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POLYTECHNIQUE

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Shielding Study against High-Energy

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Neutrons produced in a Proton Therapy "

Facility by means of Monte Carlo

-LU

Codes and On-Site Measurements

-Thèse présentée en vue de l’obtention du grade de

Docteur en Sciences de l'Ingénieur

Thibault VANAUDENHOVE

Directeur

Alain Dubus (Université Libre de Bruxelles)

Co-Promoteur

Nicolas Pauly (Université Libre de Bruxelles)

Membres du Jury

Président: Jean-Marc Sparenberg (Université Libre de Bruxelles)

Secrétaire: Gilles De Lentdecker (Université Libre de Bruxelles)

Frédéric Stichelbaut (Ion Beam Applications)

Véronique Lacoste (Institut de Radioprotection et de Sûreté Nucléaire)

Lena Lebreton (Institut de Radioprotection et de Sûreté Nucléaire)

LU

Shielding Study against High-Energy

^

Neutrons produced in a Proton Therapy ^

Facility by means of Monte Carlo

^

Codes and On-Site Measurements

-Thèse présentée en vue de l'obtention du grade de

Docteur en Sciences de l’Ingénieur

Thibault VANAUDENHOVE

Directeur

Alain Dubus (Université Libre de Bruxelles)

Co-Promoteur

Nicolas Pauly (Université Libre de Bruxelles)

Membres du Jury

Président: Jean-Marc Sparenberg (Université Libre de Bruxelles)

Secrétaire: Gilles De Lentdecker (Université Libre de Bruxelles)

Frédéric Stichelbaut (Ion Beam Applications)

Véronique Lacoste (Institut de Radioprotection et de Sûreté Nucléaire)

Lena Lebreton (Institut de Radioprotection et de Sûreté Nucléaire)

En plus d’Alain, ma gratitude se porte également sur mon co-promoteur,

Nicolas (Pauly). Je les remercie tous deux pour leur présence, leurs réflex­

ions, nos discussions, mais aussi leur confiance dans les diverses activités

de recherche et académiques que j’ai pu entreprendre. En effet, j’ai pu, à

mon plus grand bonheur, présenter voire publier mes résultats lors de con­

férences internationales en France, au Japon, en passant par Israël et, en

juillet prochain, en Espagne. Du point de vue académique, j’ai pu encadrer,

entre autres, les travaux pratiques de cours de Dosimétrie lorsque Jean-

Claude Dehaes était encore de service mais également après le passage du

flambeau à Nicolas. Je remercie également Jean-Claude pour avoir parcouru

ma thèse et donné ses remarques toujours aussi constructives.

Je tiens à exprimer mes remerciements à mes deux promoteurs, mais

également à tous les membres du service de Métrologie Nucléaire pour leur

sympathie et leur engouement aux activités liées au bien-être et aux bonnes

moems du service (en gros, les restos du mercredi midi, les drinks d’entrée

et de sortie du service, les discussions de couloir, etc.). Sans ordre préétabli,

merci donc à Laetitia, Pierre-Etienne, Yvan, Pierre, Artem, Julio, Xavier,

Farshid et Nicolas (Seignem, lui...).

Je tiens particulièrement à remercier Jonathan Derrien pour les raisons

précitées mais également pour sa lecture attentive du présent manuscrit et

des corrections qu’il a pu apporter, et aussi pour ses discussions et son esprit

critique, nos thèmes de recherche étant étroitement liés.

deux premières années de ma thèse sur de nombreux points liés à la pro-

tonthérapie, à la dosimétrie et aux codes Monte Carlo. Je lui souhaite une

merveilleuse carrière dans le domaine.

Du point de vue professionnel, je tiens finalement à dire merci à Frédéric

Stichelbaut, de chez IBA, et Valérie De Smet. C’est en effet grâce à Frédéric

que des mesures au centre de protonthérapie d’Essen ont pu être effectuées

et c’est de son travail, ses remarques, son expertise et son expérience dans la

radioprotection, la protonthérapie et les codes Monte Carlo que s’est insipré

le présent manuscrit. Enfin, le travail de Valérie et le mien étant étroite­

ment liés, une collaboration effective et fructueuse a pu se mettre en place

et mener à plusieurs présentations dans des colloques internationaux et à la

rédaction de plusieurs articles scientifiques.

En plus des lecteurs attitrés, je tiens à remercier mon père qui, même

s’« il ne comprend rien à ce qui est écrit », s’est pris la peine de parcourir

ma thèse afin de relever d’éventuelles fautes d’anglais et de syntaxe.

Les autres membres de ma famille et mes amis sont évidemment mis à

l’honneur pour leur soutien durant toute la durée de la thèse. Je pense no­

tamment à ma mère, mes frères, mes grands-parents, mes oncles et tantes,

mes cousins, ma belle-famille, mais aussi les amis du mini-foot, du tennis, et

tous ceux qui, de près ou de loin, se sont intéressés et m’ont écouté (ou au

moins fait semblant) lorsque je tentais de leur expliquer le contenu de mes

recherches.

treatment room to ensme that other people and workers received a dose as

small as possible. The dose measurement is performed with spécifie doseme-

ters such as the WENDI-II, which gives a conservative estimation of the

ambient dose équivalent up to 5 GeV. The dose in working areas may also

be estimated by means of numerical calculations by using simulation codes

of particle transport such as the GEANT4, MCNPX, FLUKA and PHITS

Monte Carlo codes.

Secondary particle yields calculated with Monte Carlo codes show dis-

crepancies when different physical models are used but are globally in good

agreement with experimental data from the literature. Neutron and photon

doses decrease exponentially through concrète shielding wall but the neutron

dose is definitely the main component behind a wall with sufficient thick-

ness. Shielding parameters, e.g. atténuation coefficients, vary as fonctions

of émission angle (regarding the incident beam direction), incident proton

energy, and target material and composition.

The WENDI-II response fonctions computed by using different hadronic

models show also some discrepancies. Thermal treatment of hydrogen in the

polyethylene composing the detector is also of great importance to calculate

the correct response fonction and the detector sensitivity.

since concrète walls are very thick in this case.

Résumé

La radiothérapie utilisant des faisceaux de protons d’énergie entre 50 MeV et

250 MeV s’est largement développée ces dernières années. Elle a l’immense

avantage de pouvoir concentrer la dose due au faisceau incident de manière

très efficace et très précise sur la tumeur, en épargnant les éventuels or­

ganes sains et sensibles aux radiations situés aux alentours. Cependant, des

rayonnements « secondaires » très énergétiques sont créés par les réactions

nucléaires subies par les protons lors de leur parcours dans les tissus, et

peuvent sortir du patient. Des blindages entourant la salle de traitement et

suffisamment épais doivent être présents afin que la dose reçue par les per­

sonnes se trouvant aux alentours soit la plus faible possible. La mesure de

la dose se fait avec des dosimètres spécifiques et sensibles aux rayonnements

de haute énergie, tels que le WENDI-II pour les neutrons. L’estimation de

cette dose, et donc la modélisation des blindages, se fait également avec des

codes de simulation numérique de transport de particules par les méthodes

de Monte Carlo, tels que GEANT4, MCNPX, FLUKA et PHITS.

