Dr Uli Weber

Dr Christian Finck

Dr Daniel Husson

Dr Marie Vanstalle

Prof Marco

I would like to thank my family and my friends. To my parents for their invaluable support. They have taught me to never give up, and to always follow my dreams. To all my friends, especially to Manon, Franci and Osnan, who always believed in me, helped in the hard moments

It has been a long and incredible journey that started more than three years ago, after exchanging some e-mails with Dr. Uli Weber. I explained to him my wish to do a Ph.D. in physics within his group at GSI. The probability of getting such a position was very low because of my engineering career, but my motivation for this work overcomes the lack of experience. After several months, Dr. Uli Weber oered to me the possibility to integrate his group as a fellow, which I accepted without hesitation. I thus started to work in the Space Radiation Physics group of the Biophysics department at GSI in September 2016, under the supervision of Uli. After six months of hard work, and countless eorts, I was granted a Ph.D. position in Physics at GSI together with the university of Strasbourg. My rst thanks goes to Dr. Uli Weber, who gave me the chance to work within his group and expand my knowledge about particle therapy. He was the rst person to believe in my capabilities of making this career, and for this, I could never thank him enough. I also own him my deepest gratitude for his supervision and incredible support across these years. I will always be grateful for all the knowledge he shared, all the time we spent preparing and doing experiments, and the invaluable discussions. Thank you for helping me all the way. I would also like to thank Dr. Christian Finck as my supervisor of the University of Strasbourg. He agreed to supervise my work and has always been involved in every step of it. He also believed in my capabilities to succeed in this thesis, helped me, and supported me during these three years. One of my biggest thanks goes to Dr. Christoph Schuy from the Biophysics department at GSI, who also supervised this work. I will always be thankful for all the time he dedicated to me, all the hours he spent teaching me programming, and helping me with the experiments. He has always been a great support during all moments, and I could always rely on his advice. I also thank him for the time we shared climbing and discussing. Many thanks to the Biophysics department at GSI, especially to Corinna Kausch and Marco Durante, who gave me the opportunity to work in such a nice group. I also would like to thank Thomas Friedrich for his support and involvement during the beam times at the UNILAC. I want to thank the support from Felix Horst and Daria Boscolo for all simulations they have performed for me. I am very grateful to the mechanical workshop at GSI and, in particular, Elko and Harry for their amazing contribution to this work. Thank you also to Jög Jöhnke for his valuable help with the electronics. I also would like to thank Yannick and Matthias from the Ion-beam Therapy Center in Marburg for their support. A particular thanks goes to my colleagues from GSI, who I respect scientically and personally. Thank you to Uli, Christoph, Felix, Francesca, Daria, Alex, Tabea, and all those who shared with me this journey. Many thanks also to Stéphanie, Frédéric, and the CBM team for the lunch and coee times together.

Introduction

Cancer is one of the main causes of death in the world and is expected to further increase because of the growth and aging of the population. Based on Global Cancer Observatory estimates, 18.1 million new cancer cases and 9.6 million cancer death occurred in 2018 worldwide [START_REF] Ferlay | Estimating the global cancer incidence and mortality in 2018: GLOBOCAN sources and methods[END_REF]. The risk of getting cancer before the age of 70 is about 20% and the probability to die from this disease is about 10%. Prostate cancer is the most frequent form of cancer for males while breast cancer is the most common for females. For both males and females, lung cancer is highly diagnosed and appears to be one of the cancer inducing the most mortality. Nowadays, three main treatments are used against cancer: surgery, chemotherapy and radiotherapy. Other less common treatments such as immunotherapy and targeted alpha therapy can also be employed for tumor treatment. The combination of several methods can be required for successful cancer treatments such as surgery followed by radiotherapy or typically radioimmunotherapy [START_REF] Durante | Harnessing radiation to improve immunotherapy: better with particles?[END_REF], which combines immunotherapy and radiotherapy. From all patients with a localized tumor, 50% are treated by means of radiation [START_REF] Durante | Charged particles in radiation oncology[END_REF] with a dose delivered generally in several fractions over 67 weeks.

The aim of radiotherapy is to deliver a dened homogeneous dose inside the tumor and spare the surrounding healthy tissues. The role of this treatment method is to inactivate cancer cells by exposing them to ionizing radiation that damages the DNA of the cell and lead to its death. Conventional therapy uses high energy photons produced by linear accelerators but the use of heavy charged particles for tumor treatment is also very attractive [START_REF] Durante | Charged-particle therapy in cancer: clinical uses and future perspectives[END_REF]. The use of particles is more complex and more expensive compared to the use of photons but their physical and biological properties oer several advantages, especially for deep-seated or radio-resistant tumors [START_REF] Schardt | Heavy-ion tumor therapy: Physical and radiobiological benets[END_REF].

In radiotherapy, and in particular in heavy charged particle therapy, high precision in every step of the treatment is mandatory in order to deliver a conformal dose. Uncertainties, which can lead to severe consequences, can rise on the one hand from the beam side and the treatment planning and on the other hand from patient mispositioning and organ motions. To reduce these uncertainties, high precision measurements are required to establish a reliable database for particle therapy treatment and several methods are employed to precisely position the patient and to verify the tumor movements.

INTRODUCTION

to the MAPS generation [START_REF] Turchetta | CMOS Monolithic Active Pixel Sensors (MAPS): New 'eyes' for science[END_REF] and are commonly used for tracking and vertexing in the eld of high energy physics. The sensors used in this work are called Mimosa-28 [START_REF] Valin | A reticle size CMOS pixel sensor dedicated to the STAR HFT[END_REF] and were developed by the Physics with Integrated Cmos Sensors and ELectron machines (PICSEL) group at the Institut Pluridisciplinaire Hubert Curien (IPHC) located in Strasbourg. In this work, a set of these sensors was used during dierent experiments in order to determine charged particle trajectories.

The Mimosa-28 sensors have been used for dierent tests in the past years at GSI. However, the optimum track resolution could not be reached due to mechanical instabilities of the setup during the experiments. In this work, the experimental setup is intended to be used in dierent facilities for several clinical applications. In order to do this, a portable and mechanically stable setup is required. The rst aim of this work is to optimize the experimental setup in order to transport and build it easily in dierent facilities and to improve its stability for mechanical precision and robustness. The mechanical optimization of the setup was developed to exploit the micrometer precision possible to reach with the sensors.

A tracker system composed of Mimosa-28 delivers high resolution positions from ionizing particles that pass through the sensors. The particle trajectories can then be reconstructed with a spatial resolution better than 10 µm by means of several sensors that are precisely aligned with respect to each other. A few micrometers alignment precision can be reached after performing an alignment procedure that corrects the mechanical misalignment of the sensors by software. The originally implemented alignment algorithm in the reconstruction software Qapivi [START_REF] Finck | Study for online range monitoring with the interaction vertex imaging method[END_REF] is based on an iterative procedure. The latter is time consuming and the algorithm does not always converge properly. In this work, it was intended to develop a reliable alignment procedure that corrects the mechanical misalignment of the sensors through a global χ 2 minimization. This procedure aims to be low time consuming and to converge properly for any setup congurations consisting of several pixel sensors placed along the beam axis.

The response of the Mimosa-28 sensor to dierent ion species and energies, with dierent energy losses, has not been fully characterized yet. This sensor, based on CMOS technology, is composed of almost 1 million pixels. The number of pixels red by a charged particle varies as a function of the particle characteristics. The response of previous pixel sensor generations (Mimosa-18 and Mimosa-26) was investigated by [START_REF] Spiriti | CMOS active pixel sensors response to low energy light ions[END_REF] [START_REF] Spiriti | CMOS active pixel sensors response to low energy light ions[END_REF]. During this PhD thesis, the characterization of the Mimosa-28 against dierent ion species and energies aims to extend the experimental data sets of the previous study in order to improve the understanding of the sensor response and exploit these informations for an improvement in data analysis.

During several experiments for ion-beam therapy, low particle beam intensities are required due to detector constraints. However, under such conditions the beam monitoring detectors, used in clinics, are not able to provide the beam characteristics due to the low signal produced in the detectors. The Mimosa-28 sensors are intended to be used for beam monitoring in the frame of this work to evaluate the beam proles when performing experiments at low intensities. A stand alone online tool for beam monitoring, with the use INTRODUCTION of Mimosa-28, was then important to be developed. From this online beam monitoring, a real time information of the beam characteristics can be provided.

The characterization of pencil beams for clinical applications was performed at low intensity with the use of several Mimosa-28 sensors placed along the beam axis. This measurement method aims to provide the beam divergence and angular distribution in both lateral directions. In a treatment room, the beam prole is well dened at the isocenter position. However, since the particle beam is non-parallel, the beam prole varies along the longitudinal axis. This work also aims to determine the lateral beam spread along the beam axis, by using the transport code Scattman [START_REF] Schardt | Heavy-ion tumor therapy: Physical and radiobiological benets[END_REF][START_REF] Weber | Volumenkonforme Bestrahlung mit Kohlensto-Ionen zur Vorbereitung einer Strahlentherapie[END_REF], based on the ion optical parameters of a non-parallel beam.

The Mimosa-28 could also be exploited for another clinical application related to the patient positioning using ducial markers. For particle therapy treatment, one crucial step is the precise positioning of the patient inside the treatment room. A small mispositioning of the patient can lead to range shifts of the particle beam, creating under-and overdosage inside the tumor and organs at risk, respectively. The patient is precisely positioned in the treatment room, in most cases, by means of the bony structure position of the patient visible on the daily imaging method. However, for the case of interfractional moving tumors, ducial markers are used for image guidance. These markers are implanted inside or close to the tumor volume and are composed of materials dense enough to be visible on the dierent imaging methods used during the patient treatment. Even though, the ducial markers are small (< 0.5 mm diameter), they induce dose inhomogeneities due to edge-scattering eects. Several studies have been performed with Monte Carlo simulations and experimental measurements using radiochromic lms. The latter experiments mainly investigated proton beams and were only performed at some positions along the beam axis. The aim of this work is to provide a measurement method that delivers a three dimensional uence (respectively dose) distribution to quantify precisely uence perturbations due to ducial markers. With such purpose, the measurements were intended to be performed with a tracker system composed of several Mimosa-28 sensors. This new measurement concept was rst tested with the use of thick targets to verify the usability of the method and was later applied to ducial markers commercially available. Through this concept, the maximum perturbation can be quantied as well as its position along the beam axis.

This manuscript is divided in four chapters. The rst one describes the scientic background behind charged particle therapy with the physical and biological aspects necessary for the elaboration of a precise treatment plan. It also comprises the description of tumor movements and the methods used to compensate the uncertainties coming from these motions. In the second chapter, the CMOS pixel sensor Mimosa-28 used during the dierent experiments as well as the optimization of the experimental setup are described. In the third part, the beam time campaigns performed at dierent facilities are detailed with a description of the experimental setups and the methods employed for the data analysis. In the last chapter, the results obtained from this work are described and discussed.

Chapter 1

Ion-beam therapy

This chapter describes the scientic background of particle therapy, the properties of heavy charged particles and their advantages for radiotherapy applications. A short history, relating the dierent discoveries that made possible cancer treatment with heavy ions, introduces the chapter. The physical and biological aspects necessary for planning cancer therapy are explained, followed by several descriptions of the treatment complexities and the use of ducial markers for image guidance in particle therapy.

1.1 History 1.1.1 From X-rays to heavy-ion therapy

Radiotherapy for cancer treatment started in the 19 th century, shortly after the discovery of X-rays in 1895 when Röntgen was operating a Crookes tube and observed that a nearby screen was glowing [START_REF] Röntgen | Über eine neue Art von Strahlen[END_REF]. In the same year, Becquerel discovered the phenomena of radioactivity [START_REF] Becquerel | Sur les radiations invisibles émises par les corps phosphorescents[END_REF], followed by that of the Curies of the Radium in 1898 [START_REF] Curie | Radioactive substances, especially radium[END_REF]. From these ndings, the use of X-rays and radium for treating diseases were considered [START_REF] Lederman | The early history of radiotherapy: 18951939[END_REF]. During the rst decades, the notion of dose was not clear and the measurement methods were not reliable. Biological eects were not well understood at that time, which led to high morbidity and poor results [START_REF] Kaplan | Basic principles in radiation oncology[END_REF]. From the 1920s, several discoveries signicantly improved the results of radiotherapy. First, with the invention of Coolidge in 1913 [START_REF] Coolidge | A powerful Röntgen ray tube with a pure electron discharge[END_REF], the X-ray energies could reach 180200 kV. In the same era, the dose was quantied and its physical units dened as the röntgen followed by the rad. After series of experiments, fractionated radiotherapy showed its benets with a better repair of the healthy tissues. Based on the Coolidge X-ray tube, linear accelerators were developed in 1928 by Wideröe where energies higher than 500 kV could be reached [START_REF] Robison | The Race For Megavoltage X-Rays Versus Telegamma[END_REF].

The invention of the electrostatic generator, with megavoltage potential by Van de Graaf in 1929 [START_REF] Van De Graa | The Electrostatic Production of High Voltage for Nuclear Investigations[END_REF], led to the development of the rst cyclotron by Lawrence in 1932 [START_REF] Lawrence | The production of high speed light ions without the use of high voltages[END_REF]. In parallel, neutron radiation for medical treatment was used after its discovery in 1932 by Chadwick [START_REF] Chadwick | Possible existence of a neutron[END_REF]. Electrons also became an option for radiotherapy after the development of the rst betatron in 1940 by Kerst [START_REF] Kerst | The acceleration of electrons by magnetic induction[END_REF]. During the following years, medical research was sidelined due to World War II. However, important achievements during this period were made with the development of a new particle accelerator type: the synchrotron [START_REF] Mcmillan | The synchrotrona proposed high energy particle accelerator[END_REF].

HISTORY

From the 1950s until mid of 1980s, the need of techniques for treating tumors located in deep tissues pushed the development of cobalt therapy [START_REF] Johns | 1,000-Curie Cobalt-60 units for radiation therapy[END_REF] and linear electron accelerators [START_REF] Karzmark | Electron linear accelerators for radiation therapy: history, principles and contemporary developments[END_REF]. A greater penetration depth was thus possible to reach, improving the skin sparing. However, X-rays and gamma rays were dicult to control since they pass through the patient, leading to overdoses in healthy tissues. Multield irradiation was introduced by the medical physicists but the lack of tumor control was still present. Over the years, treatment plans based on intensity modulated radiotherapy (IMRT) [START_REF] Brahme | Solution of an integral equation encountered in rotation therapy[END_REF] were computed, yielding a better control and conformity of the dose inside the tumor volume.

Within a century of research from laboratories and clinics, several developments continuously improved patient treatments by delivering a more conformal dose to the tumor and minimizing the secondary eects.

History of Ion-beam therapy

The construction of the rst cyclotron in 1932 enabled the acceleration of charged particles to over a million electron volts for the rst time, with the acceleration of protons to 1.22 MeV. In 1939, larger machines were built, able to accelerate deuterons to 20 MeV and alpha particles to 40 MeV [START_REF] Courant | Early Milestones in the Evolution of Accelerators[END_REF]. Heavy ions for radiotherapy applications were rst considered in 1946 when Wilson investigated the depth-dose prole of proton beams [START_REF] Wilson | Radiological use of fast protons[END_REF].

