U N I V E R SITÉ LIBRE DE
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)
Il y a approximativement 4 ans, alors que j’entamai mon blocus du MA2 Ingénieur Civil Physicien, le professeur Alain Dubus, alors co-promoteur de mon mémoire, me proposa d’entamer une thèse sous le financement de l’Association Vinçotte Nuclear (que je remercie également) dans le domaine de la sureté nucléaire et de la radioprotection. Le financement m’ayant été octroyé et la thèse menée à terme, je voudrais remercier Alain, devenu mon promoteur de thèse, pour m’avoir offert l’opportunité d’un travail de recherche dans un domaine qui m’intéresse énormément, à savoir la radio-protection. Depuis, il m’a toujours soutenu avec enthousiasme et confiance et ce, durant ces 3 ans et demi de thèse.
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 discussréflex-ions, 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 moeurs 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-Étienne, Yvan, Pierre, Artem, Julio, Xavier, Farshid et Nicolas (Seigneur, 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.
Over the last few decades, radiotherapy using high-energy proton beams over the range from 50 MeV to 250 MeV has been increasingly used and developed. Indeed, it offers the possibility to focus the dose in a very narrow area around the tumor cells. The tumor control is improved compared to radiotherapy using photon beams and the healthy cells around the tumor are not irradiated since the range of charged particles is limited. However, due to nuclear reactions of the incident charged particles in the tissue, secondary high-energy radiations, essentially photons and neutrons, are produced and irradiate the treatment room.
As a consequence, thick concrete shielding walls are placed around the treatment room to ensure that other people and workers received a dose as small as possible. The dose measurement is performed with specific doseme-ters such as the WENDI-II, which gives a conservative estimation of the ambient dose equivalent 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 concrete shielding wall but the neutron dose is definitely the main component behind a wall with sufficient thick-ness. Shielding parameters, e.g. attenuation coefficients, vary as functions of emission angle (regarding the incident beam direction), incident proton energy, and target material and composition.
The WENDI-II response functions 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 function and the detector sensitivity.
since concrete 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 GEANT4 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 Presentations & Posters
1. T. Vanaudenhove, A. Dubus and N. Pauly
1 poster: WENDI-II Fast Neutron Detector Modelization with the Monte Carlo Simulation Toolkit Geant4
2nd International Workshop on Fast Neutron Detectors and Applica-tions (FNDA 2011), Ein Gedi, Israël, 6-11/11/2011.
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
2-7/09/2012.
3. V. De Smet, F. Stichelbaut, T. Vanaudenhove, G. Mathot, I. Gerardy, G. De Lentdecker, A. Dubus and N. Pauly 1 poster: Comparison between Monte Carlo simulations and H∗(10) measurements performed with a WENDI-2 detector inside a proton therapy facility
12th Neutron and Ion Dosimetry Symposium (NEUDOS-12), Aix-en-Provence, France, 3-7/06/2013.
4. V. De Smet, F. Stichelbaut, T. Vanaudenhove, G. De Lent-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 Attenuation 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 Attenuation 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 function 134 3.1 Neutron Detector and Dosemeter Description . . . 136
3.2 Monte Carlo Simulations of the WENDI-II Response Function147 3.3 Conclusion . . . 159
4 Comparing Numerical and Experimental Evaluations of Am-bient Dose Equivalent in a Proton Therapy Center 166 4.1 Proton Therapy Facility Description . . . 168
4.4 Ambient Dose Equivalent Rate in the Treatment Room in DS mode. . . 198
4.5 Conclusion . . . 203
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 attenuation 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, electron and proton beams. . . 28
1.8 Radiation weighting factors wR for neutrons . . . 30
1.9 Schematic representation of an oriented and expanded radia-tion field and the ICRU sphere for the ambient-dose-equivalent definition . . . 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 Beryllium target irradiated by a 113-MeV proton beam . . . 60
2.6 Differential energy spectra of neutron leaving the Aluminum target irradiated by a 113-MeV proton beam . . . 62
2.7 Differential energy spectra of neutron leaving the Aluminum target irradiated by a 256-MeV proton beam . . . 62
2.8 Differential energy spectra of neutron leaving the Iron target irradiated by a 113-MeV proton beam . . . 63
2.9 Differential energy spectra of neutron leaving the Iron target irradiated by a 256-MeV proton beam . . . 63
2.10 Differential energy spectra of neutron leaving the Uranium target irradiated by a 113-MeV proton beam . . . 64
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 emission from PMMA for a 160-MeV proton beam and from Lucite for a 40-MeV proton beam . . . 71
energy, for a 250-MeV proton beam on Iron target . . . 75