La production de rayonnements secondaires calculée à l’aide de codes

Monte Carlo montre des écarts significatifs lorsque différents modèles d’inter­

actions physiques sont utilisés, mais est en bon accord avec des données

expérimentales de référence. L’atténuation de la dose due aux neutrons et

aux photons secondaires à travers un blindage composé de béton est expo­

nentielle. De plus, la dose due aux neutrons est clairement la composante

dominante au-delà d’une certaine épaisseur. Les paramètres d’atténuation,

comme par exemple le coefficient d’atténuation, dépendent de l’angle d’émis­

sion (par rapport à la direction du faisceau incident), de l’énergie des protons

incidents et de la nature et la composition de la cible.

Publications

1. T. Vanaudenhove, A. Dubus and N. Pauly

Comparing GEANT4 Hadronic Models for the WENDI-II Rem Meter

Response Function

Radiation Protection Dosimetry 154(3), pp. 340-345, 2013,

doi:10.1093/rpd/ncs240.

2. T. Vanaudenhove, F. Stichelbaut, A. Dubus, N. Pauly and

V. De Smet

Monte Carlo Calculations with MCNPX and CEANTf for General

Shielding Study — Application to a Protontherapy Center

Progress in Nuclear Science and Technology 4, pp. 422-426, 2014,

www.aesj.or.jp.

3. V. De Smet, F. Stichelbaut, T. Vanaudenhove, G. Mathot,

I. Gerardy, G. De Lentdecker, A. Dubus and N. Pauly

Neutron H* (10) inside a Proton Therapy Facility — Comparison be-

tween Monte Carlo Simulations and WENDI-2 Measurements

Radiation Protection Dosimetry, Advance Access published, November

19th, 2013,

doi:10.1093/rpd/nct289.

Oral Présentations &: Posters

1. T. Vanaudenhove, A. Dubus and N. Pauly

1 poster: WENDI-II Fast Neutron Detector Modelization with the

Monte Carlo Simulation Toolkit Geantf

2nd International Workshop on Fast Neutron Detectors and Applica­

tions (FNDA 2011), Fin Gedi, Israël, 6-1I/11/20II.

