evaluation I . . . . . . . . . . . . . . . . . . . . . . . . 213.5.2 Evaluation II . . . . . . . . . . . . . . . . . . . . . . . 223.5.3 Evaluation III . . . . . . . . . . . . . . . . . . . . . . . 243.5.4 Evaluation IV . . . . . . . . . . . . . . . . . . . . . . . 25

4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1 EGSnrc collection of programs . . . . . . . . . . . . . . . . . 274.2 Monte Carlo simulations . . . . . . . . . . . . . . . . . . . . . 27

4.2.1 Models, uncertainties and variance reduction . . . . . 274.2.2 fw,air . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.4 Experimental measurements . . . . . . . . . . . . . . . . . . . 284.5 Evaluations of dose ratios and ionization ratios . . . . . . . . 294.6 Future aspects . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

iii

Nomenclature

BeamNRC � Built around the core EGSnrc Monte Carlo simulation software, themain application of BEAMnrc is modeling the treatment head of ra-diotherapy linear accelerators.

CPU � Central Processing Unit; A collection of integrated circuits combinedto carry out computational instructions such as program executionand/or calculations.

CPE � Charged Particle Equilibrium; A state which can occur in a mediumwhen the number of charged particles, of each type, that leave a givenvolume of medium are equal to the number of identical particles (samekind and energy) entering said volume.

CS � Correlated Sampling; See the chapter on variance reduction tech-niques.

EGS - Electron Gamma Shower; A set of Monte Carlo based coupled trans-port codes for electrons and photons originally created at the StanfordLinear Accelerator Center.

FORTRAN � A general purpose programming language especially suited for appli-cations in numerical and scienti�c computations.

gcc � The GNU Compiler Collection

GNU � GNU's Not Unix, a set of highly specialized programs for UNIX-like operating systems. Often used in relation to compiling computersoftware

IC � Ionization Chamber; A commonly used type of gas-�lled radiationdetector.

IMRT - Intensity Modulated Radiation Therapy; A radio therapy deliverymethod which enables an improved ability to conform the treatmentvolume to speci�c tumor shapes.

IPSS - Intermediate Phase-Space Scoring; See the chapter on variance re-duction techniques.

iv

CONTENTS Monte Carlo simulation of...

MLC - Multi-Leaf Collimator; Thin sheets, made out of high atomic numbermaterial (often tungsten), that can move independently of one anotherin order to shape the radiation �eld.

NRC - National Research Council (Canada)

PEGS4 - Preprocessor for EGS; A stand-alone utility program written in Mor-tran which in part is used to generate materials data for the EGS code.

RR � Range Rejection; See the chapter on variance reduction techniques.

SSD - Source Surface Distance; The distance from the accelerator target inthe accelerator head to the surface of the patient or phantom.

VMAT - Volumetric Modulated Arc Therapy; A method which is used to de-liver radiation by rotating the gantry of a linear accelerator whilstkeeping the radiation beam on during one or more full rotations. Dur-ing the rotation the dose is shaped using a number of parameters suchas MLC aperture shape, �uence-output rate (dose rate), gantry rota-tion speed and MLC orientation.

VRT - Variance Reduction Technique; See the chapter on variance reductiontechniques.

XCSE - Photon Cross-Section Enhancement; See the chapter on variance re-duction techniques.

v

Chapter 1

Introduction

High energy photon beams are commonly used in external beam radiother-apy for treatment of cancer. The dose is delivered by using di�erent �eld-sizes, shapes and gantry angles. It is of signi�cant importance to be able todetermine the amount of energy transferred to the target volume with highprecision. In order to describe and predict with high accuracy this energytransfer, it is of importance to correctly understand the properties of theradiation �eld and its e�ect on the target volume.

Ionization chambers are widely used in radiotherapy for characterizationof the radiation beam, i.e. experimental determination of dose pro�les, depthdose curves and output factors as well as the determination of the referencedose. The conversion of the measured ionization to absorbed dose to water(a representative material for human tissue) is well established in condi-tions where electron equilibrium exists (for example in �eld sizes larger than3x3cm2 incident on homogeneous material at depths beyond the build-up andin non-penumbra regions). However the interpretation of measurements, un-der non-reference conditions where lack of electron equilibrium is present, isnot trivial and the use of certain correction factors (e.g. kQ,Q0 from TRS

398[1]) may not always be correct. Such conditions arise, for example, in thebuild-up and the penumbra regions as well as in small radiation �elds lessthan 3x3 cm2.

Advanced irradiation techniques used in external beam radiotherapy withphoton beams, (i.e. conventional IMRT and VMAT), consist of a numberof small dynamic �elds. Thus, in order to interpret QA measurements, in-vestigations are needed regarding the ionization chamber response in smallradiation �elds.

1.1 fw,air

Using Spencer-Attix cavity theory[2] it is possible to derive the absorbeddose to water (Dw) using the dose deposited inside an air cavity (Dair) in

1

P Andersson CHAPTER 1. INTRODUCTION

an ionization chamber. This relation can be expressed as

Dw = Dair · sw,air ·∏i

pi (1.1)

where sw,air represents the mass collision stopping-power ratio betweenwater and air, pi are di�erent factors used to correct for the perturbatione�ect caused by the presence of the ionization chamber in the measurementmedium. Subsequently, it is possible to rewrite equation (1.1) to de�ne atotal correction factor as the ratio between the absorbed dose to water overthe dose deposited in air[3, 4]. The total correction can then be expressed as

fw,air =Dw

Dair(1.2)

It should be noted that Dw represents an estimate of the amount ofenergy deposited to water at the point of interest with the absence of theionization chamber. Dair is an estimate of the dose deposited to air insidethe air cavity of the ionization chamber when the chamber is present in theradiation beam. To determine a potential change in perturbation factors andstopping-power ratio between a reference and non-reference situation, a newcorrection factor c can be de�ned [4] as

c =fnonrefw,air

f refw,air

=(Dw(nonref)

Dair(nonref))

(Dw(ref)

Dair(ref))

(1.3)

Using eq. (1.3) it is possible to describe the di�erence in dosimetrybetween the reference and non-reference situation. The correction factorc can be related to the kQ,Q0 correction factor in dosimetry protocols, forexample the IAEA TRS 398, which state that for a given beam quality Qthe correction factor kQ,Q0 can be written as

kQ(ref),Q0 =(sw,air)Q(ref)

(sw,air)Q0

pQ(ref)

pQ0

(1.4)

However, this relation requires that the perturbation e�ects and thestopping-power ratio in eq. (1.4) are of reasonable accuracy and are in-dependent of the �eld size. In cases where such requirements are not met,an additional correction factor c must be applied as follows

kQ(nonref),Q0 = kQ(ref),Q0 · c (1.5)

1.2 Aim

The aim of this project was to study the response of the cylindrical ionizationchamber CC13 manufactured by IBA Dosimetry, Schwarzenbruck, Germany.