2.22 Total ambient dose equivalent HSfor a 100-MeV proton beam on Iron target . . . 76
2.23 Total ambient dose equivalent HSfor a 250-MeV proton beam on Iron target . . . 76
2.24 Source term for monoenergetic neutrons in concrete as a func-tion of neutron energy . . . 78
2.25 Attenuation length for monoenergetic neutrons in concrete as a function of neutron energy. . . 79
2.26 Attenuation length calculations for monoenergetic neutrons in concrete as a function of neutron energy . . . 79
2.27 Shielding concrete sphere and variance reduction by impor-tance sampling for neutrons . . . 82
2.28 Neutron and photon ambient dose equivalent through a spher-ical concrete shield for a 100-MeV proton beam on iron target 84
2.29 Neutron and photon ambient dose equivalent through a spher-ical concrete shield for a 250-MeV proton beam on iron target 84
2.30 Neutron and photon ambient dose equivalent through a spher-ical concrete 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 equivalent through a spher-ical concrete 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
MeV proton beam on Iron target . . . 89
2.37 Neutron ambient dose equivalent through a spherical concrete shield for a 250-MeV proton beam on Iron target, multiplied by the distance from the source . . . 91
2.38 Source terms H1 for neutrons in concrete, for a 250-MeV pro-ton beam on Iron target . . . 94
2.39 Source terms H1 for neutrons in concrete, for a 250-MeV
pro-ton beam on Iron target . . . 95
2.40 Source terms Hout for neutrons in concrete, for a 250-MeV
proton beam on Iron target . . . 95
2.41 Attenuation lengths for neutrons in concrete, for a 250-MeV proton beam on Iron target . . . 97
2.42 Neutron ambient dose equivalent compared with semi-empirical laws at 60-70◦ solid angle . . . 99
2.43 Intermediate d-value between the first and the second expo-nential curves of the dose attenuation law, for a 250-MeV proton beam on Iron target. . . 99
2.44 Attenuation length in the first meter of concrete as a function of emission angle and incident proton energy for a tissue target103
2.45 Attenuation length in the first meter of concrete as a function of emission angle and incident proton energy for a Nickel target104
2.46 Attenuation length in the first meter of concrete as a function of emission angle and incident proton energy for a Tantalum target . . . 104
2.47 Attenuation length in the first meter of concrete as a function of emission angle and incident proton energy for tissue, Nickel and Tantalum targets . . . 105
2.48 Attenuation length at equilibrium as a function of emission angle and incident proton energy for a tissue target . . . 106
2.49 Attenuation length at equilibrium as a function of emission angle and incident proton energy for a Nickel target . . . 107
talum targets . . . 108
2.52 Dose at the shield entrance as a function of emission angle and incident proton energy for a tissue target . . . 109
2.53 Dose at the shield entrance as a function of emission angle and incident proton energy for a Nickel target . . . 110
2.54 Dose at the shield entrance as a function of emission angle and incident proton energy for a Tantalum target . . . 110
2.55 Dose at the shield entrance as a function of emission angle and incident proton energy for tissue, Nickel and Tantalum targets . . . 111
2.56 Source term in the first meter of concrete as a function of emission angle and incident proton energy for a tissue target 112
2.57 Source term in the first meter of concrete as a function of emission angle and incident proton energy for a Nickel target 113
2.58 Source term in the first meter of concrete as a function of emission angle and incident proton energy for a Tantalum target . . . 113
2.59 Source term in the first meter of concrete as a function of emission angle and incident proton energy for tissue, Nickel and Tantalum targets . . . 114
2.60 Source term at equilibrium as a function of emission angle and incident proton energy for a tissue target . . . 115
2.61 Source term at equilibrium as a function of emission angle and incident proton energy for a Nickel target . . . 116
2.62 Source term at equilibrium as a function of emission angle and incident proton energy for a Tantalum target . . . 116
2.63 Source term at equilibrium as a function of emission angle and incident proton energy for tissue, Nickel and Tantalum targets . . . 117
2.64 Dose at the shield exit as a function of emission angle and incident proton energy for a tissue target . . . 118
2.67 Dose at the shield exit as a function of emission angle and incident proton energy for tissue, Nickel and Tantalum targets120
3.1 Ratio of the response function and the ambient-dose-equivalent conversion function for the Andersson-Braun and the Leake
rem counter. . . 143
3.2 Schematic view of the Leake neutron detector. . . 143
3.3 Response to lateral irradiation of the A-B rem counter with and without 1-cm Pb around the boron plastic attenuator.. . 145
3.4 Rem meter response functions (normalized at 2 MeV) relative 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 3He(n,p)3H reaction over the energy inside the active volume of the WENDI-II detector151 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 a252Cf 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 Selection 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 pole of AVF cyclotron, no spiral angle and spiral shape175
