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

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Key Data for the Reference and Relative

Dosimetry of Radiotherapy and

Diagnostic and Interventional Radiology Beams

Hamza Benmakhlouf

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Cover image:

Examples of detailed detector geometries in the Monte Carlo calculations of this work, built with 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 2015 ISBN 978-91-7649-111-9

Printed in Sweden by Publit Sweden AB, Stockholm 2015 Distributor: Department of Physics, Stockholm University

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Key Data for the Reference and Relative Dosimetry of

Radiotherapy and Diagnostic and Interventional Radiology Beams

Hamza Benmakhlouf

Doctoral thesis submitted to the Department of Physics at Stockholm University

Supervisor Professor Pedro Andreo, Stockholm University

Co-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 University

Committee member Professor Anders Ahnesjö, Uppsala University

Committee member Associate Professor Åsa Carlsson-Tedgren, Linköping University

and Karolinska University Hospital, Stockholm

Committee member Associate Professor Anne Thilander-Klang, University of Gothenburg

and Sahlgrenska University Hospital, Gothenburg

Committee member Associate Professor Alejandro Sanchez-Crespo, Stockholm University

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Abstract

Accurate dosimetry is a fundamental requirement for the safe and efficient use of radiation in medical applications. International Codes of Practice, such as IAEA TRS-398 (2000) for radiotherapy 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 radiotherapy small 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 safety and treatment efficiency.

The aim of this thesis is to investigate and determine key data for the reference and relative dosimetry 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 and a number of experimental determinations have also been made. A review of the key data for radiotherapy beams published after the release of IAEA TRS-398 was conducted, and in some cases the considerable differences found were questioned under the criterion of data consistency throughout the dosimetry chain (from standards laboratories to the user). A modified concept of output factor, defined in a new international formalism for the dosimetry of small photon beams, requires corrections to dosimeter readings for the dose determination in small beams

used clinically. In this work, output correction factors were determined, for Varian Clinac R

6 MV photon beams and Leksell Gamma Knife R _PerfexionTM 60_{Co γ-ray beams, for a large}

number 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 Carlo with 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. A database of these quantities was created for a broad range of monoenergetic photon beams and computer codes developed to convolve the data with clinical spectra, thus enabling the determination 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 inom strålterapi och röntgendiagnostik är en korrekt bestämning av stråldosen. De internationella stråldosprotokollen IAEA TRS-398 samt TRS-457 beskriver metoden för referens- och relat-ivdosimetri, samt tillhandahåller data som krävs för att implementera protokollen. Dock har senare tids forskning och utveckling fastslagit att nödvändig data saknas för vissa stråltera-peutiska samt röntgendiagnostiska tillämpningar. Bristen på sådan data kan både innebära en patientrisk 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 Carlo koden PENELOPE använts, i vissa fall tillsammans med experimentella metoder. Arbetet in-leds med att utvärdera nyckeldata för referensdosimetri vid strålterapi, som publicerats upp till tio år efter publiceringen av IAEA TRS-398 protokollet. Flera publikationer tyder på att en del av den data som ges i protokollet bör ändras. Dock är en sådan förändring problematisk då den skulle påverka hela den väletablerade dosimetrikedjan. Korrektionsfaktorer som krävs för att 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 för

smala60Co fotonstrålar från en Leksell Gammakniv. Korrektionsfaktorerna har beräknats för

ett antal detektorer, luftjonkammare, diamantdetektorer samt kiseldioder, potentiellt användbara för 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 beräkna avgörande faktorer och koefficienter för godtyckliga rötngenstrålar av olika kvaliteter.

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

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List of Papers

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

I. Benmakhlouf H and Andreo P 2011 Ten years after: Impact of recent research in photon and 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 and mass 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 and material 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 small field detectors in 6 MV radiation therapy photon beams: A PENELOPE Monte Carlo study Med. Phys. 41 041711 1-12

V. Omar A, Benmakhlouf H, Marteinsdottir M, Bujila R, Nowik P and Andreo P 2014 Monte 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 and experimentally determined output correction factors for small field detectors in Leksell Gamma 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 kfclin

Q 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 kfclin

Q

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 small

radiation therapy photon beams. SSM Report 2014:26 (Stockholm: Swedish Radiation

Safety Authority)

vi. Benmaklouf H, Sempau J and Andreo P 2014 Monte Carlo calculated output correction factors 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 dede-tectors 17thInternational Leksell Gamma

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Acknowledgements

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

I am indebted to Associate Professor Annette Fransson for giving me the opportunity to start with 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 Giovanna Gagliardi for your continuous encouragement, support and advice.