2

CHAPTER 1. INTRODUCTION Monte Carlo simulation of...

This chamber is used for dose determinations in high-energy photon beams.In particular, the aim was to estimate the total correction fw,air = Dw/Dair

needed to convert the measured charge using the ionization chamber to ab-sorbed dose to water for di�erent �eld-chamber geometries and �eld sizes.The following tasks are carried out

• Set up the Monte Carlo code package EGSnrc

• Study the di�erent modules in EGSnrc and in particular egs_chamber

• Develop a geometrical model of the ionization chamber according tothe technical speci�cation

• Validate egs_chamber results with other software

• Perform Monte Carlo simulations of the irradiation of the chamberwith di�erent beams in water

• Perform experimental measurements

• Perform data processing including comparison of simulated results withexperimental measurements

Furthermore, the work on this project intends to serve as a basis, i.e. astarting point for MC dosimetry which opens a new �eld for the department.

1.3 Monte Carlo method

The use of Monte Carlo methods and techniques in science has been aroundsince the early 1950's and is becoming increasingly common. In 2013 morethan 104 scienti�c works involving MC simulations were published. Approx-imately 103 of these were set in the �eld of medicine or medical physics[5].According to Rogers (2006) a search for 'Monte Carlo' on PubMed resulted in

14452 hits[6]. As of May 2014 the same search term (http://www.ncbi.nlm.nih.gov/pubmed/?term=monte+carlo) results in 36809 hits.

The Monte Carlo method is often used for simulating stochastic pro-cesses, for example the interaction of radiation with matter. There are var-ious implementations of Monte Carlo methods but the general principlesoften remain the same.

Initially a domain of possible events is de�ned. Next, random inputs aregenerated from a probability distribution over the domain and the processevolution is computed for each input. Finally, the results are summed up andthe mean value and statistical accuracy of the quantity of interest presented.

The randomly generated inputs are sometimes referred to as historiesand the number of histories used in a simulation has a direct impact on theaccuracy of the simulated scenario but also on the time needed to calculate

3


it. In order to determine a suitable number of histories to simulate for agiven scenario one should take into account the amount of processing poweravailable and the needed accuracy. It should also be noted that even thougha target number of histories to be simulated are set, does not require thesimulation to process all of them. For example if a desired accuracy hasbeen reached before running the target number of histories, the simulationcan be considered completed.

1.3.1 Variance reduction techniques

In order to signi�cantly improve the e�ciency of a simulation one or morevariance reduction techniques (VRT) may be employed. In Monte Carlosimulations the uncertainty of a calculation depends on the variance of theestimated quantity and is calculated by

σ(X) =

√V ar(X)

N(1.6)

in which N is the number of simulated histories and V ar(X) is the vari-ance of the estimated quantity. Additionally, the e�ciency ε of an MCsimulation can be calculated by

ε =1

T · σ2(1.7)

where T is the CPU time required to calculate a quantity of interestwithin the estimated statistical uncertainty σ [7]. This means that σ(X) canbe improved by either lowering the variance of the estimated quantity or byincreasing the number of histories calculated. Any technique which leadsto an increase in ε without introducing systematic calculation errors canbe considered a variance reduction technique[7]. In this thesis the quantityof interest is the amount of energy deposited (absorbed dose) to air in theionization chamber sensitive volume.

1.3.1.1 Photon Splitting (PS)

Photon splitting works by dividing a photon into Ns sub-photons with a uni-form distribution of interaction sites along the initial direction. The weightof each split photon is adjusted to be that of w0

Nswhere w0 is the original

weight of the incident photon[7]. Ns is user de�ned and can be optimizedtowards e�ciency.

1.3.1.2 Range Rejection (RR)

The basic idea behind range rejection is that any charged particle having arange shorter than its distance to the scoring volume is discarded. A userde�ned threshold is given in order to control this approximation.

4

CHAPTER 1. INTRODUCTION Monte Carlo simulation of...

1.3.1.3 Correlated Sampling (CS) and Intermediate Phase-SpaceScoring (IPSS)

Correlated Sampling is based on the idea that the information on particletransport common to several geometries of interest can be recycled. A re-gion is de�ned large enough to enclose all the scoring geometries. Particlesentering the CS region are stored into an intermediate phase space for lateruse and re-use.

1.3.1.4 Photon Cross-Section Enhancement (XCSE)

One of the key reasons behind the implementation of XCSE is that theinteraction density of the photons in the cavity medium is low. The resultof XCSE VRT is similar to that of photon splitting explained previously.The shower of particles in a region around the scoring volume is ampli�ed.There are strict rules to obey to assure an unbiased result and equal particleweighting. For that matter, particle splitting and Russian roulette are playedin such a way that each particle type carry a unique statistical weight givenby the XCSE factor. In order to be considered optimal by today's standardsMonte Carlo simulations should employ all of the above mentioned variancereduction techniques.

For a more in-depth explanation of these four VRT's please see ref.[5]

chapters 3.2 and 4 with additional information in �gure 4.4 p. 52 or ref.[7]

chapter II p. 1329.

1.3.2 Simulation of radiation source

When using the EGSnrc MC code package there are two basic ways of simu-lating the radiation source in the accelerator head. One is to model the linearaccelerator head using BeamNRC allowing for greater �exibility when gener-ating di�erent �eld geometries. The other method is to use a pre-calculatedphase space �le. A phase space is a virtual plane placed at a certain dis-tance from the actual radiation source and containing the characteristics ofall particles passing the plane.

1.3.3 EGSnrc

EGSnrc is a continuation of the EGS (Electron Gamma Shower) softwarepackage originally developed at the Stanford Linear Accelerator Center. It iscurrently maintained by the Ionizing Radiation Standards Group at the Insti-tute for National Measurement Standards at the National Research Councilof Canada.

EGSnrc is considered by many to be a powerful tool in medical physics.It includes an accurate electron transport model which in particular results

5


in a more precise simulation of the electron trajectory at material interface.This enables artefact-free simulation of ionization chamber irradiation.