A couple of years later, the rst synchrotron for medical purpose was built at Lawrence Berkeley Laboratory in USA, where experiments were performed to study the physical and biological properties of proton beams [START_REF] Tobias | Heavy charged particles in cancer therapy[END_REF]. In 1954, patient treatments started with protons followed by helium ions. Several years later, heavier particles and in particular 670 MeV/u 20 Ne ions, produced at the Bevalac in Berkeley, were used due to their strong biological eects and low oxygen enhancement ratio [START_REF] Chen | Heavy charged particle radiotherapy[END_REF].

A variety of beam delivery techniques were also developed, such as passive beam shaping, collimators and modulators [START_REF] Chu | Instrumentation for treatment of cancer using proton and light-ion beams[END_REF] and several medical facilities using mainly proton beams were constructed in the world [START_REF] Boone | Introduction to the use of protons and heavy ions in radiation therapy: Historical perspective[END_REF]. When sucient computer resources were available, three dimensional computed tomography (CT) imaging could be performed, improving the treatment planning capabilities [START_REF] Goitein | Planning treatment with heavy charged particles[END_REF]. Patient positioning techniques were developed [START_REF] Verhey | Precise positioning of patients for radiation therapy[END_REF] for proton therapy since higher precision was required due to the sharp dose fall-o of protons compared to photons. In 1994, the Heavy Ion Medical Accelerator (HIMAC) [START_REF] Hirao | Heavy ion synchrotron for medical useHIMAC project at NIRS-Japan[END_REF] was built at the National Institute of Radiological Science (NIRS) in Japan, delivering carbon ion beams using innovative beam delivery techniques by means of passive systems. Advanced techniques were developed with the implementation of active beam scanning using spot scanning [START_REF] Pedroni | The 200-MeV proton therapy project at the Paul Scherrer Institute: Conceptual design and practical realization[END_REF] at the Paul-Scherrer-Institute (PSI) in Switzerland and raster scanning [START_REF] Haberer | Magnetic scanning system for heavy ion therapy[END_REF] at the Helmholtzzentrum für Schwerionenforschung (GSI) in Germany. The latter became a pioneer in heavy ion-beam therapy from 1997 on, when a pilot project was conducted until 2008 with the use of carbon ions for the rst time in Europe, under the leadership of Pr. Gerhard Kraft from the Biophysics department at GSI. For this project, the treatment planning system TRiP98 [START_REF] Krämer | Treatment planning for heavy-ion radiotherapy: physical beam model and dose optimization[END_REF] (Treatment planning for particles, 1998 edition) was developed including the Local Eect Model (LEM) [START_REF] Scholz | Calculation of Heavy Ion Inactivation Probabilities Based on Track Structure, X Ray Sensitivity and Target Size[END_REF]. A raster scanning system was used for delivering precisely the dose to the tumor volume. An online Photon Emission Tomography (PET) system [START_REF] Parodi | PET imaging for treatment verication of ion therapy: Implementation and experience at GSI Darmstadt and MGH Boston[END_REF] was placed in-room and could measure the range of the ion beams shortly after the treatment. After ten years of clinical trials, more than 400 patients were successfully treated,

GENERAL ASPECTS

showing the benet of carbon ion beams. Therefore, the Ion-beam Therapy Center in Heidelberg (HIT) was constructed as part of the university clinic Heidelberg with the help of GSI. The HIT facility and the treatment planning system used are based on the ones developed for the pilot project at GSI. But still, a lot of research is needed for better accuracy and precision of ion-beam therapy treatments.

General aspects

The main rationale of using heavy ions in tumor therapy compared to electromagnetic radiation (e.g., X-rays) relies on their favorable depth-dose prole [START_REF] Schardt | Heavy-ion tumor therapy: Physical and radiobiological benets[END_REF]. In contrast to photons, used in conventional therapy, the dose of ions at the entrance channel is small and increases along their path until they release a maximum dose at the end of their range, forming a distinct and narrow peak called Bragg peak. In Figure 1.1, the depth-dose proles of 6 MV photons, 170 MeV protons and 325 MeV/u carbon ions in water are illustrated. The primary energies of protons and carbon ions were chosen to adjust the Bragg peak position to 20 cm depth. For the photon curve, an energy-uence spectrum was simulated using the data set from a 6 MV Varian Linac [START_REF] Sheikh-Bagheri | Monte Carlo calculation of nine megavoltage photon beam spectra using the BEAM code[END_REF].

The position of the Bragg peak can be precisely adjusted to the proper depth by varying the energy of the incident ions. By superimposing single energy irradiations, a spread out Bragg peak (SOBP) can be created and a uniform dose can be delivered over a target volume by means of a single eld irradiation, but typically more than one eld are used in particle therapy. Figure 1.2 shows a SOBP created with carbon ions is shown, covering 5 cm in depth.

In the past years, innovative techniques such as raster scanning were developed, permitting the modulation of beam energies and intensities within a short time. Intensity modulated particle therapy (IMPT) uses several irradiation elds, where the dose can be modulated and optimized for all elds enabling the treatment complex tumor volumes with high precision. To fully exploit the physical advantages of ion-beam therapy, high precision is an absolute necessity during all steps. Therefore, several aspects such as precise patient positioning, beam monitoring and treatment planning system database need to be accurate. the SOBP (blue line). The data were generated with the Monte Carlo code Fluka [START_REF] Battistoni | The FLUKA Code: An Accurate Simulation Tool for Particle Therapy[END_REF]. A ripple lter was included in the simulation in order to reduce the number of energy steps. Data courtesy of Dr. Felix Horst.

Physical aspects 1.3.1 Interaction mechanisms

A charged particle passing through matter interacts via dierent mechanisms. To deliver a conformal dose to the patient, it is necessary to consider the dierent mechanisms that are responsible for this dose. In particle therapy, three main processes are relevant: the elastic Coulomb interactions with the nucleus, the inelastic Coulomb interactions with the atomic electrons and the inelastic nuclear interactions (Figure 1.3).

Elastic Coulomb interactions

When a heavy charged particle passes through a medium, it undergoes elastic Coulomb interactions and is slightly deected by a few mrad due to a repulsive force with the target nuclei. This interaction is sketched in Figure 1.3 (a), and is responsible for the lateral spread of the beam, explained in section 1.3.4.

Inelastic Coulomb interactions

Inelastic Coulomb interactions are due to the attractive Coulomb force between the positively charged projectile and the target atoms. In such collisions, the energy transfer of the primary ion to the atom causes an ionization or excitation process. Figure 1.3 (b) illustrates an inelastic interaction leading to the ionization of the target atoms. The ejected electrons can undergo a large impulse and have enough energy to create further ionizations. In such case, these high energetic liberated electrons are called δ-electrons. Inelastic Coulomb interactions are mainly responsible for the energy deposition of the particle inside a medium, detailed in section 1.3.2.

Inelastic nuclear interactions

Inelastic nuclear interactions are less likely than the interactions described above, but their contribution to the dose in a target volume is not negligible. Peripheral collisions are the most frequent nuclear reactions and lead to the loss of one or several nucleons of the primary ion. Nuclear fragmentation can yield projectile and target fragments, as illustrated in Figure 1.3 (c), which also contribute to the dose inside the target. The probability for a certain reaction to occur, due to inelastic nuclear interaction, is dened by its cross section, described in section 1.3.6. For heavy ions, with atomic number Z > 2, these collisions are well described by the abrasion-ablation model [START_REF] Serber | Nuclear reactions at high energies[END_REF][START_REF] Gaimard | A reexamination of the abrasion-ablation model for the description of the nuclear fragmentation reaction[END_REF] that is a two-step process. In the rst one, an overlap zone is dened where the projectile and target nucleons are abraded, forming a reball while the remaining projectile and target pieces of the nonoverlapping zone are the spectators. In the next step, the reball and spectators deexcite by evaporation of nucleons, protons and light nuclei as well as the emission of photons. In the case of protons and helium ions, this model is not valid anymore. For protons at therapeutic energies, only target fragments are produced during nuclear interactions while the secondary protons are deected [START_REF] Newhauser | The physics of proton therapy[END_REF]. For helium ions, the nuclear fragmentation follows a one-step process due to its unique internal structure. The dierent interactions of helium ions are well described by [START_REF] Cucinotta | Description of alpha-nucleus interaction cross sections for cosmic ray shielding studies[END_REF] [START_REF] Cucinotta | Description of alpha-nucleus interaction cross sections for cosmic ray shielding studies[END_REF].

Energy deposition

A heavy charged particle passing through matter mainly loses its energy by electronic interactions with the atoms of the medium. The energy loss per unit path length, also called stopping power, depends on the energy and type of the projectile and on the characteristics of the target material. When traversing a medium, the particle beam slows down until it loses a maximum energy at the end of its path before dropping down to zero (Figure 1.1), induced by inelastic interactions with the target electrons (section 1.3.1.2). The curve describing the trend of the energy loss per unit path length is called Bragg curve and can be calculated using the Bethe-Bloch formula [START_REF] Bethe | Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie[END_REF][START_REF] Bloch | Zur Bremsung rasch bewegter Teilchen beim Durchgang durch Materie[END_REF]:

- dE dx = 4πN A r 2 e m e c 2 ρ Z A z 2 β 2 ln 2m e c 2 γ 2 β 2 I -β 2 - δ 2 - C Z , (1.1)
where the parameters are listed in Table 1.1.

The energy loss per unit path length of a heavy charged particle is proportional to the square of the projectile charge z and increases with the slowing down of the particle due to the velocity parameter of the projectile β. This means that for heavier ions than protons such as carbon ions, the energy loss is higher for the same traveled distance and increases along its path. Equation 1.1 is valid for high energy particles that are fully stripped [START_REF] Herault | Stopping powers of gases for heavy ions (O, Ar, Kr, Xe) at intermediate energy (20100 MeV/u). Vanishing of the gassolid eect[END_REF].

For lower energies than 1 MeV/u, the energy loss of the projectile becomes smaller due to the decrease of the eective charge when the primary particle captures the absorber electrons. The atomic number of the projectile z in Equation 1.1 is thus replaced by the eective charge z ef f and can be approximated with the Barkas formula [START_REF] Barkas | Techniques and theory[END_REF] as:

z ef f = z 1 -exp -125βz -2 3 . (1.2)

C

Shell correction

The stopping power of dierent ion beams in water as a function of their kinetic energy is illustrated in Figure 1.4. Energy loss in H 2 O (MeV cm 2 /g) protons 4 He ions 12 C ions 16 O ions 20 Ne ions

Mean range & energy straggling

As explained in the previous section, the energy loss function, described by the Bethe-Bloch formula (equation 1.1), shows a narrow peak just before that the primary ion stops in the medium. Since the interaction processes with the target material occur in a statistical way, the energy loss varies for each independent particle. This eect is called energy-loss straggling and induces a broadening of the Bragg peak. The range of a particle is dened as the path length traveled in a given absorber until it comes to rest. In reality, the particle follows a complex path due to multiple Coulomb scattering. However, the latter eect is relatively small for heavy charged particles and the total path length can be approximated by a straight line. Even though the multiple scattering is not relevant for this range, a range straggling eect arises due to the stochastic variations of the energy loss. For simple applications, these uctuations can be neglected and the range R of a particle at a given energy can be approximated by the continuous slowing down approximation (CSDA) [START_REF] Ashley | Inelastic Interactions of Electrons with Polystyrene: Calculations of Mean Free Paths, Stopping Powers, and CSDA Ranges[END_REF], and is calculated by integrating the reciprocal energy loss per unit path length dE/dx over the full energy range:

R = E 0 0 dE dx -1 dE . (1.3)
For a given velocity and for a same medium, the CSDA range is proportional to A/z 2 , which means that in general, the heavier the particle is, the smaller is the range, except for protons and helium ions that have the same range. The CSDA range in water as a function of the energy for dierent ion species is illustrated in Figure 1.5. protons, 4 He ions 12 C ions 16 O ions 20 Ne ions

Lateral beam spread

The deections of ions, due to multiple Coulomb scattering, are accurately described by the Molière's theory [START_REF] Molière | Theorie der Streuung schneller geladener Teilchen II Mehrfach-und Vielfachstreuung[END_REF]. The latter is algebraically complicated and can be approximated by a Gaussian distribution much easier to evaluate. The angular width of the Gaussian distribution σ α , given in mrad, can be dened by the Highland approximation [START_REF] Highland | Some practical remarks on multiple scattering[END_REF]54]:

σ α = 14.1 βpc z ρd L rad 1 + 1 9 log 10 ρd L rad , (1.4)
where p is the projectile momentum and ρ, d and L rad are the density in g/cm 3 , the thickness in cm and the radiation length in g/cm 2 of the absorber, respectively. The Highland formula scales with z/A of the projectile, which means that the multiple scattering is stronger for protons than carbon ions at a given energy. Heavy absorber materials induce stronger deections than lighter ones for a given thickness. Figure 1.6 illustrates the FWHM of several pencil beams as a function of the depth, for protons and carbon ions at therapeutic energies. Scattman [START_REF] Schardt | Heavy-ion tumor therapy: Physical and radiobiological benets[END_REF][START_REF] Weber | Volumenkonforme Bestrahlung mit Kohlensto-Ionen zur Vorbereitung einer Strahlentherapie[END_REF].

The FWHM was evaluated by the analytical code Scattman [START_REF] Schardt | Heavy-ion tumor therapy: Physical and radiobiological benets[END_REF][START_REF] Weber | Volumenkonforme Bestrahlung mit Kohlensto-Ionen zur Vorbereitung einer Strahlentherapie[END_REF], described in section 3.4.2.1, which transports the particle based on the multiple Coulomb scattering calculated by the Highland approximation (equation 1.4). For the calculations presented in Figure 1.6, a 5 mm FWHM parallel pencil beam passes through a set of detectors, called beam nozzle, and impinges a water phantom of 40 cm thickness, which fully stops the particle beam. The beam nozzle represents the beam monitoring system used in the therapy centers in Heidelberg (HIT) and Marburg (MIT) and has a water equivalent length of 2 mm. As shown in Figure 1.6 (top panel), protons scatter more than carbon ions for a given range. For a certain ion species, the scattering becomes stronger when the particle energy decreases. To correctly estimate the multiple scattering, it is necessary to take into account the energy loss of the primary beam along its path. The strong rise of the beam width at the end of its range is due to the decrease of the particle energy, especially when impinging on the water phantom.

Edge-scattering eects

A particle beam passing perpendicularly through strong density gradients and edges suers inhomogeneous scattering, creating then an over-and undershoot. In Figure 1.7, the basic principle of edge-scattering eects induced by a target with a sharp edge is depicted. This gure was obtained by analytical calculations of several overlapping Gaussian beams that are dierently scattered. The strength of the perturbation due to edge-scattering eects depends on several parameters relative to the beam and to the density gradient. On the one hand, high density and thick target materials induce strong particle deections due to multiple Coulomb scattering. On the other hand, the lower and the lighter the beam energy and particle species are, 1.3. PHYSICAL ASPECTS the larger is the scattering eect. Consequently, a particle beam of a given energy, passing through high density gradients from a target placed inside a certain medium, suers stronger perturbations than for low density gradients. The position of the perturbation behind the target also depends on these parameters: for small deections, the over-and undershoot are created at further positions than for strong deections.