2. T. Vanaudenhove, F. Stichelbaut, A. Dubus, N. Pauly and

V. De Smet

1 oral communication: Monte Carlo Calculations with MCNPX and

GEANT4 for General Shielding Study — Application to a Protonther­

apy Center

decker, I. Gerardy, A. Dubus and N. Pauly

1 oral communication: Study of several uncertainties in Monte Carlo

shielding simulations for proton therapy facilities

Introduction

1

1 Physics for Radiation Protection

9

1.1

Interactions of Charged Particles with Matter... 11

1.2 Photon Interactions with Matter... 15

1.3 Neutron Interactions with Matter... 20

1.4 Dosimetry and Radiation Protection... 27

2 Monte Carlo Simulations of Secondary Particle Yield and

Atténuation for Proton Beam on Thick Targets

41

2.1

Monte Carlo Simulation Codes... 43

2.2

Secondary-Particle Production for Proton Beam Impinging

on Thick Target... 55

2.3 Dose Atténuation Through Shielding Wall for Iron Target . .

74

2.4 Systematic Shielding Study for Different Target Materials

Ir-radiated by a Proton Beam... 102

2.5

Conclusion ... 121

3 Neutron Dosemeter Characterization and Monte Carlo sim­

ulations of the WENDI-II-rem-meter response fonction 134

3.1

Neutron Detector and Dosemeter Description... 136

3.2 Monte Carlo Simulations of the WENDI-II Response Function 147

3.3

Conclusion ... 159

4 Comparing Numerical and Experimental Evaluations of Am­

biant Dose Equivalent in a Proton Therapy Center

166

4.1

Proton Therapy Facility Description... 168

1

Radiation effects on biological cells... 2

2

Typical proton therapy treatment, Spread-Out Bragg Peak,

and photon beam treatment... 3

3

Clinical dose distributions for photon and charged particle

therapy... 4

1.1 Electron mass stopping powers for Carbon, Copper and Lead 13

1.2 Proton mass stopping powers for Carbon, Copper and Lead .

14

1.3 Photon mass atténuation coefficients for Carbon, Copper and

Lead... 19

1.4 Neutron cross-sections for Carbon, Copper and Lead... 23

1.5 Schematic view of nuclear cascade... 25

1.6 Schematic view of spallation reaction... 26

1.7 Depth dose curves in tissue for photon, électron and proton

beams... 28

1.8 Radiation weighting factors

for neutrons... 30

1.9 Schematic représentation of an oriented and expanded radia­

tion field and the ICRU sphere for the ambient-dose-equivalent

définition... 32

1.10 Conversion coefficients for the photon effective dose... 33

1.11 Conversion coefficients for the neutron effective dose... 35

2.1 Proton beam on thick cylindrical target... 55

2.2 Neutron multiplicity for Carbon, Copper, Tin and Tungsten .

57

2.3 Differential energy spectra of neutron leaving the Béryllium

target irradiated by a 113-MeV proton beam ... 60

2.11 Differential energy spectra of neutron leaving the Uranium

target irradiated by a 256-MeV proton beam ... 64

2.12 Double differential neutron yield for a 250-MeV proton beam

impinging on an thick Iron target for different INC models

used in GEANT4... 65

2.13 Double differential distributions of neutrons from the inter­

action of 150-MeV and 250-MeV proton beams with a thick

Iron target, calculated with the FLUKA code... 66

2.14 Double differential neutron yield divided to the material

den-sity, at 30° and for a 113-MeV proton beam... 68

2.15 Double differential neutron yield divided to the material

den-sity, at 150° and for a 113-MeV proton beam... 68

2.16 Double differential neutron yield divided to the material

den-sity, at 30° and for a 256-MeV proton beam... 69

2.17 Double differential neutron yield divided to the material

den-sity, at 150° and for a 256-MeV proton beam... 69

2.18 Photon multiplicity for Carbon, Copper, Tin and Tungsten . 70

2.19 Measured and calculated gamma prompt émission from PMMA

for a 160-MeV proton beam and from Lucite for a 40-MeV

proton beam ... 71

2.20 Differential energy spectra of photons leaving the PMMA tar­

energy, for a 250-MeV proton beam on Iron target... 75

2.22 Total ambient dose équivalent Hs for a 100-MeV proton beam

on Iron target... 76

2.23 Total ambient dose équivalent H s for a 250-MeV proton beam

on Iron target... 76

2.24 Somrce term for monoenergetic neutrons in concrète as a func­

tion of neutron energy... 78

2.25 Atténuation length for monoenergetic neutrons in concrète as

a function of neutron energy... 79

2.26 Atténuation length calculations for monoenergetic neutrons

in concrète as a function of neutron energy ... 79

2.27 Shielding concrète sphere and variance réduction by impor­

tance sampling for neutrons... 82

2.28 Neutron and photon ambient dose équivalent through a

spher-ical concrète shield for a 100-MeV proton beam on iron target 84

2.29 Neutron and photon ambient dose équivalent through a

spher-ical concrète shield for a 250-MeV proton beam on iron target 84

2.30 Neutron and photon ambient dose équivalent through a

spher-ical concrète shield for a 100-MeV proton beam on iron target,

multiplied by the square of the distance from the source ... 85

2.31 Neutron and photon ambient dose équivalent through a

spher-ical concrète shield for a 250-MeV proton beam on iron target,

multiplied by the distance from the source... 85

2.32 Differential neutron fluence multiplied by the energy as a

function of shield depth, at 170°-180°

... 86

2.33 Normalized differential neutron fluence multiplied by the en­

ergy as a function of shield depth... 86

2.34 Low- and high-energy-neutron contributions to the neutron

dose as a function of the shield depth at 170°-180°... 88

2.35 Relative neutron and photon contributions to the ambient

2.41 Atténuation lengths for neutrons in concrète, for a 250-MeV

proton beam on Iron target... 97

2.42 Neutron ambient dose équivalent compared with semi-empirical

laws at 60-70° solid angle... 99

2.43 Intermediate d-value between the first and the second

expo-nential cmves of the dose atténuation law, for a 250-MeV

proton beam on Iron target... 99

2.44 Atténuation length in the first meter of concrète as a function

of émission angle and incident proton energy for a tissue target 103

2.45 Atténuation length in the first meter of concrète as a function

of émission angle and incident proton energy for a Nickel target 104

2.46 Atténuation length in the first meter of concrète as a function

of émission angle and incident proton energy for a Tantalum

target...104

2.47 Atténuation length in the first meter of concrète as a function

of émission angle and incident proton energy for tissue. Nickel

and Tantalum targets ... 105

2.48 Atténuation length at equilibrium as a function of émission

angle and incident proton energy for a tissue target... 106

2.49 Atténuation length at equilibrium as a function of émission

angle and incident proton energy for a Nickel target ...107

2.50 Atténuation length at equilibrium as a function of émission

talum targets... 108

2.52 Dose at the shield entrance as a function of émission angle

and incident proton energy for a tissue target... 109

2.53 Dose at the shield entrance as a function of émission angle

and incident proton energy for a Nickel target... 110

2.54 Dose at the shield entrance as a function of émission angle

and incident proton energy for a Tantalum target...110

2.55 Dose at the shield entrance as a function of émission angle

and incident proton energy for tissue, Nickel and Tantalum

targets... 111

2.56 Source terni in the first meter of concrète as a function of

émission angle and incident proton energy for a tissue target 112

2.57 Source term in the first meter of concrète as a function of

émission angle and incident proton energy for a Nickel target 113

2.58 Source term in the first meter of concrète as a function of

émission angle and incident proton energy for a Tantalum

target... 113

2.59 Source term in the first meter of concrète as a function of

émission angle and incident proton energy for tissue, Nickel

and Tantalum targets ... 114

2.60 Source term at equilibrium as a function of émission angle

and incident proton energy for a tissue target... 115

2.61 Source term at equilibrium as a function of émission angle

and incident proton energy for a Nickel target... 116

2.62 Source term at equilibrium as a function of émission angle

and incident proton energy for a Tantalum target...116

2.63 Source term at equilibrium as a function of émission angle

and incident proton energy for tissue. Nickel and Tantalum

targets... 117

2.64 Dose at the shield exit as a function of émission angle and

incident proton energy for a tissue target ... 118

2.65 Dose at the shield exit as a function of émission angle and

to H* (10) and NCRP-38 fluence-to-dose conversion functions. 146

3.5 WENDI-38 rem meter schematic side view... 148

3.6 WENDI-II rem meter schematic cutaways view...149

3.7 Typical distribution of counts per ^He(n,p)^H reaction over

the energy inside the active volume of the WENDI-II detector 151

3.8 Thermal neutron cross-sections for hydrogen in polyethylene . 153

3.9 Number of counts per unit fluence as a function of neutron

energy by considering the free-gas model and the thermal

treatment... 154

3.10 Number of counts per unit fluence as a function of neutron

energy by considering the different hadronic inelastic models . 156

3.11 Absolute and relative (normalised to 2 MeV) total response

