key data for the reference and relative dosimetry of ...792325/fulltext03.pdf · radiotherapy and...

Key Data for the Reference and RelativeDosimetry of Radiotherapy andDiagnostic and Interventional Radiology Beams

Hamza Benmakhlouf

Doctoral Thesis inMedical Radiation Physics at StockholmUniversity, Sweden 2015

Cover image:Examples of detailed detector geometries in the Monte Carlo calculations of this work, builtwith the PENELOPE geometry package pengeom using information provided by the manufac-turers; colours correspond to the different materials in each device.

c© Hamza Benmakhlouf, Stockholm 2015ISBN 978-91-7649-111-9Printed in Sweden by Publit Sweden AB, Stockholm 2015Distributor: Department of Physics, Stockholm University

Key Data for the Reference and Relative Dosimetry ofRadiotherapy and Diagnostic and Interventional Radiology Beams

Hamza BenmakhloufDoctoral thesis submitted to the Department of Physics at Stockholm University

Supervisor Professor Pedro Andreo, Stockholm UniversityCo-supervisor Associate Professor Josep Sempau, Polytechnic University of

Catalonia, Barcelona, Spain

Examination Board:Opponent Professor Klemens Zink, University of Applied Sciences,

Giessen, Germany

Committee chair Professor Per-Erik Tegnér, Stockholm UniversityCommittee member Professor Anders Ahnesjö, Uppsala UniversityCommittee member Associate Professor Åsa Carlsson-Tedgren, Linköping University

and Karolinska University Hospital, StockholmCommittee member Associate Professor Anne Thilander-Klang, University of Gothenburg

and Sahlgrenska University Hospital, GothenburgCommittee member Associate Professor Alejandro Sanchez-Crespo, Stockholm University(supplant) and Karolinska University Hospital, Stockholm

Contents

Abstract iii

List of Papers v

Acknowledgements vii

Quantities and symbols ix

Acronyms and abbreviations xiii

1 Introduction 1

2 Background 52.1 The dosimetry framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Monte Carlo calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Basic concepts on the physics of small MV photon beams . . . . . . . . . . . . 9

3 Radiation therapy dosimetry framework 133.1 Reference dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Beam quality correction factor . . . . . . . . . . . . . . . . . . . . . . 143.1.2 Configuration correction factor . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Key data for reference dosimetry: beam quality factors . . . . . . . . . . . . . 153.3 Relative dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.4 Key data for relative dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4.1 Output correction factors for 6 MV linac beams . . . . . . . . . . . . . 183.4.2 Output correction factors for LGK PerfexionTM beams . . . . . . . . . 20

4 Diagnostic radiology dosimetry framework 234.1 Reference dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Key data for reference dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2.1 Backscatter factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2.2 Mass energy-absorption coefficients . . . . . . . . . . . . . . . . . . . 27

4.3 Relative dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.4 Key data for relative dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.4.1 Thickness correction factors . . . . . . . . . . . . . . . . . . . . . . . 294.4.2 Material correction factors . . . . . . . . . . . . . . . . . . . . . . . . 30

5 Changes in the fundamental data of PENELOPE 335.1 Photoelectric effect cross sections . . . . . . . . . . . . . . . . . . . . . . . . 335.2 Mass energy-absorption coefficients . . . . . . . . . . . . . . . . . . . . . . . 355.3 Mass electronic stopping powers . . . . . . . . . . . . . . . . . . . . . . . . . 37

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ii CONTENTS

6 Additional Monte Carlo calculations 396.1 Backscatter factors for kilovoltage x-ray beams . . . . . . . . . . . . . . . . . 396.2 Absorbed dose in megavoltage photon beams . . . . . . . . . . . . . . . . . . 416.3 Spectral distributions in small-field detectors in 6 MV beams . . . . . . . . . . 42

6.3.1 Photon fluence spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 436.3.2 Electron fluence spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 44

7 Summary and conclusions 51

8 References 55

Appendices 63

Abstract

Accurate dosimetry is a fundamental requirement for the safe and efficient use of radiationin medical applications. International Codes of Practice, such as IAEA TRS-398 (2000) forradiotherapy beams and IAEA TRS-457 (2007) for diagnostic radiology beams, provide the ne-cessary formulation for reference and relative dosimetry and the data required for their imple-mentation. Research in recent years has highlighted the shortage of such data for radiotherapysmall photon beams and for surface dose estimations in diagnostic and interventional radiology,leading to significant dosimetric errors that in some instances have jeopardized patient’s safetyand treatment efficiency.

The aim of this thesis is to investigate and determine key data for the reference and relativedosimetry of radiotherapy and radiodiagnostics beams. For that purpose the Monte Carlo sys-tem PENELOPE has been used to simulate the transport of radiation in different media anda number of experimental determinations have also been made. A review of the key data forradiotherapy beams published after the release of IAEA TRS-398 was conducted, and in somecases the considerable differences found were questioned under the criterion of data consistencythroughout the dosimetry chain (from standards laboratories to the user). A modified conceptof output factor, defined in a new international formalism for the dosimetry of small photonbeams, requires corrections to dosimeter readings for the dose determination in small beamsused clinically. In this work, output correction factors were determined, for Varian Clinac R©

6 MV photon beams and Leksell Gamma Knife R© PerfexionTM 60Co γ-ray beams, for a largenumber of small field detectors, including air and liquid ionization chambers, shielded and un-shielded silicon diodes and diamond detectors, all of which were simulated by Monte Carlowith great detail.

Backscatter factors and ratios of mass energy-absorption coefficients required for surface (skin)determinations in diagnostic and interventional radiology applications were also determined,as well as their extension to account for non-standard phantom thicknesses and materials. Adatabase of these quantities was created for a broad range of monoenergetic photon beamsand computer codes developed to convolve the data with clinical spectra, thus enabling thedetermination of key data for arbitrary beam qualities.

Data presented in this thesis has been contributed to the IAEA international dosimetry recom-mendations for small radiotherapy beams and for diagnostic radiology in paediatric patients.

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iv ABSTRACT

Sammanfattning

En grundläggande förutsättning för en patientsäker tillämpning av joniserande strålning inomstrålterapi och röntgendiagnostik är en korrekt bestämning av stråldosen. De internationellastråldosprotokollen IAEA TRS-398 samt TRS-457 beskriver metoden för referens- och relat-ivdosimetri, samt tillhandahåller data som krävs för att implementera protokollen. Dock harsenare tids forskning och utveckling fastslagit att nödvändig data saknas för vissa stråltera-peutiska samt röntgendiagnostiska tillämpningar. Bristen på sådan data kan både innebära enpatientrisk samt påverka behandlingseffektiviteten.

Denna avhandling syftar till att bestämma nyckeldatan som behövs för referens- och relativ-dosimetri för strålterapi samt röngendiagnostiska strålfält. För detta har främst Monte Carlokoden PENELOPE använts, i vissa fall tillsammans med experimentella metoder. Arbetet in-leds med att utvärdera nyckeldata för referensdosimetri vid strålterapi, som publicerats upp tilltio år efter publiceringen av IAEA TRS-398 protokollet. Flera publikationer tyder på att en delav den data som ges i protokollet bör ändras. Dock är en sådan förändring problematisk dåden skulle påverka hela den väletablerade dosimetrikedjan. Korrektionsfaktorer som krävs föratt bestämma output faktorer för små strålfält har definierats av en ny internationell formalism.Dessa har bestämts för fotonstrålfält från en Varian Clinac 6 MV linjäraccelerator, samt försmala 60Co fotonstrålar från en Leksell Gammakniv. Korrektionsfaktorerna har beräknats förett antal detektorer, luftjonkammare, diamantdetektorer samt kiseldioder, potentiellt användbaraför små strålfält, genom att simulera dessa noggrant med hjälp av Monte Carlo beräkningar.

Vidare beräknades bakåtspridningsfaktorer samt massenergiöverföringskoefficienter för låg-energifotoner för olika material och tjocklekar för tillämpningar inom röntgendiagnostik. Slut-produkten är en databas med dessa värden för olika energier, vilka kan användas för att beräknaavgörande faktorer och koefficienter för godtyckliga rötngenstrålar av olika kvaliteter.

Data som presenteras i denna avhandling utgör därmed ett betydande bidrag till internationelladosimetriprotokoll och rekommendationer.

List of Papers

The thesis is based on the following papers, which are referred to in the text by their Romannumerals:

I. Benmakhlouf H and Andreo P 2011 Ten years after: Impact of recent research in photonand electron beam dosimetry on the IAEA TRS-398 Code of Practice, in Standards, Ap-plications, and Quality Assurance in Medical Radiation Dosimetry (IAEA Int. Symp.2010) Vol. 1 (Vienna: International Atomic Energy Agency) 139-152

II. Benmakhlouf H, Bouchard H, Fransson A and Andreo P 2011 Backscatter factors andmass energy-absorption coefficient ratios for diagnostic radiology dosimetry Phys. Med.Biol. 56 7179-7204

III. Benmakhlouf H, Fransson A and Andreo P 2013 Influence of phantom thickness andmaterial on the backscatter factors for diagnostic x-ray beam dosimetry Phys. Med. Biol.58 247-260

IV. Benmakhlouf H, Sempau J and Andreo P 2014 Output correction factors for nine smallfield detectors in 6 MV radiation therapy photon beams: A PENELOPE Monte Carlostudy Med. Phys. 41 041711 1-12

V. Omar A, Benmakhlouf H, Marteinsdottir M, Bujila R, Nowik P and Andreo P 2014Monte Carlo investigation of backscatter factors for skin dose determination in interven-tional neuroradiology procedures, in Physics of Medical Imaging (San Diego, Feb. 2014)Vol 9033 (Bellingham: International Society for Optics and Photonics) 1-8

VI. Benmakhlouf H, Johansson J, Paddick I and Andreo P 2015 Monte Carlo calculated andexperimentally determined output correction factors for small field detectors in LeksellGamma Knife Perfexion beams Phys. Med. Biol. 60 3959-3973

Reprints were made with permission from the publishers.

Related publications not included in the thesis:

i. Benmakhlouf H, Fransson H and Andreo P 2011 Backscatter factors and mass energy-absorption coefficient ratios for surface dose determination in diagnostic radiology Ka-rolinska Hospital Physics Report KS-ASF-201101-IR, Stockholm

ii. Benmakhlouf H, Johansson J and Andreo P 2012 Monte Carlo calculated detector correc-tions kfclinQ for determination of output factors for the Leksell Gamma Knife Med. Phys.39 3709 (abstract)

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vi LIST OF PAPERS

iii. Almén A, Andreo P, Benmakhlouf H, Chapple C-L, Delis H I, Fransson A et al. Dosi-metry in Diagnostic Radiology for Paediatric Patients IAEA Human Health Series No.24 (Vienna: International Atomic Energy Agency) 2013 (the author contributed to Ap-pendix III).

iv. Benmakhlouf H, Sempau J and Andreo P 2013 Monte Carlo calculated corrections kfclinQ

for output factors of Varian Clinac iX 6 MV beams Med. Phys. 40 209 (abstract)

v. Andreo P and Benmakhlouf H 2014 Improved reference and relative dosimetry of smallradiation therapy photon beams. SSM Report 2014:26 (Stockholm: Swedish RadiationSafety Authority)

vi. Benmaklouf H, Sempau J and Andreo P 2014 Monte Carlo calculated output correctionfactors for nine small field detectors in Varian Clinac IX 6MV photon beams Radiother-apy and Oncology 111 Suppl. 1 211 (abstract)

vii. Benmakhlouf H, Johansson J, Paddick I and Andreo P 2014 Perfexion Gamma Knife de-tector reading ratios measured with 12 PTW detectors 17th International Leksell GammaKnife Society Meeting, New York (abstract)

Acknowledgements

I would like to thank my supervisor, mentor and dear friend Professor Pedro Andreo for givingme the opportunity to be your doctoral student. You have shared your knowledge, taught meabout life, advised me during difficult times and generously shared your valuable time. I amgrateful for your exemplary guidance and for everything you have done for me. I also thankmy co-supervisor Associate Professor Josep Sempau who has helped and guided me throughthe Monte Carlo calculations of this thesis. You always shared your time despite your busyschedule.

I am indebted to Associate Professor Annette Fransson for giving me the opportunity to startwith the research projects that led to this doctoral thesis. You have always encouraged and sup-ported me in my research and clinical work. I am also grateful to Associate Professor GiovannaGagliardi for your continuous encouragement, support and advice.

Robert Bujila, Jenny Ljungqvist, Maria Marteinsdottir and Artur Omar are acknowledged foryour many suggestions that have resulted in improvements of this work.

IBA and PTW are thanked for providing detector blueprints for the Monte Carlo simulations ofsmall radiotherapy photon beams.

Last but not least I would like to thank my family who have always encouraged me to pursueacademic studies and supported me with everything I needed.

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viii ACKNOWLEDGEMENTS

Quantities and symbols

Roman letter symbols

B backscatter factor in kV x-ray beamsBQ,air air-determined backscatter factor from a phantom at the beam quality Q

D absorbed doseDmed absorbed dose to a medium ‘med’Dw absorbed dose to waterDdet mean absorbed dose to the sensitive material of a detectorDfclin

Qclinabsorbed dose to water in the clinical field fclin, for a beam of quality Qclin

Dfmsr

Qmsrabsorbed dose to water in the field fmsr, for a beam of quality Qmsr

DfrefQ0

absorbed dose to water in the field fref , for a beam of quality Q0

E kinetic energy of charged particlesE mean energy of a charged particle spectrum

FGS Goudsmidt-Saunderson angular distributionfclin clinical fieldfmsr machine specific reference (msr) field)fref conventional broad reference beam (10 cm × 10 cm)fdet,Q chamber- or detector-quality factor, defined as the product of the stopping-

power ratio and perturbation correction factors at the beam quality Q

g radiative fraction, the fraction of the kinetic energy transferred to chargedparticles by photons that is subsequently lost on average in radiative processesas the charged particles slow to rest in the material (ICRU 2011). Related tothe radiation yield, Y (E)

HVL half-value layer of a kV x-ray spectrumHVL1, HVL2 first and second half-value layersh homogeneity index of a kV x-ray spectrum (h = HVL1/HVL2)

I mean excitation energy (also known as the I-value of a medium)Iwater I-value of water

K kerma

ix

x QUANTITIES AND SYMBOLS

Kcol collision kermaKair,k air kerma photon spectrum or differential air kerma(Kair,Q)air air kerma at the quality Q determined in air(Kair,Q)surf air kerma at the quality Q determined at the entrance surface of a phantom(Kmed,Q)surf kerma in medium ‘med’ at the quality Q determined at the entrance surface

of a phantomkV kilovoltage, for x-rays spectra produced by electrons with energies in the keV

range (x-ray tube potential)k photon energyk mean energy of a photon spectrumkmax maximum energy of a photon spectrumki generic factors to correct the departure from laboratory conditions to hospital

conditionskP detector correction factor for pressurekT detector correction factor for temperaturekpol detector correction factor for polarity effectsks detector correction factor for recombination or lack of saturationkt phantom thickness correction factorkmed phantom material correction factorkQ,Q0 beam quality correction factorkfmsr,frefQmsr,Q

configuration correction factor to account for the difference between the con-ventional broad reference beam fref (10 cm × 10 cm) of quality Q and themsr field of quality Qmsr

kfclin,fmsr

Qclin,Qmsroutput correction factor for a beam clin relative to the msr field

Mlab detector reading at the laboratoryMhosp detector reading at the hospitalMair,Q detector reading in air, corrected for influence quantities, in a beam of qual-

ity QMw,Q detector reading at a given depth in water, corrected for influence quantities,

in a beam of quality QM fclin

Qclindetector reading in the clinical field fclin, in a beam of quality Qclin, correctedfor influence quantities

M fmsr

Qmsras above for the field fmsr and beam quality Qmsr

M frefQref

as above for the reference field fref and reference beam quality Qref

MV megavoltage, for photon spectra produced by electrons in the MeV range(nominal accelerator potential of an accelerator)