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

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

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

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Quantities and symbols

Roman letter symbols

B backscatter factor in kV x-ray beams

BQ,air air-determined backscatter factor from a phantom at the beam quality Q

D absorbed dose

Dmed absorbed dose to a medium ‘med’

Dw absorbed dose to water

¯

Ddet mean absorbed dose to the sensitive material of a detector

Dfclin

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

Dfmsr

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

Dfref

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

E kinetic energy of charged particles

¯

E mean energy of a charged particle spectrum

FGS Goudsmidt-Saunderson angular distribution

fclin clinical field

fmsr 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 charged

particles by photons that is subsequently lost on average in radiative processes as the charged particles slow to rest in the material (ICRU 2011). Related to the radiation yield, Y (E)

HVL half-value layer of a kV x-ray spectrum

HVL1, HVL2 first and second half-value layers

h 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

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x QUANTITIES AND SYMBOLS

Kcol collision kerma

Kair,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 phantom

kV kilovoltage, for x-rays spectra produced by electrons with energies in the keV

range (x-ray tube potential)

k photon energy

¯

k mean energy of a photon spectrum

kmax maximum energy of a photon spectrum

ki generic factors to correct the departure from laboratory conditions to hospital

conditions

kP detector correction factor for pressure

kT detector correction factor for temperature

kpol detector correction factor for polarity effects

ks detector correction factor for recombination or lack of saturation

kt phantom thickness correction factor

kmed phantom material correction factor

kQ,Q0 beam quality correction factor

kfmsr,fref

Qmsr,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 the

msrfield of quality Qmsr

kfclin,fmsr

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

Mlab detector reading at the laboratory

Mhosp detector reading at the hospital

Mair,Q detector reading in air, corrected for influence quantities, in a beam of

qual-ity Q

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

in a beam of quality Q

Mfclin

Qclin detector reading in the clinical field fclin, in a beam of quality Qclin, corrected

for influence quantities

Mfmsr

Qmsr as above for the field fmsrand beam quality Qmsr

Mfref

Qref 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 Q

ND,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 cm

pdet,Q overall perturbation correction factor for a detector at radiation quality Q

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xi

pcav electron fluence perturbation correction factor

pcel perturbation correction factor for the central electrode of an ionization

cham-ber

pdis displacement or replacement perturbation correction factor

pwall perturbation correction factor for the lack of equivalence to water of the

ma-terial of an ionization chamber wall

Q radiation beam quality

Q0 reference radiation beam quality

Qfield radiation beam quality of a specific field (ref, msr or clin)

RCSDA continuous slowing down (CSDA) range of charged particles

R50 half-value depth (or range) of an electron beam

rLEE 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 power

Srad/ρ mass radiative stopping power

Srad(∆b)/ρ mass restricted radiative stopping power

Stot/ρ mass total stopping power

SDD source-to-detector distance

SSD source-to-phantom surface distance

smed1,med2 Spencer-Attix mass restricted stopping-power ratio medium1/medium2,

aver-aged over the charged particle spectrum

T temperature in◦ C

TPR20,10 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 energy

UK K-edge energy (electron binding energy of the K-shell)

uA Type-A standard uncertainty

uB Type-B standard uncertainty

uc 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 Q

WCC energy cut-off between soft and hard inelastic collisions

WCR energy cut-off between soft and hard radiative collisions

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

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xii QUANTITIES AND SYMBOLS

zmax depth of maximum dose

zref reference depth for beam calibration

Greek letter symbols

∆ charged-particle energy-loss cut-off

∆b energy-loss cut-off for bremsstrahlung

MC efficiency of a Monte Carlo calculation

µen/ρ photon mass energy-absorption coefficient

µtr/ρ photon mass energy-transfer coefficient

[µen/ρ]med1,med2 ratio of mass energy-absorption coefficients, medium1/medium2, averaged

over a photon spectrum h

(µen/ρ)_Q

ip+b

med,air ratio of mass energy-absorption coefficients, medium/air, averaged over a

photon spectrum of quality Q at the phantom surface (primary incident beam plus backscattered radiation)

Q

i

product of i factors

ρ mass density

ρe(r) radial distribution of the atomic electron density

σ microscopic cross section (cm2₎

σannih cross section for in-flight positron annihilation

σbrem bremsstrahlung cross section of charged particles

σelast elastic scattering cross section of charged particles

σinel inelastic scattering cross section of charged particles

Φ particle fluence

ΦE electron fluence differential in energy (electron energy spectrum)

Φk photon fluence differential in energy (photon energy spectrum)