Cross section

The inelastic collisions between two nuclei, presented in section 1.3.1.3, can be described in terms of cross section. The latter quanties the probability of a reaction to occur per unit area, given in barn. When a primary beam impinges a thin target, particles are scattered out within a certain solid angle. The dierential cross section is given as followed [START_REF] Leo | Techniques for nuclear and particle physics experiments: a How-to Approach[END_REF]:

dσ dΩ (E, Ω) = 1 Φ dN dΩ , (1.5)
where dσ/dΩ represents the fraction of particles dN scattered into the solid angle dΩ per unit uence Φ. This value varies as a function of the primary beam energy and the scattered angle. The total cross section of a reaction at a given energy is calculated by integrating equation 1.5 over all solid angles:

dσ(E) = dσ dΩ dΩ , (1.6)
Cross section measurements are essential for transport codes applied to ion-beam therapy.

Semi-empirical models are used to describe total cross sections as a function of the charge and mass of the projectile and target, and also depend on the energy of the colliding system. The parametrization in these models is well characterized by means of experimental data.

The geometrical model based on the Bradt-Peters formula [START_REF] Bradt | The heavy nuclei of the primary cosmic radiation[END_REF], and enhanced with the consideration of the energy dependence [START_REF] Townsend | Energy-dependent parameterization of heavy-ion absorption cross sections[END_REF], describes the total reaction cross section σ R as follows:

σ R = π r 2 0 c 1 (E) (A 1/3 P + A 1/3 T -c 2 (E)) 2 , (1.7)
where r 0 ≈ 1.2 fm is the nucleon radius used for the calculation of the nuclear radius as r = r 0 • A 1/3 . The A P and A T terms represent the mass number of the projectile and target, respectively, and c 1 (E) and c 2 (E) are energy-dependent parameters. As explained in section 1.3.1.3, nuclear collisions produce fragments that contribute to the dose. Moreover, they have dierent biological eects than the primary beam, which need to be considered in order to deliver a conformal dose to the patient. Several studies have been performed to measure cross sections of dierent reactions (e.g., Dudouet et [START_REF] Haettner | Experimental study of nuclear fragmentation of 200 and 400 MeV/u 12 C ions in water for applications in particle therapy[END_REF]) in order to tune the models used for particle transport calculations.

Absorbed dose

The absorbed dose or physical dose is dened as the mean energy deposited dE per mass element dm [START_REF]ICRU. Quantities and units in radiation protection dosimetry[END_REF]:

D = dE dm , (1.8)
where D is given in Gray (1 Gy = 1 J/kg). Considering the energy loss per path length from equation 1.1, the absorbed dose can be calculated as:

D = 1.6 • 10 -9 Φ dE dx 1 ρ , (1.9)
where Φ is the uence of the primary beam per unit area in cm -2 , and ρ is the density of the target material in g/cm 3 . The linear energy transfer (LET), given in keV/µm, is dened as the energy locally deposited per path length [START_REF][END_REF] and is similar to the electronic stopping power described in equation 1.1. The latter determines the ability of an absorber to slow down a certain particle, while the LET corresponds to the energy transferred from the particle to the medium. The LET may refer to a restricted stopping power in the case that an energy cut-o ∆ is applied to the produced δ-electrons and is dened as follows:

LET ∆ = dE ∆ dx . (1.10)
In the case of heavy charged particles, the LET ∞ (∆ → ∞) is practically identical to the electronic stopping power since radiative energy losses such as bremsstrahlung [START_REF] Leo | Techniques for nuclear and particle physics experiments: a How-to Approach[END_REF] are negligible. The LET inuences the biological eects [START_REF] Wambersie | The future of high-let radiation in cancer therapy. justication of the heavy-ion therapy programmes[END_REF], detailed in the next section.

Biological aspects

The aim of radiotherapy is to inactivate and avoid the multiplication of tumor cells by damaging their deoxyribonucleic acid (DNA). The latter is comprised inside the cell nucleus of about 2 µm diameter for a total cell size of 20 µm diameter [START_REF] Alberts | Molecular Biology of the Cell[END_REF]. DNA damages can occur via direct or indirect actions [START_REF] Hall | Radiobiology for the Radiologist[END_REF]. In the case of direct damages, the produced δelectrons interact immediately with the DNA structure by destroying its helix. For the case of indirect damages, a free radical is created, in most cases by creation of a group hydroxyl through hydrolysis of water, and can diuse far enough to damage the DNA structure. Lesions of the DNA can be induced either through base or strand damages. In the rst case, the DNA structure is damaged with the loss or the modication of a base. In the second case, two main break types can occur: the single strand break (SSB) and the double strand break (DSB), which are simple and more complex lesions, respectively. Cells have dierent ways to repair ionizing radiation-induced damages depending on the type of lesion. In the case of base damages and SSBs, the DNA can be repaired without errors due to the simplicity of the lesions. For DSB cases, and especially spatially clustered DSBs, the damage can be complex enough that no available mechanisms can repair the DNA successfully. In such case, cell mutations can happen or the cell dies and cannot multiply anymore.

Track structure

The track structure of a particle determines its spatial energy distribution at a microscopic level. Another characteristic of heavy charged particles compared to photons, in addition to their depth-dose prole (Figure 1.1), is their advantageous track structure for tumor therapy. For high energy photons, produced by a linear accelerator, photoelectric eect and Compton scattering processes dominate [START_REF] Schardt | Heavy-ion tumor therapy: Physical and radiobiological benets[END_REF]. The photons interact with the target electrons of the medium that damage the DNA. Electromagnetic radiation produces then indirect ionizations while heavy charged particles can also create direct ionizations. In the case of photons, the interaction processes happen with low probability and the number of indirect ionizations per cell is small. In the case of heavy charged particles, ionizations have a high probability, and the track is denser. The red points describe the ionizations due to the primary particle while the blue points are the ionizations created by the secondary δ-electrons. The simulations were performed with the Monte Carlo transport code Trax [START_REF] Krämer | Calculations of heavy-ion track structure[END_REF]. Data courtesy of Dr. Daria Boscolo.

Electromagnetic radiations are thus dened as low-LET radiations due to their sparsely ionizing property, while heavy charged particles are considered as high-LET radiations since they produce dense tracks. The track density, which denes the spatial energy distribution, 1.4. BIOLOGICAL ASPECTS also varies as a function of the particle type and energy. In Figure 1.8, the track structures, of a proton (left panel) and a carbon ion (right panel) at 10 MeV/u in a water medium, are illustrated. The spatial energy distribution inuences the biological eects on the cells. It is thus an essential criterion to take into account for the optimization of the delivered dose to the patient.

Biological eects

Since the track structure from ionizing particles varies as a function of the ion species and energy, the biological eects depend strongly on the ionization density around the particle trajectory [START_REF] Kraft | Tumor therapy and track structure[END_REF]. As the number of ionizations increases for ions compared to photons, the probability of creating complex DNA damages is enhanced. For densely ionizing particles, such as carbon ions, the number of DSBs increases, which leads to higher biological effects. To study these eects, cell survival curves as a function of the absorbed dose are established [START_REF] Fertil | Mean inactivation dose: a useful concept for intercomparison of human cell survival curves[END_REF]. The linear-quadratic model is the most common parametrization for cell survival S and is given as the following:

S = exp(-αD -βD 2 ) , (1.11)
where D is the absorbed dose and α and β are the linear and quadratic parameters, which are experimentally determined. In this model, the linear and quadratic components α and β scale with the dose and the square of the dose, respectively. One of the most common interpretation explains that for low doses, cell death by single hits are responsible for the linear component while for high doses, the multiple hits for cell killing may result from the interaction of dierent particles describing the quadratic component [START_REF] Mcmahon | The linear quadratic model: usage, interpretation and challenges[END_REF]. The two contributions of cell killing are identical for a dose equal to the α/β ratio. The latter is an important criterion for cell killing and inuences the repair process of the cells. A small α/β ratio is connected to a pronounced shoulder of the survival curve and a high radioresistance. For sensitive cell lines, the shoulder of the survival curve is less pronounced and is dened by a large α/β ratio. The relative biological eectiveness (RBE) is the quantity that denes the biological eects and is dened as follows:

RBE = D ref D ion , (1.12)
where D ion is the ion dose needed to create the same biological eect as the reference dose D ref applied with photons. The RBE can be determined from survival curves (Figure 1.9 (left panel)), and is commonly shown as a function of the deposited energy per path length illustrated in Figure 1.9 (right panel).

The biological eectiveness increases for high-LET radiation until reaching a saturation point, where it decreases again due to overkill eect. For protons, the RBE value is considered as 1.1 [START_REF] Paganetti | Relative biological eectiveness (RBE) values for proton beam therapy[END_REF]. For carbon ions, this quantity varies signicantly along its path and can be calculated based on dierent models such as the Local Eect Model (LEM) developed at GSI [START_REF] Scholz | Calculation of Heavy Ion Inactivation Probabilities Based on Track Structure, X Ray Sensitivity and Target Size[END_REF]. Additionally, the LET of carbon ions where the RBE is maximum corresponds to the LET at the Bragg peak position [START_REF] Friedrich | Systematic analysis of RBE and related quantities using a database of cell survival experiments with ion beam irradiation[END_REF]. The RBE is a complex biological quantity, which depends on the particle species, energy and absorbed dose but also on the 4 He ions (blue line) and 20 Ne ions (green line). Data redrawn from [START_REF] Schardt | Heavy-ion tumor therapy: Physical and radiobiological benets[END_REF].

cell line and oxygenation level. Tumors in hypoxic conditions are more radio-resistant; therefore, heavy particles such as carbon ions seem to be more ecient in the treatment.

Treatment procedure

The aim of tumor treatment is to establish the best possible procedure to ensure the killing of the tumor and to spare the surrounding healthy tissues. With this purpose, diagnostic tools are used to evaluate the specic patient case and to decide whether to employ radiotherapy for tumor treatment. In such a case, several steps are followed to precisely and eciently remove the tumor.

Planning CT & volume denitions

In a rst step, a three dimensional (3D) computed tomography (CT) is performed for the patient in the same conditions than the later treatment. From the treatment planning CT information, the physician can delineate the gross tumor volume (GTV). The clinical target volume (CTV) includes the GTV and the microscopic spread of the disease. The physician prescribes the dose that needs to be delivered to the tumor and additional constraints to organs at risk (OAR). The treatment planning CT serves as a representation for the treatment delivery and is included into the treatment planning system (TPS). The latter takes into account the beam specic information such as particle ranges, deposited energies and beam angles as well as patient geometry to design the best possible treatment.

Patient positioning, inter-and intrafractional motions lead to uncertainties on the delivered dose. The TPS also considers these uncertainties related to the shift of the tumor during the treatment compared to the tumor position on the planning CT. Therefore, safety margins are applied around the target volume to ensure that the whole CTV is covered. The target volume with the applied margins is called planning target volume (PTV).

Treatment planning systems

The TPS calculations are normally performed using a pencil beam algorithm for dose optimization. Nowadays, TPSs based on Monte Carlo (MC) transport codes are also used. They lead to more accurate dose optimization but are also more time consuming. During the pilot project at GSI, mentioned in section 1.1.2, the TPS TRiP98 [START_REF] Krämer | Treatment planning for heavy-ion radiotherapy: physical beam model and dose optimization[END_REF][START_REF] Krämer | Treatment planning for heavy-ion radiotherapy: calculation and optimization of biologically eective dose[END_REF] was developed for the use of carbon ions, delivered with a raster scanning system. This TPS considers both absorbed dose and biological dose. TRiP98 resulted to successful patient treatments and was later used as base for the commercial TPS from Siemens. Pencil beam algorithms are based on basic data, provided by MC simulations or by transport codes, and include depth-dose proles, lateral dose distributions, fragmentation processes and RBE tables. The biological dose D biol at position -→ r can be calculated as the following [START_REF] Gunzert-Marx | Secondary beam fragments produced by 200 MeV u -1 12 C ions in water and their dose contributions in carbon ion radiotherapy[END_REF]:

D biol ( - → r ) = zp z=1 Emax 0 Φ(z, E, - → r ) LET (z, E) RBE(z, E) 1 ρ( - → r ) dE , (1.13)
where Φ is the particle uence of the primary ions and all fragments of energy E and ρ is the target material density. The biological dose is optimized according to the prescribed dose given by the radio-oncologist for covering the target volume and spare the healthy tissues. The RBE is determined for each particle, energy and tissue, based on a table containing values calculated beforehand with a modeling code.

In Figure 1.10, a treatment plan for a head and neck tumor was calculated by using photons (left panel) and carbon ions (right panel). Both plans were computed with the software matRad [START_REF] Wieser | Development of the open-source dose calculation and optimization toolkit matRad[END_REF] for a single fraction dose of 2.3 GyE in the main PTV and 2.1 GyE in the second PTV, with a total dose of 70 GyE and 63 GyE, respectively, delivered in 30 fractions. This comparison demonstrate that a better dose conformality can be achieved with 12 C ions than with photons. In the latter case, the left parotid (white contours) needed to be irradiated for a homogeneous dose in the PTV while in the case of carbon ions, both parotids could be spared.

In ion-beam therapy, a verication of the plan is typically performed before the patient treatment. For this, the planned treatment is delivered to a water phantom, and the dose conformality is veried with several detectors such as ionization chambers.

Treatment delivery & Tumor control

The patient receives the treatment delivered in a number of fractions that was specied from the clinician and optimized by the TPS. Typically, the radiotherapy treatment is performed over several weeks. During this time, the patient plan can be re-evaluated to ensure that the treatment is still appropriate to the tumor characteristics such as its size and to verify the unexpected toxicities. In case large dierences are found, compared to the original planning, a new planning CT is performed and a new treatment plan is calculated. At the beginning of every fraction, the patient is precisely positioned in the treatment room to guaranty a reproducible treatment. Magnetic resonance imaging (MRI) is used to follow up the patient treatment, by verifying that the tumor has shrunk and is not regrowing. The control of the patient is usually done during a period of 5 years after the end of the treatment, in general every 6 months, to verify that there is no recurrence from the tumor.

Interfractional tumor motions

Ion-beam therapy can deliver conformal doses with sharp dose fall-o to complex target volumes. For static targets, range uncertainties can be estimated and the irradiated volume is delimited in order to cover the full tumor. Patient positioning is one of the most important steps during the patient treatment and is optimized by using several methods to precisely align the patient with respect to the beam axis. Several studies have investigated inter-and intrafractional motions as well as the patient positioning [START_REF] Langen | Organ motion and its management[END_REF]. In this section, the use of ducial markers for image guidance of interfractional organ motions and their dosimetric consequences are introduced.