4.10 Dee/Counter-Dee acceleration structure . . . 175
4.11 Half-view of an IBA 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 implementation of the cyclotron room. . . 183
4.18 Ambient dose equivalent in the south and west walls of the cyclotron room. . . 184
4.19 Ambient dose equivalent in the maze walls of the cyclotron room. . . 185
4.20 Detector positions and variance reduction 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 equivalent rate in maze legs of the cyclotron room. . . 190
4.23 Diffusion and transmission of the ambient dose equivalent rate in maze legs of the cyclotron room. . . 191
4.24 GEANT4 implementation 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 equivalent rate in the maze legs of the gantry room in PBS mode. . . 197
4.28 GEANT4 implementation of the gantry treatment room in DS mode. . . 198
4.29 Internal structure of the nozzle as simulated in GEANT4. . . 199
1.1 Radiation weighting factors wR . . . 29
1.2 Recommended dose limits in planned exposure situations . . 36
2.1 Simulated secondary particle 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 Concrete 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 252Cf neutron field. . . . 160
4.1 Most recent shielding studies for proton therapy facility . . . 169
4.2 Ambient dose equivalent rates in the cyclotron room, calcu-lated with GEANT4 . . . 189
4.3 Ambient dose equivalent rates in the cyclotron room: mea-sured with the WENDI-II, calculated with MCNPX and com-pared with GEANT4 . . . 189
4.6 Measured ambient dose equivalent rates in the gantry room in DS mode . . . 201
Hadron beams (proton, neutron and ion) with energy up to hundreds of MeV have been used for decades in many kinds of applications. Indeed, charged hadrons are particularly suitable for cancer therapy in specific cases, e.g. ocular and prostate treatments, for which they definitely compete with conventional photon and electron 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 all countries around the world. Today, about 50 hadron therapy facilities are in operation, 25 are under construction and more than 100 000 patients have 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 emission of electrons and, in the case of biological cells, these may interact with cell elements 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 proliferation, radio-induced cancer may occur, while if the radiation exposition is lethal for the cell, it may be useful for tumor treatment, this is the so-called radiation therapy.
Figure 1: Radiation effects on biological cells. Direct and indirect effects to the DNA of atomic electrons 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 depends on the initial proton energy. As a consequence, 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 penetration 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 deposition processes are described inChapter 1.
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 lines) 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. From [Levin et al.,2005].
Figure 3: Clinical dose distributions for photon and charged particle therapy [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 have been studied since the beginning of the use of particle accelera-tors: specific detectors have been developed and used to give an estimation of the risk, shielding walls have been designed and located around acceler-ators and treatment rooms, etc. When secondary-particle detection 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-culated and experimental results overestimate the real quantity which is evaluated.
The first approach is the most difficult 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 sufficiently precision to implement them in the simulations. In the context of this work, physical models dealing with the secondary emission, more partic-ularly photons and neutrons, are compared inChapter 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 attenuation 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 specific to the secondaries produced in proton therapy centers and similar facilities. More particularly, it focuses on a specific 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 function 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 function and sensitivity are computed by using different physical models available in Monte Carlo codes, showing sometimes large discrepancies.
facility building process and should obviously be checked and validated a posteriori, i.e. when the facility is constructed and operational, by experi-mental data. Therefore, experiexperi-mental evaluations of the dose are performed with the dosemeter studied in Chapter 3 at the proton therapy center of Essen, Germany, and compared with numerical results in order to evaluate discrepancies and validate models and geometries considered in the simula-tions. This step is of course crucial for a radiation protection study because it should give confidence in the designing of shielding walls by means of numerical tools but also for further shielding calculations of similar particle accelerator facilities.
