Development of an external beam line for radiobiology experiments and microdosimetry applications at the 18 MeV proton cyclotron facility at CNA

Universidad de Sevilla Ph.D. Thesis Doctoral Programme in Physical Sciences and Technologies Faculty of Physics / National Centre of Accelerators Development of an external beam line for radiobiology experiments and microdosimetry applications at the 18 MeV proton cyclotron facility at CNA Author: Anna Baratto Roldán Directors: Prof. Miguel Antonio Cortés Giraldo Dr. María del Carmen Jiménez Ramos Prof. José Manuel Espino Navas November 2020 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 A mi familia Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Acknowledgements The accomplishment of this long desired objective in my academic career would not have been possible without the advice, support, help and encouragement of the many people I crossed paths with during these last four years. I am extremely grateful for all the experiences and opportunities I was gifted with, but also for the challenges I had to face; all of them made me grow as a researcher and, more importantly, as person. First of all, I would like to express my sincere gratitude to my supervisors, A/Prof. Dr. Miguel Antonio Cortés Giraldo, Dr. María del Carmen Jiménez Ramos and A/Prof. Dr. José Manuel Espino Navas, for believing in me and encouraging me to go beyond my own limits. Their guidance and support were fundamental for the completion of this work, and I owe them most of the knowledge I acquired during my doctoral studies. I am especially thankful for the friendship they have always demonstrated, for the patience with which they listened to me during the bad times and for the enthusiasm with which they celebrated the many good ones. My special appreciation and thanks go to Prof. Dr. María Isabel Gallardo Fuentes, for her contagious curiosity and endless desire to learn. She has been a great inspiration and mentor, keeping the flame of my enthusiasm alight. I would also like to show my deep gratitude to Prof. Dr. Joaquín Gómez Camacho, who put his trust in me, and fought the bureaucracy to give me the opportunity to teach. Along these lines, I wish to express my gratitude to all the other colleagues and personnel of the Department of Atomic, Molecular and Nuclear physics, for the warmth with which they welcomed me, making me feel as a part of the family. This work would not have been possible without the help and involvement of many collaborators from different institutions. In the first place, I would like to thank Prof. Dr. Francisco Javier García López and Dr. Begoña Fernández Martínez, from the CNA, for being always available to help during experimental measurements and for retrieving and lending the necessary material and equipment. Secondly, my sincere gratitude goes to A/Prof. Alejandro Cárabe Fernández, from the Hospital of the University of Pennsylvania; without him the content of the third chapter of this v Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 thesis would have never come to existence. The discussions and the sharing of ideas we had during our meetings, and the team working with my colleagues Dr. Alvaro Perales Molina and Dr. Alejandro Bertolet Reina, were very prolific and exciting, opening a whole new line of research. In this context, I would also like to thank Dr. Giorgio Baiocco and Dr. Sofia Barbieri, who dedicated their time and effort to produce simulation results to be compared with ours. Then, I wish to acknowledge Dr. Consuelo Guardiola (CNRS - Paris, France) and Dr. Dieter Schardt (GSI - Darmstadt, Germany), for their sincere interest in my thesis work and for the many advices and ideas they shared with us. Finally, my deepest gratitude goes to A/Prof. Dr. Sonia Jimeno González and A/Prof. Dr. Pablo Huertas Sánchez, from CABIMER, for offering their expertise, laboratories and time to make the irradiation of cell cultures at the cyclotron happen. I would like to express my deepest gratitude to Prof. Dr. Carsten Welsch and to all the partners of the OMA project, for believing in it and making it real: they created an outstanding network that was a countless source of knowledge, collaborations and training experiences. Being an OMA fellow was, without any doubt, the most precious gift of these doctoral years, and I hope that the friendship and companionship I found in the network will accompany me throughout my life. A special mention goes to our project managers, Magdalena and Samantha, who gave all their best to organise the meetings and to make sure that everything was fine among us. I found in them careful listeners and supportive friends, and more than once they encouraged me to not give up. And of course, this project would not have existed without the brilliance and liveliness of its fellows, the true heart of OMA, who became my dearest friends. A sincere thank goes especially to Ewa, Sud, Jacinta, Navrit, Michelle, Laurent and Roland, for all the laughters and the great moments we shared together. I am extremely thankful to Dr. Michael Scholz, Prof. Dr. Marco Durante, and all the people of the GSI biophysics department, for welcoming me during my secondment and making me feel at home. I really enjoyed the time I spent there, the continuous occasions for learning and improvement, and the stimulant environment. A special thank goes to Dr. Olga Sokol, who patiently introduced me to the world of radiobiology, spending many hours with me under the flow hood to guide my hands for the preparation of cell samples. I consider her a great teacher and a precious friend. I had the chance to meet many wonderful people during my time at the GSI, but Francesca and Claire deserve a special mention. Even if we could just spend a short time together, their friendship was, and still is, an unexpected and amazing treasure. They gave me strength, enthusiasm, self-confidence and countless happy memories. Concludere questo lavoro di tesi, durante i mesi di isolamento ed incertezza portati vi Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 dal COVID-19, sarebbe stato estremamente difficile senza l’appoggio di tutti i miei amici dall’Italia. Nonostante la lontananza e la solitudine forzata, non c’è stato un giorno in cui mi abbiano fatto mancare il loro affetto e la loro presenza. In particolare desidero ringraziare Valeria, per essere sempre rimasta al mio fianco e avermi capita, sostenuta e spronata a non mollare. La sua vivacitá, il suo coraggio e la sua determinazione sono per me una fonte di ispirazione. Sono estremamente grata per l’affetto che ci unisce e so di poter contare su di lei, come lei su di me. Le nostre interminabili telefonate sono state il balsamo che ha alleviato la mia solitudine. Grazie di cuore a Martina e alle nostre colazioni virtuali in quarantena. Nonostante la conosca da una vita riesce sempre a sorprendermi e a farmi mettere in discussione. Il suo spirito genuino, la sua allegria e il suo grande cuore sono la ricetta infallibile per il buonumore. Grazie anche a Francesca, per essermi stata vicina e per il suo appoggio e incoraggiamento. La ammiro per la sua forza, la sua resilienza e la sua capacitá di rimettersi sempre in gioco, e sono grata di poter fare affidamento sulla sua amicizia. E come dimenticare i miei cari "papiri", Elena, Luca, Camilla, Luca (DM), Francesco (Coach), Stefano, Eugenio (dove sarà Eugenio?), Francesco, Andrea e Enrico. I nostri ritrovi bisettimanali su meet e la loro compagnia mi hanno aiutato a scandire il passaggio del tempo e sono stati un dono prezioso in questi tempi stranianti che stiamo vivendo. Infine, grazie ad Alberto, Francis e a tutti gli altri amici che mi sono stati accanto in questo tempo di scrittura e nel percorso che mi ha portato fin qui. Siviglia "tiene un color especial", come dicono qui, e mi ha incantata con la sua bellezza, i suoi sgargianti colori e la sua gente. Ma anche in un posto cosí accogliente e meraviglioso è inevitabile sentire, di tanto in tanto, nostalgia. Per questo ringrazio di cuore la mia piccola comunità di donne italiane a Siviglia, Cristina, Laura e Ilaria, con le quali ho potuto esprimere e condividere la mia italianitá e dalle quali mi sono sentita capita. Durante mis años en Sevilla he tenido la suerte de cruzarme con personas maravillosas, que me han acogido con los brazos abiertos y cuya presencia me ha enriquecido. Gracias ante todo a los "mongolfiera", en especial Jorge, Mario, Cristina, Andrés, Mercedes, Carlos, Laura, Miguel, y Carlos, por ayudarme a emprender los primeros pasos en el camino del doctorado y hacerme sentir arropada. No bastan las palabras para expresar la gratitud que siento hacia mis compañeros del "despachito", Damián, Tere y Llanlle. Su llegada marcó un giro tanto en mi formación doctoral como en mi vida. Con ellos he compartido fracasos y logros, llantos y alegrías, momentos serios e incontables tonterías. Echaré muchísimo de menos nuestros momentos de complicidad en el despacho, aunque sé que seguirán estando a mi lado allá donde yo vaya. En especial, quiero agradecer a Damián todo el tiempo que me vii Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 ha dedicado y la enorme ayuda que me ha proporcionado en el desarrollo de mi tesis. Su apoyo y sus palabras me han sostenido en los momentos difíciles, haciéndome creer en mí misma. Un gracias de todo corazón va a las personas que han compartido piso conmigo en estos años, convirtiendose en mi familia. A Elena, a mi adorable perrita Lana y a Bea, por su amistad y por hacerme descubrir Sevilla y a su gente. A mi querida luchadora Alessandra y a la dulcísima Jila, por haber dejado una huella en mi corazón. A Ibon, porque es el mejor amigo que podría desear y mi punto de referencia. Siempre ha estado presente para escucharme, animarme y darme todo su apoyo. Su amistad es un puerto seguro y una flor que deseo cultivar para toda mi vida. A Agata y a Rocío, por haberme acompañado en la última etapa de mi tesis doctoral, con lo que eso ha conllevado. Especialmente, quiero agradecer a Rocío la paciencia y la comprensión demostradas por mi creciente dejadez en las labores domésticas. Pero, sobre todo, le estoy inmensamente agradecida por su amistad, su complicidad y su capacidad de alegrarme siempre el día. Finalmente, gracias a Alex, mi futuro "compañero de piso" y el más inesperado de los regalos en este 2020 tan extraño. Su cariño y su apoyo me han dado la carga y el entusiasmo para acabar este trabajo y empezar una nueva aventura. Un agradecimiento y un recuerdo especial van a Morgan, Boris y a toda la familia del CrossFit Macarena Box. No sé qué habría hecho sin ellos y sin las agotadoras sesiones de entrenamiento en cuarentena. Me han animado a ser tenaz, constante y a sobrepasar mis limites. Gracias a ellos he descubierto que soy más fuerte de lo que pensaba y que todo se puede consiguir con aplicación y esfuerzo. Los entrenamientos en el Macarena Box han sido, y son, mi momento desahogo y mi medicina; una ayuda valiosísima para mantenerme centrada y aclarar mi mente. Gracias de todo corazón a mio tío Ángel, a mi tía Paqui y a mis primas Alicia y María. Su cercanía y su afecto me han hecho sentir menos sola y han sido mi hogar de referencia en estos años lejos de casa. Finalmente, no habría llegado donde estoy hoy sin mi familia y su incondicional apoyo. Mi madre, mi padre y mi hermano Silvio son el faro que me guía cuando estoy a la deriva y el hogar en el que me siento segura. Gracias a mi madre, mi modelo a seguir y la mujer que más admiro. Aunque ambas suframos por la distancia que nos separa, le estaré siempre agradecida por las alas que me ha dado y por velar mi vuelo. Gracias a mi padre, por su sabiduría y su don para tranquilizarme y transmitirme serenidad. Sé que puedo confiar en él en todo momento y conservo como un tesoro todos sus consejos. Y gracias a Silvio, la chispa de la casa. Cada día estoy más orgullosa del hombre en el que se está convirtiendo y de la determinación con la que prosigue su camino. Le agradezco su incansable y contagioso entusiasmo, que es la pimienta que da sabor a nuestro día a día. viii Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Abstract Cancer is one of the leading causes of mortality world-wide, killing more than one million people per year just in Europe. Nowadays, proton therapy is one of the most promising techniques in the fight against cancer, being two the main bases of its success: (1) the physical advantages of protons with respect to conventional radiotherapy with photons, resulting in a more selective energy deposition in depth; (2) the increased biological effectiveness of protons with respect to photons and their denser pattern of energy deposition in matter, usually determining a more lethal damage to the DNA. The biological effect of protons and other ions with respect to photons is described in terms of the Relative Biological Effectiveness (RBE), i.e., the ratio between the doses of the reference and studied radiation determining the same effect. In clinical proton therapy, a RBE value of 1.1 is currently used. However, there is an increasing awareness that proton RBE is not a constant, but seems to increase linearly with the Linear Energy Transfer ( LD ) of the proton as it slows down in tissues, especially close to the distal region of the Bragg peak, possibly leading to toxicity in healthy tissue beyond the target. In this context, recent studies aim at including dose-averaged LET objective functions in treatment planning optimization to take full advantage of the increased RBE in protons beams. This last problem, and the characterisation of RBE, can be addressed with the formalism of microdosimetry, which, on one hand, permits the calculation of RBE from a microscopic approach by means of the microdosimetric kinetic model (MKM) and, on the other hand, provides physical concepts and computational tools to calculate macroscopic LD distributions. The rationale behind this thesis project is, therefore, given by the necessity of performing studies of proton RBE at low energies, close to the Bragg peak region of clinical proton beams (below 40 MeV ), which would help reaching a consensus on the variation of proton RBE with LET. To do so, two main objectives were foreseen: (1) the design and mounting of a low energy proton facility at CNA (proton kinetic energy below 18 MeV ) for the experimental study of RBE in mono-layer cell cultures and (2) the development of a simulation tool to study the patterns of energy deposition of protons in water at a micrometric scale, for the computation of microdosimetric quantities. ix Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.1. Introduction Figure 1.1: Comparison of the profiles of energy deposition in water as a function of depth (Physical dose) of an X-ray beam and high-energy charged particles. While an X-ray beam exhibits an exponential decrease of energy deposition at depths greater than few cm (approximately 1.5 cm for a 6 MV clinical beam), charged particles deposit most of their energy at the end of their path, defining a region usually called Bragg peak, while sparing both proximal and distal located normal tissues (taken from [11]). dimensional shape of the tumour, by modulating the intensity of the radiation beam. Typically, multiple fields coming from different directions are combined to deliver a patient specific radiation dose: maximised in the tumour and minimised in the adjacent normal tissues [7]. However, since the aim of any treatment modality is to kill as many cancerous cells as possible, while minimising damage to the healthytissues, in some situations conventional radiotherapy is not sufficient due to the tumour location close to organs at risks, that sometimes results in the delivery of a radiation dose above their tolerance. The urge for clinical solutions to treat these cases has stimulated in the last twenty years both remarkable technological developments in conventional photon therapy and an increasing enthusiasm in the use of particle beams for radiation therapy, which could not be fully exploited before the achievement of these advances [8]. The article in Radiology [9], published by Robert Wilson in 1946 about the therapeutic interest of protons for treating cancer, is usually considered as the starting point of 2 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy Figure 1.2: Comparison of saggital images of proton and photon treatment plans for a pediatric patient treated with craniospinal radiation. On the right, the excess dose deposited from photon treatment is highlighted (taken from [12]). particle therapy: less than ten years later, in 1954, the first treatments with protons took place in the Lawrence Berkeley Laboratory (Berkeley, CA, USA). Today, particle therapy has grown into an advanced clinical modality, counting more than 100 000 patients treated worldwide with protons since the establishment in 1990 of the first hospital-based treatment centre in Loma Linda (California, USA) and more than 10 000 treated with heavier ions, generally carbon [10]. The clinical interest in particle therapy comes from the favourable physical properties of charged particles, especially their characteristic curve of energy deposition in depth, which allows precise delivery of radiotherapy treatments. As emerges from Figure 1.1, while an X-ray beam deposits energy slowly and mainly exponentially as it penetrates tissue, the energy deposition of charged particles increases with penetration depth, reaches a maximum just before coming at rest in the region called the Bragg peak and then exhibits a rapid fall-off. Since the Bragg peak position in depth increases with the kinetic energy of the incident particle, it is possible to target a well-defined region at a certain depth in the body, tuning the position of the Bragg peak by adjusting the energy of the incident particle beam, while sparing 3 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.1. Introduction both proximal and deeper located normal tissues, as shown in Figure 1.2. As already mentioned, tumour indications for particle therapy are generally those close to organs at risk, being chordomas and chondrosarcomas of the base of the skull and eye tumours some typical cases [13]. However, other indications exist, for example for patients where the reduction of the radiation dose received by normal tissues is essential: children treated with curative intent and patients with genetic, radiosensitive syndromes [13]. More generally, the high-precision and non-invasiveness of the Bragg peak would be beneficial for most cancer cases. However, in some situations the clinical benefit is not significant enough, while substantial differences in cost exist between X-ray-based therapy and particle therapy, being the latter more expensive both in terms of initial investment and cost per treatment, making the issue of cost-benefit ratio highly controversial [14]. In addition to the physical advantages derived from the energy loss mechanism that characterises the interaction of protons and other ions with matter, the use of particle therapy is associated with important biological advantages, which can be exploited in the clinics. The biological properties of any type of radiation are derived from the energy deposition pattern: if compared to photons, charged particles (especially light ions) exhibit a more condensed ionisation pattern in traversed cells, resulting in the induction of more complex damages and different cellular responses, which can be exploited in particle therapy. This is usually quantified by the Relative Biological Effectiveness (RBE), defined for a given radiation type as the ratio between a reference radiation dose (generally 60 Co, γ -rays or 250 keV X-rays) and the dose of the radiation type considered that produces the same biological effect. While for heavy ions like carbon the increase in RBE is clearly advantageous for treatments, the case of protons is not fully understood and a lot of uncertainties exist both in experimental measurements and models of proton RBE [16]. In clinical practice with protons, a fixed RBE value of 1.1 is used [15], despite the evidences suggesting that the RBE changes along the Bragg curve, but that is justified by the fact that the available biological data are insufficient to support the implementation of other proposed RBE models in clinical environment [17–22]. The work presented in this thesis is inserted into this context and has two main objectives: (1) the design and mounting of a low energy proton facility (proton kinetic energy below 18 MeV ) for the experimental study of RBE in mono-layer cell cultures, as described in Chapter 2; and (2) the development of a simulation tool to study the patterns of energy deposition events of protons in water at a micrometric level, useful to infer the biological effects of protons at a macroscopic scale through specific models as described in Chapters 3 and 4. In the following sections, the physics fundamentals and the radiobiological bases of 4 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy proton therapy will be described in details; followed by a brief overview about Monte Carlo methods and radiation detectors for dosimetry in particle therapy. 1.2 Physical aspects The phenomena associated with the interaction of ionising radiation with matter include a wide variety of physical mechanisms, whose knowledge is of fundamental importance to allow the widespread of new techniques and applications. Radiation interacts with matter in terms of its fundamental elements: atoms, nuclei and their individual constituents, with a probability that is governed by quantum mechanics and depends on radiation nature, energy and type of material. The type of processes occurring for each type of radiation define its propagation through matter, its detection characteristics as well as its effects on biological organisms. The most common processes which take place when charged particles or photons pass through matter are governed by electromagnetic interactions. Light ions undergo energy losses mainly due to excitation and ionisation of the atoms of the medium close to their trajectory. Electrons and positrons also lose energy by radiating photons. Finally, photons are attenuated in matter by single scattering with atomic electrons of the medium or by a few subsequent interactions mainly governed by Compton scattering, photoelectric effect and pair production, the last two eventually leading to full absorption of the photon in matter [23]. In this section, the physical principles of the interaction of protons with matter, relevant to therapeutic applications, are discussed. Two are the main processes that characterise the passage of these particles through a material: energy loss and deflection from the particle original direction. Protons interact with matter primarily through Coulomb forces between their positive charge and the negative charge of the electrons of the absorber atoms. Depending on the closeness of such interactions, the impulse felt by the electrons from the attractive Coulomb force may be sufficient either to raise the electron to a higher-lying shell within the atom (excitation) or to remove it completely from the atom (ionisation) [26], subsequently causing new ionisations as the freed electron travels and interacts with other neighbouring atoms. In the slowing down process, most protons travel in a nearly straight line and no significant deflections of their trajectory are observed, as their rest mass is approximately 2000 times greater than that of an electron. In contrast, a proton passing close to the atomic nucleus of the absorber, whose mass is much bigger, experiences a repulsive elastic Coulomb interaction, that deflects the proton from its original trajectory. Although such interactions occur rarely, when they take place the target nucleus absorbs a very little amount of energy while the incident particle is scattered, causing a deflection of its trajectory. For example, for a 1 MeV proton 5 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.2. Physical aspects impinging on a carbon nucleus, the maximum scattering angle is approximately 5° with an interaction probability of only about 0.1% that decreases with increasing energy. Therefore, elastic nuclear interactions only play a small role towards the very end of the proton path [24]. In the following, the two main processes of proton interaction with matter, which can be generally identified as stopping and scattering, will be discussed in detail. A third type of process contributes to determine the shape of the Bragg peak: the nuclear interaction of proton projectiles with the target nuclei. This type of interaction leads to the excitation of the target nucleus, to the formation of a compound nucleus or to a direct interaction with an individual component of the nucleus. The result is an energy loss of many MeV per collision, eventually accompanied by the emission of secondary particles and by a significant change in the flight direction of the proton. The probability for non-elastic nuclear reactions increases rapidly with increasing proton energy being about 1% for a 25 MeV proton and up to 25% for a 200 MeV proton [24,25]. However, since for the energies considered for the purpose of this thesis (below 18 MeV ) head-on collisions of protons with nuclei are very rare, their contribution will be neglected. 