Patient positioning

To cover the target volume with the prescribed dose and to spare healthy tissues, the patient must be aligned compared to the beam axis with high precision to minimize range and lateral uncertainties. These uncertainties have a stronger impact for ion beams than for photons, and a mispositioning of the patient can lead to severe underdosage in the tumor and overdosage in the healthy tissues. In this case, tumor recurrence could occur and organs at risk could receive unwanted doses. The patient is generally treated for several weeks and needs to be precisely positioned each day of the treatment. Systematic and statistical patient setup errors need to be taken into account for the treatment. Systematic uncertainties describe all causes for changes in the patient position, shape and size, for instance, weight change and target average displacement during the treatment. Statistical patient setup errors dene unpredictable interfractional changes of the patient positioning due to mechanical uctuations related to the treatment equipment or the setup methodology used for the daily treatment. At the beginning of every fraction, the patient is xed to the couch through several methods, such as using a stereotactic mask for the treatment of brain or head and neck tumors. A 3D image such as cone beam computed tomography (CBCT) or a two dimensional (2D) X-ray projection image is recorded to verify the position of the patient. The daily image is used to compare the position of the patient with the CT recorded for the treatment plan by checking, for example, the bony structure position. With this information, the patient can be re-aligned with a precision better than 1 mm [START_REF] Nairz | Accuracy of robotic patient positioners used in ion beam therapy[END_REF] compared to the absolute coordinates system of the treatment room, and therefore to the beam axis.

Fiducial markers for image guidance

In some cases, the tumor can move between two consecutive fractions due to anatomical changes. For instance, several studies showed that the prostate may move in the range of 02 cm in-between the fractions [START_REF] Balter | Measurement of prostate movement over the course of routine radiotherapy using implanted markers[END_REF][START_REF] Crook | Prostate motion during standard radiotherapy as assessed by ducial markers[END_REF][START_REF] Haken | Treatment planning issues related to prostate movement in response to dierential lling of the rectum and bladder[END_REF], due to the lling of the bladder and the rectum with an average displacement of around 5 mm. For such motions, the bony structures of the patient can not be used anymore for precise positioning. Therefore, ducial markers are used to verify the interfractional tumor displacements. The markers are surgically implanted inside or at the border of the tumor before the treatment, and their positions are recorded during the treatment planning CT. They are used to verify the tumor movement by comparing their positions on the planning CT, and the daily image performed most of the time by X-ray projections. In case the ducial markers indicate a signicant movement of the tumor, the treatment can be stopped and a new treatment planning CT will be recorded in order to re-calculate a proper treatment plan with the new tumor position.

The spatial stability of the ducial markers was investigated with two or three implanted markers [START_REF] Kupelian | Intraprostatic ducials for localization of the prostate gland: monitoring intermarker distances during radiation therapy to test for marker stability[END_REF]. In 99% of all cases, their movement was smaller than 4 mm. Fiducial markers must respect three essential criteria. First, they should produce low streak artifacts on the treatment planning CT [START_REF] Handseld | Determination of optimal ducial marker across image-guided radiation therapy (IGRT) modalities: visibility and artifact analysis of gold, carbon, and polymer ducial markers[END_REF] to not induce wrong density information, which could lead to a wrongly calculated dose distribution. Secondly, they must be visible on the dierent daily imaging methods used for the patient positioning [START_REF] Habermehl | Evaluation of dierent ducial markers for image-guided radiotherapy and particle therapy[END_REF]. The last criterion is that ducial markers should produce a low dose perturbation during the radiotherapy treatment [START_REF] Newhauser | Monte Carlo simulations of the dosimetric impact of radiopaque ducial markers for proton radiotherapy of the prostate[END_REF]. As described in section 1.3.5, a particle beam suers inhomogeneous scattering when passing through strong density gradients and edges, creating uence perturbations. Since the dose scales with the uence, the edge-scattering eects induce cold and hot spots in terms of dose. Therefore, ducial markers can cause unwanted dose inhomogeneities. To fulll the above criteria, size and shape of the ducial markers as well as the Z and ρ of the material need to be optimized.

Dose perturbations due to ducial markers

During the last years, mainly high density (e.g., gold) and relatively large (> 1 mm diameter) ducial markers were used for position verication since they can easily be seen on the X-ray projection. However, these types of markers induce signicant artifacts on CTs [START_REF] Habermehl | Evaluation of dierent ducial markers for image-guided radiotherapy and particle therapy[END_REF] and also cause cold and hot spots (dose perturbations) during the treatment due to inhomogeneous scattering of the particle beam. Other markers with lower density and atomic number (e.g., carbon-coated ZrO 2 ) can reduce these inhomogeneities. However, they are not always visible on the X-ray projection performed during the daily treatment.

It is also important to note that the fractionation of the treatment will lead to a wash-out of the dose inhomogeneities produced behind the ducial markers.

Several studies investigated the severeness of the dose perturbations induced by ducial markers with MC simulations [START_REF] Newhauser | Monte Carlo simulations of the dosimetric impact of radiopaque ducial markers for proton radiotherapy of the prostate[END_REF][START_REF] Giebeler | Dose perturbations from implanted helical gold markers in proton therapy of prostate cancer[END_REF][START_REF] Herrmann | Investigation of the dosimetric impact of a Ni-Ti ducial marker in carbon ion and proton beams[END_REF] and/or measurements performed with radiochromic lms [START_REF] Cheung | Dose perturbations and image artifacts caused by carbon-coated ceramic and stainless steel ducials used in proton therapy for prostate cancer[END_REF][START_REF] Huang | Investigation of dose perturbations and the radiographic visibility of potential ducials for proton radiation therapy of the prostate[END_REF]. These studies have demonstrated that the dose perturbations depend on the marker material, thickness, position and orientation inside the phantom. The bigger and heavier the material is, the stronger is the inhomogeneous scattering eect, which creates thus larger and stronger cold and hot spots. Another MC simulation study showed that the dose perturbations due to the markers could be partly reduced using several elds [START_REF] Matsuura | Biological eect of dose distortion by ducial markers in spotscanning proton therapy with a limited number of elds: A simulation study[END_REF]. The measurements performed with radiochromic lms were mainly done for proton beams and with several lms placed along the beam axis. However, it is dicult to predict where to place them exactly along the longitudinal axis to precisely measure the maximum dose perturbation induced by the markers.

Chapter 2

CMOS pixel sensors: Mimosa-28

This chapter relates in a rst part the general characteristics of CMOS pixel sensors and the evolution of the MAPS generation for particle tracking purpose. In a second part, the Mimosa-28 pixel sensor used in this work is described, followed by a section explaining the detector characterization and the mechanical setup optimization, performed during this PhD thesis.

CMOS pixel sensors

In the eld of particle physics, single-sided microstrip detectors were initially used as vertex detectors in collider and xed target experiments [START_REF] Heijne | A silicon surface barrier microstrip detector designed for high energy physics[END_REF]. This type of semiconductor detector is fabricated through a planar process by oxide passivation, photo engraving and ion implantation [START_REF] Kemmer | Fabrication of low noise silicon radiation detectors by the planar process[END_REF]. The growing requirements for high precision tracking in particle physics, such as the study of short-lived particles and the high particle collision rates, pushed the development of high granularity pixel detectors, able to detect multiple tracks with high spatial and time resolution. One of the proposed candidate to fulll these requirements was a monolithic active pixel sensor (MAPS) [START_REF] Turchetta | CMOS Monolithic Active Pixel Sensors (MAPS): New 'eyes' for science[END_REF], based on complementary metal-oxide-semiconductor (CMOS) technology.

General aspects

Semiconductor materials are such that their electrical conductivity is between the one of a conductor material and the one of an insulator material. The detection principle of semiconductors is the same as e.g., gas-lled ionization chambers. The energy needed to create an electronhole pair in such a chamber is about 20 eV while only 3.6 eV is required for silicon material. This has the advantage that semiconductors have a better energy resolution.

The conductivity can be modied by introducing impurities (doping) into the semiconductor, either by adding electrons (n-type) or holes (p-type). A pn-junction is an interface between p-type and n-type semiconductors creating an electric eld at the boundary region. Metal-oxide-semiconductor eld-eect transistors (MOSFET or MOS) are a common semiconductor device used in the electronics industry. They consist of a metal gate, an oxide insulation and a semiconductor, and are composed of four dierent terminals: the source (S), the drain (D), the grid (D) and the substrate (B). The MOSFETs can be used in dierent operation modes depending on the applied voltage between the source and the drain: the weak-inversion mode, the linear mode and the saturation mode. MOS transistors can be either p-type (p-MOS) or n-type (n-MOS), and the combination of both types is called CMOS. This technology is used for dierent electronic components, but also for active-pixel sensors (CMOS sensors).

Originally used as an alternative to charge-couple devices (CCDs) in image sensors [START_REF] Theuwissen | CMOS image sensors: State-of-the-art[END_REF], CMOS detectors were proposed for particle tracking in the eld of particle physics, and also were of interest for medical physics applications, with the development of MAPSs. The latter are composed of a low-resistivity monolithic epitaxial layer with an embedded amplier per pixel to buer the output signal. MAPSs became attractive with their good compromise between granularity, readout speed, material budget, radiation tolerance and power dissipation.

Charged particle detection

Monolithic CMOS sensors are composed of a thin epitaxial layer moderately p-doped (P-) located between a highly p-doped substrate (P++) and P-well (P++). A pn-junction is created between the epitaxial layer and the implanted N-well (N++) in the top of each pixel, creating a collection diode. When a particle traverses the sensor, electron-hole pairs are produced by ionization and trapped in the epitaxial layer. Since the epitaxial layer is not fully depleted, the electrons diuse thermally and are collected by the N-well region of the pixel. Because of the dierent doping concentrations of the layers, build-in voltages are induced at the boundaries of the epitaxial layer with the substrate and the N-well, which allow the electrons to move towards the collection diode. The signal is then stored in a diode-parasitic capacitance before being amplied for each pixel. A schematic cross-section of a monolithic active pixel sensor is sketched in Figure 2.1.

Substrate P++ Metal layers & Polysilicon

Epitaxial layer P-N+ N-well P-well

+ + + + + _ _ _ _ _ _ + P-well

Evolution of Mimosa sensors

In 1999, a rst prototype of MAPS, called Mimosa (Minimum Ionizing particle MOS Active Pixel Sensor)-1, was designed for particle tracking applications [START_REF] Turchetta | A monolithic active pixel sensor for charged particle tracking and imaging using standard VLSI CMOS technology[END_REF]. This prototype sensor was fabricated in AMS-0.6 µm CMOS process with an epitaxial layer of 15 µm, and was an analog sensor made of four matrix arrays of 64 × 64 pixels each with a pitch of 20 µm. Even though the collection process was dominated by thermal diusion, a charge collection of about 1000 electrons by 3 × 3 pixels in less than 100 ns was obtained with simulated and experimental data [START_REF] Deptuch | Simulation and measurements of charge collection in monolithic active pixel sensors[END_REF]. The tracking performance of this rst prototype was evaluated for a high energy beam, yielding a detection eciency close to 100% and a signal to noise ratio (SNR) of 30 [START_REF] Claus | Particle tracking using CMOS monolithic active pixel sensor[END_REF]. The potential of this prototype pushed the research and development of several other prototypes based on CMOS processes, leading to the design of Mimosa-5. This sensor was the rst device in wafer scale composed of four matrix arrays of 510 × 512 pixels each one, and a pixel pitch of 17 µm [START_REF] Deptuch | Development of monolithic active pixel sensors for charged particle tracking[END_REF]. These analog sensors showed good performance for particle tracking with a single point resolution ∼ 2 µm [START_REF] Gay | High-resolution CMOS sensors for a vertex detector at the Linear Collider[END_REF].

The readout time per frame of such pixel detectors was in the range of 110 ms.

During the following years, several prototypes of Mimosa, mainly fabricated in AMS-0.35 µm CMOS process, were initially developed for the vertex detector [START_REF] Gaycken | Monolithic active pixel sensors for fast and high resolution vertex detectors[END_REF][START_REF] Szelezniak | Application-specic architectures of CMOS monolithic active pixel sensors[END_REF][START_REF] Besson | A vertex detector for the International Linear Collider based on CMOS sensors[END_REF] of the STAR experiment at RHIC and the International Linear Collider (ILC) [START_REF] Adams | Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions[END_REF]. This new sensor generation was equipped with a more complex electronics with an in-pixel amplication and correlated double sampling (CDS), to suppress the pixel-to-pixel pedestal variations [START_REF] Deptuch | Monolithic active pixel sensors with in-pixel double sampling operation and column-level discrimination[END_REF]. The dierential output signal was read out in parallel by column-level discrimination with oset compensation [START_REF] Deerli | Low-power autozeroed high-speed comparator for the readout chain of a CMOS monolithic active pixel sensor based vertex detector[END_REF]. These MAPS also integrated a binary output, improving signicantly the readout speed of the detector [START_REF] Deerli | Performance of a fast binary readout CMOS active pixel sensor chip designed for charged particle detection[END_REF]. The study of the charge collection and SNR as a function of the integrated radiation dose for dierent pitch sizes showed that reducing the pitch from 40 to 20 µm improved the radiation hardness of the sensor signicantly [START_REF] Deveaux | Charge collection properties of Monolithic Active Pixel Sensors (MAPS) irradiated with non-ionising radiation[END_REF].

In 2006, the EUDET-JRA1 project (Detector R&D programme for a future international linear collider) [START_REF] Haas | A pixel telescope for detector R&D for an international linear collider[END_REF] was proposed to provide a test beam area for a telescope of high resolution pixel sensors, located at the facility in DESY near Hamburg (Germany). Mimosa-16 was the rst prototype for this project, using the architecture of Mimosa-8 with a new pixel design [START_REF] Deerli | Development of binary readout CMOS monolithic sensors for MIP tracking[END_REF]. The promising results of this prototype were followed by the fabrication of a larger sensor, Mimosa-22, with ∼ 25 mm 2 active area. Mimosa-22 was characterized and showed good performance with a high spatial resolution, good detection eciency and low noise [START_REF] Gélin | Intermediate digital monolithic pixel sensor for the EUDET high resolution beam telescope[END_REF]. Nevertheless, a concern about the radiation hardness led to the development of other sensors, investigating dierent pixel architectures and the epitaxial layer resistivity [START_REF] Orsini | A radiation hard digital monolithic pixel sensor for the EUDET-JRA1 project[END_REF]. The requirements for the EUDET project and the STAR vertex detector also needed a fast readout with integrated zero suppression to reduce the data ow [START_REF] Hu-Guo | CMOS pixel sensor development: a fast read-out architecture with integrated zero suppression[END_REF].