Bibliography
S. Agosteo, C. Birattari, M. Caravaggio, M. Silari, and G. Tosi. Secondary neutron and photon dose in proton therapy. Radiotherapy and Oncology, 48:293–305, 1998.
H. Aït 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 Mama-terials, 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, J. 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.
PTCRi. Introduction. Particle Therapy Cancer Research Institute (PTCRi), part of the Oxford Martin School, University of Oxford. Website
A. R. Smith. Proton therapy. Physics in Medicine and Biology, 51:R491– R504, 2006.
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 Penetration Depth. . . 13
1.2 Photon Interactions with Matter . . . . 15 1.2.1 Photoelectric Absorption . . . 15
1.2.2 Coherent or Rayleigh Scattering . . . 16
1.2.3 Incoherent 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 1.4.1 Absorbed Dose . . . 27
1.4.2 Dose Equivalent . . . 28
1.4.4 Ambient Dose Equivalent . . . 31
1.4.5 Principles of Radiological Protection . . . 34 Radiation beams are often composed of photons, electrons, neutrons, protons or ions. Their physical properties and interaction processes with other particles depend on their nature and energy. The way to understand how a particle beam can be used to treat tumor and how radiation protection constraints must be specified is then not straightforward.
Thus, this chapter defines some basics of particle physics needed for the good understanding of this work. The first three sections describe charged particle, photon and neutron interaction processes. The fourth section de-scribes the biological effects and the ability of these particles to treat dis-eases, as well as definitions and concepts about radiation protection and dosimetry. Topics included in this chapter can be found in main references such asEvans[1955], Attix[1986], Martin[2010], NCRP[2003],Podgoršak
1.1
Interactions of Charged Particles with Matter
1.1.1 Collision Stopping PowerCharged particles, such as ions, protons and electrons, passing through some material, have Coulomb-force interactions with atomic electrons 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 electrons 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 ρ, the collision stopping power Scol is defined. The mass collision stopping power Scol/ρ is approximately represented by the Bethe-Bloch formula
Scol ρ = dT ρdx col = C 1 β2 Z A z2 (1.1)
where β = v/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), Scol/ρ behaves similarly. Depending on the mass of the incident particle, electron 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-effect correction. The first effect occurs when the particle velocity is lower than the atomic electron velocity and then less atomic electrons contribute to the interaction and Scol 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 Scol/ρ.
1.1.2 Radiative Stopping Power
the nucleus. The particle acceleration through the nuclear electric field may lead to energy loss by radiation emission, called Bremsstrahlung, and is proportional to 1/m where m is the mass of the incident particle. This loss of energy is then only relatively important for electrons and often negligible for heavy charged particles. The mass radiative stopping power Srad/ρ is approximately given by Srad ρ = B Z2 A ! T (1.2)
where B is a very slowly varying function of T and Z. As the (Z/A) ratio is relatively constant, Srad/ρ is approximately proportional to Z and T . 1.1.3 Nuclear Collisions
Direct collision of the charged particle with the atomic nucleus, i.e. an impact parameter less than the nuclear radius, leads essentially to elastic scattering. For electrons, the transfer of energy with the nucleus 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 nucleus may occur. The incident parinelas-ticle goes into the nucleus and one or more individual nucleons may be struck and driven out of the nucleus, collimated strongly in the forward direction. After this in-tranuclear cascade process, the resultant highly-excited nucleus decays from its excited state by emission of so-called evaporation particles (mostly nu-cleons of relatively low energy) and photons. More details on this nuclear reaction and the related physical models are discussed in the section1.3.4.
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
and is represented in figures 1.1 and 1.2 for electron and proton, respec-tively, from databases available on the website of the National Institute of Standards and Technology (NIST). For electrons over the MeV region, the mass stopping power in all materials is approximately 2 ± 1 MeV cm2/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.