N calibration coefficient of a detector (generic)NK,Q air-kerma calibration coefficient of a detector at the beam quality QND,w,Q0 absorbed-dose-to-water calibration coefficient of a detector at the beam qual-

ity Q0

P pressure (in kPa)PDD(z) percentage depth-dose at the depth z, usually at SSD = 100 cmpdet,Q overall perturbation correction factor for a detector at radiation quality Qpi perturbation correction factors, assumed to be independent and small

xi

pcav electron fluence perturbation correction factorpcel perturbation correction factor for the central electrode of an ionization cham-

berpdis displacement or replacement perturbation correction factorpwall perturbation correction factor for the lack of equivalence to water of the ma-

terial of an ionization chamber wall

Q radiation beam qualityQ0 reference radiation beam qualityQfield radiation beam quality of a specific field (ref, msr or clin)

RCSDA continuous slowing down (CSDA) range of charged particlesR50 half-value depth (or range) of an electron beamrLEE lateral electron equilibrium radius (for achieving LCPE)

S generic reference quantity used at the standards laboratory (K or Dw)Sel/ρ mass electronic stopping power (also known as collision stopping power,

Scol/ρ)Sel(∆)/ρ mass restricted electronic stopping powerSrad/ρ mass radiative stopping powerSrad(∆b)/ρ mass restricted radiative stopping powerStot/ρ mass total stopping powerSDD source-to-detector distanceSSD source-to-phantom surface distancesmed1,med2 Spencer-Attix mass restricted stopping-power ratio medium1/medium2, aver-

aged over the charged particle spectrum

T temperature in CTPR20,10 Tissue Phantom Ratio, for a field size of 10 cm × 10 cm at the depths of

20 cm and 10 cm (photon beam quality specifier)t thickness

UB electron shell binding energyUK K-edge energy (electron binding energy of the K-shell)uA Type-A standard uncertaintyuB Type-B standard uncertaintyuc combined standard uncertainty

V (r) interaction potential at distance r

Wair,Q mean energy expended in dry air per ion pair formed, at the beam quality QWCC energy cut-off between soft and hard inelastic collisionsWCR energy cut-off between soft and hard radiative collisions

Y (E) radiation yield or bremsstrahlung efficiency (see also g)

Z atomic number

xii QUANTITIES AND SYMBOLS

zmax depth of maximum dosezref reference depth for beam calibration

Greek letter symbols

∆ charged-particle energy-loss cut-off∆b energy-loss cut-off for bremsstrahlung

εMC efficiency of a Monte Carlo calculation

µen/ρ photon mass energy-absorption coefficientµtr/ρ photon mass energy-transfer coefficient[µen/ρ]med1,med2

ratio of mass energy-absorption coefficients, medium1/medium2, averagedover a photon spectrum[

(µen/ρ)Q

]p+b

med,airratio of mass energy-absorption coefficients, medium/air, averaged over aphoton spectrum of quality Q at the phantom surface (primary incident beamplus backscattered radiation)∏

i

product of i factors

ρ mass densityρe(r) radial distribution of the atomic electron density

σ microscopic cross section (cm2)σannih cross section for in-flight positron annihilationσbrem bremsstrahlung cross section of charged particlesσelast elastic scattering cross section of charged particlesσinel inelastic scattering cross section of charged particles

Φ particle fluenceΦE electron fluence differential in energy (electron energy spectrum)Φk photon fluence differential in energy (photon energy spectrum)Φpk primary (incident) photon fluence

Φp+bk total (primary plus backscattered) photon fluence

Ψ photon energy fluenceΨk photon energy fluence differential in energy (energy fluence spectrum)

Ωfclin,fmsr

Qclin,Qmsrfield output factor for a clinical beam relative to the msr field

Ωfclin,frefQclin,Qref

field output factor for a clinical beam relative to the reference field

∅ diameter of a circular field

Acronyms and abbreviations

AAPM American Association of Physicists in MedicineABS Acrylonitrile butadiene styrene (water-equivalent plastic)CHT Condensed history techniqueCPE Charged particle equilibriumDCS Differential cross sectionDICOM Digital Imaging and Communications in MedicineDHFS Dirac-Hartree-Fock-SlaterDWBA Distorted–wave Born approximationEFD Electron field detectorEPDL Evaluated Photon Data LibraryFWHM Full width at half maximumGOS Generalized oscillator strengthIAEA International Atomic Energy AgencyIBA Ion Beam Applications SALCPE Lateral charged particle equilibriumICRU International Commission on Radiation Units and MeasurementsIMRT Intensity modulated radiation therapyIROC Imaging and Radiation Oncology Core (USA)LLNL Lawrence Livermore National Laboratory (USA)LIC Liquid ionization chamberLiF Lithium fluorideLGK Leksell Gamma Knife R©

MAD Mean Absolute DifferenceMC Monte CarloMSR Machine-specific-reference (field)MV MegavoltageNACP Nordic Association of Clinical PhysicsNEMA National Electrical Manufacturers Association (USA)NIST National Institute of Standards and Technology (USA)OAR Off-axis ratioOF Output factorPDD Percentage depth-dosePFD Photon field detectorPMMA Polymethyl methacrylate (Lucite, Perspex or Plexiglas)PTB Physikalisch-Technische Bundesanstalt (Germany)PTW Physikalisch-Technische Werkstaetten Dr. Pychlau GmbHPWBA Partial–wave Born approximation

xiii

xiv ACRONYMS AND ABBREVIATIONS

QA Quality AssuranceRDSR Radiation DICOM Structured ReportRMSD Root Mean Square DifferenceROI Region of interestRPC Radiological Physics Center (USA)SAD Source–to–axis distanceSFD Stereotactic field detectorSSD Source–to–surface distanceSW Solid Water R© (water-equivalent plastic)TLD Thermoluminescent dosimeterTPR Tissue phantom ratioTRS Technical Report Series (IAEA)VRT Variance reduction techniques

Chapter 1

Introduction

The estimation of the absorbed dose of radiation, determined before or after an exposure toionizing radiation, is of importance to assure the safe use of radiation; applications in radiationmedicine aim at determining the dose delivered to patients as accurately as possible. Not beinga quantitative concept, accuracy is prone to different meanings and we will follow the Guide tothe expression of Uncertainty in Measurement (the GUM, JCGM 2008), which defines accuracyas the closeness of the agreement between a result (e.g. dose delivered) and a true value (e.g.the prescribed dose or a limit dose)1.

The modality of medical exposure, which in this work includes radiotherapy and diagnostic andinterventional radiology procedures, sets the requirements for the accuracy with which radi-ation dose should be delivered. These are different for the various modalities mainly due to theconsiderable difference in the dose levels involved, of several orders of magnitude, but otherarguments are also of significance. In therapeutic exposures, for example, accuracy in dosedelivery is important not only to reduce the risk of harming a patient, but also to ensure thatprescribed doses are correctly delivered to specific targets so that the balance between tumourcontrol and normal-tissue damage, the complication-free control, is optimized (c.f. Holthusen1936, Steel 2002, etc). A limit of ±5% for the accuracy needed in radiotherapy was givenin report 24 of the International Commission on Radiation Units and Measurements (ICRU1976), based on clinical evidence for certain types of tumour and noting that limits as low as±2% could be necessary in certain cases “but at the present time it is virtually impossible toachieve such a standard”. An updated analysis of data made 25 years later by the InternationalCommission on Radiological Protection (ICRP 2000) on the lowest dose differences clinicallydetectable concluded that the accuracy in radiotherapy dose delivery should be in the order of±5%−±10%, depending on tumour type, site, size and other factors. The lower doses deliveredduring diagnostic and interventional radiology exposures decrease the required accuracy due tothe large uncertainty in the risk for long-term stochastic effects (e.g. induction of cancers orgenetic damages). For example, the dosimetry recommendations by the International AtomicEnergy Agency for this type of x-ray beams (IAEA TRS-457, 2007) quote a target accuracy of

1This definition is taken from the International Vocabulary of Basic and General Terms in Metrology (VIM) pub-lished by the International Organization for Standardization (ISO 1993). The GUM clarifies that a result can bevery accurate (i.e. be close to the reference value, or have a negligible error) but may have a large uncertainty.Accuracy (characterized by a single value) and uncertainty (characterized by a distribution) are two different con-cepts, but often they are used interchangeably creating confusion. The same occurs with the term precision, whichthe GUM emphasizes should not be used for accuracy as it defines repeatability and reproducibility.

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2 CHAPTER 1. INTRODUCTION

20% in exposures where only stochastic effects are of concern; most types of diagnostic radi-ology examinations can generally be included in this category. The limit is lowered to 7% whenthe dose delivered exceeds the threshold for deterministic effects, such as some interventionalangiography procedures where skin doses often reach orders of several grays. A different butcomplementary aspect to the required accuracy is the uncertainty with which dose can be de-livered, as the uncertainty may narrow the limits of the achievable accuracy (termed correctedtolerance interval in Andreo 2011).

Achieving these accuracy levels at the end of an entire dose delivery process is a formidabletask, as multiple intermediate steps are required from the prescription to the delivery of the ac-tual patient exposure, each having its own accuracy and uncertainty. The first step at a hospitalis to determine the absorbed dose under so-called reference conditions, to a point in a me-dium similar in composition to the patient; hence the term reference dosimetry. This requiresa reference detector calibrated at a standards laboratory in terms of a given quantity, absorbeddose to water or air kerma, determined using absolute dosimetry. The next step is to relate thereference dose to that being used at the clinic using non-reference conditions, e.g. other fieldsize, energy, position, phantom, etc., which is termed relative dosimetry. The process of cal-ibrating a detector establishes a consistent link (traceability) in the chain between primary andsecondary standards laboratories and hospitals, thereby establishing a robust way of comparingthe dosimetry of different beams at different sites. Absolute dosimetry, reference dosimetry,and relative dosimetry form what will henceforth be referred to as the dosimetry frameworkwhich, if implemented correctly, will contribute to the optimization of the accuracy and uncer-tainty of the dose delivered to patients. This is in general the area where the work presentedin this thesis is addressed. It is of interest to point out that, for radiation therapy, ICRP report86 (ICRP 2000) estimated a 6% combined standard uncertainty in the clinical dose deliveryof high-energy photon beams including all the different steps of a treatment. Approximatelyone third of this figure corresponds to reference and relative dosimetry, which represents a sub-stantial contribution to the total uncertainty. For diagnostic and interventional radiology no suchcomprehensive uncertainty estimates have been made, but for example, for reference dosimetry,IAEA TRS-457 has provided a standard uncertainty range between 2.7% and 6.3%, dependingon the laboratory or hospital level scenario.

Procedures for the reference dosimetry of radiotherapy photon and electron beams have beenrecommended by different national, regional and international organizations in the form of so-called dosimetry protocols or codes of practice. Formerly, these recommendations were basedon ionization chambers calibrated in terms of air kerma free-in-air, e.g. those published byAAPM TG-21 (Schulz et al. 1983), IAEA TRS-277 (Andreo et al. 1987), DIN (1997) andothers. New dosimetry procedures, based on ion chamber calibration coefficients in terms ofabsorbed dose to water, were developed later such as AAPM TG-51 (Almond et al. 1999),IAEA TRS-398 (Andreo et al. 2000), DIN (2008) and others, which replaced the air kerma-based recommendations. Even if both methods yield similar uncertainty in the reference dose,as can be inferred comparing the uncertainty budgets of each method (see e.g. Huq and Andreo2001, Huq et al. 2001, Andreo et al. 2002, etc), the absorbed dose to water formalism hassimplified reference dosimetry considerably. This is because the metrology system is based ondifferent types of primary standards, water and graphite calorimetry and ionization chamberdosimetry, making it more robust than the air kerma based system that relies on a single type ofstandard (ionization chamber). In diagnostic and interventional radiology dosimetry, procedureshave been recommended by ICRU report 74 (ICRU 2005), IAEA TRS-457 (Alm-Carlsson et

3

al. 2007) and others, based on detector calibration coefficients in terms of air kerma.

To implement the recommendations for reference and non-reference dosimetry at the hospital,a number of correction factors and coefficients are required throughout the processes; they arehere referred to as key data. Depending on the intended correction, key data relates to beamquality, beam configuration, detector type, irradiation geometry, etc. Examples of key dataare beam quality correction factors for radiotherapy dosimetry and backscatter factors for dia-gnostic radiology dosimetry, both to be described in detail in the following chapters. Manypublications have so far been devoted to determining key data for reference and relative do-simetry using experimental techniques, analytical calculations, Monte Carlo (MC) radiationtransport computer simulations, or a combination of these methods. In early days, when com-puters were not so widely available, the common practice was to determine key data analyticallyor experimentally. The former had the disadvantage of being often based on simplified models,in some cases proven later to be inadequate; measurements at hospitals had the disadvantageof being frequently associated to large uncertainties and sometimes results have been misinter-preted. Recent advances in computer power and the development of fast MC codes now allowaccurate determination of key data using MC simulations where both the radiation beam andthe detector geometry can be simulated with great detail.

Techniques in radiotherapy and radiology procedures have evolved considerably, although un-fortunately some of the new techniques have been affected by poor dose accuracy and large un-certainties. In radiotherapy, for example, an internal report from 2009 by the audit service of theImaging and Radiation Oncology Core (IROC) Houston QA Center (formerly the RadiologicalPhysics Center, RPC) documented that the dosimetry of Intensity Modulated Radiation Ther-apy (IMRT) treatments was not properly established in many centres in the USA, and as manyas 58% of the participating centres failed to pass a widely accepted criteria for head-and-necktreatments. Errors in dose delivery in treatments using small photon beams were highlighted inICRP Publication 112 (ICRP 2010), where a reported accident in France was caused by meas-urements with an inappropriate detector. Novotny et al. (2011) also found that the referenceon-site dose of 70 Leksell Gamma Knife R© (LGK) PerfexionTM 60Co γ-ray beams, estimatedby the local physicist, differed by up to 3% with standardized alanine measurements. Theseexamples and many others show that the dosimetry status of small radiotherapy photon beamsand non-uniform beams formed by the superposition of small fields is far from satisfactory.

In radiology procedures, Balter et al. (2010) claimed that skin doses in x-ray exposures were notlikely to be determined with accuracies better than 50% using conventional dosimetry methodslike those relying on backscatter factors (to be described in Chapter 4). This claim was reiteratedby Sukupova et al. (2011), who used a generic backscatter factor of 1.3 for all kinds of field con-figurations. Jones et al. (2014), however, showed that it is possible to determine skin doses withaccuracies of the order of 35%. These poor accuracies in skin dose estimations were mainly dueto the limited procedure-related data (beam configuration, patient position, etc.) accessible tousers. A standard by the USA National Electrical Manufacturers Association (NEMA) (RDSR2005) has made procedure-related parameters available to users, enabling more accurate skindose estimations, and manufacturers of angiography systems are today required to implementthis standard. Johnson et al. (2011) developed a skin dose mapping software based on theRDSR standard, using backscatter factor data from ICRU (2005) and mass energy-absorptioncoefficient values from Hubbell and Seltzer (1996), and determined skin dose with accuraciesconsiderably better than the mentioned 35%. Despite this improvement, in the opening sessionof the International Symposium on Standards, Applications and Quality Assurance in Medical

4 CHAPTER 1. INTRODUCTION

Radiation Dosimetry, Vienna 2010, it was highlighted that backscatter factors given in ICRUreport 74 (2005) and IAEA TRS-457 (2007) cover only about one third of the clinical beamqualities currently used at hospitals (see Figure 5 in Andreo 2011).