After successful achievements [START_REF] Winter | Achievements and perspectives of CMOS pixel sensors for charged particle tracking[END_REF], the full scale sensor Mimosa-26 was fabricated within the EUDET project. This reticular sensor was composed of 576 × 1152 pixels, with a pitch of 18.4 µm and a readout time 200 µs [START_REF] Hu-Guo | First reticule size MAPS with digital output and integrated zero suppression for the EUDET-JRA1 beam telescope[END_REF]. The detection performance of this sensor was assessed with minimum ionizing particles. Several tests were performed at the CERN-SPS with a 120 GeV π -beam [START_REF] Baudot | First test results of MIMOSA-26, a fast CMOS sensor with integrated zero suppression and digitized output[END_REF], resulting in a low temporal noise, a low fake rate, a detection eciency ∼ 99.5% and a single point resolution better than 3 µm. Another full scale sensor Mimosa-28, based on the Mimosa-26 architecture and optimized for the STAR experiment [START_REF] Deveaux | Radiation tolerance of a column parallel CMOS sensor with high resistivity epitaxial layer[END_REF][START_REF] Dorokhov | High resistivity CMOS pixel sensors and their application to the STAR PXL detector[END_REF], was the rst vertex detector based on CMOS technology. The physics run in 2014 for the STAR experiment [START_REF] Schambach | A MAPS Based Micro-Vertex Detector for the STAR Experiment[END_REF]118] at RHIC validated the use of MAPS 2.2. MIMOSA-28 as vertex detectors. Since then, CMOS pixel sensors also became of interest in the eld of applied physics: Mimosa-26 was used during the FIRST experiment [START_REF] Pleskac | The FIRST experiment at GSI[END_REF][START_REF] Agodi | FIRST experiment: Fragmentation of Ions Relevant for Space and Therapy[END_REF] with heavy charged particle, and Mimosa-28 is foreseen to be used in the FOOT experiment [START_REF] Valle | FOOT: a new experiment to measure nuclear fragmentation at intermediate energies[END_REF] for ion-beam therapy and space radiation applications. Nowadays, silicon sensors have become a standard for vertex detectors in high energy physics [START_REF] Snoeys | Development of monolithic sensors for high energy physics in commercial CMOS technologies[END_REF]. Further designs of CMOS pixel sensors are exploited [START_REF] Deveaux | Development of CMOS Monolithic Active Pixel Sensors for the ALICE-ITS Outer Barrel and for the CBM-MVD[END_REF] in order to provide adequate performance required for dierent experiments such as the ALICE [START_REF] Collaboration | The ALICE experiment at the CERN LHC[END_REF] inner tracking system upgrade at CERN [START_REF] Besson | From vertex detectors to inner trackers with CMOS pixel sensors[END_REF][START_REF] Mauro | The new inner tracking system for the ALICE upgrade at the LHC[END_REF] or the micro-vertex detector of the future Compressed Baryon Matter (CBM) experiment at FAIR [START_REF] Ablyazimov | Challenges in QCD matter physicsThe scientic programme of the Compressed Baryonic Matter experiment at FAIR[END_REF].

Mimosa-28

Mimosa-28 (or Ultimate) [START_REF] Valin | A reticle size CMOS pixel sensor dedicated to the STAR HFT[END_REF] is fabricated in AMS-0.35 µm CMOS process, using 4 metaland 2 polylayers. It is composed of 928 rows × 960 columns with a square pixel of 20.7 µm pitch covering an active area of ∼ 3.8 cm 2 . was evaluated with a 120 GeV π -beam, where the single point resolution of the detector was found to be better than 4 µm [START_REF] Valin | A reticle size CMOS pixel sensor dedicated to the STAR HFT[END_REF]. At room temperature, the power dissipation of the chip is around 150 mW/cm 2 and the fake hit rate per readout frame is < 10 -4 for a threshold set at ve times the noise. The radiation tolerance of this sensor is around 150 krad (or 1500 Gy) for ionizing dose, which means that the sensor could be damaged after some hours of irradiation in clinical conditions. However, for the primary beam energies and intensities used in this work, the sensor could be continuously operated for some years without serious eect. The non-ionizing damaging uence has been proven to be 3 × 10 12 n eq /cm 2 for Mimosa-28.

Architecture

Pixel

The pixel architecture of the Ultimate sensor is described in Figure 2.3 (left panel). The sensitive part is composed of a self-biased diode, where the reverse biased collection diode D 1 is reset by the forward biased diode D 2 . The sensitive element and the amplication stage are biased with a common source. The load transistor amplier M 2 is biased with another transistor M 3 , increasing the gain about a factor 2 [START_REF] Dorokhov | Optimization of ampliers for monolithic active pixel sensors[END_REF].

Sel_Row [0]
Sel_Row [START_REF] Kaplan | Basic principles in radiation oncology[END_REF] 16 pixels

Sel_Grp [0] Sel_Row [912]
Sel_Grp [START_REF] Townsend | Energy-dependent parameterization of heavy-ion absorption cross sections[END_REF] Sel_Row A feedback, creating a low-pass lter with a large time constant, is formed by the transistor M 4 and the capacitor C 1 , compensating the leakage current of the diode D 1 . The MOS capacitor M 5 and the MOS switch M 6 compose the CDS element, which removes the oset and reduces the noise due to the circuitry. This is done via resetting the clamping node at the gate M 7 to a pre-dened voltage at each readout cycle. The transistor M 7 is followed 2.2. MIMOSA-28 by an output source follower M 8 , whose current is provided by a current source, located at the end of the column and shared by all pixels inside the same column. To reduce the capacitance at the output node, each column is split in 58 groups of 16 pixels, and each group has a common switch (Figure 2.3 (right panel)).

Discriminator

To provide a high precision signal, the discriminator is based on a dierential architecture (Figure 2.4 (top panel)) with oset compensation, and comprises three dierential gain stages and a dynamic latch. The auto-zero functionality is performed via the two phases Calib and Read, where the amplier osets are rst stored by the capacitors C 1 , C 2 , C 3 and C 4 to be then canceled in the second phase. The pixel output is reset by the Clamp signal, controlling the in-pixel CDS element. As observed on the time diagram sketched in Figure 2.4 (bottom panel), the pixel oset stored in the Calib phase is subtracted from the pixel output signal superimposed to the same oset recorded during the Read phase. The same operation is performed concerning the threshold signal, coming from the difference between V ref 1 and V ref 2 stored during the Read and Calib phases, respectively. During the Latch phase, the latch performs the dierence between the pixel output signal and its corresponding threshold. The binary output signal is obtained after amplication and digitization of this dierence.

V clamp Pixel V ref1 V ref2 V clamp Calib Read Calib Read Read Read Read Read A1 A2 A3 Latch Q Q _ Latch C 1 C 2 C 3 C 4

Clock

MIMOSA-28

A total of 960 discriminators are used in the Mimosa-28, which can suer from stray capacitance of the MOS devices used as switches. To ensure the minimization of these eects and reduce the capacitance of the output node, the sensor is divided in four blocks of 240 discriminators (Figure 2.2) with an adjustable threshold per block. By means of a characterization procedure, detailed in section 2.2.2, the noise levels of each block can be evaluated to later set appropriate threshold values to the sensor. The performance of Mimosa-28, evaluated with minimum ionizing particles as a function of the noise threshold measured at 30 • C, are represented in Figure 2.5. For a threshold set at six times the noise value, a detection eciency ∼ 100% is found with a single point resolution < 4 µm, and a fake hit rate < 10 -6 per pixel per readout frame.

Zero suppression

The data ow from such pixel detector can reach up to several Gbit/s, slowing down the readout speed. The Ultimate sensor is equipped with zero suppression, located at the end of the discriminators, and is based on a row by row sparse data scan readout in order to only store the information from the red pixels. In a rst stage, the digital signals are processed in parallel on 15 blocks of 64 columns. Each block describes 1 status group (4-bit), up to 6 states (11-bit per state), and 1 overlap (1-bit). The status group indicates the number of states for one block with its line address. A state contains the information of up to 4 contiguous red pixels; the number of contiguous pixels are described by the rst 2-bit, while the next 11-bit encode the column address of the rst pixel. In a second stage, the outcome of the 15 blocks is read by a multiplexer composed of 3 dierent modules, resulting in 1 status and 9 states encoded on 16-bit each. The status contains the number of states and the line address, while each state contains the number of red pixels and the column address. In a last stage, data are stored in memory, containing 2 buers to perform read and write operations, simultaneously, allowing a continuous readout of the sensor. The data are transmitted to the acquisition system via 2 low voltage dierential signal (LVDS) outputs, with a frequency of 160 MHz. In Figure 2.6 (top panel), a sequence example of pixels red from a line of one block is sketched. The middle and bottom panels describe the coding of the status and the state of the binary data, respectively.

0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1

Characterization

During the characterization of Mimosa-28, it is possible to test the circuitry of the chip, to determine the number of broken pixels, and to verify the uniformity of the sensor response. This procedure also aims to determine the noise level of all pixels in order to apply consistent thresholds during operation. As explained in section 2. In a previous study [START_REF] Spiriti | CMOS active pixel sensors response to low energy light ions[END_REF], the cluster size was investigated for the analog sensor Mimosa-18 [START_REF] Dulinski | Beam telescope for medium energy particles based on thin, submicron precision MAPS[END_REF], and for the digital sensor Mimosa-26 [START_REF] Hu-Guo | First reticule size MAPS with digital output and integrated zero suppression for the EUDET-JRA1 beam telescope[END_REF], with 80 MeV proton, and 80 and 400 MeV/u carbon ion beams. An empirical model was developed and used to t the collected data of Mimosa-18, expressing the cluster size as a function of the energy deposition.

In this work, an extension of this study was performed with the Mimosa-28 sensor. With this goal, two generations of Mimosa-28 sensor were used, where the noise repartition of the sensor is distributed more uniformly in the second generation, after improvements implemented by the PICSEL group at IPHC in Strasbourg.

Data acquisition system

The data acquisition (DAQ) system uses the PXI platform, and is based on National Instruments (NI) hardware. The DAQ software used for Ultimate was developed in Labview [START_REF] Kalkman | LabVIEW: a software system for data acquisition, data analysis, and instrument control[END_REF], and the management of the DAQ operations is performed via a FlexRIO board driver. The JTAG protocol is generated on the CPU board parallel port in order to congure the sensors. The DAQ system is equipped with a eld programmable gate arrays (FPGA) on a NI FlexRIO board and a NI LVDS adaptor module for the acquisition of serial data stream.

In Figure 2.8, a schematic of the DAQ system used to operate several Mimosa-28 sensors is sketched. The sensor proximity printed circuit board (PCB) comprises four ports: the power connector supplying +5 V, the Jtag port to provide the slow control protocol for conguration, the Ctrl port for the clock and synchronization and the Data port for the clock, synchronization and data streaming. The JTAG protocol and the Control signals are provided by the DAQ system via a parallel port, and translated by the JTAG interface board into LVDS signals transmitted to the sensor via RJ45 connectors. The Data port of the sensor is connected to a digital interface board via RJ45 connectors, while the connection between the interface board and the FlexRIO front-end module is done via VHDCI connectors. To be able to run more than one sensor at the same time, additional JTAG and CTRL distribution boards are needed.

To synchronize the readout of several Mimosa-28 sensors, a specic starting procedure is followed. In a rst step, the DAQ generates start and clock signals distributed to all sensors. The DAQ system receives then the clock and a synchronization signal from one of the sensors, provided via the digital interface board. In a last step, the 160 MHz clock is provided by the DAQ system to the Ctrl connector through an adaptor card connected to the DAQ adaptor module via VHDCI cable. The recorded data are nally saved on a RAID of disk connected to the PXIe system.

Mechanical setup for Mimosa-28

The mechanical stability of the setup is one of the main concerns for high spatial resolution pixel sensors, since small deviations can lead to severe problems during the data analysis.

In this work, the mechanical setup for Mimosa-28 has been optimized in order to perform experiments in dierent facilities. Main goals were having a setup relatively easy to handle, fast to mount and as stable as possible. The dierent parts detailed in this section were designed, in the frame of this work, with CATIA V5 [START_REF] Koh | Catia V5 design fundamentals[END_REF], and manufactured by the mechanical workshop at GSI.

Sensor holder

The sensor holders were designed to be light-tight, and to tightly accommodate the proximity board. This brings stability to the system by restricting the sensor movements. Even though aluminum is a standard material used for shielding in dierent electrical applications, the sensor holders developed in this work are made of trubidur plastic (PVC). The reason for this choice was because plastic is a lighter material with small eective atomic number. This reduces unwanted secondary fragment production from the primary beam interactions with the holders. The latter are composed of one support part, where the sensor PCB can be xed with ve screws, and one cover part attached to the support. On both parts, two holes slightly bigger than the dimensions of the sensor were manufactured to remove any additional material in front and behind the sensor.

In Figure 2.9, a drawing of the holder, developed in this work, for Mimosa-28 sensor is depicted. Antistatic black tape was used to cover the holes for making the holder light-tight.

Figure 2.9: Holder for the Mimosa-28 sensor, designed with CATIA V5 [START_REF] Koh | Catia V5 design fundamentals[END_REF].

After being xed inside their holder, the sensors were scanned with a resolution of 600 dpi to evaluate precisely their position compared to the holder dimensions. After analyzing the scanned images with ImageJ [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF], the position (0,0) in x and y, dened as the center of the sensor, could be precisely quantied compared to the holder coordinates. To locate the sensor position in (x, y and z) inside its holder, marks were drawn on each holder, with a precision better than 0.5 mm.

Setup optimization

The complete setup to be mounted during an experiment for running Ultimate sensors is relatively complex. The DAQ system uses multiple boards and several tens of cables, as mentioned in the previous section. To optimize such a setup, it was necessary to employ a concept where the setup could be pre-cabled and prepared as compact as possible (Figure 2.10). In this work, the JTAG interface card, the two distribution boards, the adaptor card and the digital interface board were tted inside a 19-inch rack drawer, with all cables and interconnections pre-connected. Several holes have been made on the front and back sides of the box to create an interface between all cards that will be connected to the PXIe crate and the sensors during the experiment. For this, RJ45 feed-through connectors were xed in the front of the rack drawer.

For stability and precision purposes, the sensors are placed on an optical bench (Qioptic manufacturer). The RJ45 shielded cables attached to the sensor proximity boards are six meters long, which make them relatively heavy. To avoid any movement of the holder due to cable strain, each of them, as well as each power cable, is clamped to a cage built from aluminum proles. In Figure 2.11, a picture of an experimental setup, using six Mimosa-28 sensors, illustrates the dierent components used to improve the stability of the setup. Chapter 3

Materials & Methods

In this work, several experiments have been performed with the goal of providing high precision experimental data for ion-beam therapy. Due to the high spatial resolution of Mimosa-28, the sensors have been used in dierent experimental conditions. The rst part of this chapter describes the software package of this pixel sensor, the alignment procedure that was developed during this PhD thesis as well as a description of the response of Mimosa-28 sensor to heavy charged particles. These steps are necessary to obtain high precision measurements. The beam proles of therapeutic beams and the uence perturbation due to ducial markers were measured with high resolution. In this chapter, the experimental setups used for these measurements are described.

Software package for Mimosa-28 sensors

The analysis of the data, obtained with the Mimosa-28 sensors, was performed using the object-oriented Qapivi software [START_REF] Finck | Study for online range monitoring with the interaction vertex imaging method[END_REF], written in C++. This code contains a reconstruction and a simulation part, based on the Root [START_REF] Brun | ROOT an object oriented data analysis framework[END_REF] and Geant4 [START_REF] Agostinelli | Geant4a simulation toolkit[END_REF] libraries.

In the frame of this work, the reconstruction package was modied to improve the eciency and precision of the data analysis. This section explains the dierent steps followed of Qapivi, regarding the reconstruction and simulation parts.

Reconstruction

The reconstruction part of Qapivi aims to reconstruct the trajectories of charged particles passing through several sensors (also referred to as planes). The dierent steps, required for the data analysis of Mimosa-28, are detailed with the conversion of raw data to hit pixels, the clustering, the tracking and the vertexing.