1.3.4 The egs_chamber user code

This recent addition to the EGSnrc family of user codes was developed byWul� et al. in 2008[7] and is a modi�ed version of the original EGSnrccode 'cavity'. In egs_chamber a number of advanced variance reductiontechniques are introduced to achieve an improved e�ciency with respect tothe calculation of perturbation factors and ion chamber dose at more thanone position inside a phantom[8].

6

Chapter 2

Materials and methods

This chapter describes the three main steps taken during the present work. 1)Set-up and con�guration of the simulation hardware and software; 2) creationand simulation of the irradiation geometries; 3) performing experimentalmeasurements.

2.1 Monte Carlo simulations

The computer simulation environment was setup on a HP EliteDesk 800 G1using Ubuntu 13.10 (GNU/Linux 3.11.0-20-generic x86_64). The centralprocessing unit of the EliteDesk 800 G1 was an Intel(R) Core(TM) i7-4770CPU at 3.40 GHz (boost). The system was �tted with a total of four memorysticks. Two Hynix/Hyundai 4 GiB (HMT351U6EFR8C-PB) and two Sam-sung 4 GiB (M378B5273DH0-CK0) giving the system a total of 16 GiB 64bits DIMM DDR3 Synchronous 1600 MHz (0.6 ns) random access memory.

2.1.1 EGSnrc and BEAMnrc

The EGSnrc software package was obtained as a download from the NRCwebsite[9] and installed using GNU Fortran and gcc (both of Ubuntu/Linaro4.8.1-10ubuntu9). Additional programs such as egs_gui, egs_view and user-developed codes such as egs_chamber were also employed. Additionally,BEAMnrc was also employed in order to generate radiation sources withdynamic energies and geometries.

Initially the radiation �eld information was stored in the form of phasespace �les which in turn served as input to the egs_chamber simulations.However this was found to be ine�cient and not �t for the purpose of thisproject. Instead, the previously developed BEAMnrc models of the ClinaciX accelerator for 6 MV[10] and 15 MV[11] were employed as simulationradiation sources.

7

P Andersson CHAPTER 2. MATERIALS AND METHODS

2.1.2 Modeling the CC13 chamber

The ionization chamber (IC) was modeled and con�gured in the Monte Carlocode system EGSnrc according to its technical data speci�cation. The modelwas created using four virtual planes, three cylinders (central electrode, innerand outer wall) and two spheres (inner and outer wall at the top of thechamber).

For simulations of the absorbed dose to water the IC model materialswere de�ned as the default material in the cross-section library PEGS4(H2O521ICRU). For simulations of dose to air the IC model consisted oftwo materials, C552 (Shonka plastic) and AIR521ICRU. The C552 materialwas created using the chemical composition of the Shonka plastic (H:2.4%,C:50.2%, O:0.5%, F:46.5%, Si:0.4%) of the actual CC13. Prior to the di�er-ent simulations, one of the two versions of the CC13 model described abovewas implemented in the input �le.

Several variance reduction techniques were employed. Photon cross-section enhancement (XCSE) was employed using an additional geometrywhich encapsulated the basic CC13 model in a 1 cm thick shell. Further-more an IPSS VRT which included photon splitting and range rejection, wasde�ned using two planes and a cylinder. The IPSS VRT geometry was setto encapsulate the CC13 IC with a very small margin of 0.001 cm in radius.

2.1.3 Implementation of the irradiation geometries

Simulations using the egs_chamber user code were performed at 6 MV and15 MV for geometries at SSD 90 cm and SSD 100 cm for four �eld sizes(20x20 cm2, 10x10 cm2, 2x10 cm2 and 2x2 cm2), at depths 1.5 cm (6 MV),2.5 cm (15 MV) and 10 cm (6 MV and 15 MV).

In order to maximize computation time two main batch �les were de-veloped (see appendix A1). Parallel_batch.sh was used to execute theegs_chamber command with proper runtime arguments in order to dis-tribute the computational load over several CPU cores (using the -b -P

# -j command line arguments of egs_chamber)[12, 13]. Additionally thebatch_simulation.sh script was used to setup the consecutive execution ofseveral parallel_batch.sh. Because of this it was possible to automaticallystart a new distributed simulation as soon as the previous one had �nished.

2.1.4 Input �le development

The egs_chamber program is used in conjunction with a set of instructionson how to model the simulation. These instructions are collected in a �lecalled an input �le which is passed to egs_chamber at runtime along witha PEGS4 materials �le and other possible command line arguments. Eachinput �le consists of several sections of speci�c instructions of which the

8

CHAPTER 2. MATERIALS AND METHODS Monte Carlo simulation of...

important de�nitions are geometry, source, run control, scoring options, cal-culation, variance reduction and mc transport parameters.

The work of developing input �les started with the creation of a basicmodel consisting of a cylinder made of water and placed in a cube also con-sisting of water. This basic model was later extended to include several morecylinders and eventually also spheres in order to shape the CC13 chamberaccording to its actual dimensions. Finally, when an input �le with a modelof acceptable accuracy had been developed, it was re-used in order to createnew simulations with di�erent geometries and ionization chamber positions.In each simulation the CC13 model was oriented parallel to the y-axis (de-�ned by the upper jaws movement) and positioned with the electrode tipcentered at a certain depth. In some simulations an o�-axis position wasalso set. An illustration of geometries and IC positions can be seen in �gure2.1a and 2.1b.

During this work a total of 64 input �les were developed. The decisionto develop several smaller and somewhat simpler input �les rather than afew more complex ones were that it allowed for greater control and �exibilityin situations when new simulations with the same or similar properties wereneeded.

A target of 107 histories were set for each scenario. Several variance re-duction techniques were employed as follows. Photon splitting (=50), RangeRejection (=100) and XCSE (=128).

Figure 2.1.a: Overview illustration of a

simulation scenario. A 10x10 cm2 radi-

ation �eld impinges on a water phantom

with each side 30 cm in length.

Figure 2.1.b: A closer look at di�er-

ent ionization chamber positions from �g.

2.1a. The illustration shows the positions

of ionization chambers at 2.5 cm and 10

cm depths at central axis and o�-axis po-

sitions in a 10x10 cm2 �eld at 15 MV.

9


2.1.5 Cavity dose and Per Incident Particle

The egs_chamber program calculates the dose in units Gy per incident par-ticle, i.e. per electron incident on the accelerator target. Thus, the cavitydose reported by egs_chamber should be seen as the dose deposited in thesensitive volume of the ionization chamber per primary history.