per unit fluence as a function of neutron energy... 157

3.12 Neutron source strength per unit lethargy from a ^^^Cf

spon-taneous fission source...159

4.1 Footprint of the West-German Proton-therapy center, Essen

(WPE)... 169

4.2 Cyclotron of the WPE... 170

4.3 Energy Sélection System of the WPE... 170

4.4 Beam line of the WPE... 171

4.5 Fixed-Beam Treatment Room of the WPE... 171

4.6 Gantry Treatment Room, number 2, of the WPE...172

4.9 Magnet pôle of AVF cyclotron, no spiral angle and spiral shapel75

4.10 Dee/Counter-Dee accélération structure... 175

4.11 Half-view of an IB A 230-MeV cyclotron...176

4.12 Extraction of high-energy protons from cyclotron using

elec-trostatic septum... 177

4.13 Proton beam line from cyclotron to treatment room... 178

4.14 Schematic drawing of the nozzle...179

4.15 Principle of Double Scattering delivery mode...179

4.16 Principle of pencil beam scanning delivery mode...180

4.17 GEANT4 implémentation of the cyclotron room...183

4.18 Ambient dose équivalent in the south and west walls of the

cyclotron room...184

4.19 Ambient dose équivalent in the maze walls of the cyclotron

room... 185

4.20 Detector positions and variance réduction techniques in the

maze and control room of cyclotron room...186

4.21 WENDI-II positions in the maze and the control room of the

cyclotron room...187

4.22 Ambient dose équivalent rate in maze legs of the cyclotron

room... 190

4.23 Diffusion and transmission of the ambient dose équivalent rate

in maze legs of the cyclotron room... 191

4.24 GEANT4 implémentation of the gantry treatment room in

PBS mode...193

4.25 Water phantom and nozzle position in the gantry treatment

room... 194

4.26 WENDI-II positions in the maze and the control room of the

gantry room, and in the west gantry room, in PBS mode ... 195

4.27 Ambient dose équivalent rate in the maze legs of the gantry

room in PBS mode...197

4.28 GEANT4 implémentation of the gantry treatment room in

DS mode... 198

4.29 Internai structure of the nozzle as simulated in GEANT4. . . 199

1.1 Radiation weighting factors

... 29

1.2 Recommended dose limits in planned exposure situations . . 36

2.1

Simulated secondary partiale multiplicity for a 160 MeV pro­

ton beam impinging on a PMMA target... 56

2.2 Proton range and cylinder height for different target materials 57

2.3 References for neutron yield from thick targets irradiated by

a proton beam... 58

2.4 Target characteristics for a 113 MeV proton beam ... 59

2.5 Target characteristics for a 256 MeV proton beam ... 59

2.6 Concrète atomic composition from NIST... 80

2.7 References for shielding parameter measurement for thick tar­

gets irradiated by a proton beam... 92

2.8 Atomic composition and mass fraction of target materials for

the shielding systematic study... 102

3.1

Neutron and gamma-ray interaction probabilities in typical

gas proportional counters and scintillators... 142

3.2 WENDI-II sensitivity calculated in a ^^^Cf neutron field. . . . 160

4.1

Most recent shielding studies for proton therapy facility ... 169

4.2 Ambient dose équivalent rates in the cyclotron room, calcu­

lated with GEANT4 ... 189

4.3 Ambient dose équivalent rates in the cyclotron room:

mea-sured with the WENDI-II, calculated with MCNPX and com-

pared with GEANT4...189

4.4 Measured ambient dose équivalent rates in the gantry room

Hadron beams (proton, neutron and ion) with energy up to hundreds of

MeV bave been used for décades in many kinds of applications. Indeed,

charged hadrons are particularly suitable for cancer therapy in spécifie cases,

e.g. ocular and prostate treatments, for which they definitely compete with

conventional photon and électron beams. The main advantage is their ability

to treat tumor by not irradiating healthy and radiation-sensitive cells located

around the tumor. On the other hand, producing high-energy hadron beams

requires huge and expensive installations and advanced technologies, even

while many efforts are done to make hadron therapy facilities affordable for

ail countries around the world. Today, about 50 hadron therapy facilities are

in operation, 25 are under construction and more than 100 000 patients hâve

been treated [PTCOG, 2014]. In few years, two proton therapy facilities will

be installed in Belgium.

Interactions of radiation beams may lead to transfer of their energy to

matter. In most cases, the energy transfer leads to the émission of électrons

and, in the case of biological cells, these may interact with cell éléments

and more particularly with the DeoxyriboNucleic Acid (DNA) — directly or

indirectly through radiolysis of water and free radicals (OH“) production

— see figure 1 [Morgan and Sowa, 2005]. If damages to the DNA lead to

the cell prolifération, radio-induced cancer may occur, while if the radiation

exposition is léthal for the cell, it may be useful for tumor treatment, this

is the so-called radiation therapy.

Figure 1: Radiation eiïects on biological cells. Direct and indirect effects to

the DNA of atomic électrons freed by radiation beam [Morgan and Sowa,

2005].

to reach a maximum, called Bragg peak, after which the particles stop and

no energy is deposited further, see figure 2 [Levin et al., 2005]. The depth

of the Bragg peak dépends on the initial proton energy. As a conséquence,

varying the proton energy allows to irradiate an extended target volume, this

is called Spread-Out Bragg Peak (SOBP). On the contrary, photon beams

deposit their energy in such a way that the depth-dose profile decreases ex-

ponentially with the pénétration depth, except near the skin surface where

an increasing part, called build-up, occurs. A large part of tissue and or-

gans located outside the target volume are then irradiated, see also figure

3 [PTCRi, 2014], and that shows the greatest advantage of using protons

instead of photons for radiation therapy [Smith, 2006; Suit et al., 2010]. Par-

ticle interactions with matter and energy déposition processes are described

in Chapter 1.

beam direction I ^

Figure 2: Typical proton therapy treatment, Spread-Out Bragg Peak

(SOBP, dashed blue line) and photon beam treatment (red line). The SOBP

is the sum of several individual Bragg peaks (thin blue Unes) at staggered

depths. The pink area represents the additional dose delivered by photon

therapy which can be the source of damage to normal tissues and of sec-

ondary cancers, especially of the skin. Prom [Levin et ah, 2005].

[PTCRi, 2014],

operators [Binns and Hough, 1997]. This work focuses on this second aspect.

Which kinds of particles are emitted during treatment? What is the risk

for potentially-exposed people? How to quantify and minimize it? These

issues hâve been studied since the beginning of the use of particle accelera-

tors: spécifie detectors hâve been developed and used to give an estimation

of the risk, shielding walls hâve been designed and located around acceler-

ators and treatment rooms, etc. When secondary-particle détection is not

possible because the point of interest is not reachable or the facility is sim-

ply not in operation yet, advanced numerical codes can be used instead to

estimate radiation protection quantities. The most common codes are the

particle-transportation simulation codes based on the Monte Carlo methods

which are described at the beginning of Chapter 2. These codes are very

useful to calculate and optimize the shielding design of a proton therapy

center (wall thickness, maze geometry, etc.) by minimizing the dose due to

secondary radiations in frequented areas. However, shielding walls should

not be as thick as possible because of obvious economical reasons. There-

fore, numerical simulations should be sufficiently accurate to estimate the

dose and ensure it to be below the legal limits.

Monte Carlo codes use theoretical and empirical physical models to

transport subatomic particles over a large energy range and in complex

structures. However, results calculated by using these codes must be vali-

dated by experimental data, but two non-exclusive approaches can be con-

sidered:

• and the protection, or conservative, approach, expecting that both cal-

cnlated and experimental results overestimate the real quantity which

is evaluated.

The first approach is the most difhcult to deal with but definitely the most in-

teresting since it challenges physical models used in simulation codes. How-

ever, it needs also to know the experimental conditions with sufhciently

précision to implement them in the simulations. In the context of this

work, physical models dealing with the secondary émission, more partic-

ularly photons and neutrons, are compared in Chapter 2 by using the scien-

tific approach. Comparisons with experimental results from the literature

are made when possible. Extensive simulations are also performed in this

chapter in order to estimate the atténuation of these secondary radiations

through a shielding wall with a simplified geometry. For instance, doses

before and behind the shield are computed as functions of the initial proton

energy and the target material, which may be useful to estimate, as a first

approximation, the dose behind shielding walls in more complex geometries.