1.2.1 The stopping power and the Bragg peak As previously mentioned, the energy loss of protons in matter is mostly described by their electromagnetic collisions with the target electrons, which are statistical in nature. The amount of energy transferred after each collision is a very small fraction of the kinetic energy of the incident particle. However, depending on the density of the material traversed by the protons, the number of interactions per unit of length might be very large. It is then possible to define an average energy loss per unit path length, the so-called stopping power dE/dx , where dE is the mean energy loss and dx is the distance traversed by the particle in the medium. The energy loss rate is described by the Bethe [27] and Bloch [28] formula reported here in the relativistic version described by Fano [29]: −dE dx= 4πNAr2 emec2ρZt A Z2 p β2ln 2mec2γ2β2 hIi−β2−C Zt−δ 2,(1.1) where NA is Avogadro’s number, re , me and e are the electron classical radius, mass and charge, Zt and Zp denote the atomic numbers of the target and the projectile, A is the atomic weight of the target material and ρ its mass density, β = v/c , where v is the particle velocity and c is the speed of light, γ = (1 −β2 ) −1/2 , and hIi is the mean excitation potential of the target material. The terms C and δ are two correction factors which are derived from relativistic theory and quantum 6 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy Figure 1.3: Variation of −dE/dx as a function of the proton kinetic energy in water (blue circles) and in Polymethyl methacrylate (PMMA, ρ = 1.19 g cm−3 , orange triangles). Data extracted from the National Institute of Standard and Technologies (NIST, Maryland, MD, USA) Standard Reference Database PSTAR [31]. mechanics, and need to be considered respectively when projectiles at very low (below few MeV for protons [23]) or very high energy (close to 1 GeV for protons in biological materials [30]) are used in calculations. The shell correction C arises as the incident particle velocity gets closer to the velocity of atomic electrons. In this energy region, many complex phenomena take place, the most important of them being the electronic capture by the incident particle, that determines a decrease of its charge state and consequently of its stopping power. The density effect δ , instead, originates from the electric field produced by the incident particle, which tends to polarise the electrons of the medium along its path. This effect increases with the particle energy, meaning that further electrons feel a shielded electric field and give a lower contribution to the energy loss. At high velocities the atomic electrons are completely stripped off and the projectile charge is equal to the atomic charge Zp . At lower velocity, below about 10 MeV u−1 for light ions, the mean charge state decreases due to the interplay of ionisation and recombination (electron exchange) processes. To account for this phenomenon, Barkas [32] proposed to replace Zp by a projectile effective charge Zeff , parametrised as a function of β and Zp of the incident particle with the following empirical formula: 7 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.2. Physical aspects Figure 1.4: A typical Bragg curve, showing the variation of −dE/dx as a function of the penetration depth for protons having a kinetic energy of 70 MeV in water. Computed with the Monte Carlo code Geant4 (see Section 1.4). Zeff =Zph1−exp −125βZ−2/3 pi.(1.2) Some interesting considerations can be done by observing the dependences of the energy loss on the projectile and material characteristics in Equation (1.1). Indeed, dE/dx is proportional to the inverse square of the velocity of the incident particle and on the square of its charge, and there is no dependence on the projectile mass. On the other side, Equation (1.1) puts in evidence the strong influence of the target material on the energy loss rate. In fact, the stopping power is proportional to the electron density NAρZt/A of the target material, and depends on its hIi value, which varies from about 19 eV for hydrogen to about 820 eV for lead, being 78 eV the one of water [33]. However, since this last dependence goes with the logarithm of hIi−1 , its effect is diminished, and the strongest elements affecting the energy loss in the human body are the material density, which can vary by about three orders of magnitude from air in the lung to cortical bone, and the particle velocity, which can cause the stopping power in water to vary by a factor of 60 for proton energies between 1 and 250 MeV [34] (see Figure 1.3). Taking into account the aforementioned considerations, as a light ion slows down inside matter, its rate of energy loss changes, determining a greater amount of energy deposited per unit length at the end of its path rather than at its beginning. This 8 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy Figure 1.5: Example of the method of summing up different Bragg peaks with different energies and weights, to build the SOBP (taken from [35]). effect is shown in Figure 1.4, which represents the amount of energy deposited by a proton as a function of its position along its slowing-down path. The curve is known as Bragg curve and its maximum is usually indicated as Bragg peak. In the clinical practice, the aim is usually to obtain an irradiation profile broader than the individual Bragg peak, in order to achieve a better coverage of the tumour volume. This is done by superimposing different beams with slightly different energies and fluence weights, as depicted in Figure 1.5, generating a spread out Bragg peak (SOBP) that deposits the required radiation dose in the treatment volume. Until now, proton energy loss has been described in an approximate way on the assumptions that a proton loses energy along a linear trajectory and that the energy loss is continuous. However, the absorption of this energy occurs in a threedimensional volume, and the random fluctuations in the location and size of primary ionisation events result in a proton ionisation track with an irregular three-dimensional structure. Indeed, some of the recoil electrons produced by the proton interaction, usually defined as δ -rays, are sufficiently energetic to create small spur tracks of ionisation emanating from the main track. The maximum possible energy transfer to a δ -ray ( Eδ max ) following the collision of a proton with an unbound stationary electron is: Eδ max = 2mec2β2γ21+2γme M+me M2−1 ,(1.3) where M is the mass of proton. Even for very energetic protons, the secondary electrons do not acquire enough energy to travel more than a few millimetres from the proton track; for example, a 250 MeV proton can transfer to an electron a maximum energy of ∼600 keV resulting in a maximum travelled distance from the proton track in water of about 2 mm . For targets having atomic numbers ranging between Zt = 6 and Zt = 92 in the δ -ray energy range 0.7 keV −30 MeV , the 9 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.2. Physical aspects maximum distance travelled by secondary electrons ( Rδ max ) can be calculated by a semi-empirical equation developed by Tabata et al. [36]: Rδ max =a1     1 a2 ln 1 + a2 Eδ max mec2− a3 Eδ max mec2 1 + a4Eδ max mec2a5     ,(1.4) where the parameters ai are given by simple functions of the atomic number Zt and the mass number A of the target material. The expressions for the parameters ai are listed here: a1=b1A/Zb2 t, a2=b3Zt, a3=b4−b5Zt,(1.5) a4=b6−b7Zt, a5=b8/Zb9 t, where the symbols bi are constants, independent on the target material, which have been determined by Tabata et al. [36] and whose values are listed in Table 1.1. Table 1.1: Values of the constants bi(i= 1,2, ..., 9) of Equation (1.5). Reprinted from [36] i bi 10.2335 21.209 31.78 ×10−4 40.9891 53.01 ×10−4 61.468 71.180 ×10−2 81.232 90.109 If Equation (1.4) is applied to materials that are mixtures or compounds, the atomic and mass number should be replaced by respective effective values (Z∗ tand A∗): 10 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy Z∗ t=X i fiZi,(1.6) A∗=Z∗ t X i fi Zi Ai!−1 , where fi is the fraction by weight of the constituent elements with atomic number Zi and atomic weight Ai . For a water medium, for example, Z∗ t = 7 . 22 and A∗ = 13 . 0. The spatial characteristics of secondary electrons should, in principle, be taken into account near material interfaces and in cases where the radiation quality is of interest, as it happens in the microdosimetric characterisation of individual energy deposition events, which will be described in Section 1.3.3. 1.2.2 Range and energy straggling The peculiar shape of the stopping power distribution as a function of the material penetration depth has led to the conception, and later on the development, of proton therapy as a technique in cancer research and therapy. Indeed, a key aspect of proton therapy is the precise knowledge of the beam range, a distance beyond which no primary particle will penetrate. Assuming the energy loss to be continuous, this distance should be a well defined magnitude, the same for all identical particles with the same initial energy in the same medium. However, as shown in Figure 1.6, this is not necessarily true as the incident protons stop within a certain interval of thicknesses. This behaviour, known as range straggling, is due to the fact that the energy loss has a statistical nature, which leads to an approximately Gaussian distribution of the range. Consequently, the range is an average quantity, defined for a beam and not for individual particles. Since the path of most protons in matter is nearly a straight line, on average their true path length is approximately equal to their projected path length and range. This fact makes many proton range calculations resolvable with relatively simple numerical or analytical approaches. Bearing in mind the previous considerations and under the hypothesis of Continuous Slowing Down Approximation (CSDA), from a theoretical point of view the range R ( E0 )of an incident particle with energy E0 can be calculated integrating the Bethe and Bloch formula as follows: R(E0) = ZR 0 dx(E) = Z0 E0 dx dEdE=Z0 E0dE dx−1 dE. (1.7) For any given particle, however, the path-length or equivalently the amount of energy loss per unit path length will not generally be equal to its mean value, due to the 11 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.3. Radiobiological aspects energy locally given to the medium, rather than on the energy lost by the incident particle. As for the electronic stopping power, the LET is defined as the mean energy dE lost in the target medium by a slowing-down particle in a track segment of length dl, and it is usually expressed in keV µm−1: LET =dE dl.(1.14) The LET defined in this way is called unrestricted. In some practical cases, it can be useful to exclude interactions that carry energy far away from the original track, imposing an upper threshold ∆for the energy of secondary electrons. This is usually referred to as restricted LET (LET ∆ ), and tends to the unrestricted LET (thus to the electronic stopping power) if the threshold tends to infinity [51]. The physical absorbed dose and the LET are strictly related; indeed, for a parallel beam with particle fluence Φ, the dose deposited in a thin slice of an absorber material with mass density ρcan be calculated as: D= 1.6×10−9×Φ×LET ×1 ρ.(1.15) The LET depends on the energy of a particle and, in the usual case of a beam with a broad energy spectrum, a distribution of LET will be observed in the exposed material. Therefore, to characterise the radiation field by a single parameter, a mean LET value must be used. There are two common ways of specifying LET distribution and, consequently, two different mean values: the frequency distribution, defined in terms of the total track length (which decreases as particles are stopped) of the incident particle or, equivalently, in terms of the particle fluence, and the dose distribution, defined in terms of the absorbed dose deposited by the particle at a specified LET [50,51]. •Frequency distribution Let F ( L )be the distribution function of the fraction of the total track length that is associated with a LET not larger than L: F(L) = φL φ,(1.16) where φ is the total fluence and φL is the fluence of particles with LET not exceeding L . The density of LET in track length or fluence is denoted by f ( L ) = dF ( L ) /dL , being the frequency- (or track-)averaged LET, LF , its mean value: 18 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy LF=ZLf(L)dL. (1.17) •Dose distribution Let D(L)be the distribution function of the fraction of absorbed dose due to particles with linear energy transfer not larger than L: D(L) = DL D,(1.18) where D is the total absorbed dose, and DL is the absorbed dose due to particles with LET not exceeding L . The corresponding density of LET in dose is denoted by d ( L ) = dD ( L ) /dL . The dose-averaged (or weighted-averaged) LET LDis: LD=ZLd(L)dL. (1.19) The dose and frequency distributions of LET are related as follows: d(L) = Lf(L) LF .(1.20) Accordingly, the dose-averaged LET can be expressed in terms of the first two moments of f(L): LD=1 LFZL2f(L)dL=L2 F LF .(1.21) 1.3.2 Survival curves and Relative Biological Effectiveness A common way to analyse the different effects of photons and light ions on living materials is by means of cell survival curves. A cell survival curve describes the relationship between the physical dose and the portion of cells that survives. The word survival can take different meanings depending on the context, but usually refers to the capability of a certain cell type to preserve a specific function. In the case of proliferating cells, such as cancerous ones, the response of the cells to ionising radiation, in vitro, is frequently quantified in terms of the probability of clonogenic survival, where clonogenic refers to the ability of the survivor to maintain the reproductive integrity and duplicate to form a large colony. Cell survival experiments are relatively easy to perform: cells from an actively growing stock culture are irradiated and then incubated for 1 or 2 weeks before being fixed and stained. Then, cell proliferation is analysed counting as survivors only 19 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.3. Radiobiological aspects Figure 1.11: Survival curve for photons (solid black line) and ions (red dashed line), and determination of RBE at 10% and 1% survival level (taken from [42]). those cells which have formed colonies with more than a certain threshold of daughter cells, usually set to 50. Finally the surviving fraction is given by normalisation to the number of seeded cells [47]. Survival curves are usually reported plotting the dose on a linear scale and the surviving fraction on a logarithmic scale, as shown in Figure 1.11. Qualitatively, the shape of the survival curve can be described in simple terms: • For low-LET radiation qualities, on the log-linear plot, the survival curve starts with a finite initial slope, bends for higher doses and finally straightens again for very high doses. • For densely ionising or high-LET radiation qualities, the cell survival curve is linear in the log-linear plot throughout the whole dose range. Therefore, the most common way to parametrise the cell survival curve is by means of an exponential function, theorised in the frame of the Linear Quadratic (LQ) model: S(D) = exp(−αD −βD2),(1.22) where S is the survival fraction, D is the absorbed dose and α and β are experimentally determined parameters. The LQ model assumes that there are two components to 20 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy cell killing by radiation, respectively proportional to the dose and to the square of the dose, which in some way depend on the severity of DNA damage. The ratio α/β determines the shoulder of the survival curve, i.e. the radiation sensitivity, and corresponds to the dose at which the linear and quadratic contributions to cell killing are equal. For a given endpoint, the dose-response curves from proton radiation are steeper than those for photon radiation (higher α/β ), probably indicating a lower damage repair probability. This effect becomes more pronounced at low proton energies and, specifically, α typically increases with increasing LET while β is not significantly affected [25]. Even if the LQ model is rather accurate in the classical dose range of conventional radiotherapy, the picture just presented is greatly simplified, and a universal theory of radiation cell killing is not yet available [52,53]. As mentioned in Section 1.3.1, the biological effects of radiation cannot be predicted only by means of the absorbed dose. In order to take into account the different biological effects induced by different radiation types for the same physical dose, the Relative Biological Effectiveness (RBE) coefficient has been defined: the ratio between the absorbed dose of a reference radiation (generally 60 Co, γ -rays or 250 keV X-rays) and that of the test radiation (for example light ions), required to produce the same biological effect (isoeffect): RBE =Dref Dtest iso .(1.23) Typically, the RBE is determined from cell survival curves, using for example the 10% survival fraction as isoeffect, as shown in Figure 1.11. It is important to note that the statement of a RBE value requires both the specifications of the reference radiation and the level of the biological effect. Usually, RBE values reported in literature use different types of reference photon energies, from mega-voltage to kilo-voltage [19]. As emerges from Figure 1.12, however, different photon energies are subject to a different LET, which for neutral beams is defined via the respective secondary electrons and charged products. Therefore, when reporting a RBE value, it is mandatory to give also the information about the reference radiation. In spite of its simple definition, the RBE is a very complex radiobiological concept, which depends on several factors and variables. In the specific case of proton therapy treatments, however, a proton RBE relative to high-energy photons equal to 1.1 is currently assumed, neglecting any dependency of RBE on dose, biological endpoint or proton beam properties [19]. Nevertheless, it is well known that the RBE is not a constant, but clinical data can neither indicate that the use of a generic RBE of 1.1 is unreasonable nor confirm that it is correct [25]. Recently, efforts have been made to include a variable RBE scheme in proton therapy treatment planning, and several 21 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.3. Radiobiological aspects Figure 1.12: Dose-averaged LET of the resulting secondary electrons as a function of the nominal photon energy (taken from [19]). Figure 1.13: RBE at 10% survival of different monoenergetic particle beams as a function of LET, grouped in different α/β sensitivity ranges (taken from [54]). 22 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy Figure 1.14: Variation of the RBE α = αtest/αref as a function of the particle type and the LET, where αref and αtest are the linear part of the survival curve for photons and ions, respectively (taken from [48]). models have been proposed for proton RBE prediction [21]. Indeed, evidences exist that a generic RBE value of 1.1 could under- or overestimate the RBE for certain tumours or organs at risk, having a potential impact on the clinical efficacy of proton therapy [19]. In order to implement RBE variations in treatment planning, a deep understanding of the relationship between RBE and LET, dose and biological endpoint is necessary. In general, as emerges from Figure 1.13, for light ions, the RBE increases with increasing LET up to a certain maximum, and then decreases due to a saturation effect for LET values above 100 keV µm−1 . This is related to the fact that, for very high LET, a single-particle traversal is sufficient to reduce the cell survival probability, making further ionisations unnecessary, leading to an "overkill" effect and to a decrease of RBE with increasing LET. For protons, the maximum RBE occurs at extremely low proton energies and a linear relation can be assumed between RBE and LET, with a slope depending on the biological endpoint [25]. The position of the RBE maximum is also influenced by the particle type, being shifted towards higher LET values for heavier particles as shown in Figure 1.14. For example, comparing protons and alpha particles in the LET region from 20 to 30 keV µm−1 , the first show a higher effectiveness. This is related to the different track structure of the two particles: at equal LET, alpha particles have a higher 23 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.3. Radiobiological aspects Figure 1.15: Proton RBE values calculated as a function of α/β for 2 Gy (full dots) and 6 Gy (open circles) (taken from [25]). An increase in RBE for late responding tissues ( α/β < 4 Gy ) is observed for lower doses. energy, resulting in broader tracks wih lower ionisation density in the centre, leading to a lower RBE. Finally, by definition, the RBE depends on the dose and on the chosen level of effect, which can vary strongly based on the biological system considered. For example, normal and malignant cells respond differently due to differences in their repair and cell re-population mechanisms; furthermore, oxygenation is decisive, especially for indirect effects, as low oxygen levels may determine a greater resistance to radiation [47]. Usually, different cell lines and tissues are classified depending on the α/β ratio of the photon survival curve. Two main groups can be identified: early responding tissues (high α/β values above 4 Gy ) and late responding tissues (low α/β values between 1and 4 Gy ), depending on their damage repair capability. The dependence of proton RBE on the α/β ratio has been extensively studied using experimental data and theoretical models [19]. Figure 1.15 shows that the RBE for late responding tissues seems to be higher than for early responding ones, and the biggest variations in RBE are expected to be observed for low α/β ratios at low doses. This, for example, can be advantageous in prostate (low α/β ) treatment with proton therapy, but disadvantageous for other treatment sites, if for example the spinal cord has to be irradiated to achieve sufficient tumour coverage [25]. Some studies have been performed in the past, trying to include a variable RBE scheme in proton therapy treatment planning [21], based on different phenomenological models for RBE prediction [55,56]. Despite starting from different model assumptions, these studies have shown the importance of considering RBE corrections in treatment 24 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy plans, as consistent deviations to the current practice of proton therapy biological planning with a constant RBE of 1.1 have been observed [57 – 59]. These findings suggest that considering at least main RBE dependencies, i.e. dose, LET and α/β , would be beneficial for treatment planning, especially in correspondence to organs at risk and for late responding tissues. Therefore, the development of computational tools for the modelling of such variable RBE would be strongly advisable. An alternative possibility with respect to the implementation of a variable RBE in proton therapy could be the use of a dose distribution optimisation based on physical quantities that can be predicted with higher accuracy. An example of this could be a LET-guided plan optimisation capable to maximise dose-averaged LET in the tumour while minimising it in the normal tissue, exploiting the linear dependence of the RBE on the LET [60,61]. 