It should be noted that the dose to the cavity for the total number ofsimulated histories can not be directly compared to the dose measured byan ionization chamber although both may be expressed in Gy. Additionalcalculations are needed to relate the number of primary histories to acceler-ator MU, (i.e. how many electrons incident on the target correspond to oneMU).

2.1.6 Calculation of fw,air

The correction factors were obtained by calculating the dose to the IC cavityassuming water or air as cavity material. Calculations were carried out usingthe simulated results and according to the steps described in chapter 1.1.Propagation of simulation uncertainties was also performed according to thesteps in chapter 2.1.7.

2.1.7 Error propagation

Error propagation was performed using a simpli�ed expression for error prop-agation in uncorrelated variables. A function f was de�ned as the ratio oftwo uncorrelated variables a and b

f =a

b(2.1)

The simpli�ed expression for error propagation then states that the un-certainty σ2f can be written as

σ2f = (df

da)2 · σ2a + (

df

db)2 · σ2b =

= (1

b)2 · σ2a + (

a

b2)2 · σ2b =

σf =

√(1

b)2 · σ2a + (

a

b2)2 · σ2b

(2.2)

The relative error σfrel was then obtained by

σfrel =σfa/b

(2.3)

where a and b are MC simulated doses with their respective uncertaintiesσa and σb.

10


2.1.8 Validation of egs_chamber dose calculations

The egs_chamber simulations were validated using the dosxyznrc softwareprogram. Comparisons of the dosxyznrc results with measurements havebeen reported previously (Rogers et al 1995, Kapur et al 1998, Ma 1998,

Zhang et al 1999, Ma et al 1999a, 2000a)[14]. In the dosxyznrc simulations a5x5x5 mm3 voxel was used to approximate the volume of the CC13 chamber.Validation simulations using dosxyznrc were carried out for a select numberof egs_chamber scenarios in both AIR521ICRU and H2O521ICRU PEGS4materials. Additionally, it is should be noted that the dosxyznrc software isnot designed to handle chamber geometries and can not be regarded as analternative method for calculation of ionization chamber response.

2.2 Experimental measurements

The experimental measurements were made using a Varian Clinac iX linearaccelerator (Varian Medical Systems, Palo Alto, CA, USA), treatment roomno. 10 at Sahlgrenska University Hospital. The measurements were per-formed at a source surface distance of 90 cm and 100 cm using di�erent �eldsizes and depths in 6 MV and 15 MV photon beams in analogy with MC sim-ulations. During each measurement the CC13 chamber was exposed to 120MU. Due to similarities in the measurement setup and geometries investi-gated, the value for uncertainties (0.3%, expressed as coe�cient of variation)

presented by Swanpalmer and Johansson[15] was used in the present work.

2.2.1 CC13 chamber

The air-�lled cylindrical ionization chamber CC13 manufactured by IBADosimetry (Schwarzenbruck, Germany) have a central electrode and wallmade of Shonka plastic (C-552). The diameter and length of the air cavity

of this chamber are 6.0 mm and 5.8 mm, respectively[16]. Measurementswere performed using the e�ective point of measurement of the chamber (Peff ).

2.2.2 Blue Phantom

The Blue Phantom manufactured by IBA Dosimetry was used throughoutthe experimental measurements. The CC13 ionization chamber was posi-tioned at di�erent depths and o�-axis distances. The Blue Phantom has apositioning uncertainty of 0.5 mm. Initially (as seen in �g. 2.2a and �g.2.2b) a leveling cap was used to position the chamber relative to the watersurface.

11


Figure 2.2.a: Initial position of the CC13

with the leveling cap in place for accurate

positioning in reference to the water sur-

face.

Figure 2.2.b: The CC13 chamber was

aligned to the water surface manually us-

ing the 3-axis motor controlled position-

ing system in the Blue Phantom.

2.3 Data analysis

The results from simulations and experimental measurements were studiedin four evaluations.

2.3.1 Evaluation I

A comparison of the results from calculations of fw,air was carried out bystudying the ratio described in eq. (1.3). The evaluation was performed inorder to determine if fw,air deviate when comparing the non-reference andreference situations.

2.3.2 Evaluation II

The second evaluation compared the ratios of results at depths of 1.5 cm (6MV) or 2.5 cm (15 MV) with that of 10 cm (both energies) for MC simulateddoses and experimentally determined ionization. This evaluation was carriedout at SSD 90 cm and SSD 100 cm in �eld sizes of 10x10 cm2, 2x2 cm2 and2x10 cm2 in the central axis and in the penumbra region. For instance inthe 6 MV beam the relation between MC simulated doses can be expressedas

QDair1.5/10

= DairMC1.5

/DairMC10

(2.4)

where DairMC1.5

and DairMC10

are the results from MC simulations at depth1.5 cm and 10 cm at the central axis of the beam or in the penumbra region.The purpose of this evaluation was to make an overview of results which en-abled a side-by-side comparison between MC doses and measured ionizations

12


at di�erent depths.

2.3.3 Evaluation III

Evaluation three was carried out in order to examine the consistency of theMC ratios with the ratios of experimental results. The relation studied canbe expressed as

QDair

1.5/10

Iair1.5/10

=Dair

MC1.5/Dair

MC10

IairXP1.5/IairXP10

(2.5)

where the included variables are represented as described in previouschapters. The purpose of this evaluation was to study the accuracy of MCsimulations when compared to experimental data.

2.3.4 Evaluation IV

In order to determine the relative di�erence in cavity dose and ionization be-tween the central axis and in the penumbra region a comparison between MCsimulations and experimental data was carried out by studying the relation

QDMCrelIXPrel

=Dair

MCCAX/Dair

MCPNM

IairXPCAX/IairXPPNM

(2.6)

where DMCCAX, DMCPNM

, IXPCAXand IXPPNM

represent the dose inMC simulation to air and the ionization measured by the CC13 during experi-mental measurements at the central axis (CAX) and o�-axis in the penumbraregion (PNM) for a certain beam energy, SSD, �eld size and depth.

13

Chapter 3

Results

3.1 CC13 model

The egs_view software was used to verify shapes and regions of the �nalCC13 model. Fig. 3.1a shows the CC13 when viewed from outside thechamber and with the opacity of the water region colour turned down closeto zero. Figure 3.1b shows a cross-section along the Y-axis of the CC13revealing the air (PEGS4 material AIR521ICRU) volume inside. Also inFigure 3.1b, the blue water region and red Shonka plastic region are shown.