10−2 10−1 100 101 102 103 10−1 100 101 102 103 Pb Cu C
Electron Energy [MeV]
Mass Stop ping P o w er [Me V cm 2 /g]
Collision Stopping Power Radiative Stopping Power Total Stopping Power
Figure 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 Penetration Depth
FollowingAttix [1986]: « The range R of a charged particle of a given type
10−3 10−2 10−1 100 101 102 103 104 10−1 100 101 102 103 Pb Pb Cu Cu C C
Proton Energy [MeV]
Mass Stop ping P o w er [Me V cm 2 /g]
Electronic Stopping Power Nuclear Stopping Power Total Stopping Power
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 RCSDA can be expressed as ρRCSDA= Z T 0 1 Stot/ρ dT. (1.4)
Attix [1986] defines also a second quantity related to the first: « The pro-jected range of a charged particle of a given type and initial energy in a given medium is the expectation value of the farthest depth of penetration 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 electrons, nuclei, atoms or molecules, depending on its wave-length, i.e. its energy. In the context of this work, only interactions leading to a subsequent transfer of energy are discussed, i.e. X-ray and γ-ray inter-actions. X-rays are photons produced by deexcitation of atomic electrons or during a charged-particle slowing-down process, typically over the range from 100 eV to 1 MeV, while γ-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 σ. The cross-section units are [cm2] or barns which equal 10−24 cm2, and the numerical value may be interpreted as the interaction probability if the target was uniformly distributed on a 1-cm2 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 electron is then ejected with a kinetic energy equal to the initial photon energy minus the electron binding energy. The ejected electron coming from an inner atomic shell is ejected with a higher probability, provided that the photon energy is higher than the correspond-ing bindcorrespond-ing energy. Therefore, as the photon energy decreases, the atomic cross-section aσph plummets discontinuously when the photon energy be-comes insufficient to release an atomic electron from its shell.
The mass atomic cross-section aσph/ρ for photoelectric absorption is approximately given by
aσph
ρ ∝
Z3−3.6
(hν)3−1 (1.5)
where h is the Planck constant, ν is the photon frequency, hν is then the photon energy and am−n means that the quantity a has an exponent
1.2.2 Coherent or Rayleigh Scattering
Rayleigh scattering consists in a coherent diffusion of the photon, i.e. the photon loses essentially none of its energy and is usually redirected through only a small angle. The corresponding mass atomic cross-sectionaσcoh/ρ is given by
aσcoh
ρ ∝
Z
(hν)2. (1.6)
1.2.3 Incoherent and Compton Scatterings
A photon undergoes an incoherent scattering when it gives up part of its energy during interaction with an atom or an atomic electron, and then is diffused. For photon energy above about 0.1 MeV, the incoherent diffusion is well described by the Compton scattering theory which considers the interaction between the incident photon and a weakly-bound electron, i.e. an atomic electron from an outer shell. The photon is diffused and a part of its energy is given to the electron. The kinetic energy of this electron 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 electron and as this fraction increases, the electron scattering angle gradually decreases from π/2 to 0 while the photon angle increases from 0 to π. 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 hν, i.e. more than 1.022 MeV, may interact with nuclear and electronic electric fields and disappear by giving rise to an electron and a positron (electron antiparticle) with kinetic energies T− and T+, respectively, such that
hν = 2mec2+ T−+ T++ TR (1.7)
where meis the electron rest mass and TRis the recoil energy of the host par-ticle. TR 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 electron field, leading to a triplet production.
Kinematic laws give the following results. Only photon with energy above 2mec2 and 4mec2 can interact in the nuclear and electronic field, re-spectively. For photon energies far above this energy threshold, the electron and the positron coming from pair production are forward directed while for triplet production, the three particles may depart in various directions.
The nuclear pair-production cross-section σpnis evaluated from a theory due to Bethe and Heitler and is approximately given by
σpn
ρ ∝ Z (1.8)
and the photon-energy dependence of the cross-section is roughly logarith-mic, see figure1.3.
The electronic triplet-production cross-section σpe is very small, usually negligible, compared to the pair-production cross-section in the field of an atomic nucleus, and the corresponding mass cross-section is approximately independent of Z.
Finally the total pair-production cross-section σpair is given by σpair ρ = σpn ρ + σpe ρ . (1.9)
The produced positron can interact with an atomic electron by giving rise to the production of two photons sharing an energy of 2mec2 + T0
and then the photons are often emitted with opposite directions because of the momentum-conservation law.
1.2.5 Photonuclear Absorption
When the photon energy exceeds the binding energy of a nucleon (8 ± 1 MeV), it can be absorbed in a nuclear reaction, resulting in the ejection of one or more nucleons. The cross-section for the photonuclear effect depends on both atomic number Z and atomic mass A, and thus on the isotopic abun-dance in a sample of a given element. Nevertheless it can contribute only between 2% for high-Z elements and 6% for low-Z elements to the total cross-section.