1.3.3 Microdosimetry When describing the energy loss on a cellular level, the LET concept is only a crude approximation, because the pattern of energy deposition events, which are stochastic in nature, plays a role in defining the radiobiological properties of radiations with similar LET. Indeed, the LET is a macroscopic parameter that, by definition, describes the energy lost by an incident particle per unit path length, and it is not well suited to describe the energy actually deposited in sub-cellular volumes. On the other side, the biological effect of radiation depends strongly on the information about the energy distribution in microscopic structures and in the local concentration of radiation-induced ionisations. To study the fluctuations of energy depositions in the tracks of charged particles, and the resulting biological effectiveness of radiation, the formalisms of microdosimetry was introduced by Rossi and co-workers [62 – 64]. Microdosimetry postulates that the biological effect of radiation is determined by the amount of energy deposited in certain sensitive cellular structures called sites. The basic microdosimetric quantities are the energy imparted,  , the specific energy, z and the lineal energy, y , defined in a site Sof a specified shape and size, usually having micron dimensions [65]. The energy imparted is the sum of all energy transfers iwithin S: =X i i.(1.24) The energy imparted is a random variable, and its value varies with repeated irradiations, being the fluctuations greater for small sites, densely ionising radiations and small doses. Therefore, predictions can be only made on the basis of probability distributions. 25 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.3. Radiobiological aspects The specific energy zis closely related to the energy imparted and it is defined as: z= m(1.25) where m is the mass of the site. The specific energy can be considered as the stochastic microscopic analogous of the absorbed dose, and in the SI it is given in Gy as well. Finally the lineal energy y is somehow the stochastic analogous of the LET, and it is defined by the quotient: y=s l,(1.26) where s is the energy imparted to the site by a single energy-deposition event, and l is the mean chord length of the site. The chord length l is a stochastic quantity and represents the length of a particle track within a site. It depends on the shape and dimensions of the site and, if the track is considered as a straight line, l is defined as the mean length of randomly oriented chords in the site, whose determination is a purely geometric problem. An important concept in microdosimetry is that of event in a site, defined as the energy deposition due to particles that are statistically correlated, e.g. a charged particle and all the secondary electrons generated by its interaction with matter. The single-event distribution f ( s )of the energy imparted is defined as the distribution of energy deposited in the site by exactly one event: f(s) = Ns,ds N,(1.27) where Ns,ds is the number of events with energy imparted in the interval [ s, s + ds ], and Nis the overall number of events. The expectation value of s following f ( s )is called frequency-mean imparted energy per event sF, and it is given by: sF =Z∞ 0 sf(s)ds.(1.28) For radiobiological considerations, it is also useful to consider the weighted or dose distribution d ( s )of the energy imparted per event, where the contribution of each event is weighted by the energy it deposits: d(s) = sf(s) sF .(1.29) The expectation value of s following d ( s )is called dose-mean imparted energy per 26 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy event sD, and it is given by: sD =Z∞ 0 sd(s)ds=1 sF Z∞ 0 2 sf(s)ds=2 sF sF .(1.30) From Equation (1.30) it is possible to relate both averages through: sD =sF +σ2 s sF ,(1.31) where σ2 sis the variance of f(s). Since s = zs·m = y·l , where zs = s/m is the single event specific energy, frequency and dose mean specific and lineal energy can be defined in an analogous way: zsD =z2 sF zsF , yD=y2 F yF .(1.32) The frequency mean lineal energy, yF , is approximately analogous to the frequency mean LET, LF , introduced in Section 1.3.1. If energy-loss straggling and the lateral escape of δ -rays out of the site are negligible, and if the range of the ionising particle is sufficiently large, the two mean values tend to be equal and LF = yF . As demonstrated by A. Kellerer in different works [66 – 68], a relation between the dose-averaged LET, LD , and its microdosimetric equivalent, yD , can also be derived. The demonstration, however, is not straightforward and will be discussed in more detail in Chapter 3. Microdosimetric Kinetic Model One of the main advantages of the microdosimetry theory is that it permits the calculation of RBE from a microscopic approach by means of the Microdosimetric- Kinetic Model (MKM) [69 – 71]. The foundations of this model lay on the theory of dual radiation action [72], which predicts that the observable effect of ionising radiation is determined by the combined action of sub-lesions, generated in the cell by a specific pattern of energy deposition, interacting in pairs to produce lethal lesions. Based on this concept, the following fundamental assumptions are made in the MK model [73]: 1. a cell nucleus can be divided into a number of microscopic volumes called domains; 2. following radiation exposure, two types of DNA damage are created in cell nuclei, named lethal and sub-lethal; 27 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.5. Radiation Dosimeters (a) (b) Figure 1.17: Working principle of a p-n junction without (a) and with (b) the application of an inverse bias voltage to increase the size of the depletion zone. are swept out by the electric field and, if electrical contacts are placed on either end of the junction, a current signal proportional to the ionisation can be detected, as shown in Figure 1.17a (bottom panel). In order to increase the depth of the depletion zone and the sensitive volume of the detector, an inverse bias voltage is usually applied to the junction, as shown in Figure 1.17b. The maximum voltage that can be applied, however, is limited by the resistance of the semiconductor. In radiotherapy applications, p-type silicon is generally used for dosimetry [86], as it is less affected by radiation damage and has a small dark current, i.e. a small fluctuating current that flows through the junction when the voltage is applied, contributing to the signal noise. Silicon dosimeters are very sensitive and small in size, being particularly useful for measurements in phantoms with small fields and high dose gradients. However, they can be employed only for relative dosimetry, since they are affected by radiation damage and their sensitivity might change with repeated use. For the experimental measurements conducted in this thesis, a lithium-drifted silicon detector was used. One drawback of silicon detectors is the difficulty of achieving a depletion zone thicker than a few millimetres, necessary to stop a proton beam of tens of MeV. This problem is solved with lithium-drifted silicon detectors [37], which can reach a depletion zone with thicknesses up to 10 −15 MeV. 34 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy 1.5.3 Radiochromic films Radiochromic films are extensively employed in radiation therapy for quality assurance measurements [87]. These films are mainly used for photon dosimetry because their response is independent on the energy of the incident clinical photons. This is not true in the case of proton irradiation, where an energy dependence emerges if the highly ionising region of the Bragg peak falls inside the active layer of the film [88–93]. The most widely used radiochromic films in recent years are the Gafchromic EBT films (Gafchromic, International Specialty Products, Wayne, New Jersey, USA), which show a significantly increased sensitivity with respect to the previous models available [94]. Different EBT type films exist, such as EBT2 and the most recent EBT3 and EBT-XD [95], each of them having different properties and dynamic ranges. For the measurements performed in this work, EBT3 films were used. EBT3 type films are made of a single 28 µm thick active layer (56.8% H, 27.6% C, 13.3% O, 1.6% Al and 0.6% Li, with a mass density of 1.2 g cm−3 [96] compatible with Lucite), mounted between two 125 µm thick polyester substrates. Their composition is nearly tissue equivalent [86, 87] and they contain a special dye that is polymerised under exposure to ionising radiation developing a blue colour. The polymer absorbs light, whose transmission through the film can be measured with a suitable densitometer such as a flatbed scanner. EBT3 films are self-developing films and do not require post exposure processing. The full colour development of these films is usually very rapid, occurring in a few milliseconds. However, some chemical processes require more time, minutes and even hours after irradiation, to reach completion. Therefore, a time window of 24 h is usually recommended before scanning [97]. The dynamic dose range of these films goes from 0.1 Gy to 20 Gy , but the optimum dose range lays between 0.2 Gy and 10 Gy . Above 10 Gy the EBT3 dose response curves show a shallow slope, which may lead to increased uncertainties at higher doses [98]. The working principle of radiochromic films is based on the colour change after radiation exposure, which is somehow proportional to the absorbed dose. The response of a radiochromic film to irradiation is commonly expressed in terms of the change in its net optical density (netOD), that represents the difference in optical densities of the same film piece sampled after and before irradiation, where the optical density is computed as the logarithm of the inverse transmission. To compute the netOD, pixel values ( PV ) of the film scanned in transmission mode are sampled over predefined regions of interest and the following formula is applied: 35 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.5. Radiation Dosimeters Figure 1.18: EBT3 dose response curves (left) and first derivatives (right) for dose values up to 40 Gy , plotted for the three colour channels that compose the image: red, green and blue (taken from [99]). netOD =ODf−ODi= log10 PV0 PVf−log10 PV0 PVi = log PVi PVf ,(1.37) where PV0 represents the pixel value of a non attenuated beam and for a 16-bit image is equal to 2 16 , and PVi and PVf are the pixel values of the film before and after irradiation, respectively. As can be observed in Figure 1.18, each colour channel of a scanned EBT3 film shows a different slope in the netOD-to-dose curve, related to the different ratio between the dose dependent and dose independent portion of the signal [99]. The red channel has a higher response from 0 to 10 Gy , visible from the derivative of its response curve in this dose range, which is higher than the green and blue ones. Above 10 Gy , the use of the green channel would be preferable, while the blue channel is generally less useful for dose measurements. Recently, dosimetric methods have been proposed for the combined used of all colour channels for the computation of the dose [100,101]; however, the discussion of these methods is beyond the scope of this thesis. Radiochromic films are known to show a significant under-response in dose for higher LET radiation in the proximity of the Bragg peak [88 – 93]. This effect, known as quenching, is related to the local saturation of the polymerisation process: the number of radiation-induced activated polimerysation sites increases with LET until, eventually, no more sites are available for activation and the polimerysation stops locally. Therefore, corrections must be applied if films are used for dose determination in the Bragg peak region or, more generally, in low energy ion beams [92,93]. 36 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 1. Principles of Proton Therapy 1.6 Work outline The work performed during this doctoral thesis was framed in the context of proton RBE variability, a topic that has been faced with two different approaches. The first one, experimental, focused on the design of a beam line for radiobiology experiments at the 18 MeV proton cyclotron installed at the National Centre of Accelerators (CNA, Seville, Spain). The second one, computational, was centred on the development of a Monte Carlo track structure application for the computation of microdosimetric quantities in water, to be used for the calculation of macroscopic dose-averaged LET distributions. The core of the thesis is divided in three main parts. Chapter 2 is dedicated to the description of the radiobiology beam line, focusing especially on the overall optimization of the beam parameters to define the best setup for the irradiation of mono-layer cell cultures. In this chapter, a Monte Carlo simulation of the beam line, realised with Geant4 and validated towards experimental measurements, is also presented. In Chapter 3 the Monte Carlo track structure application developed for the computation of microdosimetric distributions of protons in liquid water, is described. This application, based on Geant4-DNA, provides two sampling methods, uniform and weighted, for the scoring of the quantities of interest in spherical sites. Furthermore, it is used to verify the validity range of a formula that links microdosimetric quantities to the macroscopic dose-averaged LET distribution, being a powerful tool for the development of analytical models to be used in treatment planning optimisation. Chapter 4 presents the results of the first irradiation of cell cultures at the radiobiology beam line developed at the cyclotron facility. In this context, an application of the Monte Carlo code for the computation of microdosimetric quantities is shown. With this code, a theoretical derivation of the expected RBE for the experimental irradiation and cells under study could be done, through the use of the microdosimetric kinetic model. Finally, Chapter 5 collects a summary of the results obtained, followed by a brief discussion on the future perspectives of this work. 37 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2 Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA 2.1 Introduction As explained in Section 1.3.2, in current clinical practice it is assumed that proton beams are 10% more efficient than clinical photon beams as for cell-killing effectiveness; i.e., they have a constant RBE value of 1.1. However, the conventional use of this value has been questioned for some time, as the RBE varies with parameters such as tissue type, dose, biological endpoint and LET [19]. Nevertheless, the lack of accurate biological data, makes it difficult to implement biophysically optimised treatment plans in clinical practice. In this context, radiobiological investigations using particle accelerators have gained an increasing interest in the last decades [102 – 106], aiming at collecting accurate biological data especially for proton energies typically found at the Bragg peak region of clinical beams, roughly below 40 MeV , where the RBE is expected to increase [19,107]. Low energy proton accelerator facilities provide the perfect tool for this kind of studies, as they can produce high LET beams with narrow energy distributions. In fact, radiobiological experiments with low energy protons should be ideally performed at facilities providing proton beams with nominal energy below the limit mentioned, in order to minimise the straggling related to passive degradation. At the National Centre of Accelerators (CNA, Seville, Spain), two beam lines of this kind are available at the 3 MV tandem (Pelletron 9SDH-2 model) and at the cyclotron (Cyclone 18/9 model) facilities, respectively. To adapt these beam lines for radiobiological studies, special beam optimisation and dosimetric techniques 39 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.1. Introduction Figure 2.1: Picture of the experimental room. From the exit flange to the room wall there is approximately a distance of 2 m. are needed [102 – 106]. Indeed, radiobiological experiments at proton facilities pose stringent conditions both on the physical and on the biological point of view. Firstly, a homogeneous dose distribution throughout the biological sample must be ensured, with a meaningful dose rate comparable to that used in the clinic ( ≈2 Gy min−1 ). Furthermore, when dealing with low-energy accelerators, the limited particle range (lower than 5 mm in water for a proton beam of 20 MeV ) makes it difficult to irradiate samples in tissue flasks filled with medium, meaning that cells must be exposed inside open culture vessels vulnerable to bacterial contaminations. Finally, as biological targets are always made of living material, the environmental parameters such as room temperature, air pressure and humidity must be kept under control, to ensure no external factor impacts on the cell viability. In the case of the radiobiology beam line designed for the 3 MV tandem, these constraints were met by making some significant changes in the beam line, adding a manipulator for the insertion of a scattering foil in the vacuum pipe and a fast-closing valve to start and stop irradiations [106]. A specific sample holder was then designed, to irradiate cell culture plates in the vertical position, removing the growth medium immediately before exposure and treating the cells immediately afterwards to fix the 40 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA damage. Compared to the tandem, the 18 MeV cyclotron facility offered some increased challenges, mainly related to its installation environment and workflow. First, unlike the tandem beam line, the experimental beam line of the cyclotron is common to different research groups and it is devoted to multi-purpose research. Therefore, potential changes in the beam line structures should interfere neither with the experimental work of other groups nor with the normal workflow of the production of radioisotopes for Positron Emission Tomography (PET). Second, the space available in the experimental room is limited (approximately 2 m from the exit window to the wall, see Figure 2.1), and the insertion of new elements extending the length of the beam line was not feasible. In this chapter the setup proposed for the irradiation of cell samples at the cyclotron facility is presented, focusing in particular on the beam optimisation procedures and dosimetric characterization, and on the Monte Carlo simulations performed to attain these tasks. 2.2 Materials and Methods The cyclotron installed at the CNA in Seville is a Cyclone 18/9 from the IBA company (Ion Beam Applications, Louvain-La-Neuve, Belgium), which accelerates protons and deuterons to 18 and 9 MeV , respectively. This cyclotron has eight target ports: seven dedicated to the production of radioisotopes for PET and one used for the transport of the proton beam to an external beam line for interdisciplinary research. Figure 2.2: Schematic representation of the beam line (not scaled). 41 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.2. Materials and Methods In this section, the procedures and equipment used to obtain a proton beam suitable for the irradiation of cell samples are described, focusing on the characterisation of the beam energy and profile and on the optimisation of the experimental setup for radiobiological measurements. 2.2.1 Beam line As depicted in Figure 2.2, the 18 MeV proton beam, produced by the cyclotron, proceeds horizontally to the experimental room via the beam transport system. The beam line is divided into two sections, respectively located in the cyclotron bunker and in the experimental room, separated by a two meter thick concrete wall (number 9 in Figure 2.2). The first section includes a series of remote control permanent elements to monitor and define the beam current and size: 1. a retractable graphite Faraday cup for beam current monitoring (number 3); 2. a variable graphite slit (number 5 ), an XY set of magnetic steerers (number 6 ) and a quadrupole doublet (number 7, left) for beam shaping and guidance. A neutron shutter (number 8 in Figure 2.2) completes this part of the beam line, protecting the downstream elements in the experimental room from neutron radiation when the cyclotron is under operation for radioisotopes production. The second section of the beam line, in the experimental room, contains a single quadrupole magnet (number 7 , right), a circular water-cooled fixed aluminium collimator of 15 mm diameter (number 12 ), a pumping station (number 13 ) and a second retractable graphite Faraday cup (number 11 ), covered with a phosphor scintillator (ZnS–Ag) to observe the beam shape and size by means of a video camera. Finally, a pneumatic isolation valve (number 10 ) placed between the wall and the fixed collimator, and controlled manually from the control room, can be used to isolate the vacuum in the cyclotron from the beam pipe of the experimental room. All the elements described above are an integral part of the experimental beam line, and cannot be modified or replaced without interfering with the normal workflow of the facility or with other research activities. Apart from them, however, two other components complete the beam line, playing a major role in the optimisation of the system for the irradiation of cell cultures: a manipulator (not represented in Figure 2.2), for the insertion of targets in the vacuum pipe, and the exit flange (number 14 ). The target manipulator is placed between the wall and the isolation valve, at a distance of 2 m from the exit flange, and can be used to insert scattering foils of different thicknesses and materials in the beam path. It has different slots for the insertion of various targets, whose position can be changed manually. However 42 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA Figure 2.3: Graphical representation of the external beam line in the experimental room (not scaled), with a particular focus on the positioning of the two collimators. due to its placement upstream the isolation valve, the insertion of targets in the manipulator can only be done during special maintenance days, when the whole beam line and cyclotron are ventilated. For this reason, the preliminary tests for the development of the radiobiology beam line at the cyclotron facility were conducted degrading the beam directly in air, placing scattering foils of various thicknesses after the exit window. On its part, the design of the exit flange was especially developed to reduce activation of its components during irradiation, covering the internal part with a 5 mm thick absorbent layer of graphite acting as a collimator with customisable inner diameter. Therefore, on its path the beam encounters two subsequent collimators, as shown in Figure 2.3, the aluminium one of 15 mm diameter, and the graphite one with variable aperture, separated by a distance of 1.5 m . Finally, exit windows of different materials and thicknesses can be attached to this collimator, being Mylar the material chosen for the purpose of this study. As already mentioned, some major requirements must be taken into account when it comes to the irradiation of biological samples. 1. The beam intensity impinging on the sample should be of the order of tens of pA to control properly the fluence within suitable irradiation time scales. Ideally, a dose rate comparable to that used in the clinic should be achieved, of the order of 2 Gy min−1. 