The discussions above show that there is a need for additional and accurate key data for thedosimetry of radiotherapy and diagnostic and interventional radiology beams. This thesis hasaimed at deriving key data for the reference and relative dosimetry of radiotherapy and radi-ology beams, mostly using Monte Carlo techniques but also using experimental methods in oneparticular treatment unit. For radiotherapy beams, the starting point was to review the key dataincluded in the reference dosimetry Code of Practice IAEA TRS-398 published in 2000. Datapublished subsequently were compared to the data provided by TRS-398 and implications inthe reference dosimetry of photons and light and heavy charged particles discussed. An inter-national formalism for small photon field dosimetry published by Alfonso et al. (2008) camewell in time due to the increasing clinical use of these fields, and the lack of key data for this ra-diotherapy modality was emphasized. In our work, correction factors for small field dosimetryhave been calculated for Varian Clinac R© 6 MV (linac) beams and LGK PerfexionTM 60Co γ–ray beams that will contribute to making output factor estimations for the clinical dosimetryof these beams more accurate. The increased amount of information available following theimplementation of the RDSR standard, which allows more accurate skin dose estimations indiagnostic radiology procedures, requires the availability of specialized key data. Hence, thedosimetry of interventional angiographic procedures has been investigated focusing our work onskin dose estimations because of the potentially high doses delivered during these procedures.Different correction factors required for these estimates have been determined and simplifiedtools to estimate them analytically developed. Finally, updates of the fundamental data (mainlycross sections) in the most recent version of the MC system used in our calculations have beeninvestigated in order to estimate the sensitivity of our key data to these changes.

This thesis is organized as follows: Chapter 2 provides a background of the dosimetry frame-work and our Monte Carlo calculations. Chapter 3 summarizes the radiotherapy dosimetryframework for reference and relative dosimetry. Key data relevant to this framework have beeninvestigated and determined in Papers I (Benmakhlouf and Andreo 2011), IV (Benmakhlouf etal. 2014), and VI (Benmakhlouf et al. 2015), and will be described in this chapter. Some newdata not included in the published papers will also be presented in the chapter. Chapter 4 sum-marizes the diagnostic radiology framework, focused on surface dose estimations. Emphasiswill be given to the role of the backscatter factor, the main correction needed for skin doseestimations. The framework will then be extended to corrections necessary for non-referenceconditions. The data required for both steps, and determined in Papers II (Benmakhlouf et al.2011b), III (Benmakhlouf et al. 2013), and V (Omar et al. 2014), will be discussed. Chapter 5compares the cross section data in the PENELOPE version 2008, used for all the calculationsin this work, with those in the most recent version of 2014. The impact of new cross sectionson our MC calculations will be investigated by simulating cases relevant to radiotherapy andto radiodiagnostic dosimetry. In Chapter 6 new MC calculations of the particle fluence insideseveral detectors are presented for broad and narrow radiotherapy 6 MV beams, a work thatcontributes to the better understanding of detector response in these beams. Chapter 7 providesthe conclusions of this thesis, complemented with some goals for the future.

Chapter 2

Background

2.1 The dosimetry framework

The dosimetry framework is based on measured calibration coefficients under the absolute do-simetry of a primary standards laboratory, which provides radiation metrology standards to themore common secondary standards laboratories (e.g. in Sweden). A detector calibration coef-ficient N , in terms of some reference quantity S, such as air kerma (Kair) or absorbed dose towater (Dw), is determined for certain laboratory specific conditions as

N =S

Mlab

(2.1)

where Mlab is the detector reading, acquired in specific conditions of humidity, pressure, tem-perature, etc. The quantity S is primarily determined at a primary standards laboratory usingwater or graphite calorimetry, chemical (Fricke) dosimetry or ionization chamber dosimetry,and subsequently disseminated to the secondary standards laboratories. The quantity of interestin radiation medicine depends on the application, e.g. radiation protection, radiotherapy, radi-odiagnostic, etc. The calibration coefficient characterizes the detector response in the standardslaboratory.

The dosimetric quantity S is thereafter determined at the hospital using the detector calibrationcoefficient according to (c.f. ICRU 2001)

S = N Mhosp

∏i

ki (2.2)

where

- N is the calibration coefficient measured at the standards laboratory in terms of the quant-ity S

- Mhosp is the detector reading at the hospital corrected for influence quantities, e.g. tem-perature (kT ), pressure (kP ), recombination or saturation (ks), and polarity (kpol), and

- ki are other factors and/or coefficients that transfer the reference quantity in the labor-atory beam quality and conditions (resulting from N Mhosp) to other beam qualities orconditions and apply to both reference and relative dosimetry.

5

6 CHAPTER 2. BACKGROUND

The key data in Eq. (2.2) are the factors and coefficients, ki. These correct the departure fromlaboratory conditions to the hospital conditions and can be classified into two groups where themain corrections in each group are

(a) Reference dosimetry-related: beam quality correction factors (kQ,Q0), configuration geo-metry and quality correction factors (kfmsr,fref

Qmsr,Q), detector perturbation correction factors

(pdet,Q), Spencer-Attix mass restricted stopping-power ratios (smed1,med2), backscatterfactors (B), mass energy-absorption coefficient ratios ([µen/ρ]med1,med2

), etc.

(b) Relative dosimetry-related: field output factors (Ωfclin,fmsr

Qclin,Qmsr) and their correction factors

(kfclin,fmsr

Qclin,Qmsr), phantom thickness (kt) and material (kmed) correction factors, percentage

depth-doses (PDD), off-axis ratios (OAR), etc.

2.2 Monte Carlo calculations

As already mentioned, the significant increase in computer power during recent years, togetherwith the development of fast and accurate Monte Carlo codes, enable determinations of keydata using extremely detailed descriptions of the radiation beam and detector configuration andmaterials. It should be mentioned, however, that even if the achievable statistical (type-A) un-certainties can be extremely small (∼ 0.1%), MC detector simulations do not take into accountdetector-to-detector differences (of the same detector type) nor detector electronic details thatmay require significant corrections for their practical use (e.g. recombination effects in liquidionization chambers). This is the reason why experimental and MC determinations of key datarelated to detector response should complement each other.

The MC calculations made throughout this work have been done with the user code PenEasy(Sempau et al. 2011), based on the 2008 version of the PENELOPE MC system (Salvat et al.2008). PENELOPE and the EGSnrc MC system (Kawrakow et al. 2013) are so far the only MCsystems capable of simulating accurately the response of ionization chambers, both complyingwith the stringent test of verifying Fano’s theorem (Fano 1954, Smyth 1986, Seuntjens et al.2002, Sempau and Andreo 2006).

PENELOPE can simulate the transport of photons and light-charged particles (electrons andpositrons) between 50 eV and 1 GeV in any material. Photons are treated by a detailed de-scription (analogue technique) of their possible interaction modes, while charged particles aresimulated in detail, using the so-called Class II condensed history technique, CHT (Berger1963, Andreo 1981) or a combination of the two. Recall that the Class II CHT divides chargedparticle interactions into two groups, denoted in PENELOPE as hard and soft collisions. Hardinteractions are those where large energy losses and angular deflections occur, and take placeabove predetermined thresholds defined by the user as transport parameters (see below); theseinteractions are simulated using the analogue technique. Soft collisions are all those with energylosses and angular deflections below the thresholds, and are treated ‘condensing’ the interac-tion mechanisms that occur in the distance between two hard events (termed the step-length) bymultiple interaction theories like stopping power and multiple elastic scattering; these determ-ine the energy loss and angular deviation after the step-length using a random-hinge method tosplit this length and improve the condensed calculation.

2.2. MONTE CARLO CALCULATIONS 7

The cross sections and interaction data used in PENELOPE are derived from first-principlecalculations, semi-empirical expressions and standard databases, and emphasis is given to pro-cesses occurring at low energies; the system uses the most accurate models to describe thenecessary differential cross sections, DCS (c.f. Salvat and Fernández-Varea 2009). All thenecessary data for the required media are prepared beforehand using a system code called ma-terial and can be tabulated (with the code tables) for subsequent analysis, additional calculationsconsistent with the MC simulation, or for graphical representation using provided scripts. Foreach element or compound the data generated are independent of the thresholds mentioned,unlike other widely used MC systems like EGSnrc that require electron and photon threshold-dependent data for each particular case. Shell binding energies (UB) are taken from the classicCarlson (1975) compilation, modified according to recent experimental data.

For photon interactions, subshell-dependent DCSs for photoelectric absorption and anomalousscattering form factors for coherent (Rayleigh) scattering in PENELOPE 2008 are taken fromthe LLNL Evaluated Photon Data Library, EPDL (Cullen et al. 1997). The form factors takeinto account effects at energies close to the K absorption edge (UK), and relaxation data isalso adopted from the LLNL-EPDL library. Incoherent (Compton) scattering is based on therelativistic impulse approximation (Ribberfors 1983) taking into account both the momentumdistribution of Compton electrons (Doppler broadening) and binding effects. Cross sectionsfor electron-positron pair production are obtained from the widely used NIST computer codeXCOM (Berger and Hubbell 1987).

For charged particles, the DCSs for elastic scattering (σelast) are obtained from Dirac partial-wave calculations in the electrostatic potential of the target atom (V (r)), the finite size ofthe nucleus being considered by a Fermi distribution of protons and atomic electron densit-ies (ρe(r)) accounted for using a Hartree-Fock model. The database for this interaction wascreated with a code termed ELSEPA (Salvat et al. 2005), and was included in ICRU report77 (ICRU 2007). DCSs for inelastic collisions with atomic electrons (σinel) are derived underthe plane-wave Born approximation (PWBA) and use a generalized oscillator strength (GOS)model developed by Liljequist (1983, 1985); this is based on the conventional summation overthe density of oscillator strengths (number of electrons in the different ionization and excitationatomic subshells) leading to the atomic number Z (Bethe sum rule), but is characterized bya spectrum of delta-like oscillators that correspond to the resonance energy and its multiples.Inelastic collisions are not simply considered as two-body reactions, and the recoil energy dis-tribution for a specific incoming projectile energy loss is included in the GOS. DCSs for brems-strahlung emission (σbrem) are taken from the NIST database (Seltzer and Berger 1986), i.e. forhigh energies they are based on the screened Bethe-Heitler formulation, also under the Born ap-proximation, and for energies up to 2 MeV taken from the partial-wave calculations by Pratt etal. (1977). It is of interest to mention that bremsstrahlung in the energy region between 2 MeVand 50 MeV, i.e. practically the entire megavoltage radiotherapy range, is based on cross sec-tion data interpolated between these two limits. The Heitler cross section (σannih) is used as theDCS for in-flight positron annihilation yielding two-photons. The cross sections σelast, σinel andσbrem are used to derive the corresponding formulations for multiple interaction events, e.g. aGoudsmidt–Saunderson angular distribution (FGS) that naturally includes spin effects and massunrestricted and restricted electronic and radiative stopping powers (Sel/ρ, Sel(∆)/ρ, Srad/ρ,Srad(∆b)/ρ), thus guaranteeing consistency over the entire set of calculations. PENELOPE alsorelies on its own database for electron impact ionization cross sections for the ionization of K,L and M electron shells of neutral atoms, calculated under the distorted-wave Born approxim-


ation, DWBA (c.f. Bote and Salvat 2008, Bote et al. 2009).

The speed of the MC calculations is governed by a set of transport parameters selected by theuser. The main parameters in PENELOPE are (a) the cut-off energies for each particle type(photons, electrons and positrons), setting the energy below which the particle is absorbed; (b)the parameters C1 and C2, that govern the transition between detailed and condensed simulationfor elastic scattering; and (c) WCC and WCR, that modulate the limit between charged particlehard and soft inelastic collisions and bremsstrahlung emissions, respectively. WCC and WCR

can be identified with the common cut-off energies for restricted electronic (or collision) andradiative mass stopping powers, Sel(E,∆)/ρ and Srad(E,∆b)/ρ, respectively. These trans-port parameters are chosen depending on the type of simulation to be carried out in terms ofenergy, geometry, accuracy required, etc. PENELOPE also includes a powerful geometry pack-age (pengeom) where components are described by quadric surfaces (planes, spheres, cylinders,cones etc). It has been used for the design of the geometry of the different detectors simulatedthroughout this work using blue-prints from the manufacturers. Examples of some these de-tailed geometries are illustrated in Figure 2.1, which for confidentiality do not identify specificdetector types or manufacturers.

Different transport parameters and radiation sources have been used throughout our MC simu-lations, depending on the calculation type:

(a) For the radiotherapy framework, where interactions by megavoltage photons and 60Coγ-ray beams are simulated, the sources were described by phase-space files for the dif-ferent field sizes at the relevant treatment distance of a Varian Clinac R© iX 6 MV and aLeksell Gamma Knife R© PerfexionTM. These were adopted from the IAEA phase-spacedatabase for external beam radiotherapy (www-nds.iaea.org/phsp) and providedby the manufacturer (Elekta), respectively. The 6 MV calculations were done in cubic(30 cm×30 cm×30 cm) water phantoms, and the 60Co ones in spherical (16 cm dia-meter) water-equivalent plastic phantoms (ABS and SW), with the detectors positionedon the central beam axis at a depth of 10 cm and in the sphere centre, respectively. Elec-tron and positron absorption energies were set to 10 keV in a specific region of interest(ROI, a 2 cm spherical shell surrounding the detectors) and 200 keV outside the ROI1;for photons it was set to 1 keV everywhere. The parameters C1 and C2 were set to 0.1,and WCC and WCR were taken equal to the charged particle and photon absorption en-ergies, respectively (note that PENELOPE includes an additional Gaussian sampling ofenergy losses below WCC and WCR that emulates efficiently energy straggling down tolow energies).

(b) For the diagnostic and interventional radiology framework, with photons in the 5 keV–150 keV energy range where kerma was the end quantity of interest, electron transportwas disregarded by setting electron absorption energies equal to the incident photon en-ergy; all the other electron transport parameters were therefore not relevant. Note thatkerma K and collision kerma Kcol are practically identical (and so are the mass energy-transfer, µtr/ρ, and energy-absorption, µen/ρ, coefficients) at the energies considered, asbremsstrahlung production is almost negligible (see footnote #1). Photon fluence dif-ferential in energy down to 1 keV (the photon energy absorption) produced by incid-

1The continuous slowing down range,RCSDA, of 200 keV electrons in water is 0.045 cm, and its radiation yield, Y(the fraction of the electron energy converted into bremsstrahlung), is 0.1%; this is our target type-A (statistical,uA) uncertainty.

www-nds.iaea.org/phsp

2.3. BASIC CONCEPTS ON THE PHYSICS OF SMALL MV PHOTON BEAMS 9

ent photon beams was scored in a 0.01 cm×1 cm×1 cm volume placed at the surfaceof t cm×30 cm×30 cm cubic phantoms, where t was set to 15 cm for reference dosi-metry and to thicknesses between 5 cm and 40 cm for relative dosimetry, and of sphericalphantoms of 18 cm and other diameters. The phantom materials used in this frameworkwere water and PMMA.

The efficiency εMC of our calculations was speeded-up considerably with the use of variancereduction techniques (VRT) that improve the statistics of the simulations by artificially increas-ing the probability of certain events (interaction forcing and photon splitting) or disregardingparticles with a small probability of reaching the defined scoring region (outside the ROI withan absorption energy of 200 keV or playing Russian roulette). These have been widely used inall the radiotherapy detector simulations.

A new version of PENELOPE has just been released (Salvat 2014) where modifications havebeen implemented in its fundamental data. As already mentioned, these will be presented inChapter 5 and their implications on our calculated data discussed in Chapter 6.

2.3 Basic concepts on the physics of small MV photon beams

The use of small megavoltage photon beams in radiation therapy, either as a single beam or toproduce so-called intensity modulated radiotherapy (IMRT) beams, has increased considerablyin recent years but harmonized procedures for their dosimetry do not exist so far. As a con-sequence, the uncertainty of this type of dosimetry has become larger than that of conventionalbeams and in some ocassions accidents have occurred when procedures, data and detectorssuitable for large (conventional) beams have been used for the dosimetry of small beams. Inter-national Codes of Practice (IAEA) and AAPM protocols for the dosimetry of small MV photonbeams are being developed, based on the formalism published by Alfonso et al. (2008) that hasbeen used in our research and that will be described in Chapter 3, but it is of interest to describesome of the basic concepts that make this type of dosimetry particularly interesting and ratherdifferent from that for large beams (provided e.g. in IAEA TRS-398, 2000).