Validating numerical results by experimental data needs also to ensure

that dose detectors, called dosemeters, are well calibrated and give the de-

sired quantity. The Chapter 3 describes several detectors spécifie to the

secondaries produced in proton therapy centers and similar facilities. More

particularly, it focuses on a spécifie detector dedicated to neutrons with

energy up to a few GeV’s [Olsher et al., 2000] and used in Chapter 4 for

the proton-therapy-center shielding study. The response fonction of this

dosemeter was originally computed by Monte Carlo simulations while re­

cent measurements validated its response up to very high energies [Olsher

and McLean, 2008]. However, in order to study this detector, its response

fonction and sensitivity are computed by using different physical models

available in Monte Carlo codes, showing sometimes large discrepancies.

The conclusion summarizes results of the different chapters and tries to

answer the following issues: How large are the discrepancies between codes

Bibliography

S. Agosteo, C. Birattari, M. Caravaggio, M. Silari, and G. Tosi. Secondary

neutron and photon dose in proton therapy. Radiotherapy and Onœlogy,

48:293-305, 1998.

H. Alt Abderrahim, P. Kupschus, E. Malambu, P. Benoit, K. Van Tichelen,

B. Arien, F. Vermeersch, P. D’hondt, Y. Jongen, S. Ternier, and D. Vande-

plassche. MYRRHA: A multipurpose accelerator driven System for research

& development. Nuclear Instruments and Methods in Physics Research, A

463:487-494, 2001.

G. Bauer. OverView on spallation target design concepts and related ma-

terials issues. Journal of Nuclear Materials, 398:19-27, 2010.

P. Binns and J. Hough. Secondary Dose Exposures during 200 MeV Proton

Therapy. Radiation Protection Dosimetry, 70 (1-4) :441-444, 1997.

W. P. Levin, H. Kooy, .1. S. Loeffler, and T. F. DeLaney. Proton beam

therapy. British Journal of Cancer, 93:849-854, 2005.

W. F. Morgan and M. B. Sowa. Effects of ionizing radiation in nonirradi-

ated cells. Proceedings of the National Academy of Sciences (PNAS) of the

USA, 4 October 2005, 102(40):14127-14128, 2005.

R. H. Olsher and T. D. McLean. High-energy response of the PRESCILA

and WENDI-II neutron rem meters. Radiation Protection Dosimetry,

130(4):510-513, 2008.

R. H. Olsher, H. Hsu, A. Beverding, J. H. Kleck, W. H. Casson, D. G.

Vasilik, and R. T. Devine. WENDI: an improved neutron rem meter.

Health Physics, 79:170-181, 2000.

PTCOG. Particle Therapy Centers. Particle Therapy Co-Operative Group

(PTCOG), Website http://ptcog.web.psi.ch, Last update 24/03/2014,

Last consultation 09/06/2014, 2014.

Physics for Radiation

Protection

Contents______________________________________________________

1.1 Interactions of Charged Particles with Matter .

11

1.1.1

Collision Stopping Power... 11

1.1.2

Radiative Stopping Power... 11

1.1.3 Nuclear Collisions... 12

1.1.4 Total Stopping Power... 12

1.1.5 Range and Pénétration Depth... 13

1.2 Photon Interactions with Matter... 15

1.2.1

Photoelectric Absorption ... 15

1.2.2

Cohérent or Rayleigh Scattering... 16

1.2.3 Incohérent and Compton Scatterings... 16

1.2.4 Pair Production ... 17

1.2.5 Photonuclear Absorption ... 18

1.2.6 Total Cross-Section... 18

1.3 Neutron Interactions with Matter... 20

1.3.1

Energy Classification... 20

1.3.2 Interactions... 20

1.3.3

Cross-sections...22

1.3.4 Intranuclear Cascade Models... 23

1.4 Dosimetry and Radiation Protection... 27

1.1

Interactions of Charged Particles with Matter

1.1.1

Collision Stopping Power

Charged particles, such as ions, protons and électrons, passing through some

material, hâve Coulomb-force interactions with atomic électrons and nuclei

through elastic or inelastic collisions depending on their « distance », called

impact parameter, to the target atom. If this distance is greater than {soft

collision) or equal to {hard collision) the atomic radius, valence électrons can

be excited {excitation process) or released from the atom {ionizing process).

The average loss of energy dT of a charged particle with kinetic energy T

per unit of path length dx, is called the stopping power S. When the loss of

energy is due to kinetic energy transfer by collision in a medium of density

P,

the collision stopping power 5coi is defined. The mass collision stopping

power 5coi/p is approximately represented by the Bethe-Bloch formula

where /3 = u/c is the incident-particle velocity v divided by the light velocity

c, Z and A are the atomic and mass numbers of the medium, respectively,

and Z is the effective charge of the incident particle. For non-relativistic

energy, the collision stopping power falls when the particle kinetic energy

rises up. As the fraction {Z/A) decreases slowly with Z (from 0.5 for Z = 2

to 0.4 for Z — 100), S'coi/p behaves similarly. Depending on the mass of

the incident particle, électron or proton and ion, the factor C may be a

complex function of the particle velocity and takes into account the shell

correction, the relativistic rise when the particle kinetic energy becomes

higher than its rest mass, and the relativistic density-efîect correction. The

first effect occurs when the particle velocity is lower than the atomic électron

velocity and then less atomic électrons contribute to the interaction and

5coi decreases. The third effect occurs because of the electric field, i.e. the

Coulomb force, which falls due to the atomic polarization by the incident

particle, making a lower 5'coi/p.

1.1.2 Radiative Stopping Power

is relatively constant, S^ad/P is approximately proportional to Z and T.

1.1.3 Nuclear Collisions

Direct collision of the charged particle with the atomic nucléus, i.e. an

impact parameter less than the nuclear radius, leads essentially to elastic

scattering. For électrons, the transfer of energy with the nucléus is negligi­

ble, but nuclear interactions, together with electronic collisions, make their

trajectory through matter very sinuous.

For a heavy charged particle having sufficiently kinetic energy, an inelas-

tic reaction with the nucléus may occur. The incident particle goes into the

nucléus and one or more individual nucléons may be struck and driven out

of the nucléus, collimated strongly in the forward direction. After this in-

tranuclear cascade process, the résultant highly-excited nucléus decays from

its excited state by émission of so-called évaporation particles (mostly nu­

cléons of relatively low energy) and photons. More details on this nuclear

reaction and the related physical models are discussed in the section 1.3.4.

However, the average contribution of nuclear reactions to the total stop­

ping power is very small but not negligible for an accurate estimation of the

spatial deposited-energy distribution. Moreover, secondary particles pro-

duced by inelastic nuclear reactions are of great importance in a radiation

protection context, as shown further in this work.