Figure 3.1.a: The CC13 ionization cham-

ber model as viewed from outside the

chamber.

Figure 3.1.b: A cross section of the CC13

ionization chamber model. Red color in-

dicates the C552 Shonka plastic material

of the wall, stem and electrode, the green

color indicates AIR521ICRU and the blue

color indicates water.

14

CHAPTER 3. RESULTS Monte Carlo simulation of...

3.2 Validation of the method

The egs_chamber dose calculations were shown to agree well with calcula-tions using dosxyznrc. For a select group of geometries where the dosxyznrccalculated dose was used as reference, egs_chamber calculated doses devi-ated on the order of 3%.

3.2.1 Monte Carlo simulations

3.2.1.1 Cavity dose simulations

The results from the eight di�erent simulated situations are presented intables 3-1 to 3-8. In all tables CAX represents the dose at the central axisof the beam, σ the relative uncertainty in % and PNM is the dose in thepenumbra region.

Table 3.1: Results of MC simulations for the 6 MV beam at SSD90 cm using the cavity material H2O521ICRU.

6 MV, SSD 90H2O521ICRU Cavity dose (Gy/hist)a

Field Depth(cm2) (cm) CAXb σ c PNMd σ

10 x 10 10 8.541E-17 0.675 4.483E-17 0.9011.5 1.324E-16 0.542 6.410E-17 0.752

2 x 2 10 6.821E-17 0.147 3.474E-17 0.2041.5 1.186E-16 0.111 5.963E-17 0.154

2 x 10 10 7.298E-17 0.327 - -1.5 1.228E-16 0.248 - -

aPer Incident Particle

bCentral Axis

cRelative error

dPenumbra

15

P Andersson CHAPTER 3. RESULTS

Table 3.2: Results of MC simulations for the 6 MV beam at SSD90 cm using the cavity material AIR521ICRU.

6 MV, SSD 90AIR521ICRU Cavity dose (Gy/hist)

Field Depth(cm2) (cm) CAX σ PNM σ

10 x 10 10 7.998E-17 2.980 4.108E-17 4.0411.5 1.204E-16 2.327 5.361E-17 3.261

2 x 2 10 6.108E-17 0.591 3.128E-17 0.8271.5 1.054E-16 0.465 5.343E-17 0.656

2 x 10 10 6.500E-17 1.311 - -1.5 1.096E-16 1.072 - -


6 MV, SSD 100H2O521ICRU Cavity dose (Gy/hist)


10 x 10 10 7.026E-17 0.720 3.699E-17 0.9961.5 1.063E-16 0.594 5.581E-17 0.901

2 x 2 10 5.694E-17 0.163 2.910E-17 0.2251.5 9.700E-17 0.122 4.853E-17 0.169

2 x 10 10 6.108E-17 0.359 - -1.5 1.002E-16 0.272 - -

16





10 x 10 10 6.291E-17 3.139 3.613E-17 4.6641.5 9.476E-17 2.612 4.927E-17 3.639

2 x 2 10 5.106E-17 0.664 2.600E-17 0.9161.5 8.512E-17 0.515 4.343E-17 0.729

2 x 10 10 5.423E-17 1.471 - -1.5 8.875E-17 1.177 - -




10 x 10 10 6.233E-16 0.811 3.273E-16 1.0952.5 8.216E-16 0.691 4.333E-16 0.935

2 x 2 10 4.919E-16 0.172 2.564E-16 0.2342.5 6.971E-16 0.140 3.572E-16 0.190

2 x 10 10 5.552E-16 3.197 - -2.5 7.413E-16 0.323 - -

17


Table 3.6: Results of MC simulations for the 15 MV beam at SSD90 cm using cavity material AIR521ICRU.



10 x 10 10 5.474E-16 1.839 3.024E-16 2.7302.5 7.318E-16 1.593 3.780E-16 2.128

2 x 2 10 4.397E-16 0.377 2.308E-16 0.5262.5 6.233E-16 0.326 3.205E-16 0.447

2 x 10 10 4.832E-16 0.889 - -2.5 6.530E-16 0.750 - -




10 x 10 10 5.118E-16 0.888 2.698E-16 1.2322.5 6.619E-16 0.746 3.523E-16 1.045

2 x 2 10 4.162E-16 0.201 2.149E-16 0.2772.5 5.771E-16 0.160 2.949E-16 0.221

2 x 10 10 4.487E-16 0.437 - -2.5 6.080E-16 0.352 - -

18





10 x 10 10 4.751E-16 2.116 2.534E-16 2.9732.5 6.064E-16 1.782 3.166E-16 2.535

2 x 2 10 3.745E-16 0.420 1.957E-16 0.5862.5 5.137E-16 0.355 2.634E-16 0.491

2 x 10 10 4.013E-16 0.961 - -2.5 5.454E-16 0.863 - -

3.3 fw,air

The dose ratios Dw/Dair for the fw,air calculations in each simulation arepresented in tables 3.9 to 3.12. The relative uncertainty in these calculationsis on the order of 5%. In all tables CAX represents the dose at the centralaxis of the beam and PNM is the dose in the penumbra region.

Table 3.9: Correction factors fw,air forthe 6 MV beam at SSD 90 cm.

6 MVSSD 90 cm fw,air

Field Depth(cm2) (cm) CAX PNM

10 x 10 10 1.068 1.0911.5 1.100 1.196

2 x 2 10 1.117 1.1111.5 1.125 1.116

2 x 10 10 1.123 -1.5 1.120 -

Table 3.10: Correction factors fw,air

for the 6 MV beam at SSD 100 cm.



10 x 10 10 1.117 1.0241.5 1.122 1.133

2 x 2 10 1.115 1.1191.5 1.140 1.117

2 x 10 10 1.126 -1.5 1.129 -

19






10 x 10 10 1.139 1.0822.5 1.123 1.146

2 x 2 10 1.119 1.1112.5 1.118 1.115

2 x 10 10 1.149 -2.5 1.135 -





10 x 10 10 1.077 1.0652.5 1.092 1.113

2 x 2 10 1.111 1.0982.5 1.123 1.120

2 x 10 10 1.118 -2.5 1.115 -


The results of the experimental measurements using the CC13 chamber inthe 6 MV and 15 MV photon beams are shown in tables 3.13 to 3.16. Thesemeasurements are associated with an uncertainty of 0.3% as given by Swan-palmer and Johansson[15]. In all tables CAX represents the dose at thecentral axis of the beam and PNM is the dose in the penumbra region.