From raw data to hit pixels

The binary le, generated from the DAQ system, is decoded following the logic described in section 2.2.1.3 and for each event, the red pixels are moved to a memory container. The pixels that belong to this container are called hits, and the event number is equal to the frame number dened by the sensor readout. A hit is identied by its event number, sensor ID (numbered from 1 up to the number of sensors placed during the experiment) and its position. The latter is dened as the line and column numbers that were red, and are converted to (x, y) coordinates. The total number of containers depends on the number of sensors, and all red pixels from one sensor belong to the same container.

From hits to clusters

A cluster is dened as a group of neighboring pixels that were red from the same particle. For this reconstruction step, a clustering algorithm was implemented [START_REF] Rescigno | Performance of the reconstruction algorithms of the FIRST experiment pixel sensors vertex detector[END_REF], based on the rst neighbor search in an iterative way. With such purpose, all consecutive hits with a common edge are considered to be part of the same cluster. The procedure stops when no more neighboring pixels are found. The performance of this algorithm was tested by means of a random cluster generator, and the eciency was found to be better than 99%. As for the hits, a cluster is identied by its event number, sensor ID and its position. The latter is dened as the center of mass from all pixels composing the cluster, and is considered as valid when the number of pixels that belong to this cluster is bigger than a certain value set by the user. This condition is used for optimizing the time of the next step by suppressing the clusters generated by noise.

From clusters to tracks

A track is described by a regression line matching several clusters in dierent planes. The track resolution is calculated by the residuals [START_REF] Rescigno | Performance of the reconstruction algorithms of the FIRST experiment pixel sensors vertex detector[END_REF], dened as the dierence between the cluster and the track positions at a given plane. The tracking algorithm is based on the one implemented for the FIRST experiment [START_REF] Rescigno | Performance of the reconstruction algorithms of the FIRST experiment pixel sensors vertex detector[END_REF], and was improved in the context of this work. The dierent steps followed during the tracking are listed below:

All combinations of the valid clusters from the rst and the last planes are considered and a straight line is computed for each combination, which denes a preliminary track.

For every intermediate plane, the closest cluster to the computed line is added to the track candidate, and the track parameters of the regression line are updated after tting all found clusters.

A track is considered valid after being evaluated by a set of constraints:

* Three or more clusters belong to the track, and only one missing cluster is allowed. The latter point is considered since a sensor can be less sensitive than the others. This can be due to the fact that the deposited energy inside the sensor was not enough to create a signal above the threshold, or that some pixels did not produce any signal (dead pixels).

* The track residuals, evaluated for each plane, are smaller than certain thresholds. The latter are estimated for every plane with a weight calculation based on multiple Coulomb scattering, approximated by the Highland formula (equation 1.4). The weight is dened as w i = 1/σ x,i for sensor i, where they are estimated from a pencil beam passing through dierent materials. The calculation details of σx,i can be found in section 3.4.2.1.

* The deviation of the cluster size from all found clusters is smaller than a certain cut.

Non-valid tracks are re-evaluated through the previous step, where the residual constraint is set to a less strict condition. This step is repeated via several iterations until reaching a xed limit dened by the user.

In the case valid clusters are still available, all steps are re-performed with a decrement of the last plane denition in the rst step.

The algorithm stops when no valid clusters or no valid track candidates are available.

From tracks to vertices

The vertexing step is performed in case a target is placed in front or in-between the tracker system. A vertex is dened as an interaction point between two or more tracks. Vertices are determined as the mean coordinates, where the distance between the two extrapolated tracks from the front and from the back, is minimum. A valid vertex is dened when this distance is smaller than a certain value set by the user.

Monte Carlo simulation

The goal of the Monte Carlo simulations for this work is to provide comparable data sets to the ones recorded from the Mimosa-28 sensors, and to test the performance of the reconstruction code.

Geant4 [START_REF] Agostinelli | Geant4a simulation toolkit[END_REF] is an object-oriented simulation toolkit, developed by CERN. This Monte Carlo transport code can be applied to high energy, nuclear and accelerator physics, but also to medical and space radiation applications. Geant4 is a modular and exible code, whose implementation is transparent and open to the user. The main tools used for the simulations presented in this work are listed below:

The geometry denes the volumes and materials as well as their positions for the simulated geometrical structure.

The physics list considers the interaction processes used during the simulation run.

The particle gun establishes the particle species and energies that will be transported through the geometry during the simulation run.

The run decides of the actions at the beginning and at the end of the simulation.

The event considers the actions at the beginning and at the end of every primary event generated by the particle generator.

The stepping determines the actions performed at the beginning and at the end of each step that correlates to one interaction along the track of a particle.

The Mimosa-28 sensor geometry was implemented in Geant4 by means of multiple superimposed volumes, representing the dierent sensor layers. They were designed following the dimensions of the Mimosa-28 sensor, as described in section 2.2, and the sensitive volume was dened as the epitaxial layer of the sensor.

The particle gun was set to dierent ion species and energies, as the ones used for particle therapy. The primary particles were generated following a Gaussian distribution, and the initial parameters such as beam position, width and divergence could be set to values comparable to the ones used in dierent experiments.

The physics list used for the simulations was the binary cascade light ion model (BIC) [START_REF] Folger | The Binary Cascade -Nucleon nuclear reactions[END_REF] in combination with the electromagnetic processes option 3 (EMY option) [START_REF] Ivanchenko | Geant4 models for simulation of multiple scattering[END_REF], which are recommended for particle therapy applications.

The runs consisted of a certain number of particles that were generated at a dened position, and transported along the constructed geometry. The particles interacting with the sensitive volume, dened as the epitaxial layer of the sensor, are considered as candidates for the simulation output. To decide whether an event is kept or not, the deposited energy of the particle inside the sensitive volume is compared to an energy cut, which reproduces the threshold values set during the experiments. In case the energy deposition is higher than this threshold, the particle parameters are recorded, and used as input for the reconstruction code. The simulation output is based on the response of the detector, detailed in section 3.3, and is generated by means of a digitizer included in the Qapivi framework.

Alignment procedure for CMOS sensors

A tracker composed of several Mimosa-28 sensors can reach a spatial track resolution better than 10 µm [START_REF] Rescigno | Performance of the reconstruction algorithms of the FIRST experiment pixel sensors vertex detector[END_REF], due to the high intrinsic resolution of the sensor. Nevertheless, this is only possible when an alignment procedure is performed beforehand. This procedure, implemented in the reconstruction code, aims to correct the mechanical misalignment of the sensors by software. The alignment is needed to determine the translational and rotational shifts (referred to as alignment parameters) of the sensors relative to each other. During an experiment, a so-called alignment run needs to be performed, where a particle beam passes through the sensors placed along the z-axis. For this run, no target is placed in front or in-between the sensors and no magnetic eld is applied. The alignment parameters can then be determined, using the positions of the primary particles passing almost straight through the tracker.

The dierent methods developed for the alignment of several sensors are generally based on iterative procedures that sequentially process a given amount of tracks [START_REF] Blobel | Software alignment for tracking detectors[END_REF][START_REF] Karimaki | Sensor Alignment by Tracks[END_REF]. For this, the particle trajectories are tted by a linear regression, where the translational and rotational shifts of the sensors are optimized. This iterative concept has the disadvantage to be signicantly time consuming. For that reason, e.g., Blobel introduced a so-called matrix method for aligning the sensors, in which the alignment parameters are optimized in one step through matrix operations [START_REF] Blobel | A New Method for the High-Precision Alignment of Track Detectors[END_REF][START_REF] Blobel | Software alignment for tracking detectors[END_REF]. The latter algorithm is able to optimize a large number of parameters in a simultaneous linear least square t for a certain number of tracks, and uses the simultaneous optimization approach for the local and global parameters. The track parameters are dened by the local parameters (e.g., slope and intersection for a straight line), while the alignment parameters are dened by the global parameters (correction of detector positioning common for all tracks).

In the case of Mimosa-28, the alignment procedure originally implemented in Qapivi, is based on an iterative procedure that calculates the global parameters after tting a given amount of tracks. The algorithm repeats this operation until the dierence of the alignment parameters between two consecutive iterations is smaller than a given requirement.

This procedure needs many iterations and in some cases, the algorithm does not converge. For this procedure, a pre-alignment of the sensors is required in order that the tracks can be reconstructed by the tracking algorithm.

To improve the accuracy and eciency of the alignment, a new procedure was developed in the frame of this PhD thesis, and implemented in Qapivi. The procedure follows the general concept of Millepede [START_REF] Blobel | A New Method for the High-Precision Alignment of Track Detectors[END_REF], developed by Blobel et al., with a global optimization.

However, the presented procedure can be implemented easier than the one from Blobel that requires a linearization around the initial local and global alignment parameters. In addition, the developed procedure is based on the cluster positions rather than on the track positions, and is explicitly adapted to the situation of a tracker system composed of a set of parallel Mimosa-28 sensors. Since the primary particles undergo multiple scattering in the sensors and in the air gaps between them, the alignment procedure described in this work includes an event rejection loop, based on simple scattering calculations, which improves the quality of the results.

The following section reports the new alignment procedure with a full description of the alignment algorithm, the renement of the procedure and its implementation in the reconstruction code. The experimental setup and the Monte Carlo simulations, performed to test the performance of the procedure, are also detailed. The alignment procedure and its performance are published in [START_REF] Reidel | Alignment procedure of silicon pixel detectors for ion-beam therapy applications[END_REF].

Alignment algorithm

The alignment algorithm presented in this section is based on the optimization of a global χ 2 function. The local parameters are not explicitly computed, but are implicitly dependent on the global parameters that are calculated within the χ 2 function. The local parameters are dened by the linear regression parameters, and the global parameters are represented by the alignment parameters. This method is very ecient and can process a high number of events. An event is dened as the measured positions from a single particle traversing all sensors, while the linear t of these positions is referred to as a track. The alignment parameters are calculated after solving a matrix-equation, whose size is independent from the number of events processed. The χ 2 function, depending on the alignment parameters, and the resulting matrix are derived, and stepwise described in this section.

Concept

In an optimal scenario, the sensors would be placed without any misalignment along the beam axis during an experiment, and the tracks could be reconstructed without performing any alignment procedure Figure 3.1 (left panel). In a realistic case, the sensors are placed with initial mechanical misalignments that need to be corrected in order to obtain a reliable data analysis. The free alignment parameters, dened in this work, are two translations dx and dy, and one rotation dφ around the z-axis (parallel to the beam axis) per sensor. For a precise mechanical setup, the sensors can be positioned with a typical accuracy < 0.5 mm lateral to the beam axis, and < 30 mrad around the x-axis and y-axis. The impact of the latter rotations can be neglected since the geometrical correction factor is smaller than 1 -cos(0.03), and is not relevant for the Mimosa-28 dimensions of 20 × 20 mm 2 . It should also be noted that the inuence of the longitudinal parameters is very small compared to the transversal ones. For a RMS of 10 mrad for the linear track slopes, the sensitivity of the longitudinal alignment parameters is a factor 100 (1/RMS) smaller compared to the transversal parameters. Considering the two translations dx i , dy i and the rotation dφ i , the corrected coordinates (X ij ,Y ij ) relative to the original coordinates (x ij ,y ij ) of sensor i for a track j are calculated as follows:

  X ij Y ij   =   cos(dφ i ) sin(dφ i ) -sin(dφ i ) cos(dφ i )     x ij y ij   +   dx i dy i   . (3.1)
Since the rotation dφ i around the z-axis is small (dφ i 1), equation 3.1 can be simplied:

  X ij Y ij   =   1 dφ i -dφ i 1     x ij y ij   +   dx i dy i   . (3.2)

Degrees of freedom

A global coordinate system needs to be established for the tracker, which is achieved by xing several alignment parameters. For this, two translational parameters in x and two in y are restricted to constrain the translations in x and y and the rotations around the x-axis and y-axis. Since the z-shift is neglected, only one rotational parameter around the z-axis needs to be xed. In this work, the rst and the last planes are dened as references, such as dx 1 = 0, dy 1 = 0, dφ 1 = 0, dx n = 0 and dy n = 0, where n is the number of planes.

Linear regression analysis for a single track

A track is dened as the linear t, also called linear regression, of the measured positions from a particle passing through the sensors. The corresponding S is the square sum of the dierences between the measured positions and the track positions in the sensors, dened as:

S(a, b) = n i=1 w 2 i [(a + bz i ) -p i ] 2 , (3.3)
where p i is the coordinate (either x i or y i ) of the measured particle for sensor i at position z i , and w i represents the weight given by the expected uncertainty of the measured event.

In order to dene the weight, the spatial distribution σ i , induced by multiple Coulomb scattering at sensor i, is calculated as a function of the angular scattering distribution σ α from the sensors and the air gaps, as given in equation 30 by [START_REF] Gottschalk | Multiple Coulomb scattering of 160 MeV protons[END_REF] [START_REF] Gottschalk | Multiple Coulomb scattering of 160 MeV protons[END_REF].

The applied weight, such as w i = 1/σ x,i , is the same for all events, and the same in x and y since Mimosa-28 is composed of square pixels. The regression coecients a and b of the linear t are the parameters to be dened. In order to have the best possible t, the least squares method is used to estimate a and b, which minimizes S leading to χ 2 S [START_REF] Montgomery | Introduction to Linear Regression Analysis[END_REF]. The optimized regression coecients a and b become the least squares estimators â and b, and are calculated as follows:

  â b  = A -1 B      p 1 . . . p n      , (3.4)
where A is a 2×2 matrix and B is a 2×n matrix:

A =     n i=1 w 2 i n i=1 w 2 i z i n i=1 w 2 i z i n i=1 w 2 i z 2 i     , B =   w 2 1 • • • w 2 n w 2 1 z 1 • • • w 2 n z n   . (3.5)
After replacing the regression coecients by the least squares estimators, the χ 2 S function can be written as:

χ 2 S = n i=1   w i   1 z i   â b  -p i     2 . (3.6)
By combining equations (3.4) and (3.6), the χ 2 S becomes:

χ 2 S = - → w (KL -I n - → p 2 , (3.7)
where I n is the n×n identity matrix, and L is the product L = A -1 B. The symbol " " denes here the element-wise product. The n-vectors -→ w and -→ p , and the K matrix of dimension n×2, are dened as the following:

- → w =      w 1 . . . w n      , - → p =      p 1 . . . p n      , K =      1 z 1 . . . . . . 1 z n      . (3.8)
For readability simplication, the n×n matrix Q is introduced as

Q = - → w (KL -I n ),
and is constant for a given setup with certain positions z i and weights w i . Equation 3.7 is then written in the following form:

χ 2 S = Q - → p 2 .
(3.9)

Denition of the χ 2 for the global alignment parameters optimization

The alignment algorithm is based on the minimization of a global χ 2 function, which combines the linear regression analysis for all tracks. The variables X i and Y i are the corrected coordinates, explicitly depending on the searched alignment parameters dx i , dy i and dφ i (see equation 3.2), common for all tracks. For a single track, χ 2 S X and χ 2 S Y dene the optimal linear t in x and y, respectively, and are written as follows:

       χ 2 S X = n i=1 w 2 i [(â X + bX z i ) -X i ] 2 χ 2 S Y = n i=1 w 2 i [(â Y + bY z i ) -Y i ] 2 , (3.10)
where âX , bX , âY and bY are the least squares estimators for the regression line of the corrected positions X i and Y i . These parameters dier for each independent track and the global χ 2 function, containing the alignment parameters, is then the sum over all tracks k (for sensor i and track j):

χ 2 (dx i , dy i , dφ i ) = k j=1 n i=1 w 2 i [(â X j + bX j z i ) -X ij ] 2 + n i=1 w 2 i [(â Y j + bY j z i ) -Y ij ] 2 . (3.11)
This χ 2 denes the goodness of the linear t of all tracks, and yields a minimum when the searched alignment parameters are optimum. The least squares estimators âX , bX , âY and bY implicitly depend on the searched alignment parameters (equation 3.4).