Φp_k primary (incident) photon fluence

Φp+b_k total (primary plus backscattered) photon fluence

Ψ photon energy fluence

Ψk photon energy fluence differential in energy (energy fluence spectrum)

Ωfclin,fmsr

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

Ωfclin,fref

Qclin,Qref field output factor for a clinical beam relative to the reference field

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Acronyms and abbreviations

AAPM American Association of Physicists in Medicine

ABS Acrylonitrile butadiene styrene (water-equivalent plastic)

CHT Condensed history technique

CPE Charged particle equilibrium

DCS Differential cross section

DICOM Digital Imaging and Communications in Medicine

DHFS Dirac-Hartree-Fock-Slater

DWBA Distorted–wave Born approximation

EFD Electron field detector

EPDL Evaluated Photon Data Library

FWHM Full width at half maximum

GOS Generalized oscillator strength

IAEA International Atomic Energy Agency

IBA Ion Beam Applications SA

LCPE Lateral charged particle equilibrium

ICRU International Commission on Radiation Units and Measurements

IMRT Intensity modulated radiation therapy

IROC Imaging and Radiation Oncology Core (USA)

LLNL Lawrence Livermore National Laboratory (USA)

LIC Liquid ionization chamber

LiF Lithium fluoride

LGK Leksell Gamma Knife R

MAD Mean Absolute Difference

MC Monte Carlo

MSR Machine-specific-reference (field)

MV Megavoltage

NACP Nordic Association of Clinical Physics

NEMA National Electrical Manufacturers Association (USA)

NIST National Institute of Standards and Technology (USA)

OAR Off-axis ratio

OF Output factor

PDD Percentage depth-dose

PFD Photon field detector

PMMA Polymethyl methacrylate (Lucite, Perspex or Plexiglas)

PTB Physikalisch-Technische Bundesanstalt (Germany)

PTW Physikalisch-Technische Werkstaetten Dr. Pychlau GmbH

PWBA Partial–wave Born approximation

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xiv ACRONYMS AND ABBREVIATIONS

QA Quality Assurance

RDSR Radiation DICOM Structured Report

RMSD Root Mean Square Difference

ROI Region of interest

RPC Radiological Physics Center (USA)

SAD Source–to–axis distance

SFD Stereotactic field detector

SSD Source–to–surface distance

SW Solid Water R

(water-equivalent plastic)

TLD Thermoluminescent dosimeter

TPR Tissue phantom ratio

TRS Technical Report Series (IAEA)

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Chapter 1 Introduction

The estimation of the absorbed dose of radiation, determined before or after an exposure to ionizing radiation, is of importance to assure the safe use of radiation; applications in radiation medicine aim at determining the dose delivered to patients as accurately as possible. Not being a quantitative concept, accuracy is prone to different meanings and we will follow the Guide to

the expression of Uncertainty in Measurement(the GUM, JCGM 2008), which defines accuracy

as 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 and interventional 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 the considerable difference in the dose levels involved, of several orders of magnitude, but other arguments are also of significance. In therapeutic exposures, for example, accuracy in dose delivery is important not only to reduce the risk of harming a patient, but also to ensure that prescribed doses are correctly delivered to specific targets so that the balance between tumour control and normal-tissue damage, the complication-free control, is optimized (c.f. Holthusen 1936, Steel 2002, etc). A limit of ±5% for the accuracy needed in radiotherapy was given in report 24 of the International Commission on Radiation Units and Measurements (ICRU 1976), 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 to achieve such a standard”. An updated analysis of data made 25 years later by the International Commission on Radiological Protection (ICRP 2000) on the lowest dose differences clinically detectable 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 delivered during diagnostic and interventional radiology exposures decrease the required accuracy due to the large uncertainty in the risk for long-term stochastic effects (e.g. induction of cancers or genetic damages). For example, the dosimetry recommendations by the International Atomic Energy Agency for this type of x-ray beams (IAEA TRS-457, 2007) quote a target accuracy of

1_{This 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 be very 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, which the 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% when the dose delivered exceeds the threshold for deterministic effects, such as some interventional angiography procedures where skin doses often reach orders of several grays. A different but complementary 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 corrected tolerance interval in Andreo 2011).