Table 3.13: Results from the exper-imental measurements in the 6 MVbeam at SSD 90 cm.

6 MVSSD 90 cm Ionization (nC)


10 x 10 10 3.737 2.4811.5 5.753 3.538

2 x 2 10 2.904 1.8601.5 4.999 3.101

2 x 10 10 3.152 -1.5 5.269 -




10 x 10 10 3.112 2.1731.5 4.679 3.288

2 x 2 10 2.450 1.5991.5 4.105 2.615

2 x 10 10 2.636 -1.5 4.294 -

20


Table 3.15: CResults from the exper-imental measurements in the 15 MVbeam at SSD 90 cm.



10 x 10 10 3.813 2.5632.5 5.059 3.370

2 x 2 10 2.922 1.9182.5 4.090 2.614

2 x 10 10 3.250 -2.5 4.463 -




10 x 10 10 3.165 2.2112.5 4.114 2.916

2 x 2 10 2.480 1.6542.5 3.412 2.244

2 x 10 10 2.733 -2.5 3.676 -

3.5 Data analysis

3.5.1 Evaluation I

Figures 3.2a to 3.3b shows the results of the deviation in fw,air when anumber of non-reference situations are compared to the reference situationsfor the beam energies 6 MV and 15 MV at SSD 90 cm and SSD 100 cm. Therelative uncertainty in these calculations is on the order of 5%. In all �guresCAX represents the ratio at the central axis of the beam and PNM is theratio in the penumbra region.

Figure 3.2.a: Variations in fw,air for the 6

MV beam at SSD 90 cm when several non-

reference situations are compared to the ref-

erence.

Figure 3.2.b: Variations in fw,air for the 6



erence.

21


Figure 3.3.a: Variations in fw,air for the 15



erence.

Figure 3.3.b: Variations in fw,air for the 15



erence.

3.5.2 Evaluation II

The ratio of the simulated dose to air at the depth of maximum dose andthe depth of 10 cm for the central axis and penumbra region are shownin �gures 3.4 to 3.7. In the same way the ratios for the experimentallydetermined ionizations are also included in these �gures.

In the �gures of this section, R1.5, R2.5 and R10 represent the simulatedor measured dose or ionization result for a certain depth (1.5 cm, 2.5 cm,and 10.0 cm) in a water phantom. The relative uncertainties of all R1.5

R10and

R2.5R10

were calculated to be on the order of 5%.

Figure 3.4: Ratios of the results at depths 1.5 cm and 10 cm for the 6 MVbeam at SSD 90 cm and several �eld sizes.

22




23



3.5.3 Evaluation III

The percent deviation between the MC simulations and experimental mea-surements for positions in the central axis and in the penumbra region arepresented in �gures 3-11 and 3-12.

Figure 3.8: The ratios at the central axis of the beam for MC simulationswhen compared to the experimental data.

24


Figure 3.9: The ratios in the penumbra region for MC simulations whencompared to the experimental data.

3.5.4 Evaluation IV

Figures 3.10a to 3.11b present the results for calculations of the relationQDMCrel

IXPrelbetween the two ratios DMCCAX

/DMCPNMand IXPCAX

/IXPPNM.

The relative uncertainties of all QDMCrelIXPrel

were computed to be on the orderof 5%.

Figure 3.10.a: The relation between the ratio

of the simulated dose values and the exper-

imental data in the 6 MV beam at SSD 90

cm.

Figure 3.10.b: The relation between the ratio

of the simulated dose values and the experi-

mental data in the 6 MV beam at SSD 100

cm.

25


Figure 3.11.a: The relation between the ratio



cm.

Figure 3.11.b: The relation between the ratio



cm.

26

Chapter 4

Discussion

4.1 EGSnrc collection of programs

The successful development of models and input �les for the EGSnrc collec-tion of programs was greatly expedited by having a familiarity with UNIX-like environments. The information on egs++ and egs_chamber in theNRCC technical report PIRS898[8] proved to be a very important read. Theuse of EGSnrc software such as user codes can be done via a graphical userinterface. However, for the applications in this project, such a method wasnot suitable. The development of batch scripts which enabled continuoussimulations to be run on several cores and in direct succession proved to bevery important with respect to the target number of histories, the numberof scenarios simulated and the time available.

4.2 Monte Carlo simulations

4.2.1 Models, uncertainties and variance reduction

It is important to recognize that all models are approximations and funda-mentally incorrect. In MC simulations such as those carried out in this studyseveral factors a�ect the accuracy. For instance the number of histories sim-ulated, the modeling of the accelerator, beam simulations etc. In addition,as discussed by Rogers[6], the accuracy of a MC simulation is only as goodas the underlying cross sections which have an uncertainty on the order of1% or more.

With respect to the uncertainties in MC simulations it is worth notingthat the results (tables 3.1 to 3.8) show a larger uncertainty for dose toair than for the respective dose to water. This is based on the fact that theenergy deposited to the air cavity has larger �uctuations compared to energydeposited to the water cavity, i.e. the number of energy deposition events islarger for the water cavity, which leads to smaller �uctuations compared to

27

P Andersson CHAPTER 4. DISCUSSION

air cavity due to the di�erence in density of the material.

As described in ref.[10] and [11] the accelerator models used in this workare well de�ned in the central parts of the beam. However the condition inthe penumbra region is not studied in detail.

The e�ects of variance reduction were not studied during this project.However, in a brief comparison no bene�ts were noticed.

4.2.2 fw,air

The calculations of correction factors fw,air listed in tables 3.9 to 3.12 showvarying results. The values obtained range between 1.024 (6 MV, SSD 100cm, 10x10 cm2 at 10 cm depth) and 1.196 (6 MV, SSD 90 cm, 10x10 cm2 at1.5 cm depth). The variations in these correction factors re�ect the di�erentsituations. The results also indicate that the doses can vary depending onthe position of the ionization chamber in the radiation beam. These resultsare in good agreement with the �ndings reported by Capote et al.[4]. Usingthe fw,air correction factors obtained in this investigation it is possible tocalculate a new correction c described in chapter 1.1. An evaluation of thevariations of fw,air for di�erent situations was carried out in chapter 3.5.1and is discussed further in chapter 4.5.