In general terms, a megavoltage photon beam is considered to be small (or narrow) when itlacks lateral charged particle equilibrium (LCPE) within a medium, and this occurs in photonbeams if the beam half–width or radius is smaller than the maximum range of the generatedsecondary electrons. Lack of LCPE is problematic for dosimetry since the balance of chargedparticles laterally scattered in and out of the beam fails, e.g. in the presence of a cavity witha density higher than that of the medium (usually water) more particles are scatered outwardsthan inwards.

The condition to determine when a field size can be considered to be small is a function of thelateral charged particle equilibrium range (rLCPE) at a given energy or beam quality, obtainedfrom Monte Carlo simulations of the ratio D/Kcol (dose to collision kerma) in water. It hasbeen approximated by (c.f. Li et al. 1995)

rLCPE(cm) = 5.973× TPR20,10 − 2.688 (2.3)

where rLCPE is the maximum radius until which a beam can be considered to be small forthe beam quality TPR20,10 of the standard reference field, fref = 10 cm × 10 cm. The photon


beam quality index TPR20,10 is defined as the ratio of absorbed doses at 20 cm and 10 cmdepth in water, keeping constant the source-to-detector distance (SDD=100 cm) and field size(10 cm×10 cm). Small beam conditions can be assumed to exist when the external edge ofthe detector volume is at a distance from the beam edge smaller than rLCPE. Thus the beamhalf-width or radius has to be at least as large as the maximum range of the secondary electronsplus half the size of the detector volume (for a detector positioned in the beam central axis).

In practice, for small megavoltage beams produced by clinical accelerators, the necessary col-limation to reduce the field size causes a partial occlusion of the radiation source and a relativeincrease of the penumbra, both effects being related to the effective size of the radiation source,i.e. the ‘spot size’ of the electrons impinging on the target where photons are produced bybremsstrahlung. The consequences are that, contrary to the case of large beams, in small beamsthe size determined by the full width at half maximum (FWHM) of a dose profile at a typ-ical depth of 10 cm, normalized to the beam central axis, usually does not coincide with theindication of the machine collimators, and that the machine output becomes decreased.

In addition to the constraints posed by the intrinsic radiation field and beam collimation, thedetector size, relative to the dimensions of the field, plays a fundamental role. As is well-known, any detector delivers a signal Mdet proportional to the average dose in its sensitivevolume Ddet (volume-averaging effect) caused by the particle fluence crossing such a volume.If the field size is smaller than the detector dimensions and particles cross only a fraction of thesensitive volume, the detector signal averaged over its entire volume will be clearly incorrect.Mass dimensions should be borne in mind to account for the detector density, as charged particleranges are density dependent.

2.3. BASIC CONCEPTS ON THE PHYSICS OF SMALL MV PHOTON BEAMS 11

Figure 2.1: Examples of detailed detector geometries in the Monte Carlo calculations of this work, builtwith the PENELOPE geometry package pengeom using information provided by the manufacturers. Col-ours correspond to the different materials in each device but, for confidentiality, their coding is not keptconstant (specific detector models and manufacturers are not identified).

Chapter 3

Radiation therapy dosimetry framework

3.1 Reference dosimetry

In radiotherapy with external megavoltage beams, the reference dose to a point at a referencedepth in water, zref , is determined at the hospital using a detector (usually an ionization cham-ber) calibrated in terms of absorbed dose to water according to

Dfrefw,Q0

(zref) = ND,w,Q0 Mfrefw,Q0

(3.1)

where Dfrefw,Q0

is the absorbed dose to water in a beam of quality Q0, the same quality as inthe laboratory, ND,w,Q0 is the calibration coefficient in terms of absorbed dose to water andM fref

w,Q0is the detector reading in water, corrected for influence quantities. Usually the reference

irradiation conditions correspond to a specific reference field size (e.g. fref = 10 cm× 10 cm),source-to-surface distance (e.g. 90 cm or 100 cm), and the reference point is on the beam centralaxis at 5 cm or 10 cm depth in water. For simplicity, in what follows we will omit the subscript‘w’ in the detector reading, indicating the medium where measurements are made, usually waterexcept when noticed. The calibration coefficient provided by the standards laboratory can onlybe used at the hospital for a beam quality and irradiation conditions identical to those used atthe laboratory during calibration, as the detector response depends on these conditions.

In most cases the beam at the hospital for which the reference dose is to be determined differsfrom the beam used at the standards laboratory, either in terms of beam quality (i.e. Q 6= Q0),or field size (i.e. fmsr 6= fref), or in some cases both. Note that the largest field size of machinesthat cannot realize the conventional reference field size of 10 cm×10 cm, is taken to be thereference field size and has been termed machine specific-reference field (msr field) by Alfonsoet al. (2008), hence the symbol fmsr. Table 3.1 shows the beam type and reference field sizeof three frequently used radiotherapy treatment units compared to those used at the secondarystandards laboratory (in Sweden). As can be seen, the beam types (and thereby beam quality)are different for conventional linear accelerator and Cyberknife R© beams, whereas the field sizeis different for LGK and Cyberknife R© beams. These departures from the calibration conditionswill be taken into account by correction factors ki included in Eq. (2.2).

13

14 CHAPTER 3. RADIATION THERAPY DOSIMETRY FRAMEWORK

Table 3.1: Beam quality and reference field size at the Swedish Secondary Standards Dosimetry Laborat-ory and in different radiotherapy treatment units.

Unit Beam quality Reference field, fref , ormachine specific-reference field, fmsr

Standards laboratory 60Co γ-rays 10 cm ×10 cmLinear accelerator 6 MV or 15 MV 10 cm ×10 cmLeksell Gamma Knife R© 60Co γ-rays ∅ 1.6 cmCyberknife R© 6 MV ∅ 6 cm

3.1.1 Beam quality correction factor

The beam quality correction factor, kQ,Q0 , accounts for the influence of the beam quality, Q,on the calibration coefficient ND,w,Q0 determined for the laboratory reference beam quality, Q0.From this follows that the absorbed dose to a point in water irradiated by a beam of quality Qcan be determined using a Q0-calibrated detector by introducing the beam quality correctionfactor, kQ,Q0

Dfrefw,Q(zref) = ND,w,Q0 M

frefQ kQ,Q0 (3.2)

The beam quality correction factor is defined (see e.g. IAEA TRS-398) as an experimentalfactor and should be determined at the standards laboratory for a given detector to take intoaccount detector-to-detector differences. When this is not possible, beam quality correctionfactors can be estimated theoretically using stopping-power ratios and perturbation correctionfactors according to Bragg-Gray cavity theory, c.f. Andreo (1992) and IAEA TRS-398 (Andreoet al. 2000)

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

pdet,Q

pdet,Q0

(Wair

)Q(

Wair

)Q0

(3.3)

where sw,air is the Spencer-Attix stopping-power ratio water-to-air evaluated for the unperturbedelectron fluence (c.f. ICRU 1984a), pdet is a product of perturbation correction factors that ac-count for different perturbation effects of the electron fluence caused by the presence of thedetector, and Wair is the mean energy required to form an ion pair in air (introduced to take intoaccount differences in this quantity for different particles and energies). The product of perturb-ation correction factors, pdet, at a given quality Q is usually determined assuming independentand small perturbation correction factors pi accounting for different effects,

pdet =∏i

pi = pcav pdis pwall pcel (3.4)

where pcav is the detector cavity electron fluence perturbation correction factor, pdis is the dis-placement or replacement correction factor, pwall is the perturbation correction factor for thelack of equivalence to water of the detector wall, and pcel is the perturbation correction factorfor the central electrode of an ionization chamber. Although chamber-to-chamber variations areneglected by using calculated correction factors, calculated and experimentally derived beam

3.2. KEY DATA FOR REFERENCE DOSIMETRY: BEAM QUALITY FACTORS 15

quality correction factors have been shown to agree within about 0.5% for some ionizationchambers (Andreo 2000). For MC calculations, Sempau et al. (2004) defined a single chamber-quality factor, fdet,Q, as the product of the stopping-power ratio and the perturbation correctionfactors, modifying Eq. (3.3) to

kQ,Q0 =fdet,Q

fdet,Q0

(3.5)

where for a given beam qualityQ, fdet,Q was obtained as the ratio between the dose at a point inwater (approximated by a small volume) and the mean dose to the active volume of the detector(fdet,Q = Dw/Ddet).

Beam quality correction factors should be implemented in the case of linear accelerator beams(6 MV or 15 MV) or Cyberknife R© beams, as these machines generate beam qualities differentfrom the laboratory 60Co γ-rays, as shown in Table 3.1.

3.1.2 Configuration correction factor

The influence of the field size fmsr and beam qualityQmsr, as well as other irradiation conditions(e.g. phantom geometry) on the calibration coefficient, ND,w,Q0 , determined for a referencefield size, fref , and a standard geometry (e.g. a cubic water phantom of 30 cm side) is taken intoaccount by a configuration correction factor, kfmsr,fref

Qmsr,Q. The absorbed dose to water in the msr

field and in the non-standard configuration is determined by

Dfmsr

w,Qmsr(zref) = ND,w,Q0 M

fmsr

QmsrkQ,Q0 k

fmsr,frefQmsr,Q

(3.6)

Configuration correction factors should be implemented in the case of LGK and Cyberknife R©

beams, as these machines generate reference field sizes fmsr different from that used in thestandards laboratory and their dosimetry uses non-cubic reference phantoms. For example, thephantom used in the reference dosimetry measurements of LGK beams is a spherical water-equivalent plastic phantom, of ABS or Solid Water R©, having 16 cm diameter.

3.2 Key data for reference dosimetry: beam quality factors

Beam quality correction factors, converting the calibration coefficient, ND,w,Q0 , from the labor-atory calibration quality, Q0, to a hospital reference beam quality, Q, are provided by IAEATRS-398 for 53 detectors for high-energy photon beams as a function of the beam qualityTPR20,10 and for 20 detectors for high-energy electron beams as a function of the beam qualityR50;the laboratory beam quality in both cases is a 60Co γ-ray beam. Recall that TPR20,10 specifiesthe photon beam quality and was defined in Section 2.3; R50 specifies the electron beam qual-ity and is defined as the depth in water corresponding to half of the maximum depth dose,D(zmax). The beam quality correction factor data given in IAEA TRS-398 were determined us-ing Eq. (3.3), i.e. products of several independent perturbation factors and stopping powers. Forhigh-energy photon and electron beams, Table 3.2 states how each of the perturbation factors,included in IAEA TRS-398, was determined.


Table 3.2: Perturbation correction factors in the dosimetry Code of Practice IAEA TRS-398 (Andreo etal. 2000) used to determine beam quality correction factors. Perturbation factors were determined usinganalytical expressions, experimental data or Monte Carlo calculations. The second and third columns indic-ate the method used to determine the specific perturbation correction factor for photon and electron beams,respectively.

pi Photon beams Electron beamspcav Unity Analyticalpdis Analytical/experimental Unitypwall Analytical Unity (due to lack of data)pcel MC calculations MC calculations/experimental

Ten years after the publication of IAEA TRS-398, Paper I investigated how new MC-calculatedperturbation factors by different authors (published between 2000 and 2010) differed from thevalues used in the IAEA Code of Practice TRS-398. 60Co γ-rays and high-energy photon andelectron beams were considered in that study. For photon beams the investigated detector was aFarmer NE-2571 cylindrical ionization chamber, whereas a NACP plane-parallel chamber wasthe focus for high-energy electron beams, as data for these two detectors were widely available.It was shown that the new MC-calculated data yielded a combined increase in the total NE-2571perturbation factor pdet for the reference beam quality of 60Co of about 1.5%, compared withTRS-398, decreasing as the energy increased. The difference between the new values and theexperimental data for the displacement effect measured by Johansson et al. (1977), and the ana-lytical expression for the wall correction factor by Almond and Svensson (1977), both used inTRS-398, contributed more or less equally to the 1.5% increase. Note that the large increase inthe perturbation factor for this reference beam quality enters into the denominator of Eq. (3.3).For photon beam qualities not too different from 60Co, the increase in pdet both at Q and Q0

will cancel out; the increase in the ratio, and thus in kQ,Q0 , will be maximum for the highestphoton energies, reaching up to 1.2%. For high-energy electron beams the most significant dis-crepancy was found for the NACP wall perturbation factor, which in IAEA TRS-398 was takenas unity due to lack of data then available, whereas the new values differed from unity by 1% to2%. The significant increase of the perturbation factors for the quality of 60Co, which would bepresent for all types of charge particle beams, triggered a subsequent investigation by Andreo etal. (2013) and, based on the comparison of MC-calculated fdet,60Co factors with experimentalvalues, it was concluded that implementing such increase without making consistent changesin the rest of the data throughout the dosimetry chain would violate the well-established con-sistency in radiation dosimetry. It was also demonstrated that an increase in the perturbationfactors would partly be balanced by a reduction in the stopping-power values for water due tothe proposed increase in its mean excitation energy (see Chapter 5).

It should be noted that by calculating the beam quality correction factor kQ,Q0 using fdet,Q as inEq. (3.5), instead of using stopping-power ratios and perturbation correction factors, simplifiessubstantially the concept of beam quality correction factor as it makes individual perturbationcorrection factors unnecessary. Paper I also concluded that large differences exist in the calcu-lations of some perturbation factors reported in different references even using the same MCsystem, especially for NACP chambers in electron beams, where in some cases the calculateddata differed by up to 1.5%.

3.3. RELATIVE DOSIMETRY 17

3.3 Relative dosimetry

The reference absorbed dose determined in the previous section is related to the dose for otherfield sizes, keeping the reference depth and all other reference conditions unaltered, using theso-called output factor1, defined as


=Dfclin

Qclin

DfrefQref

(3.7)

The beam qualities,Qref andQclin, are included in the subscript of the output factor to emphasizethat changes in beam quality are possible when the field size is changed. Although Ωfclin,fref

Qclin,Qrefis

defined as a ratio of absorbed doses, the output factor has commonly been approximated by aratio of detector readings, i.e.


≈M fclin

Qclin

M frefQref

(3.8)

which assumes that stopping-power ratios and perturbation correction factors are independ-ent of the field size, i.e. (sw,air pdet)fclin = (sw,air pdet)fref . For large fields, larger than about4 cm×4 cm, this assumption is approximately correct and therefore Eq. (3.8) holds. For smallfields multiple authors (c.f. Czarnecki and Zink 2013, Wagner et al. 2013, Papaconstadopouloset al. 2014, etc) have shown that perturbation factors vary considerably with the field size. It istherefore necessary to determine output factors using the full Eq. (3.7) or use detector readingratios corrected with a so-called output correction factor, i.e.


=Dfclin

w,Qclin

Dfrefw,Qref

=M fclin

Qclin

M frefQref

(sw,air)fclinQclin

(sw,air)frefQref

(pdet)fclinQclin

(pdet)frefQref

=M fclin

Qclin

M frefQref

kfclin,frefQclin,Qref(3.9)

where kfclin,frefQclin,Qrefis a factor that converts the ratio of detector readings into a ratio of absorbed

doses. Note that the output correction factor should be close to unity for large field sizes. Whenthe reference field size is not the conventional 10 cm×10 cm, the msr field must be used andEqs. (3.8) and (3.9) become

Ωfclin,fmsr

Qclin,Qmsr≈M fclin

Qclin

M fmsr

Qmsr

(3.10)

Ωfclin,fmsr

Qclin,Qmsr=Dfclin

w,Qclin

Dfmsr

w,Qmsr

=M fclin

Qclin

M fmsr

Qmsr

kfclin,fmsr

Qclin,Qmsr(3.11)

The characteristics of the small field detectors investigated in this work, for which output cor-rection factors have been calculated, are summarized in Table 3.3.

1Output factors have also been termed relative dose factors or total scatter factors. In addition, the abbreviation OFhas conventionally been used for output factors, but the symbol adopted for this factor in Eq. (3.7) is consistentwith the international formalism published by Alfonso et al. (2008).


Table 3.3: Characteristics of the small field detectors investigated in this work. (Updated from Papers IVand VI, Benmakhlouf et al. 2014, 2015).