Achieving these accuracy levels at the end of an entire dose delivery process is a formidable task, 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 hospital is 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 requires a reference detector calibrated at a standards laboratory in terms of a given quantity, absorbed dose to water or air kerma, determined using absolute dosimetry. The next step is to relate the reference dose to that being used at the clinic using non-reference conditions, e.g. other field size, 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 and secondary standards laboratories and hospitals, thereby establishing a robust way of comparing the dosimetry of different beams at different sites. Absolute dosimetry, reference dosimetry, and relative dosimetry form what will henceforth be referred to as the dosimetry framework which, 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 presented in this thesis is addressed. It is of interest to point out that, for radiation therapy, ICRP report 86 (ICRP 2000) estimated a 6% combined standard uncertainty in the clinical dose delivery of high-energy photon beams including all the different steps of a treatment. Approximately one 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 such comprehensive 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%, depending on the laboratory or hospital level scenario.

Procedures for the reference dosimetry of radiotherapy photon and electron beams have been recommended by different national, regional and international organizations in the form of so-called dosimetry protocols or codes of practice. Formerly, these recommendations were based on ionization chambers calibrated in terms of air kerma free-in-air, e.g. those published by AAPM TG-21 (Schulz et al. 1983), IAEA TRS-277 (Andreo et al. 1987), DIN (1997) and others. New dosimetry procedures, based on ion chamber calibration coefficients in terms of absorbed 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 Andreo 2001, Huq et al. 2001, Andreo et al. 2002, etc), the absorbed dose to water formalism has simplified reference dosimetry considerably. This is because the metrology system is based on different types of primary standards, water and graphite calorimetry and ionization chamber dosimetry, making it more robust than the air kerma based system that relies on a single type of standard (ionization chamber). In diagnostic and interventional radiology dosimetry, procedures have been recommended by ICRU report 74 (ICRU 2005), IAEA TRS-457 (Alm-Carlsson et

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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 are here referred to as key data. Depending on the intended correction, key data relates to beam quality, beam configuration, detector type, irradiation geometry, etc. Examples of key data are 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. Many publications have so far been devoted to determining key data for reference and relative do-simetry using experimental techniques, analytical calculations, Monte Carlo (MC) radiation transport 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 analytically or 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 disadvantage of 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 allow accurate determination of key data using MC simulations where both the radiation beam and the detector geometry can be simulated with great detail.

Techniques in radiotherapy and radiology procedures have evolved considerably, although 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 the Imaging and Radiation Oncology Core (IROC) Houston QA Center (formerly the Radiological Physics 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 many as 58% of the participating centres failed to pass a widely accepted criteria for head-and-neck treatments. Errors in dose delivery in treatments using small photon beams were highlighted in ICRP 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 reference

on-site dose of 70 Leksell Gamma Knife R _{(LGK) Perfexion}TM 60_{Co γ-ray beams, estimated}

by the local physicist, differed by up to 3% with standardized alanine measurements. These examples and many others show that the dosimetry status of small radiotherapy photon beams and 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 not likely to be determined with accuracies better than 50% using conventional dosimetry methods like those relying on backscatter factors (to be described in Chapter 4). This claim was reiterated by 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 with accuracies of the order of 35%. These poor accuracies in skin dose estimations were mainly due to the limited procedure-related data (beam configuration, patient position, etc.) accessible to users. A standard by the USA National Electrical Manufacturers Association (NEMA) (RDSR 2005) has made procedure-related parameters available to users, enabling more accurate skin dose estimations, and manufacturers of angiography systems are today required to implement this standard. Johnson et al. (2011) developed a skin dose mapping software based on the RDSR standard, using backscatter factor data from ICRU (2005) and mass energy-absorption coefficient values from Hubbell and Seltzer (1996), and determined skin dose with accuracies considerably better than the mentioned 35%. Despite this improvement, in the opening session of the International Symposium on Standards, Applications and Quality Assurance in Medical

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4 CHAPTER 1. INTRODUCTION Radiation Dosimetry, Vienna 2010, it was highlighted that backscatter factors given in ICRU report 74 (2005) and IAEA TRS-457 (2007) cover only about one third of the clinical beam qualities 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 the dosimetry of radiotherapy and diagnostic and interventional radiology beams. This thesis has aimed 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 one particular treatment unit. For radiotherapy beams, the starting point was to review the key data included in the reference dosimetry Code of Practice IAEA TRS-398 published in 2000. Data published subsequently were compared to the data provided by TRS-398 and implications in the 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) came well 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 dosimetry

have been calculated for Varian Clinac R _{6 MV (linac) beams and LGK Perfexion}TM 60_{Co γ–}