4.3 Validation

The egs_chamber results for �ve di�erent cases (chosen arbitrarily but some-what evenly across the material) were validated by dosxyznrc calculationswhere a voxel with air density surrounded by water represented the cham-ber cavity. During the validation of the egs_chamber doses with dosxyznrcit was possible to conclude that doses calculated by egs_chamber deviatedfrom those calculated using dosxyznrc on the order of 3%. In order to fur-ther validate the method additional comparisons with dosxyznrc are needed.However, the uncertainty (∼ 3%) obtained was considered acceptable.


In the analyses of the experimental data two unexpected values were identi-�ed. These values were found in the ionization data for the 6 MV and 15 MVbeams at SSD 100 cm in a 2x2 cm2 �eld at 10 cm depth and were attributedto incorrect registration of the measured ionization at the time of measure-ment. The erroneous data were corrected using previous measurements andhave been validated by comparison with the remaining data in this study.The corrections made in this respect did not a�ect the �nal conclusions inthis work.

28

CHAPTER 4. DISCUSSION Monte Carlo simulation of...

4.5 Evaluations of dose ratios and ionization ratios

In order to determine the accuracy of the simulations four evaluations werecarried out by comparing the results from simulations with the experimentaldata.

Analyses in the �rst evaluation (chapter 3.5.1, �g. 3.2a to 3.3b) examinedhow values of fw,air in non-reference situations deviated from the reference(10x10 cm2 and 10 cm depth at central axis of the beam). The four largestdeviations found were for the 6 MV beam: 9.6 % in the penumbra region atSSD 90 cm, �eld size 10x10 cm2 and depth 1.5 cm; 10.6% at SSD 100 cmwith �eld size 10x10 cm2 and depth 1.5 cm; 9.1% for the 2x2 cm2 �eld withSSD 100 cm at depth 1.5 cm and 9.3% at the depth of 10 cm.

In evaluation number two (chapter 3.5.2, �g. 3.4 to 3.7) the ratio betweenthe cavity dose or measured ionization at a depth of maximum dose or ion-ization and 10 cm was examined. The purpose of this evaluation was to makean overview of results which enabled a side-by-side comparison between MCdoses and measured ionizations at di�erent depths. The results showed thatthe ratios mentioned above were similar. The relative uncertainties of all theratios in this evaluation were determined to be on the order of 5%. It alsoshould be noted that when studying the results presented in �g. 3.4 to 3.7the comparison must be made per �eld size and position both for the MCsimulations as well as for the measured ionizations.

In the third evaluation (chapter 3.5.3, �g. 3.8 to 3.9) comparisons wereperformed to examine the consistency of the MC ratios with the experimentalresults (ionization ratios), �g. 3.4 to 3.7. The present study showed thata geometric mean of all such comparisons had a relative di�erence betweenthe simulated results and the experimental measurements on the order of1.3%, not including propagation of errors. Because of this di�erence thesimulated model and the experimental measurements were considered to bein agreement.

Concerning the fourth evaluation (chapter 3.5.4, �g. 3.10a to 3.11b)the ratio between the MC dose to air at CAX and penumbra region wascompared with the corresponding ratio for the measured ionization. Theseresults showed an overall 26.5% (geometric mean) greater value for the MCsimulated dose ratio over the measured ionization ratio. It is possible thatthe greater ratio in simulation results can partially be attributed to the sharpdose gradient in the penumbra region as well as the complexity associatedwith an accurate dose determination in this region. Another possible con-tributing factor to the greater ratio could be the slight di�erence (1.8 mm)in chamber position with reference to measurement depth between the sim-ulation and the experimental set-up. The relative uncertainties concerningthese comparisons, after propagation of errors, were on the order of 5%.

29

P Andersson CHAPTER 4. DISCUSSION

4.6 Future aspects

In the present work an extensive amount of results were produced. Not allof these results were included in the analyses. In order to focus on a smallerdata set, a decision was made not to include data from one o�-axis positionfor all simulations and measurements. It was also decided to exclude the20x20 cm2 �eld data which are instead presented in appendix. However,it would have been of value to include the omitted data to strengthen theresults obtained in the present investigation.

During the experimental measurements in this work the ionization cham-ber positions in the penumbra region were estimated mathematically and val-idated using dose pro�les from previous measurements. Future work couldimprove this method by also acquiring a dose pro�le during the experimentalwork.

The information contained in an egs_chamber output �le is extensive.It was not within the scope of this project to fully understand and takeadvantage of this information. Also, a comprehensive study of the input �leparameters of egs_chamber with respect to variance reduction would be ofgreat interest.

With the availability of cheaper and faster processing power includingthe use of graphics processors to improve calculation performance, futureprojects could focus on the positional resolution in the millimeter range. Agreater resolution in ionization chamber position could perhaps enable moredetailed studies of perturbation e�ects. This understanding could then laterbe implemented in the clinical practice, for instance during interpretation ofpatient QA measurements, in order to bene�t patient treatments.

30

Chapter 5

Conclusions

Signi�cance of the work (unordered list)

• The geometry of the CC13 IC was successfully built

• Five egs_chamber simulation results were found to agree with dosxyznrcand the method was therefore considered valid

• MC results for a model of the CC13 chamber in 6 MV and 15 MVphoton beams for a variety of �eld sizes, depths and o�-axis positionswere obtained

• Experimental measurements were performed using the CC13 chamberin 6 MV and 15 MV photon beams for a variety of �eld sizes, depthsand o�-axis positions

• The factors fw,air determined in this study can be used to calculatethe correction factor c described in chapter 1.1

• Comparisons between MC simulations and experimental measurementsshow that the model can be used for accurate simulations, for instancewhen determining dose pro�les and depth dose distributions in order tointerpret the measured data in the build-up region and the penumbraregion

• A useful basis for MC simulations in radiation dosimetry is achieved,allowing better understanding of measured data in clinical geometries,e.g. phantom measurements of planned VMAT treatment of patients.

• Additional investigations with respect to positional resolution and de-tailed studies of the perturbation e�ects are required

31

P Andersson BIBLIOGRAPHY

Bibliography

[1] P. Andreo, D. T. Burns, K. Hohlfeld, M. Saiful Huq, T. Kanai, F. Laitano,V. Smyth and S. Vynckier, "Technical Report Series #398, AbsorbedDose Determination in External Beam Radiotherapy: An InternationalCode of Practice for Dosimetry based on Standards of Absorbed Dose toWater," IAEA, Vienna, 2006.

[2] L. V. Spencer and F. H. Attix, "A theory of cavity ionization," Radiat.Res. 3, pp. 239-254, 1955.