1.1.4 Total Stopping Power

The mass total stopping power Stot/P is simply defined as

'S'rad

P

and is represented in figures 1.1 and 1.2 for électron and proton, respec-

tively, from databases available on the website of the National Institute of

Standards and Technology (NIST). For électrons over the MeV région, the

mass stopping power in ail materials is approximately 2 ± 1 MeV cm^/g,

which corresponds to a stopping power of 2 MeV/cm in water and human

tissue, while the proton mass stopping power decreases continuously over

the MeV to GeV range.

Figmre 1.1: Electron mass stopping powers for Carbon {Z = 6) in red,

Copper {Z = 29) in green and Lead (Z = 82) in black. Reproduced from

Berger et al. [2011].

1.1.5 Range and Pénétration Depth

Following Attix [1986]: « The range R o/ a charged particle of a given type

and energy in a given medium is the expectation value of the pathlength that

it follows until it cornes to rest (discounting thermal motion) ». Despite hard

Figure 1.2; Proton mass stopping powers for Carbon {Z = 6) in red, Copper

{Z — 29) in green and Lead {Z = 82) in black. Reproduced from Berger

et al. [2011].

range McsDA can be expressed as

pKcsDA = /

—-j- dT.

(1.4)

JO Jtot/P

Attix [1986] defines also a second quantity related to the first: « The pro-

jected range o/ a charged particle of a given type and initial energy in a

given medium is the expectation value of the farthest depth of pénétration of

the particle in its initial direction ».

1.2

Photon Interactions with Matter

A photon is an electromagnetic field which has complex interactions with

target atomic électrons, nuclei, atoms or molécules, depending on its wave-

length, i.e. its energy. In the context of this work, only interactions leading

to a subséquent transfer of energy are discussed, i.e. X-ray and 7-ray inter­

actions. X-rays are photons produced by deexcitation of atomic électrons

or dming a charged-particle slowing-down process, typically over the range

from 100 eV to 1 MeV, while 7-rays are photons produced by deexcitation of

nuclei or by annihilation reactions between matter and antimatter, typically

over the range from 10 keV to 100 MeV.

The probability of interaction with a target entity is usually expressed

in terms of the cross-section a. The cross-section units are [cm^] or barns

which equal 10“^^ cm^, and the numerical value may be interpreted as the

interaction probability if the target was uniformly distributed on a 1-cm^

plane normal to the incident particle direction.

1.2.1 Photoelectric Absorption

The photoelectric effect consists in the total absorption of the incident pho­

ton by the atom. An atomic électron is then ejected with a kinetic energy

equal to the initial photon energy minus the électron binding energy. The

ejected électron coming from an inner atomic shell is ejected with a higher

probability, provided that the photon energy is higher than the correspond-

ing binding energy. Therefore, as the photon energy decreases, the atomic

cross-section a^^ph plummets discontinuously when the photon energy be-

comes insufficient to release an atomic électron from its shell.

The mass atomic cross-section aO"ph/p for photoelectric absorption is

approximately given by

a^ph X3-3-6

---— OC --- 5—T

P

A photon undergoes an incohérent scattering when it gives up part of its

energy during interaction with an atom or an atomic électron, and then is

diffused. For photon energy above about 0.1 MeV, the incohérent diffusion

is well described by the Compton scattering theory which considers the

interaction between the incident photon and a weakly-bound électron, i.e.

an atomic électron from an outer shell. The photon is diffused and a part

of its energy is given to the électron. The kinetic energy of this électron is

equal to the transferred energy minus its initial binding energy.

The kinematic analysis and the conservation laws give the following re-

sults. Only a maximum fraction of the photon energy can be transferred

to the électron and as this fraction increases, the électron scattering angle

gradually decreases from 7

/2 to 0 while the photon angle increases from 0 to

7T. The photon probability to be diffused in the forward direction increases

with increasing initial photon energy.

1.2.4 Pair Production

A photon with sufficient energy hu, i.e. more than 1.022 MeV, may interact

with nuclear and electronic electric fields and disappear by giving rise to an

électron and a positron (électron antiparticle) with kinetic energies T~ and

T+, respectively, such that

hu = 2meC^+ T~+T^^+Tn

(1-7)

where rue is the électron rest mass and T

is the recoil energy of the host par-

ticle. Tu is negligible when the interaction occurs in the nuclear field while

it may be sufficient for the host particle to be ejected when the interaction

occurs in an électron field, leading to a triplet production.

Kinematic laws give the following results. Only photon with energy

above 2meC^ and 4meC^ can interact in the nuclear and electronic field, re­

spectively. For photon energies far above this energy threshold, the électron

and the positron coming from pair production are forward directed while

for triplet production, the three particles may départ in varions directions.

The nuclear pair-production cross-section <Tpn is evaluated from a theory

due to Bethe and Heitler and is approximately given by

^ oc Z

(1.8)

P

and the photon-energy dependence of the cross-section is roughly logarith-

mic, see figure 1.3.

The electronic triplet-production cross-section cTpe is very small, usually

negligible, compared to the pair-production cross-section in the field of an

atomic nucléus, and the corresponding mass cross-section is approximately

independent of Z.

Finally the total pair-production cross-section o-pair is given by

^pair _ ^pn

P P P '

between 2% for high-Z éléments and 6% for low-Z éléments to the total

cross-section.

1.2.6 Total Cross-Section

By neglecting the photonuclear interaction, the total mass cross-section /i/p

for photon can be written as

M ^ l^coh ^ <^incoh ^ <^pair

P~ P P P P '

The product of the total cross-section and the atomic density iVa of

the medium, called the atténuation coefficient fxNi^, is équivalent to the

probability per unit of length for the photon to internet. So the beam

intensity I of photons which hâve not interacted after a path of length dr

decreases of a quantity dl equal to

dl = -IfiNffir.

(1.11)

Therefore the intensity of unaffected primary photons decreases as a function

of the pénétration depth in matter following

I =

= loe-''/^

(1.12)

where A = l/{fiNa) is the so-called mean free path .

energies, i.e. around 1 MeV, the Compton effect is the dominant contribu­

tion to the total cross-section but over an energy range that becomes smaller

with increasing Z, while the photoelectric effect and the pair production are

the dominant contributions for lower and higher energies, respectively.

• Epithermal neutrons hâve an energy between 1 eV and 10 keV;

• Fast neutrons hâve an energy between 10 keV and 20 MeV;

• High-Energy neutrons hâve an energy between 20 MeV and 1 GeV;

• Relativistic neutrons hâve an energy above 1 GeV, corresponding

to the mass energy of a nucléon (w 940 MeV), for which relativistic

effects become non-negligible.