ray beams that will contribute to making output factor estimations for the clinical dosimetry of these beams more accurate. The increased amount of information available following the implementation of the RDSR standard, which allows more accurate skin dose estimations in diagnostic radiology procedures, requires the availability of specialized key data. Hence, the dosimetry of interventional angiographic procedures has been investigated focusing our work on skin dose estimations because of the potentially high doses delivered during these procedures. Different correction factors required for these estimates have been determined and simplified tools to estimate them analytically developed. Finally, updates of the fundamental data (mainly cross sections) in the most recent version of the MC system used in our calculations have been investigated 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 dosimetry framework for reference and relative dosimetry. Key data relevant to this framework have been investigated and determined in Papers I (Benmakhlouf and Andreo 2011), IV (Benmakhlouf et

al. 2014), and VI (Benmakhlouf et al. 2015), and will be described in this chapter. Some new

data 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. Emphasis will be given to the role of the backscatter factor, the main correction needed for skin dose estimations. The framework will then be extended to corrections necessary for non-reference conditions. 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 5 compares the cross section data in the PENELOPE version 2008, used for all the calculations in this work, with those in the most recent version of 2014. The impact of new cross sections on our MC calculations will be investigated by simulating cases relevant to radiotherapy and to radiodiagnostic dosimetry. In Chapter 6 new MC calculations of the particle fluence inside several detectors are presented for broad and narrow radiotherapy 6 MV beams, a work that contributes to the better understanding of detector response in these beams. Chapter 7 provides the conclusions of this thesis, complemented with some goals for the future.

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Chapter 2 Background

2.1 The dosimetry framework

The dosimetry framework is based on measured calibration coefficients under the absolute

do-simetryof a primary standards laboratory, which provides radiation metrology standards to the

more 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 to

water (Dw), is determined for certain laboratory specific conditions as

N = S

Mlab

(2.1)

where Mlabis the detector reading, acquired in specific conditions of humidity, pressure,

tem-perature, etc. The quantity S is primarily determined at a primary standards laboratory using water or graphite calorimetry, chemical (Fricke) dosimetry or ionization chamber dosimetry, and subsequently disseminated to the secondary standards laboratories. The quantity of interest in radiation medicine depends on the application, e.g. radiation protection, radiotherapy, radi-odiagnostic, etc. The calibration coefficient characterizes the detector response in the standards laboratory.

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

S = N Mhosp

Y

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 or

conditions and apply to both reference and relative dosimetry. 5

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6 CHAPTER 2. BACKGROUND

The key data in Eq. (2.2) are the factors and coefficients, ki. These correct the departure from

laboratory conditions to the hospital conditions and can be classified into two groups where the main 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), backscatter

factors (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, together with the development of fast and accurate Monte Carlo codes, enable determinations of key data using extremely detailed descriptions of the radiation beam and detector configuration and materials. 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 account detector-to-detector differences (of the same detector type) nor detector electronic details that may require significant corrections for their practical use (e.g. recombination effects in liquid ionization chambers). This is the reason why experimental and MC determinations of key data related 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 MC systems capable of simulating accurately the response of ionization chambers, both complying with 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 and positrons) 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 are simulated in detail, using the so-called Class II condensed history technique, CHT (Berger 1963, Andreo 1981) or a combination of the two. Recall that the Class II CHT divides charged particle interactions into two groups, denoted in PENELOPE as hard and soft collisions. Hard interactions are those where large energy losses and angular deflections occur, and take place above predetermined thresholds defined by the user as transport parameters (see below); these interactions are simulated using the analogue technique. Soft collisions are all those with energy losses 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) by multiple 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 to split this length and improve the condensed calculation.

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2.2. MONTE CARLO CALCULATIONS 7 The cross sections and interaction data used in PENELOPE are derived from first-principle calculations, 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 the necessary differential cross sections, DCS (c.f. Salvat and Fernández-Varea 2009). All the necessary data for the required media are prepared beforehand using a system code called

ma-terialand can be tabulated (with the code tables) for subsequent analysis, additional calculations

consistent with the MC simulation, or for graphical representation using provided scripts. For each 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 classic

Carlson (1975) compilation, modified according to recent experimental data.

For photon interactions, subshell-dependent DCSs for photoelectric absorption and anomalous scattering form factors for coherent (Rayleigh) scattering in PENELOPE 2008 are taken from the LLNL Evaluated Photon Data Library, EPDL (Cullen et al. 1997). The form factors take

into account effects at energies close to the K absorption edge (UK), and relaxation data is

also adopted from the LLNL-EPDL library. Incoherent (Compton) scattering is based on the relativistic impulse approximation (Ribberfors 1983) taking into account both the momentum distribution of Compton electrons (Doppler broadening) and binding effects. Cross sections for electron-positron pair production are obtained from the widely used NIST computer code XCOM (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 of the 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 was

created with a code termed ELSEPA (Salvat et al. 2005), and was included in ICRU report