[3] A. E. Nahum, "Simulation of Dosimeter Response and Interface E�ects,"New York, Plenum, 1988, pp. 523-543.

[4] R. Capote, F. Sánches-Doblado, A. Leal, J. I. Lagares and A. R, "AnEGSnrc Monte Carlo study of the microionization chamber for referencedosimetry of narrow irregular IMRT beamlets," Med. Phys. 31 (8), pp.2416-2462, September 2004.

[5] J. Seco and F. Verhaegen , Monte Carlo Techniques in Radiation Therapy,CRC Press, 2013.

[6] D. W. O. Rogers, "Fifty years of Monte Carlo simulations for medicalphysics," Phys. Med. Biol. 51, pp. R287-R301, 3 May 2006.

[7] J. Wul�, K. Zink and I. Kawrakow, "E�ciency improvements for ionchamber calculations in high energy," Med. Phys. 35 (4), pp. 1328-1336,April 2008.

[8] K. I, M.-H. E, T. F and W. B, "EGSnrc C++ class library," NRCCReport PIRS-898.

[9] N. R. C. Canada, "EGSnrc: software tool to model ra-diation transport," NRC, 01 02 2014. [Online]. Available:http://irs.inms.nrc.ca/software/egsnrc/. [Accessed 01 02 2014].

[10] E. Hedin, J. Swanpalmer and R. Chakarova, "Monte Carlo simulationof linear accelerator Varian Clinac iX," MFR-Radfys, Gothenburg, 2010.

32

BIBLIOGRAPHY Monte Carlo simulation of...

[11] R. Chakarova, K. Müntzig, M. Krantz, E. Hedin and S. Hertzman,"Monte Carlo optimization of total body irradiation in a phantom andpatient geometry," Phys. Med. Biol., pp. 2461-2496, 2013.

[12] D. W. O. Rogers , I. Kawrakow , J. P. Seuntjens, B. R. B. Walters andE. Mainegra-Hing, "User Codes for EGSnrc," NRCC Report PIRS 702(revC), 2013.

[13] I. Kawrakow , "egspp: the EGSnrc C++ class library," NRCC ReportPIRS-899.

[14] J. S. Li, T. Pawlicki, J. Deng, S. B. Jiang, E. Mok and C.-M. Ma, "Vali-dation of a Monte Carlo dose calculation tool for radiotherapy treatmentplanning," Phys. Med. Biol 45, pp. 2969-2985, 26 June 2000.

[15] Swanpalmer J. and Johansson K-A, "The e�ect of air cavity size incylindrical ionization chambers on the measurements in high-energy ra-diotherapy photon beams � an experimental study," Phys. Med. Biol.,no. 57, p. 4671�4681, 2012.

[16] Swanpalmer J. and Johansson K-A, "Experimental investigation of thee�ect of air cavity size in cylindrical ionization chambers on the mea-surements in Co-60 radiotherapy beams," Phys. Med. Biol., no. 56, p.7093�7107, 2011.

33

Appendix

A1 - Batch scripts

Parallel_batch.sh

#!/bin /bashn=$1s h i f tcommand="$@"echo "egs−p a r a l l e l ( $n jobs ) : $command"echo " Simulat ion s t a r t ed at : "datef o r j in ` seq $n ` ; do

$command −b −P $n −j $ j >/dev/ nu l l 2>&1 &pro c e s s i d=` p r i n t f %5d $ ! `echo "LAUNCHED $pro c e s s i d : $command −b −P $n −j $ j &"

donewaitecho −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−echo "SIMULATION COMPLETED ($command)"echo " Simulat ion completed at : "date

batch_simulation.sh

#!/bin /bash# NOTE: Replace n_cores with the number o f co r e s to be usedecho "Running 4 input f i l e s with 10 000 000 h i s t o r i e s each". / para l l e l_batch . sh n_cores egs_chamber − i i n p f i l e 1 −p 521 ic ru140305. / para l l e l_batch . sh n_cores egs_chamber − i i n p f i l e 2 −p 521 ic ru140305. / para l l e l_batch . sh n_cores egs_chamber − i i n p f i l e 3 −p 521 ic ru140305. / para l l e l_batch . sh n_cores egs_chamber − i i n p f i l e 4 −p 521 ic ru140305

34


A2 Additional results

A2.1 Simulations

6 MV, SSD 90 Cavity dose (Gy/hist)

H2O521ICRU

Field cm2 Depth (cm) CAX σ PNM σ

20 x 20 10.0 9.349E-17 1.263 4.745E-17 1.713

1.5 1.361E-16 1.075 7.238E-17 1.439


AIR521ICRU


20 x 20 10.0 8.052E-17 5.530 4.678E-17 8.526

1.5 1.360E-16 4.918 6.077E-17 6.469

6 MV, SSD100 Cavity dose (Gy/hist)

H2O521ICRU


20 x 20 10.0 7.772E-17 1.403 3.962E-17 1.890

1.5 1.116E-16 1.186 5.909E-17 1.602

35



AIR521ICRU


20 x 20 10.0 6.942E-17 6.360 3.025E-17 8.360

1.5 1.021E-16 5.267 5.053E-17 7.335


H2O521ICRU


20 x 20 10.0 6.486E-16 1.600 3.395E-16 2.184

2.5 8.400E-16 1.400 4.603E-16 1.741


AIR521ICRU


20 x 20 10.0 5.912E-16 3.961 2.740E-16 4.859

2.5 7.373E-16 3.395 4.403E-16 4.693

36



H2O521ICRU


20 x 20 10.0 5.311E-16 1.675 2.837E-16 2.293

2.5 6.849E-16 1.553 3.726E-16 1.919


AIR521ICRU


20 x 20 10.0 4.440E-16 4.122 2.357E-16 5.307

2.5 6.076E-16 3.431 3.379E-16 4.833

37


A2.2 Experimental measurements

6 MV, SSD90 Ionization (nC)

Field cm2 Depth (cm) CAX PNM

20 x 20 10.0 4.127 2.775

1.5 6.058 4.243



20 x 20 10.0 3.439 2.401

1.5 4.928 3.655



20 x 20 10.0 4.053 2.762

2.5 5.346 3.755

15 MV, SSD 100 Ionization (nC)


20 x 20 10.0 3.36 2.412

2.5 4.35 3.297

38

Documents

Monte Carlo simulation of cylindrical ionization chamber ... · tally study the ionization chamber response to high-energy photon beams with aryingv eld sizes and shapes (quadratic