1.3.2 Interactions

Neutrons, just as other particles with zéro electric charge, hâve no Coulomb-

force interaction with atomic électrons and nuclei, and only nuclear reactions

may occur. Neutron interactions can be classified into 5 processes which

dépend on the neutron energy and the properties of the target material:

• Elastic scattering is a two-body interaction between the incident

neutron and a nucléus. Following the energetic and momentum con­

servation laws, a neutron of mass rrin, with an initial kinetic energy

T, collides with a nucléus of mass M, at rest, by transferring a kinetic

energy ATtr equal to

ATtr =

T

éMuin

(M + mn)2

COS^ (j)

(1.13)

where (j> is the angle of the recoil nucléus after the collision. In a head-

on collision ((;/!) = 0), the transfer of energy is maximum and is given

by

AT.

AMrtin

while the mean transfer of energy is

AT,

= T

2Mmn

(M + m^y

(1.15)

Therefore, neutrons undergo elastic collisions with subséquent trans­

fer of kinetic energy only in low-Z and hydrogenous materials such

as water, concrète and polyethylene. Indeed, if the target nucléus is

composed of one proton (^H) of mass rrip, thus M = rup « ma, the

maximum energy transfer is ATr.max ~ T and the mean energy trans­

fer is

~ T/2',

• Inelastic scattering is, in fact, a neutron capture followed by the

émission of a neutron with a lower energy and in a different direction

than the initial neutron. The target nucléus is potentially left in an

excited state and de-energizes by gamma decay channels. If the nucléus

is left in its ground state, it is considered as an elastic scattering;

• Capture process is équivalent to an inelastic scattering but with

other particles than one neutron in the exit channel. It encompasses

the émission of électron {P~), positron (,5+), proton, gamma (radiative

capture), deuteron (^H), tritium (^He), a-particle (^He) and more than

one neutron. Capture processes need the incident neutron energy to

be above some threshold spécifie to the capture reaction. If the decay

scheme has a very short decay time, called period, secondary particles

are considered as prompt while if the period is longer than seconds, up

to thousands of years, the material is considered as activateà, •

tron cross-section databases by mixing experimental results and advanced-

theory or empirical calculations. The National Nuclear Data Center (NNDC,

Brookhaven National Laboratory BNL, USA) and the Nuclear Data Ser­

vices (NDS, International Atomic Energy Agency lAEA, Austria) publish

on their website the major libraries such as those from the Evaluated Nu­

clear Data File (ENDF, USA), the Joint Evaluated Fission and Fusion Li-

brary (JEFF, Europe) and the Japanese Evaluated Nuclear Data Library

(JENDL, Japan). Most of the libraries give the neutron cross-sections over

the range from thermal to 20 MeV, but recently-added ENDF and JEFF

libraries extend to 150 MeV.

Figure 1.4 shows elastic and non-elastic cross-sections for low-, medium-

and high-Z materials. Elastic scattering is often the dominant component

to the total cross-section. However, thermal neutrons may be captured by

atomic nucléus and, depending on the nature of the target nucléus, capture

reaction (low-Z materials) or nucléus fission (high-Z materials) may occur.

Over the thermal and epithermal ranges, captine processes are character-

ized by a decreasing cross-section following a 1 /u law where v is the neutron

velocity. For non-elastic processes such as inelastic scattering (elastic chan-

nel included), capture and fission, strong discrète peaks called résonance

peaks occur at neutron energies spécifie to a particular nuclide because of

--- Carbon

--- Copper

---Lead

-iilO-iOiQ-9 10-8 10-7 10-6 10-5 10-'^ 10“^ 10“2 iQ-i 10'’ 10^ 10^

Neutron Energy [MeV]

Figure 1.4: Neutron cross-sections for Carbon {Z = 6) in green, Copper

{Z = 28) in red and Lead {Z = 82) in bine, ENDF library. Reproduced

from NNDC [2011].

1.3.4 Intranuclear Cascade Models

Nuclear reactions of high-energy heavy particles are very complex processes

but the first description was suggested by Serber [1947]. He noticed that, for

sufRciently-high-energy incident particles such as protons and neutrons, the

de Broglie wavelength Ag of the incident particle is of the order or shorter

than the average distance between nucléons (~ fm = 10-^5 m). Since the

de Broglie wavelength is dcfined by

hc

considered and experimental nucleon-nucleon cross-sections are used when-

ever possible [Bertini, 1963; Loveland et al., 2006]. However, interférence

between nucléons can be important and affect the particle-nucleon interac­

tion. These effects were taken into account by Goldberger [1948] when he

made the fîrst calculations by using the statistical model of the nucléus.

The struck nucléon can escape from the nucléus if the transfer of energy

is higher than ~ 150 MeV and the émission is strongly forward directed; but

below this energy, it may collide with other nuclear particles which in turn

may escape or interact with other nucléons, this is the so-called intranuclear

cascade (INC) represented in figure 1.5. It should be noted that non-nucleon

particles such as pion

may be produced during the cascade and escape.

A neutral pion decays into two photons while charged pion decays into a

charged muon and a neutrino. Muons are not subject to nuclear forces but

behave like heavy charged particles for ionization and excitation processes,

while neutrinos are often considered as not interacting with matter [Lieser,

1997; NCRP, 2003; PTCOG, 2010].

After the INC, the energy is distributed over the nucléus in a non-

equilibrium state, which is difScult to evaluate. Then, a description of a

pre-equilibrium phase, using the exciton model, was proposed by Griffin

[1966]. In this model, intranuclear collisions give rise to an increasing num-

ber of excited particles and holes (the excitons), accompanied by nucléon

émission, eventually leading to an equilibrated but excited nucléus [Heikki-

nen and Stepanov, 2003].

n

Figure 1.5: Schematic view of nuclear cascade [Lieser, 1997].

model assumes complété energy équilibration before particle émission, and

re-equilibration of excitation energies between successive évaporation émis­

sions, until the excitation energy of tlie nucléus falls below some cutoff en­

ergy. At this moment, the remaining excitation energy is released through

decay chains. As a resuit, the angular distribution of emitted particles is

isotropie [Heikkinen and Stepanov, 2003]. However, if fission channels are

energetically allowed, nuclear break-up may also occur.

Intranuclear cascade and pre-equilibrium, évaporation, fission and decay

phases are usually known as spallation reactions and are schematically rep-

resented in figure 1.6. The INC is a fast stage (10~^^ — 10“^^ s) while the

évaporation phase is much slower (10“^^ —10“^® s) [Heikkinen and Stepanov,

2003]. The final decay, called activation, dépends on the nature of the ex-

cited nucléus and may be very long (from part of second to thousands of

years), which is of great importance for radiation protection because it may

contribute to the radiation exposition even if no beam is running.