77 (ICRU 2007). DCSs for inelastic collisions with atomic electrons (σinel) are derived under

the 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 over the density of oscillator strengths (number of electrons in the different ionization and excitation atomic subshells) leading to the atomic number Z (Bethe sum rule), but is characterized by a 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. for

high 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 et

al. (1977). It is of interest to mention that bremsstrahlung in the energy region between 2 MeV

and 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 secsec-tion (σannih) is used as the

DCS for in-flight positron annihilation yielding two-photons. The cross sections σelast, σineland

σbrem are used to derive the corresponding formulations for multiple interaction events, e.g. a

Goudsmidt–Saunderson angular distribution (FGS) that naturally includes spin effects and mass

unrestricted 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 also

relies 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

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approxim-8 CHAPTER 2. BACKGROUND 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 the user. 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 C1and C2, that govern the transition between detailed and condensed simulation

for elastic scattering; and (c) WCC and WCR, that modulate the limit between charged particle

hard 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) and

radiative 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 of energy, 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 simulated throughout 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 specific detector 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 60Co

γ-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 a}

Leksell Gamma Knife R

PerfexionTM. These were adopted from the IAEA phase-space

database for external beam radiotherapy (www-nds.iaea.org/phsp) and provided by 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 positioned on the central beam axis at a depth of 10 cm and in the sphere centre, respectively. Elec-tron and posiElec-tron 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 of

energy losses below WCC and WCR that emulates efficiently energy straggling down to

low 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 transport was disregarded by setting electron absorption energies equal to the incident photon en-ergy; all the other electron transport parameters were therefore not relevant. Note that

kerma 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, as

bremsstrahlung production is almost negligible (see footnote #1). Photon fluence dif-ferential in energy down to 1 keV (the photon energy absorption) produced by

incid-1_{The continuous slowing down range, R}

CSDA, 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,

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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 surface of 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 dosidosi-metry, and of spherical phantoms of 18 cm and other diameters. The phantom materials used in this framework were water and PMMA.

The efficiency MC of our calculations was speeded-up considerably with the use of variance

reduction techniques (VRT) that improve the statistics of the simulations by artificially increas-ing the probability of certain events (interaction forcincreas-ing and photon splittincreas-ing) or disregardincreas-ing particles with a small probability of reaching the defined scoring region (outside the ROI with an absorption energy of 200 keV or playing Russian roulette). These have been widely used in all the radiotherapy detector simulations.

A new version of PENELOPE has just been released (Salvat 2014) where modifications have been implemented in its fundamental data. As already mentioned, these will be presented in Chapter 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 to produce so-called intensity modulated radiotherapy (IMRT) beams, has increased considerably in 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 conventional beams and in some ocassions accidents have occurred when procedures, data and detectors suitable 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 photon beams are being developed, based on the formalism published by Alfonso et al. (2008) that has been used in our research and that will be described in Chapter 3, but it is of interest to describe some of the basic concepts that make this type of dosimetry particularly interesting and rather different 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 it lacks lateral charged particle equilibrium (LCPE) within a medium, and this occurs in photon beams if the beam half–width or radius is smaller than the maximum range of the generated secondary electrons. Lack of LCPE is problematic for dosimetry since the balance of charged particles laterally scattered in and out of the beam fails, e.g. in the presence of a cavity with a density higher than that of the medium (usually water) more particles are scatered outwards than inwards.

The condition to determine when a field size can be considered to be small is a function of the

lateral charged particle equilibrium range(rLCPE) at a given energy or beam quality, obtained

from Monte Carlo simulations of the ratio D/Kcol (dose to collision kerma) in water. It has

been 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 for

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10 CHAPTER 2. BACKGROUND

beam quality index TPR20,10 is defined as the ratio of absorbed doses at 20 cm and 10 cm

depth 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 of

the detector volume is at a distance from the beam edge smaller than rLCPE. Thus the beam

half-width or radius has to be at least as large as the maximum range of the secondary electrons plus 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 relative increase 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 by bremsstrahlung. The consequences are that, contrary to the case of large beams, in small beams the 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 the indication 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, the detector 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 sensitive

volume ¯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 the sensitive 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 particle ranges are density dependent.

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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, built

with 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 kept constant (specific detector models and manufacturers are not identified).