43 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.2. Materials and Methods Figure 2.7: Setup for the measurement of the energy distribution of protons with a 5 mm thick lithium-drifted silicon detector. the points used to build the energy-channel calibration curve shown in Figure 2.6. Once calibrated, the silicon detector was used to measure the energy distribution of the beam in different configurations, by placing the detector in front of the exit window together with a graphite collimator of 1 mm diameter to avoid saturation, and by degrading the beam with tungsten scattering foils with thicknesses ranging from 50 to 320 µm. A picture of the experimental setup is shown in Figure 2.7. Finally, experimental spectra were compared to simulated ones to find the optimal values for the initial mean energy and energy spread, to be inserted as initialisation parameters in the Monte Carlo code. To this end, a point-like proton source with Gaussian energy distribution was simulated, setting the mean energy equal to 18 MeV and changing the standard deviation from 0 . 10 to 0.18 MeV in steps of 10 keV . The optimal value for the energy spread was then set as that minimising the differences between experimental and simulated data for all the experimental configurations considered. 50 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA Figure 2.8: EBT3 dose-to-optical density calibration curves under 6 MV photon irradiation, for two different lots of films identified as #1 (full dots) and #2 (full squares). The measured points have been fitted with functions of the form D = a·netOD + b·netODc ; the results of these fits are listed in Table 2.3 for the two lots (#1 full lines and #2 dotted lines) and for the three colour channels: red, green and blue. Determination of the beam profile After determining the energy distribution of the beam, various measurements were carried out to determine its spatial distribution, using Gafchromic EBT3 films previously calibrated under known photon doses at the "Virgen Macarena" University Hospital in Seville. A medical linear accelerator (Siemens ONCOR, Siemens Healthineers, Erlagen, Germany) in 6 MV photon mode was used for this calibration, irradiating stripes of a sheet of EBT3 film from the same lot used at the cyclotron, with doses in the range 0 −20 Gy , under standard conditions, i.e., 10 ×10 cm2 field size, Source to Surface Distance (SSD) equal to 10 cm and at a depth of 1.5 cm in solid water at the isocentre. Twenty-four hours after irradiation, the films were scanned with an Epson Perfection V700 photo scanner (Suwa, Nagano, Japan), and acquired images converted from colour value to net optical density (netOD). To do so, films were scanned in transmission mode with a resolution of 75 dpi, 48-bit colour mode and without any image correction, taking special attention to scan all the images in the same direction. Digitised films were saved using an uncompressed tagged image file format (tiff) to be lately analysed with ImageJ (Image processing and analysis in Java), a public domain software for image processing. Different lots of EBT3 films might have in principle different optical properties, which 51 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.2. Materials and Methods Table 2.3: Results obtained for the parameters of Equation (2.1) from the fit of the data in Figure 2.8 for the three colour channels and for the two lots used. Film Lot Parameter Red Channel Green Channel Blue Channel #1 a[Gy] 10.2±0.2 16.0±0.5 35 ±3 b[Gy] 61 ±3 33 ±2 110 ±40 c3.44 ±0.09 2.51 ±0.13 2.4±0.3 #2 a[Gy] 5.4±0.2 9.6±0.2 26 ±4 b[Gy] 57 ±2 59 ±4 180 ±60 c3.03 ±0.07 2.68 ±0.10 2.4±0.3 can also vary with time. Therefore, a different photon calibration curve should be applied every time a new lot is used, and should be ideally checked for a known dose and eventually corrected previously to any measurement. During the experimental campaigns conducted at the CNA, two lots of EBT3 films were used, whose photon calibration curves are reported and compared in Figure 2.8 for the three colour channels (red, green and blue). Fit functions of the type: D=a·netOD +b·netODc,(2.1) were used to fit the data points, as suggested in literature [108]; the results of these fits, for the different colour channels, are listed in Table 2.3. Since the irradiation of the films to obtain the calibration curves was performed in solid water, the doses reported in Figure 2.8 are intended in water. The dose-to-optical density calibration curves obtained in the red channel (most sensible in the dose range 0 −10 Gy , see Section 1.5.3) were then used to convert in a first approximation the experimental netOD profiles measured at the cyclotron to dose, with the purpose of comparing them with the ones obtained from the Monte Carlo simulation. These profiles were measured in air at various distances from the exit flange (see Figure 2.9) and with various experimental configurations, listed in Table 2.4. The average beam energy impinging on the active layer of the film ranged from 17 . 2to 13.6 MeV , as reported in Table 2.4. While the EBT3 response to photon radiation is generally independent from the energy, this is not true for proton radiation, where a saturation in the darkening, or quenching effect, emerges as the LET increases [93]. Even if the application of the same calibration curve to all the configurations considered is not strictly correct, in the energy range considered the quenching effect is very small [92], and therefore the same calibration curve has been used for all the experimental configurations. Considering the characteristics of the experimental proton beam produced, which was 52 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA Figure 2.9: Example of a setup for the measurement of the beam profiles. A piece of EBT3 film is placed at a distance of 10.9 cm from the exit flange (configuration B.2 in Table 2.4). Table 2.4: Experimental configurations for the determination of the spatial characteristics of the proton beam to be compared with Monte Carlo simulations. Two different exit flanges have been used, described in Table 2.1. All these measurements were carried out without inserting the aluminium foil in the beam line; two of them ( A.3 and A.4 ) were performed attaching a thin tungsten foil to the exit flange. The distance reported was measured from the exit window to the surface of the film. Finally, the energy corresponds to the average proton kinetic energy impinging on the active layer of the film. Configuration Film Lot Exit Flange W Foil Distance Energy A.1 #1 (A) — 48 cm 15.5 MeV A.2 #1 (A) — 63 cm 15.0 MeV A.3 #1 (A) 50 µm 48 cm 14.1 MeV A.4 #1 (A) 50 µm 63 cm 13.6 MeV B.1 #2 (B) — 0.5 cm 17.2 MeV B.2 #2 (B) — 10.9 cm 16.9 MeV B.3 #2 (B) — 15.7 cm 16.7 MeV B.4 #2 (B) — 20.5 cm 16.5 MeV B.5 #2 (B) — 25.3 cm 16.4 MeV B.6 #2 (B) — 51.5 cm 15.5 MeV B.7 #2 (B) — 65.9 cm 15.0 MeV 53 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.2. Materials and Methods (a) (b) Figure 2.10: Pictures of the experimental setup for dosimetry and irradiation of biological samples. The ionisation chamber is placed between two PMMA supports on a moving table on which a plastic board can be screwed to extend its length (see (b) ). On the back of the second holder, a custom made guide can be mounted to allow for the positioning of Petri culture dishes or pieces of EBT3 film. completely defocused and collimated with a 15 mm collimator 1.5 m upstream the exit window, two initial spatial configurations were tested in the simulation: uniform circular, with a radius of 8 mm , and Gaussian elliptical, with a sigma varying from 8 to 20 mm independently in both directions on the transversal plane. 2.2.3 Setup for the irradiation of cell samples The experimental setup for dosimetry and for the irradiation of cell samples, shown in Figure 2.10, is similar to that used in the 3 MV tandem radiobiology beam line [106]. It consists of a Polymethylmethacrylate (PMMA) holder, made of two supports of 1 cm thickness each, mounted on a table which can be moved remotely with micrometric precision. Each side of the sample holder has a circular collimator of 35 mm diameter, coinciding with the entrance and exit windows of a parallel plate ionisation chamber inserted in between. This chamber, especially designed at the GSI-Heavy Ion Research Centre laboratory (Darmstadt, Germany) for radiobiology experiments with ions, is made of three thin parallel kapton electrodes of 7.5µm with two air gaps of 6.75 mm thickness in between, operates at 400 V and it is connected to an electrometer (Unidos E, PTW, Freiburg, Germany) for charge readout. On the back of the holder, a custom made guide is mounted to allow for the positioning of Petri culture plates in the vertical position, with one plate aligned with the PMMA collimator and beam each time. This position can be also used to make dosimetric studies by means of Gafchromic EBT3 type films. Finally, to extend the length of the table and move the samples closer to the exit window, a rigid plastic board has 54 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA Table 2.5: Summary of the characteristics of the two configurations, preliminary and final, tested for the preparation of the radiobiology beam line. Preliminary Final Manipulator Out In Foil material — Aluminium Foil thickness — 500 µm Fixed Collimator In In Collimator diameter 15 mm 15 mm Exit Flange (A) (B) External Foil In Out Foil material Tungsten — Foil thickness 150-220 µm— Window-Sample distance 50 cm 25 cm been designed and built, which is screwed to the table and moves jointly with it. To attain beam homogeneity over the whole sample surface, as already mentioned in previous sections, the beam had to be scattered through foils of different thicknesses and materials, and samples placed at an appropriate distance from the exit window. In the optimisation process, two different configurations were tested, whose characteristics are summarised in Table 2.5. However, these measures alone were insufficient, since the beam needed also to be centred so that its maximum intensity reached the sample. Indeed, a slight misalignment (a) (b) Figure 2.11: Beam spots measured by attaching a piece of EBT3 film directly on the exit flange in the (a) preliminary and (b) final configurations. A misalignment of the beam with respect to the fixed collimator is clearly visible in (a) , where the spot appears to be cut on one side. This effect fades away in (b) thanks to the insertion of the aluminium foil in vacuum, which increases beam divergence. 55 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.2. Materials and Methods (a) (b) (c) (d) (e) (f) Figure 2.12: Displacement of beam maximum intensity as a function of steering magnets coordinates along x-axis. No evident displacement emerged by varying y-axis coordinates, therefore the current applied to the steering magnet along y-axis was fixed to 1.98 A while varying that applied to the x-axis magnet: (a) -3 A, (b) -2.66 A, (c) -2.33 A, (d) -2 A, (e) -1.66 A and (f) -1.33 A. In this example, configuration (d) was chosen for the subsequent irradiations. of the beam with respect to the fixed collimator could be observed, especially relevant for the preliminary configuration, as shown in Figure 2.11. Therefore, previous to the calibration, different pieces of EBT3 were irradiated for approximately the same time to centre the beam, changing by small steps the current of the steering magnet coils to slightly move the beam and find the conditions that maximised beam homogeneity at the sample position. Figure 2.12 depicts the displacement of the maximum of beam intensity as a function of the steering magnets parameters, measured with the final configuration in Table 2.5. Following the identification of the best steering magnet parameters, proton dose calibration curves were measured attaching pieces of EBT3 film to the back of the sample holder, and monitoring the fluence by means of the charge readout of the ionisation chamber. Indeed, from the charge Q collected by the ionisation chamber, the incident proton fluence φcan be derived as follows: φ=1 A·Q·W e·∆EIC ,(2.2) where A is the area of the collimator placed in front of the chamber, W = 34 eV is the ionisation potential of the gas contained in the chamber, ∆EIC is the mean energy 56 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA deposited by individual protons in the ionisation chamber and e is the elementary charge. Knowing the proton fluence, the dose deposited D can be derived with the formula: D=∆Emat ∆x·f·φ·1 ρmat ,(2.3) where ∆Emat is the mean energy deposited per proton in the thickness ∆ x of the material considered, ρmat is its density and f is a correction factor introduced to account for the fluence loss due to the broadening of the beam inside the ionisation chamber. Since the computation of the dose is done under the assumption that the proton fluence does not vary over the sample surface, Equation (2.2) is a further proof of the importance of achieving homogeneous and uniform beam profiles. Finally, to compute ∆EIC , ∆Emat and f the Monte Carlo simulation, previously validated as described in Section 2.2.2, was used. 2.3 Results 2.3.1 Validation of the Monte Carlo code In this section, the results obtained for the characterisation and benchmarking of the simulated beam are presented. Firstly, the identification of the best energy distribution is discussed, focusing in particular on the determination of the energy spread of the beam. Secondly, on the other hand, is dedicated to the characterisation of the beam spatial profile. In both cases, simulation outcomes are compared with experimental measurements, and the final result is considered as that minimising the relative differences between the two. The beam energy and spatial distributions identified from this analysis are then used in all the subsequent application of the Monte Carlo simulation of the external beam line. Beam energy distribution With the purpose of characterising the initial energy distribution of the beam, to be implemented in the Monte Carlo simulation, different measurements were carried out as described in Section 2.2.2 and summarised in Table 2.6. These measurements were then reproduced in various Monte Carlo simulations, initialising the beam as a point-like source with Gaussian energy distribution. A fixed initial proton beam energy of 18 MeV was used for these simulations, changing the initial standard deviation ( σi ) from 0.18 MeV (nominal value) to 0.10 MeV in steps of 10 keV . The comparison between experimental and Monte Carlo results is 57 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.3. Results Table 2.6: Experimental configurations used for the determination of the spectral distribution of the beam, to be compared with the simulations. In all cases the energy was measured with a 5 mm thick calibrated silicon detector at a distance of 22 mm from the exit window, intercepting the beam path with tungsten degraders of various thicknesses. The values of the mean energy and energy spread reported and their errors have been obtained from a Gaussian fit of the experimental energy distributions. W foil measured mean measured energy thickness [µm] energy (Eexp) [MeV] spread (σexp) [MeV] no foil 17.463(4) 0.143(5) 50 16.135(7) 0.188(6) 100 14.861(2) 0.201(2) 150 13.441(2) 0.232(2) 220 11.201(5) 0.283(4) 270 9.563(6) 0.364(5) 320 7.533(9) 0.402(7) shown in Figure 2.13 and Figure 2.14. Deviations of the Monte Carlo mean energy values from experimental ones are generally below 1% and always smaller than the experimental energy spread σexp , while deviations in energy spread are mostly below 5% and up to 10% in the worst case. From Figure 2.14 it emerges that a Gaussian energy distribution with mean value of 18 MeV and σi of 0.14 MeV gives the best agreement between measured and simulated energy spectra. Beam spatial distribution After tuning the Monte Carlo simulation to reproduce the initial energy distribution of the beam, its spatial distribution could be characterised. To do so, as described in Section 2.2.2, measurements of the beam profile were performed, placing EBT3 films at different distances from the exit window and in different configurations, listed in Table 2.4. Concerning the simulation, various initial spatial configurations of the beam were considered: circular uniform, circular Gaussian and elliptical Gaussian, with radius or standard deviation varying from 8 mm to 20 mm independently in the two transverse directions. A first comparison of Monte Carlo simulations with the measured lateral dose profiles is shown in Figure 2.15. In this Figure, the beam spot measured at a distance of 0.5 cm from the exit window (Figure 2.15a) is compared with the simulated ones, starting respectively from a circular uniform beam with radius ri = 8 mm (Figure 2.15b), a circular Gaussian beam with σi = 8 mm (Figure 2.15c) and an elliptical Gaussian beam with σi,x = 12 mm and σi,y = 20 mm (Figure 2.15d). Figure 2.16 shows the same comparison, where the dose profiles along the two axes have been extracted 58 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA (a) (b) Figure 2.13: (a) Comparison between experimental mean energy measured (shaded gray area and black dots) and mean energy obtained from Monte Carlo simulations (red dots) as a function of the foil thickness. The mean energy obtained at the end of the simulation, computed as the energy deposited in the silicon detector, does not depend on the initial σi of the beam. The energy width of the experimental shaded area is given by σexp . (b) Percentage deviation of the Monte Carlo mean energy (E MC ) from the experimental one (E exp ). The error bars have been computed with standard uncertainty propagation over the errors associated to the mean energies obtained from the fits. Figure 2.14: Comparison between the experimental σ measured (shaded gray area) and those obtained from the Monte Carlo code run with different initial standard deviations of the Gaussian beam σi , as a function of the foil thickness. The width of the experimental shaded area is given by the error associated to σexp. 59 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.3. Results (a) (b) (c) (d) (e) Figure 2.20: Maps of the relative percentage deviation of the netOD computed in each pixel from the average value ( |netOD −netODµ|/netODµ ). (a) Preliminary configuration with a tungsten foil of 220 µm , lot of films #1, netOD µ = 0 . 20. (b) Preliminary configuration with a tungsten foil of 150 µm , lot of films #1, netOD µ = 0 . 19. (c) Final configuration, lot of films #2, netOD µ = 0 . 16. (d) Preliminary configuration with a tungsten foil of 150 µm , lot of films #1, netODµ= 0.58.(e) Final configuration, lot of films #2, netODµ= 0.58. In general, average relative deviations from netOD µ lower than 4% were observed in all the samples, with localised maximum differences up to 20%, usually found in small spikes close to the edges of the irradiated area. For the computation of the dose, the validated Monte Carlo simulation of the beam line was used to derive the mean energies deposited in the ionisation chamber ( ∆EIC ) and in the active layer of the film (∆EAL), and the fluence fraction (f) of particles impinging on the film, to be inserted in Equation (2.2) and (2.3) . Table 2.7 collects the values of these quantities for the different experimental configurations considered, extracted from the Monte Carlo distributions shown in Figure 2.21. From the netOD µ values measured and the computed doses, calibration curves for the three colour channels were obtained and fitted with Equation (2.1) . The resulting curves are depicted in Figure 2.22 and compared to the respective photon calibration curves depending on the film lot, while fit parameters are listed in Table 2.8. As expected [92,93], a dependence of proton calibration curves on the energy emerged. For the purpose of observing better this effect, independently from the lot of films considered, a plot of the relative difference of proton calibration curves from photon ones as a function of the netOD has been built and is shown in Figure 2.23. In this plot, for the highest incident proton kinetic energy ( 12.8 MeV ) the relative difference 66 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA (a) (b) (c) Figure 2.21: Distribution of energy deposited per individual proton track in the ionisation chamber ∆ EIC (left) and in the active layer of the film ∆ EAL (right). (a) Preliminary configuration with tungsten scattering foil of 220 µm ; (b) preliminary configuration with tungsten scattering foil of 150 µm ; (c) final configuration. Mean values and standard deviations of the distributions are listed in Table 2.7. 67 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.4. Discussion Table 2.7: Mean values and associated standard deviations obtained from the distributions shown in Figure 2.21. Ekin is the kinetic energy of the protons in the centre of the active layer of the film, ∆EIC is the average energy deposited by protons in the ionisation chamber, ∆EAL is the average energy deposited by protons in the active layer of the film and f is the fraction of protons that reaches the film after having crossed the ionisation chamber. Configuration Ekin [MeV] ∆EIC [keV] ∆EAL [keV] f Preliminary 7.9±0.4 70.8±0.6 183.4±0.7 0.93 (220 µmW) Preliminary 10.6±0.3 57.3±0.6 144.0±0.7 0.93 (150 µmW) Final 12.8±0.2 50.4±0.6 125.1±0.8 0.98 increases slowly with the netOD, with values varying from 8% to 10% in the [0,0.7] netOD range. For the lower energetic protons ( 10.6 MeV ) on the other hand, this relative difference increases steeply in the [0,0.4] netOD range, going from 15% to 30%, reaches a maximum and then decreases again. 