Figure 1.6: Schematic view of spallation reaction [Pedoux, 2012],

1.4

Dosimetry and Radiation Protection

Particle interactions may modify the nature of matter by changing its Chem­

ical, and hence biological in case of tissue, properties. If the radiation affects

the DeoxyriboNucleic Acid (DNA) of a cell, directly or indirectly by means

of free radicals produced by the radiation, it may lead to the cell dysfunc-

tion or death. This can be used to defeat tumor cells, this is the so-called

radiation therapy, but it may also injme those standing near a radiative

environment.

Charged particles are considered as directly ionizing radiations since their

interactions with matter cause many excitations and other ionizations, while

neutral particles, such as photon and neutron, are indirectly ionizing ra­

diations because their interactions may produce a few secondary charged

particles that themselves directly ionize matter and finally cause the biolog­

ical effect. However, the link between the particle interactions and the cell

death is not straightforward because of the strong dependence of biological

reactions to the physical properties of the radiation beam. Extensive de­

scriptions on biological effects of ionizing radiation can be found elsewhere

[ICRP, 2007a,b], Nevertheless, some quantities are described below for the

good understanding of following chapters and can be found in reports of

the International Commission on Radiological Protection (ICRP) and the

International Commission on Radiation Units and Measurements (ICRU)

[ICRP, 1996, 2007a, 2010; ICRU, 2011].

1.4.1 Absorbed Dose

The absorbed dose D, or simply dose, at a point in a medium, is the mean

deposited energy by an ionizing radiation to matter per unit of mass, the

unit is the Gray [Gy] = [J/kg]. The dose is a physical quantity and is used

to express the local energy déposition of some radiation beam in matter.

Figure 1.7: Depth dose curves in tissue for 4-MeV photon, 20-MeV photon,

4-MeV électron and 150-MeV proton beams [Bradu and Thiéblemont, 2012],

deposited [Smith, 2006]. Depth dose profiles by using proton and ion beams

are similar. However, when ions are used, more intense dose is deposited in

the Bragg peak and a tail occurs just after it, due to the fragmentation of

the incident ion during nuclear interaction [Suit et al., 2010].

Using proton beam for cancer therapy was first suggested by Wilson

[1946] at Harvard in 1946 and the first patient was treated in 1954 at the

Lawrence Berkeley Laboratory in 1954 [Tobias et al., 1958]. Today, particle

therapy with protons, hélium, and carbon ions has gained increasing interest

because of the fast technology improvement on particle accelerators, beam

delivery Systems, imaging, etc.

1.4.2 Dose Equivalent

exposition) because of the normally-effective defense mechanisms of cells,

but it may modify the cell DNA and lead to non-directly observable effects

such as cancer or hereditary diseases, which are then stochastic.

The probability of stochastic effccts is linked to the dose but dépends also

on the type and energy of the radiation. Therefore, a radiation weighting

factor lüR is applied to the dose, so defining the dose équivalent in nuits

of Sievert [Sv] = [J/kg], given by

Jfx = X!

(1-18)

R

where D

,

is the dose averaged over the tissue or organ T due to radiation

R. This weighting factor is selected from the Relative Biological Effectiveness

(RBE) of a radiation, i.e. the inverse ratio of doses between the considered

radiation and a reference radiation, which is often photon, producing the

same degree of a defined biological end-point. Recommended values at ail

energies for different particles except neutron are shown in the table 1.1. Be­

cause of complex nuclear reactions, the RBE for neutrons reaches different

values depending on the neutron energy. Step function was first suggested

[ICRP, 1991] but last publications recommend the use of a continuous func­

tion such as shown in figure 1.8 [ICRP, 2007a, 2010]. The maximum value of

20 has been maintained for neutrons at about 1 MeV but below this energy,

the value has changed from 5 to 2.5 due to the fact that a significant frac­

tion of the absorbed dose is deposited by secondary photons mainly from the

(n,7) reaction, which reduces the biological effectiveness. Above 50 MeV,

the asymptotic value of 2.5 has been chosen based on recent calculations

[ICRP, 2007a].

Radiation type

WR

Photon

1

Electron and muon

1

Proton and charged pion

2

Alpha particle, fission

fragment and heavy ion

Neutron

20

Function of the neutron

energy, see figure 1.8.

Figure 1.8: Radiation weighting factors tWR for neutrons as a fonction of

neutron energy. The step fonction was first suggested [ICRP, 1991] but the

continuons fonction is now recommended [ICRP, 2007a, 2010].

1.4.3

Effective Dose

The values of the radiation weighting factor are independent of the irradi-

ated tissue or organ. The effectiveness of a radiation on the physiological

properties of a tissue or an organ is taken into account through tissue weight­

ing factors wr and is quantified by the effective dose E (the energy is also

denoted by E in this work, but no confusion should occur following the

context), also in units of [Sv],

E = Y,

H

:.

(1.19)

T

the effective dose may vary with the direction of the beam because of the

location of the organs in the human body.

The value of effective dose limits has changed between the ICRP [1996]

and the ICRP [2010] due to the new values of

and

, e.g. from 0.05 to

0.12 for breast, as well as the improvement of voxelized phantom modeliza-

tion in numerical simulations.

1.4.4 Ambient Dose Equivalent

Direct measurements of the équivalent dose, particularly for neutrons, and

the effective dose are not possible in practice. Therefore, operational quan­

tifies hâve been defined to give an estimation of the protection quantifies

related to an exposure. They are based on spécifie irradiation of a spécifie

body and were defined to be easily estimated or measured in area and indi-

vidual radiation monitoring. Among others, some of these quantifies are of

particular interest for this work, such as the ambient dose équivalent H* (d).

Following the ICRP [2007a]: « the ambient dose équivalent, at a point

in a radiation field, is the dose équivalent that would be produced by the

corresponding expanded and aligned field in the ICRU sphere at a depth, d,

on the radius vector opposing the direction of the aligned field ». A field is

expanded when spectral and angular distributions of the radiation hâve the

same values as those at the point of interest, in ail points of a suffidently

large volume surrounding the point of interest. The field is aligned when the

beam is unidirectional, see figure 1.9. An ICRU sphere is a tissue-equivalent

sphere with a diameter of 30 cm and a density of 1 g/cm^. For strongly

penetrating radiation, such as neutron and photon, a depth oi d = 10 mm

is recommended.

Many efforts hâve been made to give conversion coefficients between some

radiation intensity and iî*(10). The particle intensity is often expressed by

the fluence which is, at a point in a radiation field, the number of incident

particles per unit area, in units of [m~^] or [cm“^], i.e. this is the « quotient

of dN by da, where dN is the number of particles incident on a sphere of

cross-sectional area da » [ICRU, 2011]:

^ dN