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Chapter 3 Radiation therapy dosimetry framework

3.1 Reference dosimetry

In radiotherapy with external megavoltage beams, the reference dose to a point at a reference

depth 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

Dfref

w,Q0(zref) = ND,w,Q0M

fref

w,Q0 (3.1)

where Dfref

w,Q0 is the absorbed dose to water in a beam of quality Q0, the same quality as in

the laboratory, ND,w,Q0 is the calibration coefficient in terms of absorbed dose to water and

Mfref

w,Q0 is 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 central axis 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 water except when noticed. The calibration coefficient provided by the standards laboratory can only be used at the hospital for a beam quality and irradiation conditions identical to those used at the 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 differs

from the beam used at the standards laboratory, either in terms of beam quality (i.e. Q 6= Q0),

or field size (i.e. fmsr6= fref), or in some cases both. Note that the largest field size of machines

that cannot realize the conventional reference field size of 10 cm×10 cm, is taken to be the reference field size and has been termed machine specific-reference field (msr field) by Alfonso

et al. (2008), hence the symbol fmsr. Table 3.1 shows the beam type and reference field size

of three frequently used radiotherapy treatment units compared to those used at the secondary standards 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 size}

is different for LGK and Cyberknife R

beams. These departures from the calibration conditions

will be taken into account by correction factors ki included in Eq. (2.2).

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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, or

machine specific-reference field, fmsr

Standards laboratory 60_{Co γ-rays} _{10 cm ×10 cm}

Linear accelerator 6 MV or 15 MV 10 cm ×10 cm

Leksell Gamma Knife R 60_{Co γ-rays}

∅ 1.6 cm

Cyberknife 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 Q

can be determined using a Q0-calibrated detector by introducing the beam quality correction

factor, kQ,Q0

Dfref

w,Q(zref) = ND,w,Q0M

fref

Q kQ,Q0 (3.2)

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

et al.2000) kQ,Q0 = (sw,air)_Q (sw,air)_Q₀ pdet,Q pdet,Q0 ¯ Wair Q ¯ Wair Q0 (3.3)

where sw,airis the Spencer-Attix stopping-power ratio water-to-air evaluated for the unperturbed

electron 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 the

detector, and ¯Wairis the mean energy required to form an ion pair in air (introduced to take into

account 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 independent

and small perturbation correction factors piaccounting for different effects,

pdet=

Y

i

pi = pcavpdispwallpcel (3.4)

where pcav is the detector cavity electron fluence perturbation correction factor, pdisis the

dis-placement or redis-placement correction factor, pwall is the perturbation correction factor for the

lack of equivalence to water of the detector wall, and pcel is the perturbation correction factor

for the central electrode of an ionization chamber. Although chamber-to-chamber variations are neglected by using calculated correction factors, calculated and experimentally derived beam

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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 ionization chambers (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 correction

factors, modifying Eq. (3.3) to

kQ,Q0 =

fdet,Q

fdet,Q0

(3.5)

where for a given beam quality Q, fdet,Qwas obtained as the ratio between the dose at a point in

water (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 different}

from the laboratory60Co γ-rays, as shown in Table 3.1.

3.1.2 Configuration correction factor

The influence of the field size fmsrand beam quality Qmsr, as well as other irradiation conditions

(e.g. phantom geometry) on the calibration coefficient, ND,w,Q0, determined for a reference

field size, fref, and a standard geometry (e.g. a cubic water phantom of 30 cm side) is taken into

account 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,Q0M fmsr QmsrkQ,Q0k fmsr,fref Qmsr,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 the

standards laboratory and their dosimetry uses non-cubic reference phantoms. For example, the phantom 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 IAEA

TRS-398 for 53 detectors for high-energy photon beams as a function of the beam quality TPR20,10and for 20 detectors for high-energy electron beams as a function of the beam qualityR50;

the laboratory beam quality in both cases is a60_{Co γ-ray beam. Recall that TPR}

20,10 specifies

the photon beam quality and was defined in Section 2.3; R50specifies 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 stoppus-ing powers. For high-energy photon and electron beams, Table 3.2 states how each of the perturbation factors, included in IAEA TRS-398, was determined.

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16 CHAPTER 3. RADIATION THERAPY DOSIMETRY FRAMEWORK

Table 3.2: Perturbation correction factors in the dosimetry Code of Practice IAEA TRS-398 (Andreo et

al. 2000) used to determine beam quality correction factors. Perturbation factors were determined using analytical 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 beams

pcav Unity Analytical

pdis Analytical/experimental Unity

pwall 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-calculated perturbation factors by different authors (published between 2000 and 2010) differed from the

values used in the IAEA Code of Practice TRS-398. 60Co γ-rays and high-energy photon and

electron beams were considered in that study. For photon beams the investigated detector was a Farmer NE-2571 cylindrical ionization chamber, whereas a NACP plane-parallel chamber was the 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-2571

perturbation factor pdet for the reference beam quality of60Co of about 1.5%, compared with

TRS-398, decreasing as the energy increased. The difference between the new values and the experimental 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 in TRS-398, contributed more or less equally to the 1.5% increase. Note that the large increase in the perturbation factor for this reference beam quality enters into the denominator of Eq. (3.3).