2.4 Discussion In this chapter, the experimental setup for the irradiation of biological samples, designed for the cyclotron experimental beam line installed at the CNA, has been presented. The main advantage of using an 18 MeV proton beam relies in the possibility of achieving energy distributions with mean values corresponding to the Bragg peak region of a clinical proton beam with a much lower energy spread. As a drawback, however, the range of applicability of such a beam is limited to experiments with mono-layer cell cultures, for which the energy and the stopping power of protons reaching the cells can be calculated accurately. Indeed, for floating cell culture experiments, beam energy degradation along the culture itself would have to be taken into account, leading to a high variability of the stopping power in depth within the sample and subsequently to higher uncertainties in the deposited dose. In order to achieve dose homogeneity over the irradiated samples with a manageable dose rate (around 2 Gy min−1 ), the beam intensity was decreased by lowering as much as possible the extraction current of the cyclotron and by turning off all the magnets for beam optics. A further decrease in the beam intensity, as well as a broadening of the beam profile, was obtained by intercepting the beam path with scattering foils of different materials and thicknesses, and by varying the distance between the exit flange and the position of the samples. Two different setups were tested: a preliminary one, where the beam was broadened in air by attaching tungsten foils of 150 µm or 220 µm to the exit flange; and the final one, where the beam was scattered 68 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA Figure 2.22: Dose-to-netOD calibration curves for the three colour channels. Experimental data are presented together with their fit (dashed line) and compared with the corresponding photon calibration curves (solid lines). Fit parameters are reported in Table 2.8. On the left experimental data obtained with both preliminary configurations (lot #1) are plot: (1) beam broadened with a 150 µm tungsten foil (empty diamonds) and (2) with a 220 µm tungsten foil (full stars). On the right the experimental data obtained with the final configuration (empty circles) are presented. The energies indicated in the legend are the same Ekin listed in Table 2.7 Table 2.8: Results obtained for the parameters of Equation (2.1) from the fit of the data in Figure 2.22 for the three colour channels and the different experimental configurations. Since in the range covered by the measurements performed with the 220 µm tungsten foil (stars of Figure 2.22) the dose is mostly a power of the netOD, parameter a has been set equal to zero for the three channels. Configuration Parameter Red Channel Green Channel Blue Channel Preliminary a[Gy] 0 0 0 Ekin = 7.9 MeV b[Gy] 25 ±2 33 ±3 120 ±40 (lot #1) c1.38 ±0.04 1.23 ±0.05 1.4±0.1 Preliminary a[Gy] 11.8±0.4 19 ±1 39 ±8 Ekin = 10.6 MeV b[Gy] 70 ±7 41 ±6 120 ±60 (lot #1) c3.1±0.2 2.3±0.3 2.0±0.5 Final a[Gy] 5.9±0.9 10 ±2 20 ±10 Ekin = 12.8 MeV b[Gy] 65 ±9 60 ±10 110 ±30 (lot #2) c3.1±0.3 2.6±0.3 1.8±0.4 69 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.4. Discussion Figure 2.23: Relative difference of the proton dose ( Dp ) from the photon dose ( Dγ ), evaluated with the respective calibration curves, as a function of the netOD. For the more energetic incident protons ( 12.8 MeV , circles) this relative difference increases slowly and its value lays between 8% and 10%. For the 10.6 MeV , on the other hand, the relative difference increases steeply, reaches a maximum at a netOD of around 0.4, and decreases again, varying from 15% to 30%. by means of a 500 µm thick aluminium foil inserted in the manipulator mounted 2 m upstream the exit flange. Further, for dosimetry purposes, the geometry of the beam line and the irradiation setup were implemented in Geant4, developing a dedicated Monte Carlo application which was validated and benchmarked towards comparison with experimental data. Validation of the Monte Carlo code Measurements of beam energy and shape were performed with a lithium-drifted silicon detector and EBT3 films, to be compared with Monte Carlo simulations for the validation of the code. In order to determine the initial Monte Carlo beam characteristics, multiple simulations were run changing by small steps and one at a time different parameters, such as energy spread and shape of the spatial distribution, to find the set of parameters that better reproduced experimental data. An initial proton beam energy of 18 MeV with a Gaussian energy spread of 0.14 MeV gave the best agreement between experimental and simulated results, with percentage deviations generally lower than 1%. The highest discordances between measurements and Monte Carlo, relatively to the energy distribution, were observed for the thicker tungsten foils used to degrade the beam, as can be seen in Figure 2.13. This result 70 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA could have been influenced by two different factors: the lower statistics collected experimentally for these points and the uncertainty associated to the thickness of the foil, reported to be up to 10% by the manufacturer. Regarding the reproducibility of lateral dose profiles, a circular uniform Monte Carlo beam spot, having radius ri = 8 mm , gave the best agreement with the experimental profiles measured with EBT3 films. The asymmetry in some of the measured dose profiles, especially those detected at a closer distance from the exit window, was not reproduced by the Monte Carlo simulation, since it was probably related to an initial misalignment of the beam coming from the cyclotron. This effect, which could be partially corrected by resorting to the steering magnets of the beam line, fades away as the distance from the exit window increases and the broadening due to multiple Coulomb scattering in air becomes predominant. In general, differences between simulated and measured profiles were mostly below 10%, being usually Monte Carlo beam spots slightly smaller than experimental ones. These differences arose probably from the calibration curve used to scale measured netOD profiles to dose. Indeed, photon dose calibration curves were used to this purpose in the first approximation. However, since the quenching effect observed in EBT3 films under proton radiation decreases as the proton energy increases, the "true" calibration curves for the energies considered (between 13 . 6and 18 MeV ) are expected to lay between the 12.8 MeV proton curve and the photon one shown in Figure 2.22, and the quenching effect is expected to be negligible. Optimisation of the setup for the irradiation of cell samples A homogeneous lateral dose profile is beneficial in cell experiments, to ensure that the dose stays constant throughout the culture dish at a given depth. With both setups tested for the irradiation of biological samples, preliminary and final, average relative deviations from homogeneity lower than 4% were observed, with some localised maximum differences up to 20% located at the edges of the irradiated area. In Figure 2.20c, a gradient exists in the netOD profile obtained with the final configuration, whose deviation from homogeneity is still below 10% and decreases as the netOD increases, as can be seen by comparing for example with Figure 2.20e. This behaviour is probably related to the fact that, without any degradation in air with tungsten foils, the residual misalignment of the beam might still be visible in the sample, as the beam undergoes less divergence (see Figure 2.11). For this reason the initial alignment with steering magnets is crucial and must be performed before every experimental campaign, since the coil parameters that give the best alignment are not always reproducible. Furthermore, some evidences emerged, depicted in Figure 2.24, suggesting that the beam suffered a small drifting in time within the same experimental campaign, as the coils of the steering magnets heated up with 71 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.4. Discussion (a) (b) Figure 2.24: Maps of the relative percentage deviation from homogeneity of two samples having the same netOD µ = 0 . 60, but measured at the beginning (a) and at the end (b) of the experimental campaign at a distance of approximately two hours. use, determining a displacement of the beam maximum intensity. Even if this effect can be considered negligible for the film calibration and computation of the dose, it must be taken into account, and minimised when it comes to the irradiation of biological samples. Therefore, a check on beam homogeneity and a setting of the steering magnet parameters is strongly recommended before and after any irradiation of biological material. After assuring the beam homogeneity over the sample, EBT3 films were calibrated under proton irradiation and the resulting curves compared with photon ones. A dependence on the proton energy emerged, resulting in a progressive distancing of proton curves from photon ones, leading to a lower darkening of the film for the same level of absorbed dose and thus to a lower sensitivity. To study the effect of the proton energy on the calibration curve, independently from the film lot considered, the relative difference of the predicted proton dose from the photon one was plotted as a function of the netOD (see Figure 2.23). While for the more energetic protons the relative distance between the curves remains almost constant, with a small increase towards higher netOD values, for the lower energetic protons this distance increases steeply up to a maximum at a netOD of around 0.4, and then decreases. This behaviour is probably related to two factors: the quenching effect triggered by the lower energetic protons of the incident kinetic energy distribution, and the saturation of the film response to high doses. Finally, dose rates of approximately 2 −3 Gy min−1 and 5 Gy min−1 were obtained for the preliminary and final setup, respectively. The slightly higher dose rate of the final setup was probably influenced by the material of the scattering foil used. Indeed, the atomic number of aluminium is much smaller than that of tungsten ( ZAl = 13 and ZW = 74), determining a smaller multiple Coulomb scattering effect 72 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 2. Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at CNA and therefore a reduced beam loss in the different collimators constituting the beam line and the experimental setup. Furthermore, the beam settings and intensities are subject to variations from one irradiation to another, affecting the reproducibility of the dose rate. 2.5 Conclusions A beam line diagnostic and irradiation scheme, based on a completely defocused beam, a 500 µm thick aluminium scattering foil and an ionisation chamber coupled with EBT3 radiochromic films, was identified as the best setup for the irradiation of mono-layer cell cultures at the external beam line of the CNA cyclotron facility. With this setup, a homogeneous irradiation field was achieved, with average deviations from homogeneity lower than 4% in the whole sample area ( 3.5 cm diameter) for a beam energy of 12.8 MeV and a dose rate of about 5−6 Gy min−1. A specific Monte Carlo simulation was built and developed to reproduce the beam line and the experimental setup, using the Geant4 Monte Carlo code. Simulations were tested towards experimental measurements and reproduced experimental data in what concerned the beam energy distribution and dose profiles with differences lower than 1% and 10%, respectively. From the setup just described, in principle, lower proton energies with higher levels of homogeneity over the sample surface and lower dose rates could be easily achieved, by further degrading the beam with scattering foils of different materials and thicknesses and by changing the exit window to sample distance. On the other side, a proton beam energy distribution with a higher average value ( 12.8 MeV < Ekin <18 MeV ) could probably be obtained by increasing the atomic number of the scattering foil material in the manipulator while decreasing its thickness. Finally, in Chapter 4, the first irradiations of mono-layer cell cultures performed in the cyclotron radiobiology beam line will be presented. 73 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 3 Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4-DNA 3.1 Introduction Many radiobiological effects of ionising radiation can be traced back to the microscopic spatial distribution of energy deposition in irradiated media, whose stochastic nature is described quantitatively with the formalism of microdosimetry. Consequently, in recent years several studies have turned to the framework of microdosimetry to approach problems such as the characterisation of LET distributions for radiotherapy beams and the determination of their RBE. In view of the growing awareness of the variations or proton RBE with increasing LET at the distal Bragg peak region [109 – 111], recent studies aim at including LET and/or dose-averaged LET ( LD ) objective functions in treatment planning optimisation [112,113], taking advantage of the monotonic dependence of the RBE on LET for clinical proton beams. Microdosimetry, on one hand, permits the calculation of RBE from a microscopic approach by means of the Microdosimetric-Kinetic Model (MKM) [69 – 71] and, on the other hand, provides physical concepts and computational tools to calculate 75 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.3. Materials and Methods for ν -randomness, where yD is defined with the mean chord length of the respective randomness type. Straggling, on its side, is an independent factor from LET and chord length, and its distribution should not be affected by them and by the sampling method considered. 3.2.3 Macroscopic dose-averaged LET calculation method From a macroscopic point of view, the calculation of restricted and unrestricted dose-averaged LET distributions in clinical proton beams can be carried out either by means of analytical models or by Monte Carlo simulations. In both cases, calculations are usually based on the spectral fluence evaluation of primary and, sometimes, secondary particles composing the beam. In the case of Monte Carlo simulations, a step-by-step approach can be followed in the computation of LET, using the true step length and the electronic energy loss at that step. Different Monte Carlo algorithms for the computation of LD , based on a condensed history method, were compared by Cortés-Giraldo and Carabe [117] using Geant4, to test their robustness towards the variation of different parameters. The following method: LD=PN n=1 PSn s=1 ωnLsnεsn PN n=1 PSn s=1 ωnεsn (3.12) was identified as the one giving the most consistent performances, being n and s the event and step index respectively of the primary proton track simulated, Lsn the mean energy loss per unit path length in the material, εsn the energy deposited by the primary proton along the step and ωn the statistical weight of the primary proton. In this calculation, Lsn was obtained with the Geant4 method ComputeElectronicDEDX() of the G4EmCalculator class, which computes the LET from electronic stopping power tables, provided the particle type, kinetic energy and material traversed; while εsn was obtained by summing up the continuous part of the energy deposition due to the passage of the primary proton and the kinetic energy of the δ-rays released in the medium by the incident proton in the step considered. In the present work, Equation (3.12) was used to calculate macroscopically the dose-averaged LET in the simulations, to be compared with the results of the microdosimetric calculations. 3.3 Materials and Methods In this section, the main features of the Monte Carlo application developed for the computation of the microdosimetric quantities in Equation (3.9) are presented. 82 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 3. Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4-DNA Figure 3.3: Scheme of the geometry used for microdosimetry simulations (2D projection). The primary proton (red track) is generated at the surface of a cubic water volume (world volume) and travels along the Z axis. The energy transfer points (hits) are then scored in the middle of the volume (shaded area), in a slab whose thickness ( ZS ) varies depending on the dimension of the site. The spherical sites are not physically simulated, as they are virtually selected in the scoring volume with an algorithm that depends on the type of randomness considered. Finally, the half-dimension of the world volume ( Rmax ) varies according to the maximum energy of the incident protons, and is slightly greater than the maximum range of the δ-rays emitted. All the simulations were carried out with the Geant4 toolkit, by using our computing cluster hosted at Centro Informático Científico de Andalucía (CICA, Seville, Spain), consisting of 24 computational nodes, each with 2 × 12C AMD Abu Dhabi 6344 ( 2.6 GHz/6 MB ) L3. The Geant4-DNA package, available within Geant4, was used to this purpose, as it makes possible to carry track structure simulations and tracking of electrons down to ≈10 eV. 3.3.1 Geometry The geometry of the microdosimetry application is really simple, as shown in Figure 3.3. The world volume, i.e., the volume that represents the experimental area and contains all the other components, consists of a water cubic box having half dimension Rmax slightly greater than the maximum range of the δ -rays emitted by the incident protons Rδ,max . This range is calculated with Equation (1.4) , and the 83 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.3. Materials and Methods condition Rmax ≥Rδ,max is necessary to ensure intra-track electronic equilibrium. The scoring volume, i.e., the volume in which the energy transfer points (hits) are detected and stored, is a water slab positioned in the centre of the world volume with same transversal dimensions and variable thickness ZS , depending on the dimension of the site chosen. The beam (red track in Figure 3.3) originates at the surface of the cubic volume and travels along the z-axis. The physical quantities of interest are scored in randomly-placed spherical sites, with diameters ranging from 1to 10 µm . These sites are not simulated as physical volumes, but are virtually identified as regions in the scoring volume thanks to specific algorithms for the selection of their centres. For the site positioning, two sampling methods have been implemented, uniform and weighted random sampling, whose detailed description is given in Section 3.3.2. In order to study the performance of the code, simulations were initially carried out with mono-energetic proton beams with energies ranging from 10 to 90 MeV , for spherical sites with diameters of 1and 10 µm . The upper energy limit was imposed by the physics list employed for the simulations, as Geant4-DNA only allows calculations for proton energies lower than 100 MeV . On the other side, the lower energy limit was chosen to ensure that the short track segment condition was valid for all the energies and site dimensions considered. Furthermore, to understand the dependence of the simulation results on the longitudinal dimensions of the scoring slab, a preliminary study was performed by varying the size of the scoring volume for the two extreme energies and site diameters. As a general rule, to allow for the correct functioning of the scoring algorithms (see Section 3.3.2) the relation ZS> 2 d must hold, where d is the site diameter. Therefore the formula ZS = 2 d + η was used, choosing for η the values 0 . 1 d , d ,2 d and 10 d (the latest only for the 1µm diameter site). Since for the lowest energy and biggest site dimensions the maximum δ -ray range is smaller than half of the scoring volume thickness, Rδ,max < ZS/ 2, and in order to have the same proton kinetic energy distribution at the centre of the world volume for both site diameters, the decision to set Rmax = Rδ,max + ( ZS,max/ 2) for all the simulations was taken, with ZS,max = 40 µm. 3.3.2 Scoring algorithms The most intuitive way of scoring energy deposition events in micrometric sites along a proton track would be to randomly select a point −→ PC in the region of interest with a uniform probability and consider all the energy transfer points (hits) −→ Phi within a distance |−→ Phi−−→ PC| ≤ d/ 2from it. This sampling method, known as µ -randomness, is very robust and is not subject to any bias. However, this technique 84 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 3. Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4-DNA (a) (b) Figure 3.4: Graphical representation of the working principle of the two sampling algorithms: (a) uniform sampling ( µ -randomness) and (b) weighted sampling ( ν -randomness). In both cases, a hit selection region (maroon shaded area) is identified, where the centres of the sites (yellow circles) are sorted. The dimensions of this region depend on the sampling algorithm used and on the diameter of the site, as lateral margins must be left to ensure that the site is always fully included in the scoring volume. For uniform sampling this margin must be set equal to the site radius, while for weighted sampling the margin is equal to the site diameter. is likely to be highly inefficient, as the probability of selecting volumes with no hits is really high and increases for the smaller sites and higher energies. To increase the sampling efficiency, ν -randomness can be used instead. In this case, an energy transfer point −→ PH is randomly chosen with uniform probability among the hits of the simulated track. Then, the centre of the site −→ PC is sampled with uniform probability in a sphere of radius d/ 2around −→ PH , i.e at a distance |−→ PC−−→ PH| ≤ d/ 2. Finally, all the energy transfer points −→ Phi within a distance |−→ Phi−−→ PC| ≤ d/ 2 are considered for the computation of microdosimetric quantities in the site. In this way, the presence of a at least one energy transfer point −→ PH in the site is always ensured, and a 100% sampling efficiency can be achieved. As a drawback, however, this method is spatially biased towards regions of high density of hits, and a compensation factor must be introduced to account for it. As suggested in other works [118,119], this factor should be equal to the ratio of the number of hits that can be selected to the number of hits located in the randomly placed site. Both methods were implemented in our Monte Carlo code developed for the computation of microdosimetric quantities, and their working principle is graphically represented in Figure 3.4. In order to increase the sampling efficiency of the uniform random method, a while loop controlled by a flag to a maximum of 1000 loops was 85 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.3. Materials and Methods Figure 3.5: Detail of the working principle of the weighted sampling method in Figure 3.4b. The compensation factor is computed as the ratio between the number of selectable hits (with deposited energy different from zero) in the hit selection region ( Nsel ) and the number of hits in the intersection volume of the site with the hit selection region (Nint). introduced to repeat the sorting procedure on the same track until one good event was found to the expenses of computational time. In both cases a hit selection region (maroon shaded area in Figure 3.4) must be identified, in which −→ PC and −→ PH are sorted. The dimensions of this region depend on the sampling algorithm used and on the diameter of the site. The general rule is that a margin must be left, both in the longitudinal and transverse dimensions, in order to ensure that all the randomly selected sites are always fully included in the scoring volume. For the uniform random sampling, this margin must be set equal to the site radius, while for weighted sampling it is equal to the site diameter. Following the previous considerations, in the case of weighted sampling, the compensation factor must be set equal to Nsel/Nint , as shown in Figure 3.5, where Nsel is the number of hits (with energy deposited different from zero) in the hit selection region that can be randomly selected, and Nint is the number of hits in the intersection volume of the site and the hit selection region. After sorting the position of the site, three main quantities are computed: the total energy deposited in the site per event (  ), the total energy deposited for a single proton collision ( εc ) and the chord length ( l ) of the proton traversing the site. While the computation of  is straightforward, i.e., the sum of the energies deposited by each hit happening within the site, the computation of εc and l cannot be done directly and will be discussed in the following paragraphs. 86 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 3. Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4-DNA Figure 3.6: Schematic representation of the scoring method for the evaluation of the energy deposited per single proton collision in the site, εc . The primary δ -ray generated by the proton collision is identified and assigned one distinctive tag, that is then inherited by all the secondary electrons in the shower. Only the energy deposition events happening within the site are accounted for in the calculation of εc, including δ-ray influx from outside the site. Figure 3.7: Graphical representation of the possible configurations in which proton tracks (red lines) can cross a site. The black points identify the position of the proton hits, for which the spatial coordinates are known and stored. The track segment between two hits identifies a step. The solid red lines are the proton track segments to be considered for the computation of the chord length distribution. Depending on the position of the site with respect to the proton track, a step can start and end outside the site (A), have one or both ends included in the site (B), or originate (or end) at the surface of the site (C). 87 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.3. Materials and Methods Computation of energy deposited per individual proton collision In order to compute the energy imparted to the sensitive volume per each individual proton collision, the electronic showers generated by each collision must be uniquely identified. This was done by means of a Sensitive Detector class coded for this purpose, by identifying the primary electrons set in motion by a proton collision and assigning them a distinctive tag equal to their track identification number during the Geant4 simulation. By doing so, and thanks to the structure of the tracking algorithm of Geant4, all the subsequent secondary electrons created by further collisions of the electron originating the shower can be assigned the same tag. In this way, the energy deposited in the site by each δ -ray shower originating in the site or entering the site can be scored independently, as graphically represented in Figure 3.6. Computation of chord length For the computation of the chord length distribution, the length of the segments of the primary proton trajectories intercepting the site must be evaluated. If the sites were built as physical volumes in the Geant4 application, this procedure would be straightforward, as track steps are always forced to end at the interface between two volumes. This, however, does not apply in the case under consideration, as the randomly placed sites do not have a physical interface and track steps can cross the volume surface. Therefore, proton chord lengths had to be computed manually from geometric considerations, taking into account all the possible configurations in Figure 3.7. 