1.2.6 Total Cross-Section
By neglecting the photonuclear interaction, the total mass cross-section µ/ρ for photon can be written as
µ ρ = σph ρ + σcoh ρ + σincoh ρ + σpair ρ . (1.10)
The product of the total cross-section and the atomic density Na of the medium, called the attenuation coefficient µNa, is equivalent to the probability per unit of length for the photon to interact. So the beam intensity I of photons which have not interacted after a path of length dr decreases of a quantity dI equal to
dI = −IµNadr. (1.11)
Therefore the intensity of unaffected primary photons decreases as a function of the penetration depth in matter following
I = I0e−µNar = I0e−r/λ (1.12) where λ = 1/(µNa) 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-seccontribu-tion 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.
10−3 10−2 10−1 100 101 102 103 104 105 10−4 10−3 10−2 10−1 100 101 102 103 Pb Pb Pb Pb Cu Cu Cu Cu C C C C
Photon Energy [MeV]
Mass A tten uation Co efficien ts [c m 2 /g] Photoelectric Compton Rayleigh Pair Total
Figure 1.3: Photon mass attenuation coefficients for Carbon (Z = 6) in red, Copper (Z = 29) in green and Lead (Z = 82) in black. Reproduced from
1.3
Neutron Interactions with Matter
1.3.1 Energy ClassificationDepending essentially on their domain of application, neutrons are often sorted by energy as following:
• Thermal neutrons are in thermal equilibrium with the environment at T = 20oC, i.e. they have an energy less than 0.5 eV, a most-probable energy of kT = 0.025 eV, where k = 8.617 10−5eV/K is the Boltzmann constant, and a mean energy of 32kT = 0.038 eV;
• Epithermal neutrons have an energy between 1 eV and 10 keV; • Fast neutrons have an energy between 10 keV and 20 MeV;
• High-Energy neutrons have an energy between 20 MeV and 1 GeV; • Relativistic neutrons have an energy above 1 GeV, corresponding to the mass energy of a nucleon (≈ 940 MeV), for which relativistic effects become non-negligible.
1.3.2 Interactions
Neutrons, just as other particles with zero electric charge, have no Coulomb-force interaction with atomic electrons and nuclei, and only nuclear reactions may occur. Neutron interactions can be classified into 5 processes which depend on the neutron energy and the properties of the target material:
• Elastic scattering is a two-body interaction between the incident neutron and a nucleus. Following the energetic and momentum con-servation laws, a neutron of mass mn, with an initial kinetic energy T , collides with a nucleus of mass M , at rest, by transferring a kinetic energy ∆Ttr equal to
∆Ttr= T 4M mn (M + mn)2 cos
2φ (1.13)
where φ is the angle of the recoil nucleus after the collision. In a head-on collisihead-on (φ = 0), the transfer of energy is maximum and is given by
∆Ttr,max= T
4M mn (M + mn)2
while the mean transfer of energy is
∆Ttr,mean= T
2M mn (M + mn)2
(1.15) Therefore, neutrons undergo elastic collisions with subsequent trans-fer of kinetic energy only in low-Z and hydrogenous materials such as water, concrete and polyethylene. Indeed, if the target nucleus is composed of one proton (1H) of mass mp, thus M = mp ≈ mn, the maximum energy transfer is ∆Ttr,max≈ T and the mean energy trans-fer is ∆Ttr,mean ≈ T /2;
• Inelastic scattering is, in fact, a neutron capture followed by the emission of a neutron with a lower energy and in a different direction than the initial neutron. The target nucleus is potentially left in an excited state and de-energizes by gamma decay channels. If the nucleus is left in its ground state, it is considered as an elastic scattering; • Capture process is equivalent to an inelastic scattering but with
other particles than one neutron in the exit channel. It encompasses the emission of electron (β−), positron (β+), proton, gamma (radiative capture), deuteron (2H), tritium (3He), α-particle (4He) and more than one neutron. Capture processes need the incident neutron energy to be above some threshold specific 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 activated;
• Spallation reactions occur when the neutron becomes sufficiently energetic to interact with individual nucleons inside the struck nucleus. An intranuclear cascade inside that nucleus may occur and produce different kinds of high-energy particles. Details on this mechanism are given in section1.3.4.
1.3.3 Cross-sections
Many scientific crews and collaborations in the world − mainly from USA, Japan, China, Russia and Europe − have planned to produce accurate neu-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 IAEA, 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 LiLi-brary (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.