Detector Type Active volumediameter (mm) height (mm)

PTW T31002 Air ionization chamber 5.50 6.50PTW T31006 Air ionization chamber 2.00 5.00PTW T31010 Air ionization chamber 5.50 6.50PTW T31014 Air ionization chamber 2.00 5.00PTW T31015 Air ionization chamber 2.90 5.00PTW T31016 Air ionization chamber 2.90 2.90IBA CC01 Air ionization chamber 2.00 2.77PTW T31018 Liquid ionization chamber 2.50 0.35PTW T60003 Natural diamond a 2.44 0.32PTW T60019 Synthetic diamond 2.20 0.001PTW T60008 Shielded silicon diode 1.00 0.03PTW T60016 Shielded silicon diode 1.00 0.03IBA PFD Shielded silicon diode 2.00 0.06PTW T60012 Unshielded silicon diode 1.00 0.03PTW T60017 Unshielded silicon diode 1.00 0.03PTW T60018 Unshielded silicon diode 1.13 0.25IBA EFD Unshielded silicon diode 2.00 0.06IBA SFD Unshielded silicon diode 0.60 0.06a Detectors made of natural diamond show considerable detector-to-detector differences and the manufacturer

states ranges of variation of 0.1–0.4 mm for the height and 3–15 mm2 for the area of the active region. Thedimensions quoted in this table were stated in the manufacturer’s certificate of the detector used in the meas-urements of Paper VI.

3.4 Key data for relative dosimetry

3.4.1 Output correction factors for 6 MV linac beams

Output correction factors derived according to Eqs. (3.9) or (3.11) are required for the exper-imental determination of output factors for small photon fields, to convert the measured ratioof detector readings into a ratio of absorbed doses. In this work, correction factors have beendetermined by MC calculations for eleven detectors:

(a) three ionization chambers (PTW T31018 and T31016, and IBA CC01),

(b) two diamond detectors (PTW T60003 and T60019),

(c) six silicon diodes (PTW T60016, T60017 and T60018, and IBA PFD, EFD and SFD).

The results for nine of these detectors were reported in Paper IV while results for two additionaldetectors are new in this thesis; all the values are given in Table 3.4. The output correctionfactors were determined for five field sizes between 0.5 cm×0.5 cm and 10 cm×10 cm. TheMC-calculated output correction factors were determined assuming that the detector readingM f

Q is proportional to the dose deposited in the detector DfQ, i.e.

3.4. KEY DATA FOR RELATIVE DOSIMETRY 19

kfclin,frefQclin,Qref=Dfclin

w,Qclin/M fclin

Qclin

Dfrefw,Qref

/M frefQref

≈Dfclin

w,Qclin/Dfclin

Qclin

Dfrefw,Qref

/DfrefQref

(3.12)

Table 3.4: Monte Carlo calculated output correction factors, kfclin,frefQclin,Qref, for small-field detectors at the

reference depth in water of 10 cm (in the beam central axis) for the indicated field sizes of a Varian Clinac R©

iX 6 MV clinical accelerator. The values are normalized to a reference field fmsr = 10 cm×10 cm and havea type-A uncertainty of 0.15% or smaller. The field sizes (in cm) are nominal values at the surface of a30 cm×30 cm×30 cm phantom. (Updated from Paper IV, Benmakhlouf et al. 2014).

Detector Type 10×10 4×4 2×2 1×1 0.5×0.5PTW T31018 Liquid ionization chamber 1.000 1.003 1.003 0.992 1.011PTW T31016 Air ionization chamber 1.000 1.004 1.003 1.001 1.102IBA CC01 Air ionization chamber 1.000 1.000 1.002 1.003 1.050PTW T60003 Natural diamond 1.000 1.005 1.008 0.997 1.002PTW T60019 Synthetic diamond 1.000 1.003 1.002 0.991 1.004PTW T60016 Shielded silicon diode 1.000 0.998 0.996 0.956 0.910IBA PFD Shielded silicon diode 1.000 0.991 0.983 0.951 0.947PTW T60017 Unshielded silicon diode 1.000 1.014 1.016 0.992 0.949PTW T60018 Unshielded silicon diode 1.000 1.012 1.014 0.988 0.957IBA EFD Unshielded silicon diode 1.000 1.015 1.021 1.002 0.991IBA SFD Unshielded silicon diode 1.000 1.021 1.023 1.016 0.980

Output correction factors for the ionization chambers are shown in Figure 3.1(a), for the dia-mond detectors in Figure 3.1(b), and for the silicon diodes in Figure 3.1(c). Some observationscan be made on the figures:

(a) The output correction factors for air ionization chambers are extremely large, due to thepartial volume averaging resulting from their relatively large air cavities. The effect of thedetector size on the partial volume averaging can be clearly seen in Figure 3.1(a), wherecorrection factors in small fields for the PTW T31016 ion chamber are twice as large asfor the IBA CC01. This makes these detectors unsuitable for output factor measurementsbelow 2 cm×2 cm field sizes. The output correction factors for the air ion chambers areclose to unity for field sizes larger than 2 cm×2 cm indicating that detector reading ratioscan be used to determine the output factor in this range.

(b) The output correction factors for the silicon diodes show some similar global features butdepend on whether the detector is shielded or unshielded. The correction factors for thetwo shielded diodes (PTW T60016 and IBA PFD) are less than unity for all field sizesand decrease monotonically with decreasing field size. The difference between thesetwo shielded diodes in terms of output correction factors depends on their volume; thecorrection factor for the larger silicon diode (IBA PFD) falls steeper than for the smallerdiode (PTW T60016). The lack of lateral charged particle equilibrium (LCPE, resultingfrom differences in electron ranges in water and silicon) will have a greater impact on thelarger silicon diode than on the smaller diode, resulting in larger output factor corrections.All the unshielded types show correction factors larger than unity for intermediate fieldsizes and smaller than unity for the smallest field sizes. The values smaller than one are


due to the lack of LCPE effect, whereas those larger than one, for intermediate field sizes,are due to the over-response of unshielded silicon diodes in large field sizes.

(c) Figure 3.1(b) shows that the two diamond detectors (as the liquid ionization chamberin Figure 3.1(a)) have correction factors within ±1% due to the balance of the differenteffects (lack of CPE and partial volume averaging).

As stated in Table 3.4 the type-A uncertainty of our MC calculations was uA = 0.15% orsmaller. In Paper IV we estimated the type-B uncertainty (uB) of our data in combination withthe values from other authors applying the recommendations of the Guide to the expression ofUncertainty in Measurement, the GUM (JCGM 2008), to arrive at an estimation of the combinedstandard uncertainty uc ≈ 0.6%.

3.4.2 Output correction factors for LGK PerfexionTM beams

In Paper VI the output correction factors introduced in Eq. (3.11) were determined for LGKPerfexionTM 60Co γ-ray beams using both MC and experimental methods. The output correctionfactors were determined for the three collimator sizes of 4 mm, 8 mm and 16 mm and fifteensmall field detectors. The correction factors depend on the phantom material type and weredetermined for ABS plastic phantoms and Solid Water R© phantoms, both provided by the LGKmanufacturer.

The starting point was to determine the output correction factors using MC calculations, inthe same way as was done for the linear accelerator beams in the previous section (replacingin Eq. (3.12) ‘ref’ by ‘msr’ as the LGK cannot realize the standard 10 cm× 10 cm referencefield). This was done for five detectors: one liquid ionization chamber (PTW T31018), twosilicon diodes (PTW T60016 and T60017), one alanine detector (a disc 2.3 mm thick of 5mm diameter), and one TLD detector (LiF cube with 1 mm sides). It was found that the outputcorrection factors for the liquid ionization chamber (LIC) were within±0.4% for both the 8 mmand 4 mm collimator. This result confirms that using detector readings to estimate the outputfactors (i.e. using the approximation of Eq. (3.10)) with this detector type does not requirea significant correction, as the MC-calculated output correction factors are smaller than theuncertainty in the detector reading ratio. It was also found that the silicon diodes and the TLDdetector require corrections between -3% and -4% due to the reasons discussed in the previoussection. The alanine detector required a correction factor exceeding 10% due to its large volumerelative to the smallest collimator size.

Using the results from the MC calculations, the experimental determination of the output cor-rection factors can be made using a ‘correction-free detector’ (i.e. a detector having negligiblecorrection factor) as reference, using the following expression

kfclin,fmsr

Qclin,Qmsr=Dfclin

w,Qclin/M fclin

Qclin

Dfmsr

w,Qmsr/M fmsr

Qmsr

≈M fclin

Qclin(ref)/M fclin

Qclin

M fmsr

Qmsr(ref)/M fmsr

Qmsr

(3.13)

where M fQ(ref) is the reference detector (LIC) reading. The reference detector, which should

have an output correction factor close to unity, could also be some type of radiochromic film thatdoes not require significant corrections. However, as stated above, the MC-calculations estab-lished that the liquid ionization chamber had output correction factors within ±0.4%, allowing


us to use it as a ‘practical’ correction-free detector. Using Eq. (3.13) and the liquid ionizationchamber as the reference detector, output correction factors were measured for twelve PTWdetectors; six of them were air ionization chambers and six solid-state detectors. The resultingdata are given in Table 3.5.

Table 3.5: Experimentally determined detector output correction factors, kfclin,fmsr

Qclin,Qmsr, in a 16 cm dia-

meter spherical Solid Water R© phantom for the circular 60Co γ-rays fields of a PerfexionTM Leksell GammaKnife R©. The correction factors were calculated using Eq. (3.13), with the PTW T31018 liquid ionizationchamber as reference detector. The estimated combined standard uncertainty of each point is of the orderof 0.9%. (From Paper VI, Benmakhlouf et al. 2015).

Detector Type ∅ 4 mm ∅ 8 mm ∅ 16 mmPTW T31002 Ionization chamber 2.683 1.268 1.000PTW T31006 Ionization chamber 1.312 1.025 1.000PTW T31010 Ionization chamber 2.507 1.211 1.000PTW T31014 Ionization chamber 1.336 1.030 1.000PTW T31015 Ionization chamber 1.494 1.053 1.000PTW T31016 Ionization chamber (Pinpoint 3D) 1.279 1.032 1.000PTW T60008 Diode (photon/shielded) 0.951 0.971 1.000PTW T60012 Diode (electron/unshielded) 0.965 0.996 1.000PTW T60016 Diode (photon/shielded) 0.958 0.981 1.000PTW T60017 Diode (electron/unshielded) 0.961 0.997 1.000PTW T60003 Diamond detector (natural) 1.071 1.006 1.000PTW T60019 Diamond detector (synthetic) 0.993 1.005 1.000

Due to partial volume averaging effects, relatively large correction factors were obtained forall six air ionization chambers. The results confirm the inappropriateness of these detectorsfor small photon field measurements. The six solid-state detectors include four silicon diodes(two shielded and two unshielded) and two diamond detectors (one natural and one synthetic).Correction factors between -3% and -5% were found for the silicon diodes and the smallestcollimator size, whereas they decreased to -1% and -3% for the 8 mm collimator size. Asfor linear accelerators, this is caused by the lack of LCPE in the silicon diodes compared towater. The output correction factors for natural diamond detectors (PTW T60003) were 0.6%and 7.1% for the 8 mm and 4 mm collimator size, respectively, due to partial volume averaging.The correction factors for the synthetic diamond detector (PTW T60019) were within ±0.7%for both collimator sizes. The small correction factors for the synthetic diamond are due to itssmall active volume dimensions and nearly water-equivalent detector material.


Figure 3.1: Monte Carlo calculated output correction factors, kfclin,frefQclin,Qref, for (a) three ionization chambers:

PTW T31016 and T31018, and IBA CC01, (b) two diamond detectors: PTW T60003 and T60019, and (c) sixsilicon diodes: PTW T60016, T60017 and T60018, and IBA PFD, EFD and SFD. The solid lines in (b) and(c) are new (unpublished) data. The correction factors are for nominal surface square field sizes between0.5 cm×0.5 cm and 10 cm×10 cm. The smooth lines are fits to the data, intended for visual purposes. Notethat the left half of the abscissa is in logarithmic scale to display in detail the data for the smallest field sizes.Type-A uncertainties (uA, statistical) are ∼ 0.15% or lower, smaller than the size of the symbols. (Updatedfrom Paper IV, Benmakhlouf et al. 2014).

Chapter 4

Diagnostic radiology dosimetry framework

A step-by-step formalism for the determination of skin absorbed dose in diagnostic and in-terventional radiology procedures was presented in Paper II, consistent with ICRU report 74(ICRU 2005) and the IAEA Code of Practice TRS-457 (Alm-Carlsson et al. 2007), which issummarized in this chapter. That paper included a comparison between the diagnostic radi-ology and kV radiotherapy formalisms, the latter introduced by Nahum and Knight (1994) andKnight (1996), emphasizing the different definitions of backscatter factors and ratios of massenergy-absorption coefficients that enter in the equations of this chapter.

4.1 Reference dosimetry

A detector intended for use in diagnostic radiology dosimetry is calibrated at the standardslaboratory in a kV x-ray beam in terms of air kerma free-in-air1, following the principles de-scribed in Eq. (2.1). The air kerma free-in-air is subsequently determined at the hospital as

(Kair,Q)air = Mair,QNK,Q (4.1)

where Mair,Q is the detector reading free-in-air, corrected for influence quantities, in a x-raybeam of quality Q, and NK,Q is the detector calibration coefficient in terms of air kerma at thesame beam quality. If the calibration coefficient was measured at a beam quality different fromthat at the hospital then a beam quality correction factor kQ,Q0 (defined as a ratio of air kermacalibration coefficients, see IAEA TRS-457) must be added to Eq. (4.1) as was done in Eq. (3.2)for radiotherapy beams.

The next step is to include the effect of a phantom (usually water) behind the detector, yielding

1Recall that for photons of energy k, kerma is defined as K = Ψ µtr/ρ = k Φµtr/ρ, where Ψ is the photon energyfluence, Φ is the photon fluence, and µtr/ρ is the mass energy-transfer coefficient (c.f. ICRU 2011). For lowphoton energies, and in media where the radiative fraction g ≈ 1, µtr/ρ = µen/ρ and hence K = Kcol. For a kVx-ray spectrum in a medium ‘med’, this transforms into

Kmed =

kmax∫0

Ψk [µtr(k)/ρ]med dk =

kmax∫0

k Φk [µtr(k)/ρ]med dk

23

24 CHAPTER 4. DIAGNOSTIC RADIOLOGY DOSIMETRY FRAMEWORK

the air kerma at the entrance surface of the phantom

(Kair,Q)surf = Mair,QNK,QBair(Q) (4.2)

where Bair(Q) is the backscatter factor for a beam quality Q, which accounts for the contri-bution of radiation backscattered from the phantom to its surface. To determine the kerma inanother media at the phantom entrance surface, the ratio of mass-energy absorption coefficientsof the two media is used according to

(Kmed,Q)surf = Mair,QNK,QBair(Q) [µen(Q)/ρ]p+bmed,air (4.3)

where µen(Q)/ρ must be determined for the photon spectrum at the surface, i.e. including boththe incident primary spectrum and the backscattered spectrum, emphasized by the superscript‘p+b’ in Eq. (4.3).

The backscatter factor in Eqs. (4.2) and (4.3) for a photon spectrum can be determined as a ratioof air kermas

Bair(Q) =(Kair,Q)p+b

surf

(Kair,Q)pair

=

∫ kmax

0k [Φk]p+b

surf [µen(k)/ρ]air dk∫ kmax

0k [Φk]pair [µen(k)/ρ]air dk

(4.4)

where k is the photon energy, [Φk]p+bsurf is the photon fluence differential in energy in a small

volume of air on the phantom surface, which includes both primary and backscattered photons(indicated by ‘p+b’ in the superscript), [Φk]pair is the incident primary photon fluence differentialin energy in a small volume of air free-in-air (i.e. without the phantom), and [µen(k)/ρ]air

is the mass energy-absorption coefficient for air. Note that the only difference between thenumerator and the denominator in Eq. (4.4) is that the photon fluence in the numerator includesbackscattered photons whereas the photon fluence in the denominator includes only incidentprimary photons.