Calculation of the alignment parameters

The alignment parameters can be explicitly calculated after converting the χ 2 in equation 3.11 to a single matrix equation that can be solved after a matrix inversion. From equation 3.2, the coordinates X i and Y i of the corrected positions for a single event can be calculated as:

     X 1 . . . X n      =      x 1 + dφ 1 y 1 + dx 1 . . . x n + dφ n y n + dx n      ,      Y 1 . . . Y n      =      y 1 -dφ 1 x 1 + dy 1 . . . y n -dφ n x n + dy n      . (3.12)
After dening the vectors -→ X , -→ Y , -→ x and -→ y , equation 3.12 can be re-written as:

- → X = - → x + P X - → m , - → Y = - → y + P Y - → m , (3.13)
where P X and P Y are n×3n matrices dened as:

P X =      1 • • • 0 0 • • • 0 y 1 • • • 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 • • • 1 0 • • • 0 0 • • • y n      , P Y =      0 • • • 0 1 • • • 0 -x 1 • • • 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 • • • 0 0 • • • 1 0 • • • -x n      . (3.14)
The searched 3n-vector -→ m contains the alignment parameters common to all events:

- → m = ( dx 1 , • • • , dx n , dy 1 , • • • , dy n , dφ 1 , • • • , dφ n ) T . (3.15)
The combination of equations 3.4 and 3.13 results to the minima χ 2 S X and χ 2 S Y :

χ 2 S X = Q - → x + QP X - → m 2 , χ 2 S Y = Q - → y + QP Y - → m 2 .
(3.16)

By introducing the n×3n matrices C X and C Y , and the n-vectors -→ d X and -→ d Y as:

C X = QP X , C Y = QP Y , -→ d X = Q - → x , -→ d Y = Q - → y . (3.17)
The χ 2 in equation 3.11 can now be re-written as a quadratic matrix equation:

χ 2 ( - → m) = k j=1 (C X j - → m + -→ d X j ) 2 + (C Y j - → m + -→ d Y j ) 2 , (3.18)
The gradient of the χ 2 with respect to -→ m is then a term linear in -→ m:

- → ∇χ 2 ( - → m) = C m - → m + - → d m , (3.19)
where the 3n×3n matrix C m and the 3n-vector -→ d m are built by summing all events:

C m = k j=1 (C X j T C X j ) + (C X j T C X j ) T + (C Y j T C Y j ) + (C Y j T C Y j ) T , - → d m = k j=1 2 ( -→ d X j T C X j + -→ d Y j T C Y j ) T . (3.20)
As mentioned in section 3.2.1.2, ve global parameters have to be constrained in order to get a dened geometrical situation. Therefore, the alignment parameters of the rst plane, and the transversal parameters of the last plane are set to 0. These restrictions are best suited for the coarse mechanical alignment since the rst and the last sensors can be easier accessed than the intermediate ones during an experiment. After constraining the tracker in the global coordinate system, the nal gradient of the χ 2 can be expressed as the following:

- → ∇χ 2 ( - → m f ) = C f m - → m f + - → d f m , (3.21)
where the (3n-5)×(3n-5) matrix C f m and the (3n-5)-vector -→ d f m are obtained by canceling the ve degrees of freedom (i.e., dx 1 , dy 1 , dφ 1 , dx n and dy n ), and the corresponding columns, rows and elements in C m and -→ d m . The vector -→ m f contains the searched alignment parameters.

In order to obtain a minimum χ 2 , its gradient with respect to -→ m f is set to 0. By inverting the matrix C f m , the searched alignment parameters are then calculated as follows:

- → m f opt = -C f m -1-→ d f m . (3.22)
It should be noted that without the mentioned cancellation of the ve degrees of freedom, the matrix C f m would be singular and could not be inverted. The matrix C f m -1 is the socalled covariance matrix. The alignment parameters in -→ m f opt dene now an optimal correction for all events, with a minimum weighted (by the uncertainties) mean (quadratic) deviation between the corrected measured positions X ij and Y ij , and their corresponding individual regression lines. A package of script examples for the alignment algorithm is presented in the supplementary material at http: // dx. doi. org/ 10. 17632/ 9g5r3ypcb6. 2 .

Renement of the algorithm

The described algorithm is able to determine the alignment parameters in one step, after accumulation of a given number of events. The tracking is not explicitly performed, which allows the procedure to be independent of the initial misalignments. The basic assumption exploited by the algorithm is that the particles traverse the sensors following almost a straight line. Therefore, strongly scattered events degrade the quality of the results. In order to avoid a signicant inuence on the alignment parameters results due to scattered particles, two further calculation steps are performed with the same algorithm. In these steps, the alignment parameters from the previous solution are applied, and the strongly scattered events (e.g., due to nuclear interaction) are rejected. Therefore, for each particle, the measured angular deection from one sensor i to the next one is compared to the theoretical width σ i α of the angular distribution induced by the multiple Coulomb scattering at sensor i. The σ α value is calculated by the Highland approximation [START_REF] Highland | Some practical remarks on multiple scattering[END_REF]54], which considers the multiple Coulomb scattering as a Gaussian process and provides an estimate for its standard deviation. In this work, the rejection thresholds were set to 20σ i α (preltering) and 4σ i α for the second and third calculation steps, respectively. In each step, 1040% of the events are eliminated by this lter procedure, and the calculated alignment parameters become more accurate. These additional steps are especially necessary for the accuracy of the rotation parameter, which is more sensitive to the scattering. Table 3.1 quanties the accumulated angular distribution from a set of six Mimosa-28 sensors, for 150 and 300 MeV/u protons, 4 He and 12 C ions.

Evaluation of the procedure

The alignment procedure, described above, was implemented in the software Qapivi. In the frame of this work, a new class was developed, and included in the reconstruction code. In this section, the Monte Carlo simulations and the experimental setups used for testing the performance of the alignment procedure are described.

Experimental setup

Dedicated alignment measurements were performed in the experimental room at the Proton Therapy Center in Trento [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF] and at the Ion-beam Therapy Center in Heidelberg (HIT) [START_REF] Haberer | The heidelberg ion therapy center[END_REF]. An experimental setup composed of six Mimosa-28 sensors was placed at an angle of 0 • with respect to the beam axis. The sensors were mechanically aligned to the room laser by means of reference marks drawn on the sensor holders. The alignment runs were performed without target, without magnetic eld and at low intensity (< 5 kHz) to avoid pile-up in the sensors. The beam particles used were protons and helium ions, within the therapeutic energy range from 80 to 220 MeV/u. The energies and FWHM, of the beam at the room isocenter, are listed in Table 3.2 for both experiments. Two dierent setup geometries were tested: one with a distance of 35 cm between the rst and the last sensor (Figure 3.2 (top panel)), and one with a distance of 8.8 cm (Figure 3.2 (bottom panel)). For both experiments, the detector thresholds were set to six times the noise level (see section 2.2.1.2). The performance of the alignment procedure for the experimental data are evaluated after computing the total residuals, determined from all tracks. The track resolution is then dened by the width of the residual distributions in x and y. The performance of the procedure implemented in this work (referred to as ClusAlign) was compared to the ones of the algorithm originally implemented in Qapivi (referred to as TrackAlign), and to the state-of-the art algorithm Millepede II.

Data simulation

The Monte Carlo simulations for testing the alignment procedure were generated with the simulation package described in section 3.1.2, based on Geant4 version 10.04. The ion optics of the beam (FWHM and beam divergence) were adapted to reproduce comparable beam characteristics to the ones used for therapy, listed in Table 3.2. Six sensors were placed along the beam axis, and noisy pixels were randomly created as a function of the signal to noise ratio. The threshold was set to six times the noise level in order to reproduce the experimental data. Dierent ion beam congurations, listed in Table 3.3, were simulated for both setup geometries. The values of the beam divergence were dened as the angular distribution in front of the vacuum window. The position of the sensors along the beam axis are listed in Table 3.4 for a compact geometry (referred to as Geo1 ), and for a spread geometry (referred to as Geo2 ). For both geometries, the start position for the simulations was set to 50 cm upstream of the rst sensor. To test the alignment procedure, some arbitrary set-values for the misalignments dx, dy and dφ were dened for each sensor. As explained in section 3.2.1.1, the translations and the rotation of the rst sensor (primary reference plane) and the translations of the last sensor (secondary reference plane) were set to 0. Since the rotation is more sensitive and has a lower impact than the two translations, a rst study only involving the translations dx and dy (dφ set to 0) was performed. Two scenarios were simulated: one with small misalignment values, slightly bigger than the intrinsic resolution of the detector (referred to as Mis1 ), and one with larger misalignment values in the order of the mechanical positioning uncertainty during an experiment (referred to as Mis2 ) (∼1 mm) (Table 3.5).

In the presented work, the deviations δ are dened as the absolute value of the dierence between the calculated alignment parameters and the ones set for the Monte Carlo simulations (referred to as set-misalignments) such as δ = |d calc -d set |. The accuracy of the alignment algorithm as a function of the number of events ranging, from 2500 to 650000 events, was quantied with the misalignment scenarios listed in Table 3.6 (referred to as Mis3 ). The rotational misalignments are now set to non-zero values. Since the rotation matrix in equation (3.2) was approximated for small dφ values, the alignment procedure results for larger rotational misalignments (up to 10 • ) were also studied. All data sets were processed with an Intel Core i3-2100 CPU @ 3.10 GHz (2 physical cores and 4 threads).

Response of Mimosa-28

The response of Mimosa-28 is dened as the cluster size, representing the group of red pixels from the ionizations of a charged particle passing through the sensor. The cluster size is thus explained by the number of pixels per cluster. This depends on the deposited energy, and the track structure of a particle passing through the epitaxial layer of the Mimosa-28 sensor.

Experimental study

Dierent experimental setup congurations were used for the study of the detector response, where several Mimosa-28 sensors were placed along the z-axis. In some cases, the setup was mounted without any target in front or in-between, and in other cases, additional materials, e.g., water, were placed along the beam axis.

A rst study was carried out to compare the cluster size of the rst generation (referred to as Generation 1 ) and the second generation (referred to as Generation 2 ) of Mimosa-28 sensors for 80.64, 130.25 and 220.51 MeV/u helium ion beams. The experimental setup described in Figure 3.2 (bottom panel) was composed of three sensors of Generation 1 (sensors 46), and three sensors of Generation 2 (sensors 13).

A second study investigated the cluster size for dierent ion species and beam energies. In Table 3.7, the particle beams and their energies as well as the accelerator facility where the measurements were conducted are listed.

In a third study, the cluster size was studied for an experimental setup where a water target was placed in-between two sets of three sensors. In this case, the experimental setup depicted in Figure 3.4 was used, where the target was replaced by a water phantom of 4 cm thickness, with an area larger than the beam FWHM. This study aimed to evaluate the cluster size as a function of the dierent produced fragments from a 287.50 MeV/u carbon ion beam impinging on the water phantom.

Cluster size analysis

The analysis of the detector response for Mimosa-28 sensor was performed by using the clustering and tracking steps of the software Qapivi. For this analysis, it is important to select the clusters produced by the primary particles. In order to do this, the tracks were reconstructed to reduce the noise, and eliminate the clusters that are not created from the primary particles. The cluster size is dened in this work as the maximum value from the cluster size distribution of one sensor. The energy losses were calculated with the software Lise++ [START_REF] Tarasov | LISE++: Radioactive beam production with in-ight separators[END_REF] for 14 µm silicon thickness as the epitaxial layer of Mimosa-28. The energy values in Table 3.7 are the ones of the primary particles before crossing the vacuum window. In case that some material layers were placed in front of the tracker, such as the beam nozzle or a water phantom, the primary energy of the particle was re-calculated to compensate the energy losses inside these materials.

The uncertainty for the cluster size was determined from the measured distribution, which is dened as the superposition of several Landau functions from the response of the red pixels. The quartile at 15% of the distribution determines the lower limit, while the quartile at 85% determines the upper one. The uncertainty on the deposited energy inside the epitaxial layer of the Mimosa-28 sensor was quantied from the dierent energy losses in the material layers placed in front of the detector. The total uncertainty was then computed from the material thickness error, which is the main factor responsible for the energy loss variations. The spatial distributions of the energy loss, detailed in section 1.4.1, for similar ion beams as the ones presented in Table 3.7, were computed with Monte Carlo simulations. With this purpose, the software Trax [START_REF] Krämer | Calculations of heavy-ion track structure[END_REF] was used, which is a transport code at the nanoscopic level. With this code, the produced δ-electrons were tracked inside a volume material, dened as a 14 µm silicon layer. The deposited dose from the δ-electrons was calculated as a function of their distance from the primary track, and the radial dose distributions were computed.

To study the response of the Mimosa-28 sensor as a function of the dierent produced fragments, when a thick target is placed in-between two sets of sensors, as explained above, the mean cluster size was computed. The mean cluster size is dened as the mean value of the dierent clusters that belong to a track, for all reconstructed tracks. This procedure was followed for the tracker placed in front (referred to as bmtrack ) and the tracker placed behind (referred to as vttrack ) the target.

Lateral beam spread along the longitudinal axis

In this section, the lateral beam spread along the longitudinal axis is reported. The experimental setup, used for evaluating the beam settings, coincides with the one described in Figure 3.2 (top panel) of section 3.2.3.1. The beam proles were measured at several positions along the longitudinal axis, and the transport of a pencil beam was computed to reproduce the measured data, after optimization of the initial ion optical parameters of the beam.

Beam prole analysis

The beam proles were generated from the 2D cluster maps of the sensors at several positions along the beam axis. The proles in x and y, at a certain position, were obtained with the projection of the cluster map in x and y, respectively. They were then tted with a Gaussian function, whose mean and width were extracted. Regarding the lateral beam spread, calculated from the transport code, only the width parameter of the Gaussian function was used.

Particle transport

The transport code used to determine the lateral beam spread of a pencil beam was based on Scattman [START_REF] Schardt | Heavy-ion tumor therapy: Physical and radiobiological benets[END_REF][START_REF] Weber | Volumenkonforme Bestrahlung mit Kohlensto-Ionen zur Vorbereitung einer Strahlentherapie[END_REF], and implemented in C++ including the Root libraries [START_REF] Brun | ROOT an object oriented data analysis framework[END_REF], in the frame of this work.