10−1110−1010−910−810−710−610−510−410−310−210−1 100 101 102 10−5 10−4 10−3 10−2 10−1 100 101 102 103 C Cu Pb C Cu Pb Elastic γ-capture Non Elastic
Neutron Energy [MeV]
Cross-sections [barns ] Carbon Copper Lead
Figure 1.4: Neutron cross-sections for Carbon (Z = 6) in green, Copper (Z = 28) in red and Lead (Z = 82) in blue, ENDF library. Reproduced fromNNDC [2011].
1.3.4 Intranuclear Cascade Models
Nuclear reactions of high-energy heavy particles are very complex processes but the first description was suggested bySerber[1947]. He noticed that, for sufficiently-high-energy incident particles such as protons and neutrons, the de Broglie wavelength λB of the incident particle is of the order or shorter than the average distance between nucleons (∼ fm = 10−15 m). Since the de Broglie wavelength is defined by
λB=
hc
where E = m0c2 + T = m0c2/ p
1 − β2 is the total energy of the incident particle and m0c2 is its rest energy, the value of kinetic energy T becomes
T = m0c2 s 1 + hc λBm0c2 2 − 1 . (1.17)
For a proton or a neutron, with a de Broglie wavelength corresponding to the mean distance between nucleons ∼ 1.2 fm, the kinetic energy is approx-imately 450 MeV, but decreases down to 200 MeV when the wavelength is 2 fm. Above this energy, only individual nucleon-nucleon collision should be considered and experimental nucleon-nucleon cross-sections are used when-ever possible [Bertini, 1963; Loveland et al., 2006]. However, interference between nucleons can be important and affect the particle-nucleon interac-tion. These effects were taken into account by Goldberger [1948] when he made the first calculations by using the statistical model of the nucleus.
The struck nucleon can escape from the nucleus if the transfer of energy is higher than ∼ 150 MeV and the emission is strongly forward directed; but below this energy, it may collide with other nuclear particles which in turn may escape or interact with other nucleons, this is the so-called intranuclear cascade (INC) represented in figure1.5. It should be noted that non-nucleon particles such as pion π 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 nucleus in a non-equilibrium state, which is difficult 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 nucleon emission, eventually leading to an equilibrated but excited nucleus [ Heikki-nen and Stepanov,2003].
Figure 1.5: Schematic view of nuclear cascade [Lieser,1997].
model assumes complete energy equilibration before particle emission, and re-equilibration of excitation energies between successive evaporation emis-sions, until the excitation energy of the nucleus falls below some cutoff en-ergy. At this moment, the remaining excitation energy is released through decay chains. As a result, the angular distribution of emitted particles is isotropic [Heikkinen and Stepanov, 2003]. However, if fission channels are energetically allowed, nuclear break-up may also occur.
Intranuclear cascade and pre-equilibrium, evaporation, 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 (10−23− 10−22 s) while the evaporation phase is much slower (10−18−10−16s) [Heikkinen and Stepanov,
2003]. The final decay, called activation, depends on the nature of the ex-cited nucleus 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].
agreements with experimental data were reached with the calculations of
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 injure 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 deposition of some radiation beam in matter.
Figure 1.7: Depth dose curves in tissue for 4-MeV photon, 20-MeV photon, 4-MeV electron 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, helium, 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 effects is linked to the dose but depends also on the type and energy of the radiation. Therefore, a radiation weighting factor wR is applied to the dose, so defining the dose equivalent HT, in units of Sievert [Sv] = [J/kg], given by
HT = X
R
wRDT,R (1.18)
where DT,R 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 all energies for different particles except neutron are shown in the table1.1. 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 figure1.8[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,γ) 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
20 fragment and heavy ion
Neutron Function of the neutron
energy, see figure 1.8.
10
−510
−310
−110
110
30
5
10
15
20
25
Neutron Energy [MeV]
w
RFigure 1.8: Radiation weighting factors wR for neutrons as a function of neutron energy. The step function was first suggested [ICRP,1991] but the continuous function 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 wT 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 =X
T
wTHT. (1.19)
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 theICRP [1996] and theICRP[2010] due to the new values of wR and wT, e.g. from 0.05 to 0.12 for breast, as well as the improvement of voxelized phantom modeliza-tion in numerical simulamodeliza-tions.