The mass-energy absorption coefficient ratio, medium-to-air, is also determined as a ratio ofkermas in the two media

[µen(Q)/ρ]p+bmed,air =

∫ kmax

0k [Φk]p+b

surf [µen(k)/ρ]med dk∫ kmax

0k [Φk]p+b

surf [µen(k)/ρ]air dk(4.5)

where the difference between the numerator and the denominator is in the mass-energy absorp-tion coefficient of medium and air, respectively.

4.2 Key data for reference dosimetry

4.2.1 Backscatter factors

The largest correction in the framework of diagnostic and interventional radiology dosimetry isthe backscatter factor. Special emphasis was therefore given to this particular correction.

4.2. KEY DATA FOR REFERENCE DOSIMETRY 25

The starting point was to determine backscatter factors for incident monoenergetic photons byMC simulations. By convolving these with clinical photon spectra calculated with the soft-ware SpekCalc (Poludniowski et al. 2009) it is possible to determine backscatter factors forsuch beams. In order to verify the accuracy of the ‘convolved backscatter factors’, they werecompared to the results obtained using detailed clinical spectra directly as incident beams inMC calculations. Backscatter factors were also determined for cubic phantoms (15 cm heightand 30 cm width) and for cranial shaped phantoms (spheres with diameters of 18 cm), in Pa-pers II, III and V. The influence of phantom shapes on the entrance skin dose have briefly beenaddressed by Martin et al. (1994) and Compagnone et al. (2005).

4.2.1.1 Backscatter data for cubic phantoms

Extensive tables of backscatter factors for cubic water phantoms with a reference thickness(height) of 15 cm were published in Paper II. A database of backscatter factors for 30 monoen-ergetic photon beams with energies between 10 keV and 150 keV was created for five squarefield sizes ranging between 5 cm×5 cm and 35 cm×35 cm. The data are included in Figure 4.1(numerical values excerpted from Benmakhlouf et al. (2011c) are given in Table A1 of the Ap-pendix) showing backscatter factors of up to 1.7. The figure shows how the backscatter factorsincrease with field size due to the increasing amount of photons that scatter back to the surface.A clear field size and energy dependence can also be observed in the figure.

The MC-calculated database of backscatter factors for monoenergetic photons for five field sizeswas subsequently used to determine kerma-weighted backscatter factors for clinically relevantincident photon spectra of quality Q as,

Bair(Q) =

kmax∫0

Kair(k)Bair(k) dk

kmax∫0

Kair(k) dk

=

kmax∫0

k [Φk]pair [µen(k)/ρ]airBair(k) dk

kmax∫0

k [ΦE]pair [µen(k)/ρ]air dk

(4.6)

where [Φk]pair is the photon fluence differential in energy of the incident clinical spectrumcalculated with SpekCalc. Values of kerma-weighted backscatter factors for clinical spec-tra were shown in Paper II to range between 1.2–1.3, 1.2–1.5, and 1.2–1.6 for 5 cm×5 cm,10 cm×10 cm, and 35 cm×35 cm field sizes, respectively. The kerma-weighting procedure wasused to determine the backscatter factors of 143 clinical x-ray spectra of different field sizes andqualities, and are given in Table A2 of the Appendix as a function of the first half value layer(HVL1), kilovoltage potential (kV) and homogeneity index (h) of the clinical beams. Figure 4.2shows these backscatter data as a function of HVL and field size for all the beam qualities,where the large variations are illustrated; this confirms the well known limitation of using HVLas a single parameter for specifying the beam quality of kV x-ray beams. (see e.g. ICRU report10b (ICRU 1964) and Seuntjens et al. (1987)). Recall that the first half value layer is definedas the material required to reduce the air kerma to 50% of its initial value, whereas the homo-geneity index is the ratio between the first and second half value layer (the second being thethickness required to reduce the air kerma to 25%).

Kerma-weighted backscatter factors were benchmarked against MC-calculated backscatter factorsusing the detailed clinical spectra (generated by SpekCalc) as input radiation source and differ-ences within 0.6% were found. The kerma-weighting procedure was thus shown to be reliable


Figure 4.1: Monte Carlo calculated backscatter factors, Bair(k), for monoenergetic photons for the indic-ated square field sizes at the surface of a 15 cm thick water phantom as a function of the photon energy, k.The solid lines are fits to the 30 data points for each field size. The symbols correspond to the data of Petoussi-Henss et al. (1998), implemented in ICRU report 74 (ICRU 2005) and IAEA TRS-457 (Alm-Carlsson et al.2007). (From Paper II, Benmakhlouf et al. 2011b).

Figure 4.2: Monte Carlo calculated backscatter factors, Bair(Q), for clinical beam qualities used indiagnostic and interventional radiology for the indicated field sizes at the surface of a 15 cm thick waterphantom as a function of the first half-value layer, HVL1. (From Paper II, Benmakhlouf et al. 2011b).

in estimating backscatter factors and can be used when the incident photon spectrum is knownby measurement or by calculation. To simplify the estimation of backscatter factors when thespectrum is not known, as is usually the case in clinical routine, an analytical expression was fit-

4.2. KEY DATA FOR REFERENCE DOSIMETRY 27

ted to the backscatter factor data as a function of the kilovoltage potential and the first half-valuelayer. The expression is included in Paper III and has the form

[Bair(Q)]w,15 =2∑

i,j=0

ai,j kVi HVLj1 (4.7)

where ai,j are fitting parameters for each field size, kV is the kilovoltage potential and HVL1

is the first half-value layer. The differences between the analytically calculated values and thekerma-weighted data were within ±0.3%. This method is suitable when the HVL1 and the kVof the incident clinical photon beam are known.

4.2.1.2 Backscatter data for spherical (cranial) phantoms

MC-calculated backscatter factors for cranial phantoms were calculated in Paper V for sphereswith a diameter of 18 cm. The effect of including a layer of bone under the skin thickness (takenas 5 mm) was investigated by calculating the backscatter factors for boneless geometries andfor geometries including bone layers with thicknesses between 2.5 mm and 12.5 mm. Includingbones in the spherical geometry was shown to reduce the backscatter factors by up to 15%,caused by the shielding of low energy backscattered photons by the bone layer. A database,similar to that presented in the previous section, was created for monoenergetic photon beamsbetween 10 keV and 150 keV in a spherical phantom including a 6 mm bone layer belowthe skin. Figure 4.3 shows the resulting backscatter factor data for two field sizes and, forcomparison, the values of Figure 4.1 for cubic homogeneous phantoms are also included; thelower panel illustrates the ratio between the two sets. It is concluded that in a considerablerange of energies, backscatter factors calculated for cubic phantoms are larger than those forspherical phantoms with a bone insert by up to 5% and 10%, for field sizes of 5 cm×5 cm and10 cm×10 cm.

In order to improve the accuracy of skin dose estimations in cranial interventional procedures,backscatter factors calculated for cranial geometries should be implemented, as their differencewith the commonly used data for cubic phantoms are of the same order as the 7% targetedaccuracy.

4.2.2 Mass energy-absorption coefficients

To transfer the air kerma at the phantom entrance surface to water kerma (or kerma in any othermedium), the energy fluence weighted ratio of mass energy-absorption coefficients [µen(k)/ρ]w,air

is required. This was evaluated in Paper II according to Eq. (4.5) using the photon fluence ofthe previous 143 clinical spectra at the water surface (i.e. including both incident primary andbackscattered photons). Numerical values of [µen(k)/ρ]w,air for this set of clinical beams aregiven in Table A2 of the Appendix and vary between 1.02 and 1.12; they are shown in Fig-ure 4.4 for the smallest and largest field sizes. A field size dependence of the order of 4%-6%was found for the highest energies. Due to the magnitude of this coefficient compared to theaimed accuracy of 7%, it is considered a significant correction that should be implemented inskin dose estimations.


Figure 4.3: Monte Carlo calculated backscatter factors, Bair(k), for monoenergetic photons as a functionof the photon energy, k. The factors are given for the indicated field sizes at the surface of a 18 cm spher-ical water phantom containing a 6 mm thick bone layer at a depth of 5 mm. Results for a homogeneouscubic phantom, from Paper II, Benmakhlouf et al. (2011b), are included for comparison. The lower panelillustrates the ratio between the two sets. (From Paper V, Omar et al. 2014).

4.3 Relative dosimetry

The surface kerma or absorbed dose of Eq. (4.3) is most often determined using data for aspecific phantom material and thickness (e.g. a 15 cm×30 cm×30 cm water phantom). Inorder to determine the surface dose in other (non-reference) conditions correction factors forthe phantom material and thickness must be applied to that expression.

A thickness correction factor, kt,Q, for a beam of quality Q was defined in Paper III as

kt,Q =[Bair(Q)]med,t

[Bair(Q)]med,15

(4.8)

where [Bair(Q)]med,t is the backscatter factor for material “med” of thickness t and [Bair(Q)]med,15

is the backscatter factor for the same material and a 15 cm thick phantom. This correction factorcharacterizes the difference in the backscatter of incident photons in the standard 15 cm cubicphantoms and phantoms of arbitrary thickness, both of the same material. Note that the amountof material behind the reference point will determine the amount of backscattered photons andthereby the increase in the air kerma at the surface. Thickness correction factors are to be im-plemented in the estimation of skin doses to paediatric patients, which in some cases are muchthinner than 15 cm (or to patients thicker than the standard 15 cm). Our calculated backscatterfactors, including thickness correction factors, have been implemented in the IAEA recom-mendations Dosimetry in Diagnostic Radiology for Paediatric Patients (Almén et al. 2013).

IAEA TRS-457 includes backscatter data for water, PMMA and ICRU tissue for a reduced


Figure 4.4: Ratios of mass energy-absorption coefficients, water-to-air, for monoenergetic photons at thesurface of a cubic water phantom as a function of the photon energy, k. The solid lines correspond to thesurface spectra for the smallest and largest square field sizes considered in this work; the dashed line cor-responds to incident monoenergetic photons and is independent of field size. (From Paper II, Benmakhloufet al. 2011b).

number of qualities, and increasing the set of data for currently used clinical qualities was oneof the goals of this thesis work. We chose to introduce, as in the case of the thickness correctionfactor, a material correction factor to determine backscatter factors for phantom materials otherthan water (i.e. patient tissue or PMMA phantoms), which is defined as

kmed,Q =[Bair(Q)]med,15

[Bair(Q)]w,15

(4.9)

where [Bair(Q)]med,15 and [Bair(Q)]w,15 are the backscatter factors for 15 cm thick phantoms ofwater and material “med”, respectively.

4.4 Key data for relative dosimetry

4.4.1 Thickness correction factors

Thickness correction factors, defined according to Eq. (4.8) were determined in Paper III forthicknesses ranging between 5 cm and 40 cm and field sizes between 5 cm × 5 cm and 35 cm× 35 cm. Recall that the thickness correction factor converts the backscatter factor from a15 cm thick phantom to that for an arbitrary thickness. Factors were determined for six clinicalbeam qualities that cover most of the spectrum of clinical beam qualities used in interventionalangiography procedures, and the results are shown in Figure 4.5. The thickness correctionfactors were found to be significant for the largest field sizes and HVLs, reaching -12% for


5 cm thick phantoms. Note that the remark in ICRU report 74 (ICRU 2005), "For practicalpurposes in radiology, it is concluded that a phantom thickness of ∼ 8 cm is sufficient to obtaina backscatter factor > 95% of the value with full backscatter for all field sizes and radiationqualities" is confirmed by our results but, as reiterated throughout our work, omitting correctionfactors can only jeopardize the accuracy of dose estimates.

An expression of the form

kt,Q =3∑

i,j=0

ai,j HVLi1 tj (4.10)

where ai,j are fitting parameters for each field size, HVL1 is the first half-value layer, and t is thephantom thickness, was fitted to our data in order to provide an analytical expression that can beused to calculate thickness correction factors for arbitrary phantom thicknesses between 5 cmand 40 cm. Parameters for this expression were given both for water and PMMA phantoms.

4.4.2 Material correction factors

Material correction factors, defined according to Eq. (4.9) were determined in Paper III forPMMA phantoms and for the same field sizes used in the previous section. This correctionfactor, shown in Figure 4.6 as a function of HVL and kV, reaches 8%-10% for the largestfield size and lowest kV. The result of this correction factor should be implemented when QAmeasurements are performed on PMMA phantoms in order to take into account the differentscattering between PMMA and water.


Figure 4.5: Thickness correction factor, kt,Q, for water phantoms as a function of the phantom thicknessfor the indicated clinical beam qualities and 5 cm×5 cm (dashed lines) and 35 cm×35 cm (solid lines) fieldsizes. The curves for each field size correspond to beam qualities with HVL1 ranging between 2.3 and12.4 mm Al; the lowest curve of each set (i.e. the largest corrections) corresponds to the highest HVL1.(From Paper III, Benmakhlouf et al. 2013).

Figure 4.6: Phantom material correction factor, kmed,Q, for PMMA, for the indicated field sizes andclinical beam qualities with HVL1 ranging approximately between 2 mm and 13 mm aluminium. Iso-kVvalues are represented by the thin lines. (From Paper III, Benmakhlouf et al. 2013).

Chapter 5

Changes in the fundamental data ofPENELOPE

The statistics of Monte Carlo calculations characterized by type-A uncertainties can normallybe reduced by increasing the number of simulated particles. It is however of importance toemphasize that MC results can never be more accurate than the accuracy of the fundamentaldata (i.e. cross sections) used in the MC system and of the transport algorithms in the system(in terms of sampling, interface transport, variance reduction techniques, treatment of multiplescattering etc). It is therefore essential to understand the limitations of the MC system used and,whenever possible, to compare MC-calculated data to experimentally determined results and toresults from other MC systems, as to some extent has been done by Vilches et al. (2008, 2009),Faddegon et al. (2008, 2009), Koivunoro et al. (2012) and many others.

All the calculations in this thesis were done with version 2008 of the PENELOPE MC system(Salvat et al. 2008), which will henceforth be referred to as ‘PEN08’. A PENELOPE version2014, to be referred to as ‘PEN14’, has just been released (Salvat 2014) where modificationshave been implemented in its fundamental data; they had been summarized by Salvat (2013).It should be noticed that even if during the course of our work another version of PENELOPEwas released in 2011, for consistency all results presented in Papers I-VI are based on PEN08.In order to investigate the impact of the new data in PEN14 on our MC-results two types ofcalculations were done using the new version: backscatter factors for kilovoltage x-ray beamsand percentage depth-doses for megavoltage photon beams. The main modifications and im-provements will be summarized below and the results of the new calculations presented in thenext chapter.

5.1 Photoelectric effect cross sections

Cross sections for the photoelectric effect in PEN08 were based on a simplified descriptionof the atomic electron states; these were accounted for using the Dirac-Hartree-Fock-Slater(DHFS) model, where each electron is given a net potential from the atomic nucleus (attractive)and from the other electrons (repulsive). The differential cross sections (DCS) for the pho-toeffect in PEN08 were taken from the LLNL Evaluated Photon Data Library (EPDL, Cullenet al. 1997), based on the calculations of Scofield (1973) who used the DHFS approximation

33

34 CHAPTER 5. CHANGES IN THE DATA OF PENELOPE

Figure 5.1: (a) Photoelectric effect (solid lines) and total photon cross sections (dashed lines) for water inthe PENELOPE 2008 and 2014 versions, and (b) values relative to those in PENELOPE 2008. The energyrange, between 1 keV and 100 MeV, is over the interval of interest for radiotherapy and diagnostic andinterventional radiology. The vertical dashed line corresponds to 200 keV, slightly above the upper limit ofthe backscatter calculations in this work.

to describe the atomic states. Pratt et al. (1973) have shown that the difference between thecross sections based on the DHFS model and those based on more advanced models (e.g. thescreened relativistic Hartree-Fock) is a constant factor. This led to the so-called ‘renormalized’cross sections of Hubbell (1982), in wide spread use for many years. Later on, Hubbell andSeltzer (1996) found that DHFS-based data agreed better with new experimental cross sections,

5.2. MASS ENERGY-ABSORPTION COEFFICIENTS 35

and the DHFS model became widely accepted (e.g. by LLNL and NIST). Recent accuratemeasurements made at the German standards laboratory PTB by Büermann et al. (2006) forair, have shown better agreement with the renormalized cross sections, opening a debate stillunresolved. For PEN14 cross sections have been calculated in the renormalized form, expand-ing substantially the original data from Scofield (1973). The effect of these two options, shownin Figure 5.1 for water, is to decrease the DCS for the photoeffect by about 2.5% for photonenergies between 1 keV and 1 MeV. It is however important to recall that the contribution of thephotoeffect to the total DCS for photon interactions is only significant at the lowest energies ofour work, as the global impact of these changes on the total DCS is only 2.5% for photon en-ergies below 100 keV. For higher energies, the contribution of the photoeffect to the total DCSdecreases and so does the difference between the total DCS in the two PENELOPE versions.