3.3.3 Output Once the site is positioned, the different microdosimetric quantities can be computed and stored. The Monte Carlo code developed provides two ways of storing and saving the results, both in ROOT format: histograms containing the distributions of the physical quantities of interest and trees containing detailed information of each track. The ROOT tree format offers the advantage of being more flexible, as it allows to analyse the proton tracks on an event by event base after having run the simulation. To do so, a ROOT macro was developed implementing the same site positioning algorithms just described. However, the size of the outputs produced in this way might be of several GB and they are not always easy to handle. ROOT histograms, on the other side, provide a compact and more manageable output, at the expense of the information about the single events. When considering the histogram output format, the best way of representing microdosimetric distributions is to use the semi-logarithmic scale, since the energy deposited in each event has a variability of different orders of magnitude. By definition, the probability densities of the single event distributions are normalised to one. 88 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 3. Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4-DNA This normalisation must remain unchanged when f (  )is plotted on a logarithmic scale of , therefore a proper normalisation factor must be applied. Let the logarithmic scale of  be subdivided in B increments per decade, such that the i-th value of is: =0·10 i B,(3.13) where 0 is the lowest value of  to be considered in the histogram. In this case, the logarithmic increment of  is dlog ∼ 1 /B . Therefore, the content of the i -th bin of the histogram distribution becomes: ni+1 2=Zi+1 2 i f()d= ln 10 Zi+1 2 i f()dlog ∼ln 10 Bi+1 2fi+1 2,(3.14) where i+1/2=√i+1 ·iis the central value of the i-th bin. Finally, for the computation of the uncertainties associated to the averaged values extracted from the Monte Carlo simulation, an event by event approach can be used [120]: σX=v u u u t 1 N−1 PN i=1 X2 i N− PN i=1 Xi N!2 ,(3.15) where Nis the number of independent events and Xis the quantity under study. 3.3.4 Simulation of mono-energetic proton beams Our Monte Carlo code developed accepts as input proton beams with any energy distribution, thanks to a PrimaryGeneratorAction class able to import spectral fluence distributions in ROOT format and to use them as a beam generator. For the sake of testing the code performances, however, simulations were performed with mono-energetic proton beams having energies of 10,20,40,70 and 90 MeV , for site sizes of 1and 10 µmdiameter. For all the cases considered, simulations were run both with uniform and with weighted random sampling, the first serving as reference. A number of 250 000 proton tracks was simulated for every case, divided in 250 parallel jobs, and the efficiency of each sampling method was evaluated and compared, measuring also the time required by an individual job to complete the simulation. Finally, LD values were computed with Equation (3.9) from the microdosimetric quantities, and compared to the macroscopic LD computed with Equation (3.12) . Furthermore, since in the case of mono-energetic proton beams the LET distribution 89 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.4. Results (a) (b) Figure 3.8: Chord length distributions obtained for 10 MeV protons impinging on sites of 1 (a) and 10 µm(b) diameter. The distributions obtained with uniform (blue, u) and weighted random sampling (red, w) have been fitted with functions of the form fu ( l ) = p0l and fw ( l ) = p0l2 according to Table 3.1. The values obtained for the fit parameters (see Table 3.2) are in perfect agreement with the theoretical ones. can be considered as a delta function, centred at the LET of the particle for the specific energy considered, the relation LD = LF = yF should hold and was used for an extra validation. 3.4 Results The easiest way to check for the correct functioning of the sampling methods implemented in the code is to analyse the chord length distributions obtained, and compare their mean values with the theoretical ones listed in Table 3.1. An example of this comparison is shown in Figure 3.8 for sites of 1and 10 µmdiameter. The chord length distributions computed with the simulations were then fitted with the corresponding functions for uniform ( µ -randomness) and weighted ( ν -randomness) random sampling, and the obtained parameters compared with the theoretical values. Table 3.2: Fit functions and resulting parameters ( p0 ) obtained from the fit of the chord length distributions in Figure 3.8, compared with the expected parameter for the type of randomness considered. d[µm] fit function p0expected p0 1fu(l) = p0l2.00(1) µm−22/d2= 2 µm−2 fw(l) = p0l23.006(6) µm−33/d3= 3 µm−3 10 fu(l) = p0l2.000(4) ×10−2µm−22/d2= 0.02 µm−2 fw(l) = p0l23.006(6) ×10−3µm−33/d3= 0.003 µm−3 90 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 3. Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4-DNA Table 3.3: Values of the longitudinal dimensions assigned to the world volume and the scoring volume to study the dependence of the simulation results on the geometrical parameters. The longitudinal half dimension of the world volume Rmax is equal to Rδ,max + ZS,max/ 2, where Rδ,max is the maximum range of the δ -rays emitted by the incident protons and ZS,max is the maximum thickness of the scoring volume among the ones considered. Indeed, the thickness ZS of the scoring volume is variable and must be chosen according to the size of the site and the energy of the incident particle, in such a way that the short track segment condition is always preserved; however, the condition ZS> 2 d must hold. In this study ZS was set equal to 2d+η, assigning to ηthe values 0.1d,d,2dand 10d. Energy d Rδ,max Rmax ZS,max ZSη 10 MeV 1 µm 8.3µm 28.3µm 40 µm 2.1µm 0.1d 3µmd 4µm 2d 12 µm 10d 10 MeV 10 µm 8.3µm 28.3µm 40 µm 21 µm 0.1d 30 µmd 40 µm 2d 90 MeV 1 µm 410 µm 430 µm 40 µm 2.1µm 0.1d 3µmd 4µm 2d 12 µm 10d 90 MeV 10 µm 410 µm 430 µm 40 µm 21 µm 0.1d 30 µmd 40 µm 2d A perfect agreement emerged, as reported in Table 3.2. As described in Section 3.3.1, a preliminary study was performed to assess the influence of the longitudinal dimension of the scoring volume ( ZS ) on the simulation output. To do so, simulations were carried out with mono-energetic proton beams of 10 and 90 MeV on spherical sites of 1and 10 µm diameter, assigning to ZS the values listed in Table 3.3, both with uniform and weighted random sampling. For the uniform random sampling method no differences were observed in the resulting distributions of energy imparted f (  )and energy imparted per collision f ( εc ); on the contrary, the weighted sampling method showed a clear dependence of the results on the ZS selected, as emerges from Figure 3.9. In this figure, the normalised distributions of f (  ), represented in the semi-logarithmic scale, obtained for the different ZS with weighted sampling (w), are plotted together and compared with the distribution obtained with uniform random sampling (u). While distributions obtained by uniform sampling are not affected by ZS , they are strongly affected by statistics, as the efficiency of the method drastically decreases for higher energies and smaller site sizes, as can be seen in Figure 3.9c. On the other 91 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.4. Results Figure 3.15: Relative difference of LD from yF for the different site diameters (blue markers for 1µm and red markers for 10 µm ) and sampling methods considered (open markers for uniform sampling and full markers for weighted sampling). from Equation 3.10. As stated in Section 3.3.4, for mono-energetic proton beams the relation yF = LD should hold. In this context, this relation is used as a further test of the code performances, and LD values are represented in Figure 3.14 as shaded areas whose width is given by the uncertainty associated to them. Figure 3.15 represents the relative difference of LD from yF for the different site diameters and sampling methods considered. While for the 10 µm diameter site these differences are always lower than 6%, for the 1µm site the difference increases with energy, reaching values of 30%. This effect is especially evident looking at the weighted random sampling points, which are not affected by the lack of statistics that characterises the uniform sampling method at higher energies. Moreover, this increasing difference between LD and yF for the 1µm site results in an anomalous behaviour of LD if compared to the macroscopic dose-averaged LET obtained from Equation (3.12) , represented as a black shaded area in Figure 3.14. Indeed, as stated in Section 3.2.1, the LD computed with Equation (3.10) is restricted, being this statement especially true for the 1µm site, and should never be higher than the dose-averaged LET computed macroscopically, as it happens instead in Figure 3.14. To solve this problem, the concepts of effective mean chord length l∗ F and effective frequency- and dose-averaged lineal energy y∗ F,D were introduced. As done for the 98 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 3. Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4-DNA (a) (b) Figure 3.16: Variation of the mean energy imparted per event,  , as a function of l for the different energies and sites of (a) 1µm and (b) 10 µm diameter obtained with weighted random sampling. For l∼ 0, i.e proton tracks that don’t cross the site or pass tangent to it, the only contribution to  is given by the δ -ray influx. Then, for higher l ,  increases linearly with the chord length, as can be observed from the linear fit of the data (solid line). The overall frequency-averaged energies imparted per event, F obtained for each simulation considering the full data set, are reported as horizontal dashed lines, each colour corresponding to one proton energy. The intersection point of the linear fit of  as a function of land the value of Fcorresponds to the effective l∗ F. Figure 3.17: Effective mean chord length l∗ F as a function of the proton energy, obtained with uniform (open markers) and weighted (full markers) random sampling for sites of 1µm (blue triangles and diamonds) and 10 µm (red circles and stars). The true mean chord length lF= 2d/3is reported as a yellow horizontal dashed line for each site dimension. 99 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.4. Results energy imparted per single proton collision, a two dimensional plot of f (  )as a function of l was implemented in the simulation, and projections were extracted for intervals of l with width 0 . 1 d . In this way, plots of the mean energy imparted per event,  as a function of the chord length could be built, as shown in Figure 3.16. For l∼ 0, i.e proton tracks that don’t cross the site or pass tangent to it, the only contribution to  is given by the δ -ray influx. Then, for higher l ,  increases linearly with the chord length. Comparing the overall frequency-averaged energies imparted per event, F obtained for each simulation considering the full data set, and the linear fits of  as a function of l , the values of l corresponding exactly to an energy imparted per event equal to F could be obtained. This value, defined as effective mean chord length l∗ F should in principle be equal to lF . However, this is not the case as emerges from Figure 3.17, and l∗ F differs from the true value of lF = 2 d/ 3and varies with the proton energy. Using the effective chord lengths corresponding to each energy, for the computation of frequency- and dose-averaged lineal energies, the results shown in Figure 3.18 could be obtained. In this figure, a general better agreement between uniform and weighted random sampling methods emerges, if compared to Figure 3.14. Furthermore, as shown in Figure 3.19 relative differences of LD from yF lower than 6% could be observed for both site dimensions and all energies, being the only exception the points obtained for the two highest energies and 1µm diameter with uniform sampling, due to the lack of statistics. Finally, all the values of LD obtained with Equation (3.10) lay below the macroscopic unrestricted dose-averaged LET, as expected. The lower efficiency of uniform random sampling has emerged numerous times along this section, being its effects especially evident for sites of 1µm diameter and proton kinetic energies above 70 MeV . In order to quantify this effect, Table 3.6 collects the sampling efficiencies and computational times of the simulations performed with sites of 1µmdiameter with both sampling methods. While the difference in computational time is not critical when comparing the time needed to generate 1000 events, the loss in statistics is dramatic and the efficiency drops to less than 40% for the best case. Considering that with the uniform random sampling algorithm each track is sampled to a maximum of 1000 times until one event is "detected", i.e., at least one energy deposition is found inside the site, the actual efficiency of the method is even lower. To give a clearer idea of the computational cost, the time needed to achieve the same statistics (i.e. 250 000 detected events) with uniform random sampling has been extrapolated in the last column tE of Table 3.6. As emerges from these data, the time needed to achieve an equivalent statistical level with uniform random sampling grows exponentially with the energy of the incident proton energy, being more than 5 years for a beam of 90 MeV. 100 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 3. Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4-DNA Figure 3.18: Effective frequency-averaged lineal energy y∗ F as a function of the incident proton kinetic energy. Values obtained for uniform (open markers) and weighted (full markers) random sampling methods are plotted together for sites of 1(blue triangles and diamonds) and 10 µm (red circles and stars) diameter. Values of y∗ F are reported superimposed to the respective LD values derived from Equation (3.10) , represented as shaded areas whose thickness is given by the error associated to LD for each diameter site. The macroscopic LD computed with Equation (3.12) (black shaded area) is also reported as a reference. 3.5 Discussion In this chapter, a novel Monte Carlo code for the computation of microdosimetric distributions generated by proton track segments in liquid water was presented. Two different algorithms were implemented for the scoring of the quantities of interest: uniform random sampling and weighted random sampling. While the first is ideally better as it is not subject to any bias, it is also very inefficient due to the high chances of selecting sites with no energy depositions within. On the contrary, weighted random sampling has a 100% efficiency, but might be subject to biases related to the choice of the size of the scoring volume and of the weighting factor. One of the main elements of novelty of our code is the inclusion of an algorithm for the computation of the distribution of energy imparted per individual proton collision, 101 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.5. Discussion Figure 3.19: Relative difference of LD from y∗ F for the different site diameters (blue markers for 1µm and red markers for 10 µm ) and sampling methods considered (open markers for uniform sampling and full markers for weighted sampling). which has never been included in any of the Geant4-DNA examples of the official release of Geant4. This distribution, which is not easy to measure experimentally, reflects the action of energy straggling and δ -ray influx and escape on the energy deposited in the site, and it is fundamental for the computation of dose-averaged LET from microdosimetric quantities with Equation (3.9). In this study, our weighted random sampling algorithm was optimised and the dimensions of the scoring volume were chosen accordingly, so that the results obtained could be considered equivalent to uniform ones, with relative differences generally lower than 6%. Once optimised, the code was used to run various simulations with mono-energetic proton beams, with energies in the range 10 −90 MeV impinging on spherical sites of 1µm and 10 µm diameter. The lower limit of the energy range was chosen to ensure that the short track segment condition, necessary to apply Equation (3.9) , held for all the cases considered; while the upper limit of the energy range was determined by the Geant4-DNA physics list, which only allows calculations for proton energies lower than 100 MeV. Since for mono-energetic proton beams the relation LD = yF holds, frequencyaveraged lineal energy values obtained with both sampling methods were used as a reference for the validation of the code and the comparison with dose-averaged 102 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 3. Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4-DNA Table 3.6: Sampling efficiencies and computational times of the simulations performed with sites of 1µm diameter. A total of 250 000 events ( Nsim ) in batches of 1000 were generated. The sampling efficiency has been computed as the ratio between the detected events ( Ndet , at least one energy deposition in the site) and the generated ones. The times reported refer to the simulation of one batch of 1000 events, where tR is the actual time taken for the simulation and tE is the extrapolated time that would be necessary to achieve the same statistics with uniform random sampling. Efficiency Ndet/Nsim [%] Computational time per batch weighted uniform weighted uniform Energy [MeV] tRtRtE 10 100 38.4 1 h 31 min 3 h 46 min >9h 20 100 14.9 1 h 30 min 2 h 51 min >19 h 40 100 2.6 2 h 5 min 2 h 43 min >4d 70 100 0.5 3 h 13 min 3 h 27 min >30 d 90 100 0.2 3 d 15 h 3 d 15 h >5y LET values obtained with Equation (3.9) . Since the site dimensions considered were generally smaller than the maximum range of δ -rays emitted by the incident proton, the dose-averaged LET obtained with this equation was expected to be restricted. To prove this concept, microscopic LD values were compared with macroscopic ones, unrestricted, obtained with Equation (3.12). While generally no evident problems emerged in the results obtained with the 10 µm diameter site, the 1µm diameter site arose questions about the validity of Kellerer’s formula, due to the fact that the LD curve obtained intersected the macroscopic unrestricted dose-averaged LET curve. This apparent contradiction was solved introducing the concept of effective mean chord length l∗ F , i.e., the mean chord length corresponding exactly to an energy imparted per event to the site equal to F . In general, l∗ F should be equal to the true value lF = 2 d/ 3. However, this is not true in the simulations considered, and the effective value of the mean chord length not only differs slightly from the expected one, but varies with the impinging proton energy. This behaviour is probably related to the action of δ -ray influx, which affects the distribution of energy imparted to the site per event, slightly increasing the actual value of F with respect to what would be obtained only by considering direct traversals of proton tracks through the site, especially for the highest energies. By using the effective mean chord length values for the computation of frequency- and dose-averaged effective lineal energies, a general better agreement was observed, both between uniform and weighted random sampling results, and between LD and y∗ F curves. Furthermore, the nature of restricted LET emerged clearly in this case, being all the LD values computed with Kellerer’s formula below the macroscopic LD and generally lower for the 1µm diameter site compared to the 10 µm one. Indeed, 103 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.6. Conclusions the difference between the restricted dose-averaged LET values computed in the two site dimensions decreases as the energy increases, due to the fact that for the 10 µm diameter site the maximum range of δ -rays is comparable to the site dimensions for proton energies below 20 MeV . Therefore, the microscopic LD is initially unrestricted for the 10 µm diameter site, and approaches the curve of restricted dose-average LET obtained with the 1µmdiameter site as the energy increases. 3.6 Conclusions A Monte Carlo code for the computation of microdosimetric distributions generated by proton track segments in liquid water was presented. Apart from the distribution of energy imparted per event, our code computes also the distribution of energy imparted per single proton collision, a feature that is foreseen to be included in an example of one of the next official releases of Geant4. Two different sampling algorithms were implemented, uniform and weighted, the first serving as reference for the second, with the aim of obtaining an efficient and unbiased algorithm for the fast computation of microdosimetric distributions. By choosing appropriately the dimensions of the scoring volume, weighted sampling results could be considered as equivalent to uniform ones. However, the effect of the scoring volume thickness on the distribution of energy imparted per event obtained with weighted random sampling needs to be study more accurately, as the underlying mechanisms are not yet clear. Various simulations were run to test the performances of the code, and to benchmark it, by comparing dose-averaged lineal energy results with dose-averaged LET values computed with Kellerer’s formula, given by Equation (3.9) . In this context, the concept of effective mean chord length was introduced, defined as the value of chord length corresponding exactly to an energy imparted to the site per event equal to F . A very good agreement between simulation results and theoretical expectations was met, with relative percentage differences always lower than 6%. In the future, more studies are foreseen to test the robustness of the code against variations of site dimensions and shape. Indeed, the implementation of cylindrical sites would be highly interesting as many microdosimeters have this shape. Furthermore, the validity of Kellerer’s formula and the performances of the code should be tested for higher proton energies, at least comparable to the ones used in clinical applications. The results obtained with our code were used as a base for the definition of analytical microdosimetric models, whose description is given in [121,122]. Finally, an application of the code is presented in Chapter 4, where it is used for the theoretical derivation of the RBE by means of the Microdosimetric Kinetic model. 