For photon beam qualities not too different from 60_{Co, the increase in p}

det both at Q and Q0

will cancel out; the increase in the ratio, and thus in kQ,Q0, will be maximum for the highest

photon 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 taken as unity due to lack of data then available, whereas the new values differed from unity by 1% to

2%. The significant increase of the perturbation factors for the quality of60Co, which would be

present for all types of charge particle beams, triggered a subsequent investigation by Andreo et

al. (2013) and, based on the comparison of MC-calculated fdet,60_Co factors with experimental

values, it was concluded that implementing such increase without making consistent changes in 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 perturbation factors would partly be balanced by a reduction in the stopping-power values for water due to the 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,Qas in

Eq. (3.5), instead of using stopping-power ratios and perturbation correction factors, simplifies substantially the concept of beam quality correction factor as it makes individual perturbation correction 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 MC system, especially for NACP chambers in electron beams, where in some cases the calculated data differed by up to 1.5%.

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3.3. RELATIVE DOSIMETRY 17

3.3 Relative dosimetry

The reference absorbed dose determined in the previous section is related to the dose for other field sizes, keeping the reference depth and all other reference conditions unaltered, using the

so-called output factor1_{, defined as}

Ωfclin,fref Qclin,Qref = Dfclin Qclin Dfref Qref (3.7)

The beam qualities, Qref and Qclin, are included in the subscript of the output factor to emphasize

that changes in beam quality are possible when the field size is changed. Although Ωfclin,fref

Qclin,Qref is

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

Ωfclin,fref Qclin,Qref ≈ Mfclin Qclin Mfref Qref (3.8)

which assumes that stopping-power ratios and perturbation correction factors are

independ-ent of the field size, i.e. (sw,airpdet)fclin = (sw,airpdet)fref. For large fields, larger than about

4 cm×4 cm, this assumption is approximately correct and therefore Eq. (3.8) holds. For small fields multiple authors (c.f. Czarnecki and Zink 2013, Wagner et al. 2013, Papaconstadopoulos

et al.2014, etc) have shown that perturbation factors vary considerably with the field size. It is

therefore necessary to determine output factors using the full Eq. (3.7) or use detector reading ratios corrected with a so-called output correction factor, i.e.

Ωfclin,fref Qclin,Qref = Dfclin w,Qclin Dfref w,Qref = M fclin Qclin Mfref Qref

(sw,air)f_Qclin_clin

(sw,air)f_Qref

ref

(pdet)

fclin

Qclin

(pdet)f_Qref_ref

= M fclin Qclin Mfref Qref kfclin,fref Qclin,Qref (3.9)

where kfclin,fref

Qclin,Qref is 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. When the reference field size is not the conventional 10 cm×10 cm, the msr field must be used and Eqs. (3.8) and (3.9) become

Ωfclin,fmsr Qclin,Qmsr ≈ Mfclin Qclin Mfmsr Qmsr (3.10) Ωfclin,fmsr Qclin,Qmsr = Dfclin w,Qclin Dfmsr w,Qmsr = M fclin Qclin Mfmsr 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.

1_{Output factors have also been termed relative dose factors or total scatter factors. In addition, the abbreviation OF}

has conventionally been used for output factors, but the symbol adopted for this factor in Eq. (3.7) is consistent with the international formalism published by Alfonso et al. (2008).

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

Key Data for the Reference and Relative

Dosimetry of Radiotherapy and

Diagnostic and Interventional Radiology Beams

Hamza Benmakhlouf

Key Data for the Reference and Relative Dosimetry of

Radiotherapy and Diagnostic and Interventional Radiology Beams

Hamza Benmakhlouf

Doctoral thesis submitted to the Department of Physics at Stockholm University

Contents

Abstract

Sammanfattning

List of Papers

Acknowledgements

Quantities and symbols

Roman letter symbols

Greek letter symbols

Acronyms and abbreviations

Chapter 1

Introduction

Chapter 2

Background

2.1

The dosimetry framework

2.2

Monte Carlo calculations

2.3

Basic concepts on the physics of small MV photon beams

Chapter 3

Radiation therapy dosimetry framework

3.1

Reference dosimetry

3.1.1

Beam quality correction factor

3.1.2

Configuration correction factor

3.2

Key data for reference dosimetry: beam quality factors

3.3

Relative dosimetry