5.2 Mass energy-absorption coefficients

Changes in the photoelectric cross sections affect directly the values of the mass energy-ab-sorption coefficients. Recall that these were used in the determination of the energy fluence-weighted ratio [µen/ρ]w,air for kV x-ray clinical spectra, see Eq. (4.5). PEN08 did not include aseparate code for calculating µen/ρ-values, unlike later versions (a code called mutren is part ofthe PENELOPE system since the 2011 version), and for that reason values from the NIST data-base (Hubbell and Seltzer 1996) were used in our calculations; note that NIST data are availableup to 20 MeV. These were expected to be very similar to those in PEN08, as both shared thephotoelectric data from LLNL/EPDL (Cullen et al. 1997) and differences in the treatment ofCompton interactions (impulse approximation in PENELOPE versus Waller-Hartree theory inNIST), important only at low energies for high-Z materials, were not a concern. In addition,although our calculations of output correction factors at 6 MV are not explicitely based on theuse of mass energy-absorption coefficients, they are intrinsically related as the same type of fullMC simulations are performed to derive µen/ρ-values. Therefore, comparing coefficient datafrom the various sources, PEN08, NIST and PEN14, was considered to be of importance andthe code mutren has been used for extracting data from PEN11 (identical to those in PEN08)and PEN14. Note that in dosimetry calculations µen/ρ-ratios are usually the quantity of interest.

Figure 5.2(a) shows ratios of mass energy-absorption coefficients to water from the differentmaterials used in the different chapters of this work (air, carbon and silicon), and Figure 5.2(b)shows the ratios relative to the those in PEN08 (smoothed to avoid a saw-like pattern caused byinterpolation with few decimals); for homogeneity, the plots illustrate the ratio air/water, ratherthan the water/air ratio that would parallel Eq. (4.5). It can be seen that the data in PEN08 and inthe NIST database are, as expected, very close to each other, within about ±0.4%, the averagedifference being negligible. Significant differences exist, however, between PEN08 and PEN14at energies where the photoelectric effect plays a dominant role, below about 100 keV, but notat higher energies where differences are similar to those with the NIST data. The differences forair are the smallest ones, below 1% in the worst case; their role in our kV x-rays calculations istherefore expected not to be of importance. For carbon and silicon the large differences of up toabout±2%, occur only at low photon energies and hence are not expect to modify substantiallyour data for the output correction factors at 6 MV beams.


Figure 5.2: (a) Ratios of mass energy-absorption coefficients med-to-water from the different materialsused in different chapters (air, carbon and silicon) in PENELOPE 2008, the NIST database (Hubbell andSeltzer 1996) and the PENELOPE 2014 version; (b) ratios relative to the data in PENELOPE 2008. Theenergy range, between 1 keV and 100 MeV, is over the interval of interest for radiotherapy and diagnosticand interventional radiology. The vertical dashed line corresponds to 200 keV, slightly above the upper limitof the calculated backscatter and ratios of µen/ρ-values in this work.

5.3. MASS ELECTRONIC STOPPING POWERS 37

5.3 Mass electronic stopping powers

Figure 5.3(a) shows mass electronic stopping powers of electrons for water, calculated withPEN08, PEN14 and given in ICRU report 37 (ICRU 1984b), all for the mean excitation energy(I-value) of 75 eV, and with PEN14 using 78 eV, a new value, determined by Andreo et al.(2013), to be implemented in a forthcoming ICRU report on dosimetry data. Figure 5.3(b)shows the values relative to the those in PEN08. The ICRU-37 data have been extended from10 keV to 1 keV using a modified version of the code STAR/ESTAR (Berger 1993) originallydeveloped at the NIST for this dataset. Note that the mass electronic stopping power is the samequantity as the ‘mass collision stopping power’, but a change in terminology was recommendedby ICRU-85a (ICRU 2011).

It can be seen in Figure 5.3(b) that the difference between PEN08 and PEN14 using their de-fault Iwater value of 75 eV is about ±1% approximately below 5 keV, agreeing perfectly abovethis energy. PEN08 stopping powers also agree very well with those in ICRU-37, and onlyminor differences can be observed below the lower energy limit of 10 keV for which valuesare tabulated and that we have extended using ESTAR. It should be noted that both versionsof PENELOPE include shell corrections, important at low energies, in an approximate mannerthrough the electron shell energies entering in the GOS; these are not taken into account in theICRU-37 values. For PEN14 using Iwater = 78 eV (the value to be recommended in a nearfuture), where the largest differences occur, the discrepancies observed for electron energiesbelow ∼ 5 keV are up to 2%, whereas the discrepancy for energies above this limit variesbetween 0.5%–1% up to about 1 MeV, from where the two datasets converge.

The oscillating pattern of the PEN14 curves in the figure results from modifications in thetreatment of distant inelastic interactions with inner-shell electrons. In PEN08 the differentialcross sections for inelastic collisions were based on the plane-wave first Born approximation(PWBA) for the entire energy range, which neglects both distortions on the incoming projectilewave function caused by the electrostatic field of the target and exchange effects in the case ofelectrons (Salvat 2014). The use of the PWBA is only reliable for electron energies larger than∼ 30 times the shell ionization energy of the inner shell, corresponding to about 15 keV in thecase of water. PEN14 has modified the treatment of inelastic interactions by using the relativ-istic distorted wave Born approximation (DWBA), which accounts for distortion and exchangeeffects (Bote and Salvat 2008) for the lowest energies (up to around 20 times the ionization en-ergy) whereas PWBA calculations are used for higher energies. The DWBA introduces changesin the DCS compared to the PWBA at energies comparable to the resonance energy (a parameterincluded in the GOS model of Liljequist (1983)) and its multiples, which in the case of water is1.2 keV (in the figure the peaks at 1.35 keV and 2.58 keV correspond to the resonance energyand its multiples for the inner delta-oscillator.

The effect of increasing the Iwater-value from 75 eV to 78 eV can also be seen in Figure 5.3to cause a reduction of the mass electronic stopping power by about 1% at the lowest energies.These changes in the electronic stopping powers for water (and other media) are not expectedto have a significant impact on the calculations of this work as most of the modifications affectonly to electron energies below the MC cut-off energy used (10 keV).


Figure 5.3: (a) Mass electronic stopping powers for water in PENELOPE 2008, PENELOPE 2014 and inICRU report 37 based on the Iwater value of 75 eV, and in PENELOPE 2014 using 78 eV; (b) ratios relativeto the data in PENELOPE 2008. The ICRU-37 data have been extended from 10 keV to 1 keV (dashed curvein panel (b)) using the code ESTAR (Berger 1993). The energy range, between 1 keV and 100 MeV, is overthe interval of interest for radiotherapy and diagnostic and interventional radiology. The vertical dashedline corresponds to 10 keV, used as cut-off energy for electron transport in our Monte Carlo calculations.

Chapter 6

Additional Monte Carlo calculations

In order to verify the impact of the changes in fundamental data implemented in the most recentversion of PENELOPE (Salvat 2014) on our results obtained with the 2008 version, a set of sim-ulations has been made of some representative cases in the kV x-rays and MV photons energyrange and materials. These are discussed in the following sections, in addition to calculationsof photon and electron spectra inside the various detectors used throughout this work.

6.1 Backscatter factors for kilovoltage x-ray beams

MC-calculated backscatter factors calculated with PEN08 and PEN14 are shown in Figure 6.1.These were determined for 10 cm×10 cm beams at the surface of a cubic phantom having 15 cmheight and 30 cm width, for monoenergetic photon beams and for a set of x-ray clinical spectragenerated at 50 kV, 90 kV and 150 kV using different filtrations. The plots include the ratioPEN14/PEN08 with the scales shown in the right ordinate axis.

In the case of monoenergetic photons, Figure 6.1(a), which form the database used to generatebackscatter factors for kV spectra, a maximum difference of 0.9% for energies around 30 keVcan be observed; for the entire database the root mean square difference (RMSD) was 0.48%. Asis wellknown, a constraint of the RMSD is to give the same weight to the square of all the values,including outlayers, that then become ‘overweighted’, and for this reason the mean absolutedifference (MAD) is often used as an indication of the scatter of results. In this case the MADwas 0.43%, i.e. not too different. For kV x-rays clinical spectra, Figure 6.1(b), the differenceswere larger for the lowest energy and decreased when the kV was increased, in consistencywith the trend of the monoenergetic data. In this case the RMSDs were 0.75% (50 kV), 0.65%(90 kV) and 0.55% (150 kV), the MADs being identical. None of these differences is consideredto be of significance for our calculated key data in the diagnostic and interventional radiologyrange of energies.

The larger backscatter factors obtained with PEN14 can be explained in terms of the decreasedcross sections for the photoelectric effect for energies between 1 keV and 100 keV, shown inFigure 5.1. The lower cross section reduces the absorption of photons and thereby allows morephotons to scatter back to the surface, hence increasing the backscatter factors. Observe that,as the photoeffect contribution to the total cross section in water is extremely small for energiesabove 100 keV, the effect of using PEN14 can only be seen for energies below this limit, i.e. in

39

40 CHAPTER 6. ADDITIONAL MONTE CARLO CALCULATIONS

the kilovoltage range.

Figure 6.1: Backscatter factors for 10 cm×10 cm fields at the entrance surface of a 15 cm thick waterphantom for (a) monoenergetic photons as a function of the photon energy, k, and (b) kV x-rays clinicalspectra as a function of the beam quality, Q, expressed in terms of the HVL in aluminium, calculated withPENELOPE versions 2008 and 2014. The solid lines correspond to the ratios PEN14/PEN08 for each dataset(right ordinate axis). The symbols in the lower panel correspond to 50 kV (squares), 90 kV (triangles) and150 kV (circles); filled symbols are for PEN14, open symbols for PEN08.

6.2. ABSORBED DOSE IN MEGAVOLTAGE PHOTON BEAMS 41

6.2 Absorbed dose in megavoltage photon beams

Central axis depth-dose distributions in water were calculated for a 10 cm diameter divergentbeam (SSD = 100 cm) of 2 MeV monoenergetic photons. The distributions were calculatedwith PEN08 using the Iwater value of 75 eV and with PEN14 using 75 eV and 78 eV. TheMC results for the different options are shown in Figure 6.2, which also illustrates the depthdependence of the ratio of absorbed doses (right ordinate). Extremely small discrepancies werefound between the different calculations, which were well within the type-A uncertainties of thecalculations, approximately of 0.2% − 0.3%. The RMSDs were around 0.06% and the MADs0.05%. The ratio between the absorbed dose at the depths of 20 cm and 10 cm, D20/D10, inthe two calculations with PEN14 differed also by ∼ 0.2% from the value obtained with PEN08(0.567); it should be noticed that this quotient does not coincide with the beam quality indexTPR20,10, which corresponds to a constant SDD whereas the D-ratios used correspond to aconstant SSD configuration.

Figure 6.2: Central axis depth-dose distributions in water, in Gy per incident particle, calculated fora 10 cm diameter divergent beam (SSD = 100 cm) of 2 MeV monoenergetic photons. The distributionscorrespond to PENELOPE 2008 using Iwater = 75 eV and to PENELOPE 2014 with 75 eV and 78 eV. Theratios to PENELOPE 2008 are also included (right ordinate axis).

Of greater relevance for this work are absorbed doses in different materials and their ratio to thecorresponding dose in water. For this comparison a simplified cylindrical configuration was alsoused, much faster from a computation time point of view to achieve a given uncertainty; notethat this type of geometry has been used in the small field investigations of multiple authors(c.f. Paskalev et al. 2003, Scott et al. 2012, Fenwick et al. 2013). A scoring cylindricalvolume having a radius of 0.15 cm and a thickness of 0.30 cm was inserted in a cylindricalwater phantom of 15 cm radius and 30 cm height and irradiated with a 6 MV 10 cm photoncircular beam at SSD = 100 cm; the spectrum was from Mohan et al. (1985), taken from theEGSnrc package. The inserts were made of water (homogeneous case), carbon and silicon, and


they were situated at a depth of 10 cm. Calculations were done using PEN08 and PEN14 withIwater = 75 eV and PEN14 using 78 eV, and the results are shown in Table 6.1. As can be seen,differences between the different options are always of the order of 0.1%, even between the twoPEN14 cases with different Iwater-values. Note that the ratiosDmed/Dw can be considered goodestimates of the product smed,w pdet (stopping-power ratio times perturbation correction) for this6 MV photon spectrum.

Table 6.1: Monte Carlo calculated absorbed dose, in Gy per incident particle, in small inserts (∅ 0.3 cm,t = 0.3 cm) of different materials at a depth of 10 cm in a water phantom, using a 10 cm circular 6 MVphoton beam at SSD = 100 cm (spectrum from Mohan et al. 1985). The simulations were made withPENELOPE 2008 and 2014 using Iwater values of 75 eV and 78 eV.

PENELOPE Iwater insert Dmed uA ratioversion (eV) medium (10−14 Gy/i.p.) (%) Dmed/Dw PEN14/PEN08PEN08 75 water 6.9204 0.10 – –

silicon 5.9817 0.11 0.864 –carbon 6.0864 0.11 0.879 –

PEN14 75 water 6.9228 0.09 – 1.000silicon 5.9896 0.09 0.865 1.001carbon 6.0939 0.09 0.880 1.001

PEN14 78 water 6.9211 0.09 – 1.000silicon 5.9855 0.10 0.865 1.001carbon 6.0907 0.09 0.880 1.001

6.3 Spectral distributions in small-field detectors in 6 MVbeams

As shown in Figure 3.1, the dependence with field size of output correction factors kfclin,frefQclin,Qref

vary significantly with the detector type; for example, up to a 9% variation could be observedfor the silicon diodes included in Figure 3.1(c). These differences were explained in terms ofthree major effects: lack of LCPE, over-response of high-Z detectors in broad beams and partialvolume averaging. Each of these effects contributes to the output correction factor dependingon the detector dimension, material and beam size.

Differences in detector response can be investigated comparing the spectral distributions ofparticles crossing the active material of the detector or absorbed in it. Spectral distributions weretherefore calculated for the reference field and the smallest clinical field (i.e. 10 cm×10 cm and0.5 cm×0.5 cm) of 6 MV linac beams. The calculations were performed with the user-codePenEasy (Sempau et al. 2011), based on PEN08, and photon and electron spectra were scoredin all detectors included in Figure 3.1. Table 6.2 gives the mean photon and electron energy ofthe calculated spectra, where the expected increase for small fields can be seen due to the lackof low energy scattered particles, which are present in the broad beam case.

6.3. SPECTRAL DISTRIBUTIONS INSIDE DETECTORS 43

Table 6.2: Monte Carlo-calculated fluence-weighted mean energies of photon (k) and electron (E) spec-tra in a small volume of water and inside various detectors at 10 cm depth, for the nominal field sizes of10 cm×10 cm and 0.5 cm×0.5 cm of a Varian Clinac R© iX 6 MV clinical accelerator. The phantom size is30 cm×30 cm×30 cm.