104 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 4 Irradiation of mono-layer cell cultures at the cyclotron radiobiology beam line 4.1 Introduction In Chapter 2 the preparation of a radiobiology beam line at the cyclotron external beam line of the CNA was presented. This chapter, on its side, will focus on the first irradiation of cell samples carried out to test the performance of this beam line. To this end, a collaboration was established with a research group of the Andalusian Molecular Biology and Regenerative Medicine Centre (Centro Andaluz de Biología Molecular y Medicina Regenerativa-CABIMER), who made available their cell lines, laboratories and expertise to carry out a parallel irradiation of cell cultures with protons and photons using the cyclotron radiobiology beam line and a 137 Cs irradiator, respectively. During this experiment, Human Bone Osteosarcoma (U2OS) cells were irradiated with two doses (6and 10 Gy ), and the response to irradiation was studied in terms of DNA damage induction, through the analysis of γ H2AX and RPA foci with immunofluorescence microscopy. The most common way to study and compare the effects of different radiation qualities on cell cultures and tissues is to derive the RBE for a particular biological endpoint, usually chosen to be the 10% clonogenic survival, RBE 10 [54]. Clonogenic essays, and the respective cell survival curves, are performed by irradiating a controlled number of cells ( ≃ 100) with different doses and incubating them after irradiation for some time (approximately one week) to count for the remaining colonies. Then, cells are designated as survivors if they preserve their reproductive integrity after 105 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 4.2. Materials and Methods irradiation, i.e., are able to form a colony with more than at least 50 cells. With the irradiation setup proposed in Chapter 2, however, it was not possible to measure a proton cell survival curve, since the brief exposure of cells to air and the subsequent loss of sterile conditions enhanced the probabilities of bacterial infections, that could be propagated to other cultures in the incubator. In view of these considerations, and with the perspective of improving the setup to allow for the irradiation of cell cultures in a sterile environment, a theoretical derivation of the RBE was done, taking advantage of the microdosimetry code presented in Chapter 3 and of the Microdosimetric Kinetic Model (MKM) [69–71]. 4.2 Materials and Methods In this section, the main characteristics of the experiments and analysis carried out for the first irradiation of cell cultures at the cyclotron radiobiolgy beam line are presented. The U2OS cell line, which exhibits optimal characteristics for immunofluorescence microscopy [123], was used to study and compare the effects of different radiation qualities in the induction of γ H2AX and RPA foci, indicators of specific damage and repair pathways of the DNA molecule. In order to understand the experiments and the analysis performed in this chapter, a brief explanation of the main aspects of DNA structure and of the mechanisms of damage induction and repair are first given. Then the experimental setups for the irradiation of cell cultures, both with protons and photons, are described, followed by the procedures and protocols for the subsequent treatment and manipulation of the samples. Finally, the steps followed for the theoretical derivation of the RBE of U2OS cells at 10% survival are described. 4.2.1 DNA damage induction and repair The DNA is the main repository of the genetic information in the cells [124]. This macromolecule consists of two opposing strands of nucleotides linked by hydrogen bonds forming a double helical structure. Each strand is a linear chain of four bases, adenine (A), thymine (T), guanine (G) and cytosine (C), connected by sugar molecules and a phosphate group. Genetic information is encoded in the sequence of these bases, that can only bond in pairs: A with T and G with C. The two strands are therefore complementary. The DNA double helix is wrapped at regular intervals around some specific proteins called histones, forming the nucleosomes (see Figure 4.1). Other proteins are also linked to the DNA, and the ensemble of the DNA and its associated proteins is called chromatin. Finally, further levels of folding 106 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 4. Irradiation of mono-layer cell cultures at the cyclotron radiobiology beam line Figure 4.1: DNA packaging and structure of chromosomes (taken from [125]). and looping make up the structure of the chromosomes. Since the DNA is the largest molecule of the cell and is central to all cellular functions, it is also the principal target for radiation induced cell killing. Because of its importance, cells and organisms have developed a complex series of processes and pathways to ensure that the DNA remains intact and unaltered, including specialised repair systems detecting and repairing damages to bases, single strand breaks (SSBs) and double-strand breaks (DSBs). The DNA damage response is a complex and coordinated system determining the cellular outcome following DNA damage, as that induced by ionising radiation. This response is characterised by various signalling pathways, each of them controlling a different effect on the cell, and can be divided into two parts: the sensors of DNA damage and the effectors of damage response. The sensors consist of a group 107 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 4.2. Materials and Methods Table 4.4: Parameters for the identification of foci with the built-in application Granularity implemented in the MetaMorph software. Image Intensity above background Dimension [min–max] pixels Foci Nucleus Foci Nucleus γH2AX 300 300 [4–20] [80–300] RPA 800 300 [4–20] [80–300] Analysis with MetaMorph Software For the quantitative analysis of the images acquired with the microscope, the subsequent procedure was followed in the MetaMorph software. 1. First, two images were opened at a time, the γ H2AX- or RPA-stained image and the corresponding DAPI-stained one. 2. Both images were then converted to black and white (16 bit format) and their background subtracted. 3. A threshold was then selected in the DAPI-stained image to identify the contour of the nuclei and their inner region, where γ H2AX and RPA foci are located. Once the threshold was selected, a binary image was created highlighting the nuclei regions. 4. The binary image created from the DAPI-stained image was then used as a mask, superimposing it to the γ H2AX- or RPA-stained image with subtracted background. 5. Finally the foci were identified from the masked image with the built-in application Granularity, by selecting their intensity above background and their pixel size. Once established, the parameters for the identification of foci were kept fixed for all the different series of images. Their values are collected in Table 4.4. Finally, a spreadsheet file was generated, listing the information for every cell nucleus identified in the images, i.e., number of foci, total area occupied by foci, foci average and total intensity, nuclear area and nuclear average and total intensity. 4.2.5 Theoretical computation of RBE from microdosimetry As described in Section 1.3.3, the MK model assumes that the α parameter of the Linear Quadratic model for low-LET radiation is proportional to the dose mean lineal energy yD , and inversely proportional to the squared radius of the 114 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 4. Irradiation of mono-layer cell cultures at the cyclotron radiobiology beam line site considered, called domain. Therefore, in principle, once determined the linear quadratic parameters for a reference radiation and the characteristic dimension of the domain for a specific cell line, it should be possible to derive the LQ parameters for proton irradiation at a given yDvalue. This concept was applied to the U2OS cell line used for the first radiobiology experiments at the cyclotron facility to derive the theoretical survival curve under proton irradiation. In order to do so, U2OS clonogenic survival data under photon irradiation, collected by different groups of the CABIMER, were used to build a photon survival curve and extract the reference αγ and βγ parameters. Then, assuming the radius of the domain rd = 0.42 µm , equal to that of HSG cells [75], a commonly used cell line for radiobiological studies derived from a human cervix carcinoma, and using the microdosimetry code described in Chapter 3 to calculate the value of yD , it was possible to derive a rough estimation of the expected cell survival curve under proton irradiation. Photon survival curve Clonogenic survival data for U2OS cells, collected by different research groups of the CABIMER, were used to build a cell survival curve and extract the αγ and βγ of the linear quadratic model under photon irradiation. The data were fitted separately depending on the operator that collected them, as shown in Figure 4.4a, and final values of αγ and βγ were obtained computing the average and standard deviation of the respective parameters obtained from the different fits. Figure 4.4b shows the linear quadratic curve (solid line) obtained with the average α and β parameters, whose values are αγ = 0 . 20 ±0.03 Gy−1 and βγ = 0 . 06 ±0.03 Gy−2 , with an α/β ratio of 3 . 3 ±1.7 Gy . In this figure, the dashed lines correspond to the maximum range of variation of the α and β parameters, and were obtained with ( αγ−σα, βγ−σβ )for the upper curve and ( αγ + σα, βγ + σβ )for the lower curve. The α and β parameters obtained for U2OS cells are compatible, within the error, with HSG ones ( αX ( HSG ) = 0.19 Gy−1, βX ( HSG ) = 0.05 Gy−1 [75]), being both cell lines made of epithelial adherent cells. Therefore, the assumption of the same domain size rd= 0.42 µmfor U2OS seemed to be reasonable. Once known the dimension of the domain and the ( αγ, βγ )parameters, it is possible to extract the value of the parameter α0 of the MK model. To do so, however, information about the dose-averaged lineal energy for the radiation type considered is also necessary. Figure 4.5 reports the dose-averaged lineal energy distribution for 662 keV photons emitted by 137 Cs measured with a tissue equivalent proportional counter, whose average value is yD,γ= 1.85 keV µm−1[127]. 115 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 4.2. Materials and Methods (a) (b) Figure 4.4: (a) Clonogenic survival data for U2OS irradiated with the 137 Cs-irradiator, collected by different research groups from CABIMER. The colours and marker shapes distinguish the different sets of data, separated according to the operator that collected them. Each set of data was fitted separately (dashed lines) and final values of αγ and βγ parameters were computed as average values of the parameters obtained from these fits. (b) Cell survival curve (solid line) obtained with the average αγ and βγ parameters resulting from the fit of the experimental data. The dashed lines correspond to the maximum range of variation of α and β , and are obtained with ( αγ−σα, βγ−σβ )for the upper curve and ( αγ + σα, βγ + σβ )for the lower curve. In this plot, the experimental data are summarised by reporting the median value for each set, with the 25th (lower) and 75th (upper) percentiles as asymmetric error bars. Figure 4.5: Distribution of y d ( y )as a function of y for a 1µm diameter site at eight photon energies [127]. The highlighted curve represents the distribution for 662 keV photons emitted by 137Cs. 116 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 4. Irradiation of mono-layer cell cultures at the cyclotron radiobiology beam line Gathering all this information, and knowing that β0 = βγ the value of α0 could be computed from Equation (1.36) as follows: α0=αγ−βγ yD,γ ρπr2 d = 0.16 ±0.03 Gy−1.(4.1) Dose-averaged lineal energy computation from the Monte Carlo code The microdosimetry code described in Chapter 3 allows for the computation of microdosimetric quantities in water for any incident energy distribution and for spherical sites with various sizes. In order to reproduce the experimental conditions presented in Section 4.2 as realistically as possible, a simulation was run using as incident energy distribution the fluence spectrum of protons coming out from the ionisation chamber, and converting the air distance between the chamber and the cell layer ( 2.5 cm ) into a water equivalent thickness. To do so, the following formula was applied [128]: tw=tm ρmSm ρwSw ,(4.2) where tm/w , ρm/w , and Sm/w identify the thickness, mass density and average mass stopping power of the target material and water respectively. The mean energy of protons coming out from the ionisation chamber is 13.3 MeV , and corresponds to a mass stopping power of approximately 31.9 MeV cm2mg−1 in air ( Sm ) and 36.3 MeV cm2mg−1 in water ( Sw ), resulting in a water equivalent thickness tw = 26.5µm . Following these considerations, a simulation was run setting ZS = 11 µm and Rmax =tw+ZS/2 = 32 µm, with a site diameter of 0.84 µm. 4.3 Results 4.3.1 Irradiation of U2OS cell cultures Before proceeding with the actual analysis of nuclear foci with the MetaMorph software, a preliminary visual analysis was performed to derive the percentage of positive cells for the different irradiation conditions, where positive means with a number of clearly distinguishable foci equal or greater than 10. The same analysis was then performed with the results extracted from MetaMorph, to check for the proper identification of foci by the software. The results of this analysis and the comparison between visual and automated counting are collected in Table 4.5. For the sake of simplicity, in the following the labels 0 Gy , 6 Gy and 10 Gy will be used to identify the different irradiations performed both with photons and with protons, keeping in mind that the actual 117 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 4.3. Results Table 4.5: Percentage of positive cells after proton and photon irradiation. Results obtained from the visual analysis of immunofluorescence images are compared with the results extracted from the analysis of the images with MetaMorph. Dose [Gy] photons protons photons protons Visual γH2AX RPA 0 0% 0% 13% 7% 6 100% 100% 11% 36% 10 97% 100% 50% 48% MetaMorph γH2AX RPA 0 1.4% 4% 35% 17% 6 98% 97% 17% 24% 10 91% 97% 48% 40% dose received by the samples irradiated with protons was slightly higher ( 6.56 Gy and 10.93 Gy respectively, see Table 4.2 and related explanation). In general, the visual and the automated analysis with MetaMorph gave compatible results in what concerned the recognition of positive cells. The only anomalous result was the one associated with RPA foci in the controls for the photon irradiation, which were in higher number than what could be normally expected for non-irradiated cells. When comparing the different effects of proton and photon irradiation in what respects damage induction and response in terms of γ H2AX and RPA foci, various parameters can be taken into account. First, the number of foci per nucleus, which in principle is expected to increase for increasing doses for both radiation qualities. However, the higher LET of the 13.2 MeV protons with respect to photons could result in a more clustered damage, possibly leading to an overlapping of foci, which could decrease their absolute number. Therefore, the pixel average size and the total intensity of foci per nucleus could give additional information to highlight the differences in energy deposition patterns between photon and proton radiation. In Figure 4.6 and Figure 4.7 the distributions of γ H2AX and RPA foci number, average size and intensity are plotted, respectively, for the different radiation qualities. In Figure 4.8 and Figure 4.9 the median values of the distributions shown in Figure 4.6 and Figure 4.7 are plotted as a function of the dose together with their uncertainties, considering only positive cells. For the computation of the uncertainties associated to the median values, their distances to the 25th and 75th percentile of the corresponding distributions were computed. The data relative to the irradiations with 6 Gy and 10 Gy were normalised to their controls in order to directly compare proton and photon results independently from the initial foci background. No evident differences between the two radiation qualities emerged from the compari- 118 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 4. Irradiation of mono-layer cell cultures at the cyclotron radiobiology beam line H2AX foci / nucleusγnumber of 0 20 40 60 80 100 120 140 normalised counts 0 10 20 30 40 50 60 70 80 90 100 protons photons 0 Gy H2AX foci / nucleusγnumber of 0 20 40 60 80 100 120 140 normalised counts 0 5 10 15 20 25 30 protons photons 6 Gy H2AX foci / nucleusγnumber of 0 20 40 60 80 100 120 140 normalised counts 0 5 10 15 20 25 30 protons photons 10 Gy (a) Distribution of the number of γH2AX foci per nucleus H2AX foci / nucleusγaverage pixel size of 0 10 20 30 40 50 60 70 80 90 100 normalised counts 0 5 10 15 20 25 30 35 40 45 50 protons photons 0 Gy H2AX foci / nucleusγaverage pixel size of 0 10 20 30 40 50 60 70 80 90 100 normalised counts 0 5 10 15 20 25 30 35 40 45 50 protons photons 6 Gy H2AX foci / nucleusγaverage pixel size of 0 10 20 30 40 50 60 70 80 90 100 normalised counts 0 5 10 15 20 25 30 35 40 45 50 protons photons 10 Gy (b) Distribution of the average pixel size of γH2AX foci per nucleus H2AX foci / nucleusγtotal intensity of 0 200 400 600 800 1000 1200 1400 1600 1800 2000 3 10× normalised counts 0 10 20 30 40 50 60 70 80 90 100 protons photons 0 Gy H2AX foci / nucleusγtotal intensity of 0 200 400 600 800 1000 1200 1400 1600 1800 2000 3 10× normalised counts 0 2 4 6 8 10 12 14 16 18 20 protons photons 6 Gy H2AX foci / nucleusγtotal intensity of 0 200 400 600 800 1000 1200 1400 1600 1800 2000 3 10× normalised counts 0 2 4 6 8 10 12 14 16 18 20 protons photons 10 Gy (c) Distribution of the total intensity of γH2AX foci per nucleus Figure 4.6: Distribution of γ H2AX foci number (a) , average size (b) and total intensity (c) after irradiation with photons (blue) and protons (shaded red). 119 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 4.3. Results number of RPA foci / nucleus 0 10 20 30 40 50 60 70 80 90 100 normalised counts 0 10 20 30 40 50 60 protons photons 0 Gy number of RPA foci / nucleus 0 10 20 30 40 50 60 70 80 90 100 normalised counts 0 10 20 30 40 50 60 protons photons 6 Gy number of RPA foci / nucleus 0 10 20 30 40 50 60 70 80 90 100 normalised counts 0 10 20 30 40 50 60 protons photons 10 Gy (a) Distribution of the number of RPA foci per nucleus average pixel size of RPA foci / nucleus 0 10 20 30 40 50 60 70 80 90 100 normalised counts 0 5 10 15 20 25 30 35 40 45 50 protons photons 0 Gy average pixel size of RPA foci / nucleus 0 10 20 30 40 50 60 70 80 90 100 normalised counts 0 5 10 15 20 25 30 35 40 45 50 protons photons 6 Gy average pixel size of RPA foci / nucleus 0 10 20 30 40 50 60 70 80 90 100 normalised counts 0 5 10 15 20 25 30 35 40 45 50 protons photons 10 Gy (b) Distribution of the average pixel size of RPA foci per nucleus total intensity of RPA foci / nucleus 0 100 200 300 400 500 600 700 800 900 1000 3 10× normalised counts 0 10 20 30 40 50 60 70 protons photons 0 Gy total intensity of RPA foci / nucleus 0 100 200 300 400 500 600 700 800 900 1000 3 10× normalised counts 0 10 20 30 40 50 60 70 protons photons 6 Gy total intensity of RPA foci / nucleus 0 100 200 300 400 500 600 700 800 900 1000 3 10× normalised counts 0 10 20 30 40 50 60 70 protons photons 10 Gy (c) Distribution of the total intensity of RPA foci per nucleus Figure 4.7: Distribution of RPA foci number (a) , average size (b) and total intensity (c) after irradiation with photons (blue) and protons (shaded red). 120 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 4. Irradiation of mono-layer cell cultures at the cyclotron radiobiology beam line (a) (b) (c) Figure 4.8: Median (a) number of γ H2AX foci, (b) total foci intensity and (c) average foci pixel size per positive nucleus (more than 10 foci), as a function of the dose after proton (red) and photon (blue) irradiation. The asymmetric uncertainty intervals associated to the experimental points correspond to the 25th (lower) and 75th (upper) percentile of the distributions in Figure 4.6. The experimental points for the number of foci and total intensity are reported normalised to their controls and fitted with a linear function. 121 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 4.3. Results (a) (b) (c) Figure 4.9: Median (a) number of RPA foci, (b) total foci intensity and (c) average foci pixel size per positive nucleus (more than 10 foci), as a function of the dose after proton (red) and photon (blue) irradiation. The asymmetric uncertainty intervals associated to the experimental points correspond to the 25th (lower) and 75th (upper) percentile of the distributions in Figure 4.6. The experimental points for the number of foci and total intensity are reported normalised to their controls and fitted with a linear function. son of the number of γ H2AX foci per nucleus. However, the results obtained seemed to indicate a slight dependence on the incident particle of the total intensity and average size of foci per nucleus, which was anyway smaller than the errors associated to the individual points. On the other side, none of the RPA foci distributions showed any dependence on the radiation type, and the increase in the number, total intensity and average size of foci per nucleus with dose was less pronounced. 4.3.2 Derivation of RBE10 from the MKM The distributions of energy deposited in the cell layer per event, 2f (  ), obtained both with uniform and weighted random sampling are plotted in Figure 4.10. 122 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 4. Irradiation of mono-layer cell cultures at the cyclotron radiobiology beam line Figure 4.10: Distribution of 2f (  )as a function of  for a 0.84 µm diameter site at a proton energy of 13.2 MeV. The values of the dose-averaged energy deposited per collision, effective mean chord length and resulting dose-averaged lineal energy transfer, for the two sampling methods, are listed in Table 4.6. Table 4.6: Dose-averaged energy deposited per event, effective mean chord length and dose-averaged lineal energy computed with the microdosimetry Monte Carlo code (see Chapter 2) for the U2OS cell layer with uniform and weighted random sampling. D[keV] l∗ F[µm] yD[keV µm−1] uniform 2.67 ±0.08 0.521 ±0.009 5.1±0.2 weighted 2.709 ±0.006 0.5243 ±0.0005 5.17 ±0.01 Since ZS>> 2 d the results obtained with the two sampling methods were completely equivalent, and only weighted random sampling results are presented in the following discussion. Once obtained the value of the dose-averaged lineal energy of protons in the site, yD,p = 5.17 keV µm−1 , the parameter αp of the theoretical proton survival curve could be obtained with Equation 1.36 as follows: 123 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 5.1. Final remarks Preparation of a radiobiology beam line at the 18 MeV proton cyclotron facility at the CNA Two different irradiation setups for radiobiology experiments were tested at the cyclotron external beam line installed at the CNA. Both setups resorted to a passive scattering of the beam, by means of foils of different thicknesses and materials, to obtain low-intensity broad homogeneous profiles suitable for the irradiation of mono-layer cell cultures. Finally, a beam line irradiation setup, based on a completely defocused beam, a 500 µm thick aluminium scattering foil and an ionisation chamber, was identified as that giving the best results in terms of dose rate and beam homogeneity. With this configuration, a homogeneous irradiation field was achieved, with average deviations from homogeneity lower than 4% in the whole sample area ( 3.5 cm diameter) for a beam energy of 12.8 MeV and a dose rate of about 5 −6 Gy min−1 , close to the value used in the clinics (usually 2 Gy min−1 ). Furthermore, a Monte Carlo simulation of the beam line and experimental setup was developed, using the Geant4 Monte Carlo toolkit. Simulations were tested towards experimental measurements and reproduced experimental data in what concerned the beam energy distribution and dose profiles with differences lower than 1% and 10%, respectively. Finally, a protocol for the irradiation of biological samples was established, consisting in: (1) an accurate alignment of the target position with the beam axis by means of the steering magnets of the cyclotron external beam line; (2) a verification of the beam profile homogeneity, prior to irradiation, with radiochromic EBT3 films and (3) a control of the environmental parameters, such as temperature and pressure, to avoid extra stress to the cells that could lead to biased results. The results of this work were published in two journals [134,135]. Microdosimetry-based dose-averaged linear energy transfer calculation for mono-energetic proton beams: a Monte Carlo study with GEANT4- DNA A Monte Carlo code for the computation of microdosimetric distributions generated by proton track segments in liquid water was developed. With our code, the averages of the main microdosimetric variables (chord length, specific energy and lineal energy) in spherical sites can be obtained, including those of energy imparted per single proton collision, a feature that is foreseen to be included in an example of one of the next official releases of Geant4. This last quantity, in particular, is especially important, as the weighted average of the energy imparted per collision of the traversing proton can be used to obtain macroscopic dose-averaged LET as proposed by Kellerer [68]. The code implements two sampling algorithms for the scoring of the quantities of interest, uniform and weighted, the first serving as a reference for the second. By choosing appropriately the dimensions of the scoring volume, weighted sampling 130 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 Chapter 5. Conclusions and perspectives results could be considered as equivalent to uniform ones. Furthermore, with the weighted method efficient and unbiased calculations of microdosimetric distributions could be obtained, saving computational time if compared to uniform calculations. The code was tested and benchmarked by comparing dose-averaged lineal energy results with dose-averaged LET values obtained from Kellerer’s formula. A very good agreement between simulation results and theoretical expectations was met, with relative percentage differences always lower than 6%. The results obtained with our code were published in three papers [115,121,122], where they were used as a base for the definition of analytical microdosimetric models. Irradiation of mono-layer cell cultures at the cyclotron radiobiology beam line Once identified the best setup for the irradiation of cell samples, a preliminary irradiation of U2OS mono-layer cell cultures was conducted, with success. In this occasion, a concomitant irradiation with photons and protons was carried out, to compare the differences in damage response between the two radiation qualities. At the cyclotron radiobiology beam line, cells were irradiated without growth medium in the vertical position, trying to reduce as much as possible the time of exposure to air. Overall, the irradiation took approximately 30 minutes, after which the cells were immediately treated to be analysed with immunofluorescence. No major differences emerged in terms of damage response at the proton LET considered ( 3.8 keV µm−1 in water), a result that was not unexpected, since the proton RBE at those energies is close to 1 . 