1.4.4 Ambient Dose Equivalent
Direct measurements of the equivalent dose, particularly for neutrons, and the effective dose are not possible in practice. Therefore, operational quan-tities have been defined to give an estimation of the protection quanquan-tities related to an exposure. They are based on specific irradiation of a specific body and were defined to be easily estimated or measured in area and indi-vidual radiation monitoring. Among others, some of these quantities are of particular interest for this work, such as the ambient dose equivalent H∗(d). Following the ICRP [2007a]: « the ambient dose equivalent, at a point in a radiation field, is the dose equivalent 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 have the same values as those at the point of interest, in all points of a sufficiently large volume surrounding the point of interest. The field is aligned when the beam is unidirectional, see figure1.9. An ICRU sphere is a tissue-equivalent sphere with a diameter of 30 cm and a density of 1 g/cm3. For strongly penetrating radiation, such as neutron and photon, a depth of d = 10 mm is recommended.
Many efforts have been made to give conversion coefficients between some radiation intensity and H∗(10). The particle intensity is often expressed by the fluence Φ which is, at a point in a radiation field, the number of incident particles per unit area, in units of [m−2] or [cm−2], 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]:
Φ = dN
d
30 cm
Figure 1.9: Schematic representation of an aligned and expanded radiation field and the ICRU sphere. Red arrows represent the field. The ambient dose equivalent is defined as the dose at the blue point.
The ambient dose equivalent is then given by H∗(10) =
Z
hΦ(E)ΦE(E) dE (1.21)
where hΦ(E) is the fluence-to-ambient-dose-equivalent conversion coefficient function, in units of [Sv.cm2], and ΦE(E) is the distribution of the fluence with respect to energy E, in units of [cm−2MeV−1].
As said before, the aim of an operational quantity is to give an estima-tion of a protecestima-tion quantity related to a specific radiaestima-tion. However, in a radiation protection context, a conservative approach must be adopted: the measured or evaluated operational quantity has to overestimate the protec-tion quantity. Then, if the operaprotec-tional quantity is estimated below the dose limits, it ensures that the protection quantity does too.
10−2 10−1 100 101 102 103 Con v ersion Co e fficien ts [pSv.cm 2 ] EAP EPA ELLAT ERLAT EROT EISO H∗(10) ICRP[1996] H∗(10) Pelliccioni [2000] 0 0.5 1 Overestimation Underestimation E /H ∗ (10) ICRP 10−2 10−1 100 101 102 103 104 10−2 10−1 100 101 Overestimation Underestimation
Photon Energy [MeV]
E
/H
∗ (10)
P
elliccioni
Figure 1.10: Conversion coefficients for the photon effective dose fromICRP
Figure 1.11 shows the conversion coefficients for the neutron effective dose E [ICRP, 2010] and the neutron ambient dose equivalent from the
ICRP[1996] up to 200 MeV, supplemented by the calculations of Sannikov and Savitskaya[1997] over the range from 20 MeV to 5 GeV, and from Pellic-cioni[2000] who extended calculations to 10 GeV. For neutron energy below 50 MeV, H∗(10) values overestimate the effective dose for all irradiation di-rections, except between 3 MeV and 10 MeV for the AP direction where a 25% overestimation occurs. Above 50 MeV, the effective dose is underes-timated by the H∗(10), up to a factor of 2 at 200 MeV, for all irradiation directions. However, above 200 MeV, the ratio E/H∗(10) seems to decrease and reaches the unity for the values from Sannikov and Savitskaya [1997]. Thus, for high-energy accelerators where neutrons with energies higher than 50 MeV may be produced around the installation, the risk estimated with operational quantities must be analyzed carefully.
1.4.5 Principles of Radiological Protection
As said before, radiation may induce stochastic and deterministic effects on tissue or organ. From their definition, deterministic effects take place above a specific dose threshold, while stochastic effects always occur with probability increasing with the dose. Except for radiation therapy, where a high-concentrated and localized dose is mandatory, and nuclear accidents, irradiations often lead to low-dose exposures and then protection is difficult to be quantified because low-dose exposition data, with sufficient statisti-cal consistency, are scarce... fortunately. Laboratory experiments with pets can be helpful but human-irradiation data are only available from epidemi-ological studies from nuclear weapon tests at Hiroshima and Nagasaki and nuclear contaminations due to nuclear accident at Chernobyl, Three Mile Island and now Fukushima. Thus, few international commissions, such as the ICRP, publish tips and recommendations to be potentially included into laws about radiation monitoring.