Photon k (MeV) Electron E (MeV)Detector Type 10 ×10 0.5×0.5 10×10 0.5×0.5Water — 1.287 1.955 0.952 1.099PTW T31016 Air ionization chamber 1.275 1.986 0.948 1.116PTW T31018 Liquid ionization chamber 1.290 1.979 0.960 1.107PTW T60003 Natural diamond detector 1.276 1.980 0.952 1.101PTW T60016 Shielded silicon diode 1.295 1.957 0.882 0.983PTW T60017 Unshielded silicon diode 1.275 1.976 0.894 1.024PTW T60018 Unshielded silicon diode 1.276 1.973 0.891 1.015PTW T60019 Synthetic diamond detector 1.272 1.977 0.946 1.093IBA CC01 Air ionization chamber 1.277 1.978 0.961 1.125IBA PFD Shielded silicon diode 1.366 1.947 0.898 1.003IBA EFD Unshielded silicon diode 1.267 1.975 0.893 1.022IBA SFD Unshielded silicon diode 1.312 1.991 0.900 1.030

6.3.1 Photon fluence spectra

A priori, the photon fluence spectrum (Φk) scored in the active volume of the detectors is ex-pected to be identical or very similar to that in a small volume of water at the same positionexcept for potential photoabsorption or photogeneration in the detector structures surroundingits active volume.

Photon spectra for 10 cm×10 cm and 0.5 cm×0.5 cm field sizes are shown in Figures 6.3 – 6.5for eleven detectors obtained with our MC calculations. It can be seen that, compared to water,the spectra in the detectors are practically identical except for some specific devices. Smalldifferences were found for the three ionization chambers (Figure 6.3(a-c)) and the two diamonddetectors (Figure 6.4(a-b)). The effect of the shielding in the two shielded diodes can be clearlyseen in Figure 6.4(c-d); approximately 50% of the photons below 100 keV and 300 keV areshielded in the PTW T60016 and IBA PFD diodes, respectively. It can also be observed that theshielding of the IBA PFD diode reduces the low energy photon fluence more than the shieldingof the PTW T60016 due to its heavier material. A small shielding effect can also be observedin the two unshielded diodes (Figure 6.5(a-b)) PTW T60017 and T60018 that is not present inthe unshielded IBA EFD and SFD diodes (Figure 6.5(c-d)). It is worth commenting that thesedetectors are called ’unshielded’ due to the lack of thick dense materials surrounding the activevolume; however, thin layers of materials not intended to have a significant shielding effect canproduce certain filtration, as shown in the figure.

Two peaks can be observed in the photon spectra for all the shielded and unshielded silicondiodes at 20 keV–30 keV and 60 keV–70 keV. The first peak is present in all silicon diodesand for the broad beam the fluence at this energy is approximately 20 times larger than inwater for the PTW T60017 and PTW T60018 detectors (although not clearly seen in the figure).This is most likely caused by interactions of low-energy scattered photons of the broad beamin the layers adjacent to the active silicon, generating characteristic photons through atomic


relaxation (for confidentiality, material details are omitted). Recall that the DCS for photoeffectis largest when the photon energy is just above the shell energies and therefore the probability ofphotoabsorption is largest for low-energy photons (i.e. scattered photons in broad beams). Thesecond peak is the largest, and is observed only for the IBA PFD shielded diode; the fluenceat this energy is about 90 times larger than in water for the clinical field of 0.5 cm×0.5 cm.The energy of the peak coincides with the energy of characteristic photons from the shieldingmaterial.

The low-energy peaks in the photon fluence of silicon diodes will be completely absorbed dueto the large mass energy-absorption coefficients in silicon compared to water, thereby causingan over-estimation of the absorbed dose. The effect of these low-energy characteristic peaks inthe photon fluence of shielded diodes is included in our calculated output correction factors, buthad not been separated from the other components (i.e. lack of LCPE etc). For example, forthe smallest field size the peak in the photon spectrum of the IBA PFD shielded diode will yieldan over-estimation of the dose for that field size, which results in a lower than unity componentin the output correction factor; this could explain the peculiar shape of the output correctionfactors for this detector at the smallest field size, see Figure 3.1(c).

6.3.2 Electron fluence spectra

Electron fluence (ΦE) spectra scored in the active volume of the detector include both electronsgenerated outside the detector and those generated by photon interactions in the detector mater-ial. When charged particle equilibrium exists, the electron spectrum in a small volume of watershould be practically identical to the electron spectrum in the active region of a detector. Thisis achieved for large field sizes and small cavity materials that are not too different from waterin terms of their composition and density.

In the various electron spectra shown in Figure 6.6 it can be seen that CPE is achieved in thePTW T31016 (air) and PTW T31018 (liquid) ionization chambers (a), and in the PTW T60003(natural) and PTW T60019 (synthetic) diamonds (b). The electron spectra are very similar forwater and diamond in both field sizes, meaning that CPE exists in the two. Large differences areobserved however, between detector and water spectra for all shielded and unshielded silicondiodes and both field sizes (Figure 6.6(c-d)). This is due to the large difference between theelectron ranges in silicon and in water, e.g. for 2.5 MeV electrons, RCSDA(Si) = 0.65 cm andRCSDA(water) = 1.25 cm, i.e. a factor of two. The higher electron spectra in silicon will leadto more energy deposition in silicon diodes than in water. For all materials except diamond, thedifferences between the electron fluence in water and in the detector increase with decreasingfield size, which is expected as the degree of lateral charged particle equilibrium decreases withdecreasing field size.

The differences in spectra can be related to the fluence perturbation correction factors if Bragg-Gray cavity theory is to be used. As inferred from our output correction factors, some of theperturbation effects are so large that the basic principle underlying a ‘quasi Bragg-Gray de-tector’ (small fluence difference between the detector and the medium, corrected with smalland independent perturbation factors) is violated. MC calculations provide an ‘approximatelytrue’ correction independent of this assumption, an analysis left for future work. The quotesrefer to the usual approximation made in MC calculations, neglecting detector-to-detector dif-ferences (in detectors of the same kind) and limitations in their practical use (e.g. recombination


effects).


Figure 6.3: Monte Carlo calculated photon fluence spectra (Φk) scored in the active volume of ionizationchambers at 10 cm depth, as a function of the energy, for Varian Clinac R© iX 6 MV photon beams: (a) PTWT31018 liquid ion chamber, (b) PTW T31016 air ion chamber, and (c) IBA CC01 air ion chamber. The solidlines in each figure correspond to the detector spectra and the dashed lines to spectra at the same depth ina small volume of water. The large spectrum in each figure is for a 10 cm×10 cm field and the small for0.5 cm×0.5 cm.


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Chapter 7

Summary and conclusions

The purpose of this thesis has been to carry out investigations on the key data used in thedosimetry framework of megavoltage radiotherapy and diagnostic and interventional radiologykV x-ray beams. The aim has been to achieve a high level of accuracy in the determination ofthe absorbed dose and for that purpose comprehensive Monte Carlo calculations and a numberof experimental determinations have been made. It has been argued that correction factorslarger than the targeted clinical accuracy should be considered significant, and improving keydata decreases their uncertainty; we have emphasized that absorbed dose should be determinedas accurately as possible for each modality.

For radiotherapy beams, the starting point of our work (Paper I) was to evaluate the impactof recent research on reference dosimetry determined through the widely used dosimetry Codeof Practice IAEA TRS-398; this task was undertaken ten years after the publication of thisdosimetry protocol. An extensive analysis of new MC-data published during these years re-vealed significant discrepancies with some of the correction factors used in TRS-398, around1.5% for 60Co γ-ray beams, the most frequent reference beam quality to which the dosimetryof all other beams (photons, electrons, protons and heavier charged particles) is referred to.The changed posed by this difference was questioned on the light of the so far available exper-imental evidence, mostly at the level of primary standards dosimetry laboratories. It has laterbeen demonstrated that adopting the new MC-data would not be consistent with the data in cur-rent metrological standards and throughout the entire dosimetry chain (Andreo et al. 2013). InPaper I it was also found that the new MC calculations of certain correction factors (e.g. wallperturbation corrections for electrons and displacement corrections for photons) yielded resultsscattered by about 1%-2%, an unexpected difference as cross section data in the MC codes usedwill not yield discrepancies of this magnitude (as discussed in Chapter 6).

Output correction factors, to be implemented in the relative dosimetry of small megavoltagephoton beams, were determined in this work. This factor was introduced in the internationalformalism published by Alfonso et al. (2008), and have since been determined by different au-thors for several detectors and beam types. The correction factors in our work were determinedfor eleven detectors in 6 MV linac beams (Paper IV) and fifteen detectors in LGK PerfexionTM

60Co beams (Paper VI). Differences in the output correction factors were found to be up to 20%between the various detectors for the smallest field size investigated in the 6 MV beams and evenlarger differences were found for the LGK beams as detectors with large active volume wereincluded in that study. These results emphasize the attention required in choosing an adequate

51

52 CHAPTER 7. SUMMARY AND CONCLUSIONS

detector for relative measurements in small photon beams. The results of our work included inPaper IV were compared to the results by others, finding good agreement in most cases. Theresults obtained for the PTW T60019 micro-Diamond detector and the PTW T31018 microLion(a liquid ionization chamber) have shown these detectors to be near ‘correction free’ detectorsfor the relative dosimetry of small beams. These findings apply to both 6 MV linac beams andLGK PerfexionTM beams. Our work, and that of others, makes it possible for organizations likethe IAEA or the AAPM to recommend data for the relative dosimetry of small photon beams.To complement our research on these detectors, photon and electron fluence spectra inside theiractive volume have been calculated that enhance our understanding of their response in smallphoton beams.

Some challenges in the dosimetry of small photon beams still remain to be addressed and re-quire more research in the field. The beam size definition and its quality specification are notcompletely settled. There are also other issues that need to be clarified in order to make avail-able consistent data for clinically relevant conditions. These relate mainly to the effect of thecollimation device on output correction factors and the influence of the detector position (i.e.SAD or SSD-setup and detector depth of 5 cm or 10 cm) as discussed e.g. by Crop et al.(2009), Francescon et al. (2014) and others. Output correction factor data published so farhave been determined for different settings, making comparisons difficult; this could be thereason for some of the discrepancies between data from different references. The effect of non-square field shapes (circular or rectangular), remains also to be investigated further, althoughsome work has been done in this area. As already emphasized, experimental verifications ofMC-calculated data should be conducted for all detectors with in order to benchmark the MCcalculations.

Surface (skin) dose estimations for diagnostic and interventional radiology x-ray beams havebeen investigated. Backscatter factors were determined in Papers II, III and V for monoener-getic photon beams between 5 keV and 150 keV, and a database created and used to derive thesefactors for clinical spectra. Different geometries were considered in the calculation of the datato take the large differences between spherical and cubic phantoms into account. In addition,backscatter factors were calculated for different phantom thicknesses to account for the some-times large differences in backscatter in very thin phantoms (5 cm) and thick phantoms (40 cm).This resulted in the introduction of a thickness correction factor and a material correction factorin the formulation for the determination of the reference entrance surface kerma (or dose) thatprovides backscatter factors for non-reference thicknesses and materials. Our work has alsoprovided backscatter factors applicable to multiple clinical conditions (in terms of beam qual-ity, field size, and patient thickness) and will increase the accuracy in skin dose estimations.The backscatter factors calculated in our work, including thickness correction factors, havebeen implemented in the IAEA recommendations for the dosimetry in diagnostic radiology forpaediatric patients (Almén et al. 2013).

Most of the data presented in this thesis have been based on MC calculations using the 2008version of the PENELOPE system. Its differential cross sections have been updated in a 2014version where, in relation with our calculations, changes have been made for the photoeffectDCS and stopping power data for water. Increasing the mean excitation energy (the I-value)from 75 eV to 78 eV for water, as expected in a forthcoming ICRU report, will further affectboth the differential cross section for inelastic scattering and the stopping power for water.New calculations have been made showing that the changes in the cross section data in thenew PENELOPE version and the adoption of a new I-value for water may affect some of our

53

calculated backscatter factors by at most 1%, whereas output correction factors, based on ratiosof absorbed dose, remain unchanged.

To conclude, the work in this thesis has provided new key data to be implemented in referenceand relative dosimetry of radiotherapy and diagnostic and interventional radiology x-ray beams.The data will contribute to increasing the accuracy of the dosimetry of these beams and may beimplemented in new dosimetry protocols for the reference and/or relative dosimetry of broadand small radiotherapy beams and in radiological dose determinations.

54 CHAPTER 7. SUMMARY AND CONCLUSIONS

Chapter 8

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Appendices

63

65

Table A1: Monte Carlo calculated backscatter factors,Bair(E), and ratios of mass-energy absorption coef-ficients water-to-air, [µen(E)/ρ]w,air, of monoenergetic photons with energies between 5 keV and 150 keVfor square field sizes (in cm) at the entrance surface of a 15 cm×30 cm×30 cm water phantom. (FromBenmakhlouf et al. 2011b).

Bair(E) [µen(E)/ρ]w,air

Energy 5×5 10×10 20×20 25×25 35×35 5×5 10×10 20×20 25×25 35×35(keV)5 1.001 1.001 1.001 1.001 1.001 1.066 1.066 1.066 1.066 1.06610 1.010 1.009 1.009 1.010 1.010 1.043 1.043 1.043 1.043 1.04315 1.038 1.039 1.038 1.039 1.039 1.030 1.030 1.030 1.030 1.03020 1.091 1.096 1.096 1.096 1.095 1.021 1.021 1.021 1.021 1.02125 1.156 1.174 1.177 1.178 1.178 1.016 1.016 1.016 1.016 1.01630 1.214 1.261 1.277 1.278 1.279 1.013 1.013 1.013 1.013 1.01335 1.261 1.342 1.379 1.384 1.384 1.013 1.013 1.013 1.013 1.01340 1.292 1.403 1.469 1.480 1.484 1.016 1.016 1.016 1.016 1.01645 1.311 1.447 1.543 1.558 1.568 1.021 1.020 1.020 1.020 1.02050 1.318 1.474 1.595 1.617 1.631 1.028 1.027 1.026 1.026 1.02655 1.317 1.486 1.625 1.652 1.675 1.036 1.034 1.033 1.033 1.03360 1.308 1.481 1.633 1.666 1.692 1.044 1.042 1.040 1.040 1.04065 1.294 1.466 1.625 1.662 1.692 1.052 1.050 1.048 1.047 1.04770 1.281 1.451 1.616 1.653 1.686 1.060 1.057 1.054 1.054 1.05375 1.268 1.434 1.600 1.639 1.676 1.067 1.063 1.061 1.060 1.05980 1.254 1.414 1.576 1.617 1.656 1.073 1.070 1.067 1.066 1.06585 1.239 1.392 1.548 1.590 1.627 1.080 1.076 1.073 1.072 1.07190 1.226 1.372 1.524 1.566 1.606 1.085 1.081 1.078 1.077 1.07695 1.214 1.355 1.503 1.542 1.583 1.089 1.085 1.082 1.081 1.080100 1.204 1.338 1.479 1.519 1.558 1.090 1.087 1.084 1.083 1.082105 1.195 1.324 1.461 1.498 1.537 1.092 1.089 1.086 1.085 1.084110 1.186 1.310 1.443 1.479 1.519 1.093 1.091 1.088 1.087 1.086115 1.178 1.297 1.425 1.458 1.499 1.095 1.093 1.090 1.089 1.088120 1.170 1.285 1.408 1.438 1.480 1.097 1.095 1.092 1.091 1.090125 1.163 1.273 1.392 1.422 1.463 1.098 1.096 1.094 1.093 1.092130 1.156 1.261 1.378 1.406 1.447 1.100 1.098 1.096 1.095 1.094135 1.150 1.251 1.364 1.393 1.433 1.102 1.100 1.098 1.097 1.096140 1.145 1.243 1.352 1.380 1.420 1.103 1.101 1.099 1.099 1.098145 1.140 1.235 1.341 1.369 1.408 1.104 1.103 1.100 1.100 1.099150 1.136 1.229 1.332 1.358 1.396 1.105 1.104 1.102 1.101 1.100

66Ta

ble

A2:

Bac

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air

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ratio

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3.1

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2.5

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1.31

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1.01

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4.1

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4.1

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1.39

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1.49

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1.51

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cont

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next

page

69

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3.1

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10

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20

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25

35×

35

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trat

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1.38

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1.52

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1.59

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key data for the reference and relative dosimetry of ...792325/fulltext03.pdf · radiotherapy and...

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