1. This result, however, served as a proof of the validity of the cyclotron beam line for radiobiology experiments, since the irradiation conditions did not alter the outcome of the experiment and the cells did not suffer from the stress of transportation, temperature variations and exposure to air. One of the main limitations of the setup proposed is that irradiations cannot be performed in a sterile environment, enhancing the probabilities of bacterial infections. Therefore, it was not possible to perform a clonogenic essay, which is one of the most common ways to derive proton RBE. With the aim of computing a rough estimation of the expected RBE for the cell line and proton LET considered, the microdosimetric kinetic model was applied. To do so, our microdosimetry Monte Carlo code was used to extract the value of the dose-averaged lineal energy in the cell layer, reproducing in the simulation the experimental irradiation conditions. From this calculation, the expected U2OS proton survival curve could be obtained and compared with the experimental photon survival curve, resulting in an RBE at 10% survival of 1.1, as expected. 131 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 5.2. Future perspectives 5.2 Future perspectives Regarding the setup proposed for the irradiation of biological samples, various studies are foreseen to extend the energy range available for radiobiology experiments. In principle, lower energies should be easily obtained by further degrading the beam, eventually decreasing the dose rate while improving the dose homogeneity over the sample surface. With respect to higher energies, different foils with higher atomic numbers and lower thicknesses could be taken into consideration for the dispersion of the beam line in vacuum, thus achieving an increased beam aperture with lower energy degradation. A detailed study of the effects of changing the foil thickness and material will be performed in the next future, using the Monte Carlo simulation of the beam line to identify the best configuration. The addition of a second ionisation chamber, right after the exit window of the external beam line, has also been planned, to allow for a precise measurement of the beam fluence independent from Monte Carlo simulations. Furthermore, the design of a system to irradiate cell cultures within their growth medium is fundamental to exploit the potential of the radiobiology beam line, and is currently under study. Indeed, this would allow to investigate the kinetics of repair and to build clonogenic survival curves. On one hand, a system similar to that described in [136] could be built, with seeded culture plates vertically inserted in a box filled with medium and extracted only for the time of irradiation. On the other hand, customised culture plates, like the ones in [109], or commercial ones with an ultra-thin bottom could be used, in order to allow irradiations from behind with minimum energy loss. Concerning our code for the computation of microdosimetric quantities, more studies are foreseen to test its robustness against variations of site dimensions and shape. Indeed, the implementation of cylindrical sites would be highly interesting as many microdosimeters have this shape. A collaboration has also been established, to compare the results obtained with our Geant4-DNA application with the PARTRAC code [137], a well-established tool for track structure calculations. Furthermore, the validity of Kellerer’s formula and the performances of the code should be tested for higher proton energies, at least comparable to the ones used in clinical applications. At the radiobiology beam line, experimental measurements with 3D solid state microdetectors [138 – 140] are also foreseen in the future, to measure lineal energy distributions and compared them with Monte Carlo ones. This measurements would be of great interest for radiobiology experiments, as they would allow for a direct evaluation of the RBE through the MK model. Finally, following our first irradiation of cell cultures (described in this thesis), that has been carried out successfully, we espect to begin a prolific collaboration with our colleagues at the CABIMER, thus establishing new research lines in our group related to radiobiology. 132 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 List of Figures 1.1 Comparison of the profiles of energy deposition in water as a function of depth (Physical dose) of an X-ray beam and high-energy charged particles. While an X-ray beam exhibits an exponential decrease of energy deposition at depths greater than few cm (approximately 1.5 cm for a 6 MV clinical beam), charged particles deposit most of their energy at the end of their path, defining a region usually called Bragg peak, while sparing both proximal and distal located normal tissues (taken from [11]). . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Comparison of saggital images of proton and photon treatment plans for a pediatric patient treated with craniospinal radiation. On the right, the excess dose deposited from photon treatment is highlighted (takenfrom[12]).............................. 3 1.3 Variation of −dE/dx as a function of the proton kinetic energy in water (blue circles) and in Polymethyl methacrylate (PMMA, ρ = 1.19 g cm−3 , orange triangles). Data extracted from the National Institute of Standard and Technologies (NIST, Maryland, MD, USA) Standard Reference Database PSTAR [31]. . . . . . . . . . . . . . . . 7 1.4 A typical Bragg curve, showing the variation of −dE/dx as a function of the penetration depth for protons having a kinetic energy of 70 MeV in water. Computed with the Monte Carlo code Geant4 (see Section 1.4). 8 1.5 Example of the method of summing up different Bragg peaks with different energies and weights, to build the SOBP (taken from [35]). 9 1.6 Experimentally, the range can be determined by measuring the ratio of transmitted to incident particles ( I/I0 ), coming from a mono-energetic and collimated beam impinging on different thicknesses of the same material. The distribution of ranges is approximately Gaussian in form. The mean and extrapolated ranges are highlighted (taken from [37]). A typical curve, depicted in , shows this ratio as a function of the absorberthickness. ........................... 12 133 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 1.7 Experimental depth dose curves of protons and 12 C ions having the same mean range in water (taken from [42]). Due to the higher relative range straggling experienced by protons, the width of their Bragg peak is enlarged with respect to the carbon ions distribution. . . . . . . . 13 1.8 Time-scale of the effects of radiation exposure on biological systems (takenfrom[46]).............................. 15 1.9 Graphical representation of different types of DNA damage induced by ionising radiation. (taken from [48]). . . . . . . . . . . . . . . . . 16 1.10 Representation of 60 Co photon (left) and 1 MeV proton (right) energy deposition patterns inside a cubic volume, for an absorbed dose of 2 Gy (takenfrom[49])........................... 17 1.11 Survival curve for photons (solid black line) and ions (red dashed line), and determination of RBE at 10% and 1% survival level (taken from[42]).................................. 20 1.12 Dose-averaged LET of the resulting secondary electrons as a function of the nominal photon energy (taken from [19]). . . . . . . . . . . . . 22 1.13 RBE at 10% survival of different monoenergetic particle beams as a function of LET, grouped in different α/β sensitivity ranges (taken from[54]).................................. 22 1.14 Variation of the RBE α = αtest/αref as a function of the particle type and the LET, where αref and αtest are the linear part of the survival curve for photons and ions, respectively (taken from [48]). . . . . . . 23 1.15 Proton RBE values calculated as a function of α/β for 2 Gy (full dots) and 6 Gy (open circles) (taken from [25]). An increase in RBE for late responding tissues (α/β < 4 Gy) is observed for lower doses. . . . . . 24 1.16 Scheme of a typical ionisation chamber (Farmer type). In the picture, the materials used as electrodes, walls and insulators are also indicated (takenfrom[86]).............................. 33 1.17 Working principle of a p-n junction without (a) and with (b) the application of an inverse bias voltage to increase the size of the depletion zone..................................... 34 1.18 EBT3 dose response curves (left) and first derivatives (right) for dose values up to 40 Gy , plotted for the three colour channels that compose the image: red, green and blue (taken from [99]). . . . . . . . . . . . 36 2.1 Picture of the experimental room. From the exit flange to the room wall there is approximately a distance of 2 m. ............. 40 2.2 Schematic representation of the beam line (not scaled). . . . . . . . . 41 134 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.3 Graphical representation of the external beam line in the experimental room (not scaled), with a particular focus on the positioning of the twocollimators............................... 43 2.4 Geometry of the GEANT4 simulation developed to reproduce the cyclotron external beam line. . . . . . . . . . . . . . . . . . . . . . . 46 2.5 Fit of the α MCA spectrum acquired with the silicon detector. Each of the three peaks has been fitted with a Gaussian function, to extract information about the position of the mean value. These fits have been performed only on the peaks, since the Gaussian tails of the three emissions are overlapping each other and with noise. The results of these fits are reported in Table 2.2. . . . . . . . . . . . . . . . . . 48 2.6 Calibration curve energy-channel of the silicon detector. The points in Table 2.2 have been fitted with a linear equation of the form y = p0 + p1·x , where p0 = 0.01(9) MeV and p1 = 0.0236(3) MeVchannel−1 . 49 2.7 Setup for the measurement of the energy distribution of protons with a5 mm thick lithium-drifted silicon detector. . . . . . . . . . . . . . 50 2.8 EBT3 dose-to-optical density calibration curves under 6 MV photon irradiation, for two different lots of films identified as #1 (full dots) and #2 (full squares). The measured points have been fitted with functions of the form D = a·netOD + b·netODc ; the results of these fits are listed in Table 2.3 for the two lots (#1 full lines and #2 dotted lines) and for the three colour channels: red, green and blue. . . . . . 51 2.9 Example of a setup for the measurement of the beam profiles. A piece of EBT3 film is placed at a distance of 10.9 cm from the exit flange (configuration B.2 inTable2.4). .................... 53 2.10 Pictures of the experimental setup for dosimetry and irradiation of biological samples. The ionisation chamber is placed between two PMMA supports on a moving table on which a plastic board can be screwed to extend its length (see (b) ). On the back of the second holder, a custom made guide can be mounted to allow for the positioning of Petri culture dishes or pieces of EBT3 film. . . . . . . . . . . . . . . 54 2.11 Beam spots measured by attaching a piece of EBT3 film directly on the exit flange in the (a) preliminary and (b) final configurations. A misalignment of the beam with respect to the fixed collimator is clearly visible in (a) , where the spot appears to be cut on one side. This effect fades away in (b) thanks to the insertion of the aluminium foil in vacuum, which increases beam divergence. . . . . . . . . . . . 55 135 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.12 Displacement of beam maximum intensity as a function of steering magnets coordinates along x-axis. No evident displacement emerged by varying y-axis coordinates, therefore the current applied to the steering magnet along y-axis was fixed to 1.98 A while varying that applied to the x-axis magnet: (a) -3 A, (b) -2.66 A, (c) -2.33 A, (d) -2 A, (e) -1.66 A and (f) -1.33 A. In this example, configuration (d) was chosen for the subsequent irradiations. . . . . . . . . . . . . . . . 56 2.13 (a) Comparison between experimental mean energy measured (shaded gray area and black dots) and mean energy obtained from Monte Carlo simulations (red dots) as a function of the foil thickness. The mean energy obtained at the end of the simulation, computed as the energy deposited in the silicon detector, does not depend on the initial σi of the beam. The energy width of the experimental shaded area is given by σexp . (b) Percentage deviation of the Monte Carlo mean energy (E MC ) from the experimental one (E exp ). The error bars have been computed with standard uncertainty propagation over the errors associated to the mean energies obtained from the fits. . . . . . . . . 59 2.14 Comparison between the experimental σ measured (shaded gray area) and those obtained from the Monte Carlo code run with different initial standard deviations of the Gaussian beam σi , as a function of the foil thickness. The width of the experimental shaded area is given by the error associated to σexp. ..................... 59 2.15 Beam spot at a distance of 0.5 cm from the exit window (configuration B.1 of Table 2.4). The colour scale is in dose units ( Gy ). (a) Measured. (b) Simulated with a circular uniform distribution having a radius of 8 mm . (c) Simulated with a circular Gaussian distribution having σi,x = σi,y = 8 mm . (d) Beam spot simulated with an elliptical Gaussian distribution having σi,x = 12 mm and σi,y = 20 mm. . . . . 60 2.16 Lateral dose profiles along x (left) and y (right) directions, extracted from the measured (red) and Monte Carlo (blue) beam spots plotted in Figure 2.15: (a) and (b) beam simulated with a circular uniform distribution with radius of 8 mm ; (c) and (d) beam simulated with a circular Gaussian distribution with σi,x = σi,y = 8 mm (e) , (f) beam simulated with a two dimensional Gaussian distribution having σi,x = 12 mm and σi,y = 20 mm. .................... 61 136 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.17 (a) Percentage distance of the Monte Carlo standard deviation of dose profiles along the x axis ( σMC ) from the experimental one ( σx ) as a function of the proton kinetic energy in the active layer of the film. (b) Percentage distance of the Monte Carlo standard deviation of dose profiles along the y axis from the experimental one ( σy ) as a function of the proton kinetic energy in the active layer of the film. Three initial configurations of the Monte Carlo beam are compared, circular Gaussian with σi,x,y = 8 mm (yellow triangles), elliptical Gaussian with σi,x = 12 mm and σi,y = 20 mm (cyan stars) and circular uniform with ri= 8 mm (green diamonds). . . . . . . . . . . . . . . . . . . . . 62 2.18 Comparison of measured (red) and Monte Carlo dose profiles (blue) along the x-axis, whose standard deviations are those used for the calculation of the percentage distance in Figure 2.17a. The energies reported in the plots refer to the kinetic energy of protons in the active layer of the EBT3 film. For this comparison, Monte Carlo simulations have been performed with an initial circular uniform beam of radius ri = 8 mm . The following experimental configurations, listed in Table 2.4, are shown: (a) configuration B.1 ; (b) configuration B.3 ; (c) configuration B.5 ; (d) configuration A.1 ; (e) configuration A.2 ; (f) configuration B.7;(g) configuration A.3;(h) configuration A.4. 63 2.19 Comparison of measured (red) and Monte Carlo dose profiles (blue) along the y-axis, whose standard deviations are those used for the calculation of the percentage distance in Figure 2.17b. The energies reported in the plots refer to the kinetic energy of protons in the active layer of the EBT3 film. For this comparison, Monte Carlo simulations have been performed with an initial circular uniform beam of radius ri = 8 mm . The following experimental configurations, listed in Table 2.4, are shown: (a) configuration B.1 ; (b) configuration B.3 ; (c) configuration B.5 ; (d) configuration A.1 ; (e) configuration A.2 ; (f) configuration B.7;(g) configuration A.3;(h) configuration A.4. 64 2.20 Maps of the relative percentage deviation of the netOD computed in each pixel from the average value ( |netOD −netODµ|/netODµ ). (a) Preliminary configuration with a tungsten foil of 220 µm , lot of films #1, netOD µ = 0 . 20. (b) Preliminary configuration with a tungsten foil of 150 µm , lot of films #1, netOD µ = 0 . 19. (c) Final configuration, lot of films #2, netOD µ = 0 . 16. (d) Preliminary configuration with a tungsten foil of 150 µm , lot of films #1, netOD µ = 0 . 58. (e) Final configuration, lot of films #2, netODµ= 0.58.............. 66 137 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 2.21 Distribution of energy deposited per individual proton track in the ionisation chamber ∆ EIC (left) and in the active layer of the film ∆ EAL (right). (a) Preliminary configuration with tungsten scattering foil of 220 µm ; (b) preliminary configuration with tungsten scattering foil of 150 µm ; (c) final configuration. Mean values and standard deviations of the distributions are listed in Table 2.7. . . . . . . . . . 67 2.22 Dose-to-netOD calibration curves for the three colour channels. Experimental data are presented together with their fit (dashed line) and compared with the corresponding photon calibration curves (solid lines). Fit parameters are reported in Table 2.8. On the left experimental data obtained with both preliminary configurations (lot #1) are plot: (1) beam broadened with a 150 µm tungsten foil (empty diamonds) and (2) with a 220 µm tungsten foil (full stars). On the right the experimental data obtained with the final configuration (empty circles) are presented. The energies indicated in the legend are the same Ekin listedinTable2.7....................... 69 2.23 Relative difference of the proton dose ( Dp ) from the photon dose ( Dγ ), evaluated with the respective calibration curves, as a function of the netOD. For the more energetic incident protons ( 12.8 MeV , circles) this relative difference increases slowly and its value lays between 8% and 10%. For the 10.6 MeV , on the other hand, the relative difference increases steeply, reaches a maximum at a netOD of around 0.4, and decreases again, varying from 15% to 30%. . . . . . . . . . . . . . . . 70 2.24 Maps of the relative percentage deviation from homogeneity of two samples having the same netOD µ = 0 . 60, but measured at the beginning (a) and at the end (b) of the experimental campaign at a distance of approximately two hours. . . . . . . . . . . . . . . . . . . 72 3.1 Ranges of site diameters and proton energies in which other factors in addition to LET influence the energy deposition. The symbols R , S and δ identify, respectively, the domains where limited particle range, energy-loss straggling and δ -ray escape or influx are relevant. In the remaining region ( II ), the deposition of energy is approximately proportional to the (unrestricted) LET [114]. . . . . . . . . . . . . . 77 3.2 Chain or random factors that determine the energy deposition in a site[68]................................... 78 138 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 3.3 Scheme of the geometry used for microdosimetry simulations (2D projection). The primary proton (red track) is generated at the surface of a cubic water volume (world volume) and travels along the Z axis. The energy transfer points (hits) are then scored in the middle of the volume (shaded area), in a slab whose thickness ( ZS ) varies depending on the dimension of the site. The spherical sites are not physically simulated, as they are virtually selected in the scoring volume with an algorithm that depends on the type of randomness considered. Finally, the half-dimension of the world volume ( Rmax ) varies according to the maximum energy of the incident protons, and is slightly greater than the maximum range of the δ-rays emitted. . . 83 3.4 Graphical representation of the working principle of the two sampling algorithms: (a) uniform sampling ( µ -randomness) and (b) weighted sampling ( ν -randomness). In both cases, a hit selection region (maroon shaded area) is identified, where the centres of the sites (yellow circles) are sorted. The dimensions of this region depend on the sampling algorithm used and on the diameter of the site, as lateral margins must be left to ensure that the site is always fully included in the scoring volume. For uniform sampling this margin must be set equal to the site radius, while for weighted sampling the margin is equal to thesitediameter.............................. 85 3.5 Detail of the working principle of the weighted sampling method in Figure 3.4b. The compensation factor is computed as the ratio between the number of selectable hits (with deposited energy different from zero) in the hit selection region ( Nsel ) and the number of hits in the intersection volume of the site with the hit selection region (Nint). . . 86 3.6 Schematic representation of the scoring method for the evaluation of the energy deposited per single proton collision in the site, εc . The primary δ -ray generated by the proton collision is identified and assigned one distinctive tag, that is then inherited by all the secondary electrons in the shower. Only the energy deposition events happening within the site are accounted for in the calculation of εc , including δ-ray influx from outside the site. . . . . . . . . . . . . . . . . . . . . 87 139 Código seguro de Verificación : GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 | Puede verificar la integridad de este documento en la siguiente dirección : https://sede.administracionespublicas.gob.es/valida ÁMBITOPREFIJO CSV FECHA Y HORA DEL DOCUMENTO GEISER GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893 21/09/2020 08:04:43 Horario peninsular Nº registro DIRECCIÓN DE VALIDACIÓN O00008744e2000043582 https://sede.administracionespublicas.gob.es/valida GEISER-c77c-c4fa-1ae5-4a1b-8d10-36b4-c9a3-a893