Ion optics and phase space distribution

The pencil beam model used relies on a non-parallel (focused) beam with a Gaussian distribution [START_REF] Eyges | Multiple scattering with energy loss[END_REF][START_REF] Hollmark | Inuence of multiple scattering and energy loss straggling on the absorbed dose distributions of therapeutic light ion beams: I. Analytical pencil beam model[END_REF]. The description of the ion optical phase space distribution of a pencil beam at a certain position z can be written as the following [START_REF] Ringbaek | Fluence inhomogeneities due to a ripple lter induced Moiré eect[END_REF]:

f z (x, α) = C exp - 1 2 (x -kα) 2 σ 2 x + α 2 σ 2 α , (3.23)
where x is the lateral position of the beam, and α is the beam angle of the local angular distribution. The parameter k is the distance to the focus point z f ocus , as k = z -z f ocus , and is negative in the case that z is in front of the focus point. The values σ x and σ α are the widths of the spatial and angular distributions of the beam in the focal point, for a theoretically undisturbed beam (k = 0). Since the beam suers elastic interactions when passing through dierent materials, the ion optic parameters σ x , σ α and k vary along the beam axis as a function of the multiple Coulomb scattering. After estimating the width of the angular distribution dσ α of a pencil beam passing through a certain medium of distance dx by means of the Highland formula (equation 1.4) [START_REF] Highland | Some practical remarks on multiple scattering[END_REF]54], the unknown ion optic parameters at position i can be calculated as a function of the ion optic parameters at position i -1 by the following transport calculations:

σ 2 x,i = σ 2 x,i-1 + k 2 i-1 σ 2 α,i-1 dσ 2 α,i σ 2 α,i-1 + dσ 2 α,i , (3.24)
σ 2 α,i = σ 2 α,i-1 + dσ 2 α,i , (3.25)
k i = k i-1 + σ 2 α,i-1 σ 2 α,i-1 + dσ 2 α,i + d i . (3.26)
The width of the spatial distribution σx,i , which can be measured in practice at a certain position z i along the beam axis, can be written as a function of the ion optic parameters:

σx,i = σ 2 x,i + k 2 i σ 2 α,i . (3.27)
This procedure allows to calculate the envelope of a non-parallel (focused) beam, including the multiple Coulomb scattering, from a Gaussian approximation, for a sequence of targets and air gaps.

Fitting of the ion optical parameters for a focused beam

The formula described above were originally implemented in Scattman. This transport code aims to calculate the width σx,i of a pencil beam along the z-axis, based on the initial ion optic parameters σ x 0 , σ α 0 and k 0 dened for z = 0. To ensure that the calculated widths σx,i t the beam prole measurements along the z-axis, the initial ion optic parameters σ x 0 , σ α 0 and k 0 need to be optimized.

ONLINE BEAM MONITORING

In this work, the formula were re-implemented in C++, and the calculation steps are based on Root functions. The implementation of the code improved, by adding an automatic optimization of the ion optic parameters, using a χ 2 minimization.

Online beam monitoring

In the frame of this work, a software was developed for online beam monitoring. The code was programmed in Python, and directly implemented in the DAQ system running Windows. The aim of this program is to give fast information regarding the position and the width of the beam to verify the beam prole during low intensity experiments. Only the rst step of the reconstruction was implemented, where the raw data from the binary le are converted to hit pixels (detailed in section 3.1.1.1). The next reconstruction steps (e.g., clustering and tracking) would improve the precision of the beam prole information by reducing the noise. However, these steps are time consuming and can not be performed in the required time frame for online monitoring. Even though the hit pixels information is not as precise as the cluster one, beam proles based on the reconstructed hits are suited to the needed precision for online beam monitoring.

The program was developed to read the data le at the same time the DAQ system is writing it. The raw data are then reconstructed to hit pixels, which are used to display a 2D hit map after a couple of seconds. Several parameters can be adjusted by the user depending on the needs. Since the le writing is faster than the le reading, the executed program can jump to the last written line of the le to ensure that the analyzed events are the most recently recorded. Depending on the set parameters, the code can deliver a prole within 25 s after the beam extraction from the accelerator. This program was successfully used during several data taking at GSI.

Fluence perturbation due to ducial markers

The uence perturbations due to ducial markers, explained in section 1.6.3, were evaluated with a new measurement concept using a tracker system composed of six Mimosa-28 sensors. This method uses high spatial resolution pixel detectors, and can provide three dimensional uence distributions. The beam time campaign was performed at the Ion-beam Therapy Center in Marburg (MIT) [START_REF] Scheeler | Recommissioning of the Marburg Ion-beam Therapy Centre (MIT) Accelerator Facility[END_REF] in Germany, and was divided in two sessions. The rst one intended to measure edge-scattering eects in targets with pronounced and sharp density gradients with a tracker system of Mimosa-28 sensors. In the second session, several hours of beam time were dedicated to measure the uence perturbations due to ducial markers that are commercially available. Some hours were also dedicated to benchmark the measurements by using radiochromic lms, which is a standard method for dose perturbation measurements. The results of the uence perturbations from the ducial markers are published in [START_REF] Reidel | Fluence perturbation from ducial markers due to edge-scattering measured with pixel sensors for 12 C ion beams[END_REF].

Edge-scattering eects

The experimental setup used to measure the edge-scattering eects with a tracker composed of Mimosa-28 sensors and the beam prole analysis method are described in the two following sections.

Experimental setup

Two dierent targets were measured in the frame of this work, with dierent densities, shapes and thicknesses. The rst target (referred to as bone) had a block shape, simulating cortical bone material with a thickness of 3 cm, and was manufactured with a round edge in order to have a more realistic case. The second target (referred to as hammer ), made of gold had a triangular shape, with a maximal length of 18 mm, and a thickness of 0.5 mm. Figure 3.3 displays the targets and Table 3.8 describes their characteristics. The edge-scattering measurements were carried out at MIT, with 150.14 MeV proton beam.

The experimental setup, depicted in Figure 3.4, consisted of two sets of three Mimosa-28 sensors placed along the beam axis. A rst run was performed without target for alignment purpose. The target was then positioned in-between the two sets of sensors, and adjusted along the lateral beam axis using the room laser system.

In the case of the bone target, the beam impinged on the round edge, while for the gold hammer, the beam covered the full target. The purpose of the rst set of sensors was to verify the beam prole in front of the target. The second set of sensors was used for evaluating the uence perturbation due to the target edge. The beam intensity was set lower than 5 kHz to avoid pile-up eects in the sensors. Mimosa-28 sensors placed along the beam axis. The target is positioned in-between two sets of three sensors, and adjusted along the lateral axis in order that the beam impinges the target edge. The measurements were performed at MIT with 150.14 MeV proton beam.

Beam prole analysis

This experiment aimed to verify the concept of measuring uence perturbations due to edge-scattering eects, with a tracker system composed of several CMOS pixel sensors. The beam proles were analyzed from the rst sensor placed after the target (Figure 3.4). For this, the 2D beam prole (x, y) was extracted after the clustering and tracking reconstruction steps. The tracking was performed to reduce the noise contribution of the δ-electrons, which are produced from the interaction of the beam with the material layers of the setup, and therefore, considered as noise. Since these particles are emitted at large angles and generally penetrate only one sensor, the reconstructed tracks from the δ-electrons are in most cases not considered as valid ones. The beam proles were thus computed as the cluster positions from the clusters that were selected from the tracking. Since the targets used for this experiment were relatively large and thick, the prole in x was generated after integrating the 2D cluster map along the perpendicular direction y.

Fiducial markers

In this work, four common ducial markers were selected to evaluate the induced uence perturbation inside a target volume. Their characteristics are described in Table 3.9.

Experimental setup

The measurements were conducted at MIT with carbon ion beams, and two dierent methods were applied to determine the inhomogeneous scattering induced by ducial markers:

on the one hand with the Mimosa-28 pixel sensors, and on the other hand with EBT3 radiochromic lms. The latter were used to validate the new concept of measuring the uence perturbations due to ducial markers with a set of CMOS pixel sensors. The two experiments were carried out with few months in-between. In order to perform clinically relevant measurements, each ducial marker was placed inside a small water aquarium of 4 cm length and positioned at the isocenter of the treatment room. For better handling, the markers were glued to a polyethylene (referred to as PE ) plate of 1 mm thickness, and positioned along the vertical axis perpendicular to the beam. In addition, a PE block of 9 cm length was placed in front of the water aquarium to simulate the healthy tissues of a patient. The beam energies were chosen in order to cover a range of 3 cm (slightly smaller than the length of the water aquarium). The energies, FWHM and the range in water of the carbon ion beams, used during the experiments at MIT, are listed in Table 3.10. The energies and FWHM at isocenter position were assumed as the nominal values from MIT (ensured by the regular QA), while the ranges were calculated with Lise++ [START_REF] Tarasov | LISE++: Radioactive beam production with in-ight separators[END_REF].

The water equivalent path length of the experimental setup (computed with Lise++) was about 140 mm. The total range of the dierent ion beams used for the experiment was chosen to have enough energy to pass through the PE block, the water aquarium and the sensors placed after the water aquarium (see Figure 3.5 (bottom panel) in section 3.6.3.1). To measure the uence perturbation due to the ducial markers, a tracker system of six Mimosa-28 pixel sensors was placed at 0 • with respect to the beam axis. The beam intensity was set to less than 5 kHz, and monitored using a 5 mm plastic scintillator (BC-400) placed upstream of the sensors. Several beam prole measurements along the beam axis were performed for alignment purpose, and for benchmarking the measurements with other techniques (e.g., radiochromic lms). Two sets of three sensors were placed on each side of the PE block (Figure 3.5 (top panel)). The beam prole measurements were performed with and without the PE block. The two sets of sensors were then moved to each side of the water aquarium (Figure 3.5 (bottom panel)), and a measurement with and without the PE block and the water aquarium was performed. Afterwards, the ducial markers were inserted into the water aquarium through the method explained in the previous section. The rst three sensors were used to monitor the beam prole by verifying that it remains constant, while the three last sensors were used to measure the uence perturbation induced by the marker.

Radiochromic lm measurements

The experiment performed with the Mimosa-28 sensors was validated with radiochromic lms (GAFCHROMIC EBT3, Lot#: 06141702). EBT3 lms have a total thickness of 278 µm, an active layer of 28 µm and are resistant to water during short time immersion [START_REF] León-Marroquín | Investigation of EBT3 radiochromic lm's response to humidity[END_REF]. They were cut in pieces of 6.4 × 6.8 cm 2 , and protected with tape around the borders to prevent damage due to the water. During the irradiation, all lms were placed in portrait orientation to avoid any changes in the lm response due to its orientation [START_REF] Schoenfeld | The origin of the atbed scanner artifacts in radiochromic lm dosimetrykey experiments and theoretical descriptions[END_REF]. The EBT3 lms were then scanned after several hours using a VIDAR scanner (Dosimetry Pro Advantage) with a spatial resolution of 300 dpi (∼ 85 µm) and 16 bits resolution in portrait orientation [START_REF] Borca | Dosimetric characterization and use of GAFCHROMIC EBT3 lm for IMRT dose verication[END_REF].

Before the lm analysis, a calibration curve was measured to correlate the lm response to the delivered particle uence from the accelerator. Therefore, a lm from the same batch was irradiated with 8 dierent scanned squares, receiving a given uence per square, within the range of 5×10 6 3×10 9 ions/cm 2 , corresponding to a dose range of around 070 Gy, considering the lm background. The gray values of the lm were then calibrated according to the given uence, and each irradiated lm was analyzed by using the established calibration curve. The images from the lms were processed using the software ImageJ [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF].

MWPC 1 IC 1 MWPC 2 IC 2 IC 3
Beam nozzle 12 The radiochromic lms were placed along the beam axis at similar positions than the Mimosa-28 sensors, from the experiment described in section 3.6.3.1, in order to validate the measurement concept with a tracker system. The experimental setup is sketched in Figure 3.6 and the lm positions i are referred to as Fi. A 5 mm plastic plate was placed in front of the rst lm to simulate the 5 mm plastic scintillator used during the CMOS sensors experiment. The same set of measurements was conducted: the beam proles without any perturbations were measured without the 5 mm plastic, the PE block and the water aquarium. They were then measured with the addition of the 5 mm plastic, the PE block and the water aquarium. The perturbations from the ducial markers were later on measured by placing the marker inside the water aquarium at isocenter position (Figure 3.6), using the same technique as the one described in section 3.6.3.1. For the measurements with the ducial markers, an additional lm was inserted inside the water aquarium placed at 5 mm in front of the marker. This lm is not represented in Figure 3.6 but was used to verify the stability of the beam prole during the measurements.

3.6.3.3 Beam prole analysis: Mimosa-28 vs. radiochromic lms

The experiment for the uence perturbation due to ducial markers using several CMOS pixel sensors aimed to provide a new measurement concept, which aords high precision measurements. The new measurement concept with the use of a tracker system was benchmarked against a standard measurement method with radiochromic lms. In a rst step, the beam proles were analyzed from the measurements without perturbation, and in a second step they were analyzed from the measurements with the ducial markers for the CMOS and lm experiments (see Figures 3.5 and 3.6).

The Mimosa-28 sensors data were processed by using Qapivi, where the tracks could be reconstructed as described in section 3.1.1. Data from the radiochromic lms were obtained from the scans, and calibrated as explained in section 3.6.3.2. From the reconstructed tracks, a 2D beam prole (x, y) can be extracted at any position along the z-axis.

For both experiments, the beam proles in x and y were obtained by integrating the distribution over the perpendicular directions y and x, respectively. Without perturbation due to the markers, the proles were integrated over the full distribution. However, in the case that a ducial marker was placed inside the water aquarium, the proles in x were integrated over a smaller area in y that correlates to the length of the marker in order to evaluate its perturbation. The data sets from the tracker and the lms were analyzed independently, and normalized as a function of the prole integral in order to compare both measurement techniques. The normalization and shift of each x and y beam prole was performed by means of a cumulative distribution function (also referred to as Gaussian integral function Φ). In the case of the Mimosa-28 beam prole analysis, each entry of the histogram was weighted as a function of the cluster size (see section 3.3). The applied weight was calculated following equation 3 of Spiriti et al. (2017) [START_REF] Spiriti | CMOS active pixel sensors response to low energy light ions[END_REF]. Since the absorbed dose is proportional to the deposited energy, this quantity is also correlated to the cluster size of Mimosa-28. However, the energy resolution of the detector is low since the Mimosa-28 output is a binary signal.

The applied weight is thus a rough correction to the uence proles obtained with the CMOS sensors in order to get a more realistic comparison with the radiochromic lms.

Fluence distribution measured with Mimosa-28 sensors

The goal of this analysis part is to quantify the maximum value of the cold spot induced by the ducial markers, and to determine its position along the beam axis with a precise and ecient method. With such purpose, a 3D uence distribution is reconstructed after performing the tracking, which denes the trajectory of each single particle crossing the sensors. This 3D distribution is computed from all tracks, dened by 3D vectors, which can be reconstructed with the tracker placed after the water aquarium. For this, 10 × 10 × 100 µm 3 voxels are computed, and the uence in each voxel is specied by the sum of all tracks passing through this voxel. The 3D uence distributions are, therefore, the scoring of the total number of intersections between the reconstructed tracks and the voxels. The 2D uence distribution (referred to as uence map), presented in this study, illustrates the propagation of the perturbation in the (x, z) plane, integrated over a certain area along the y-axis. For the case of large targets, as the ones used for the experiment described in section 3.6.1, the integration was performed over the full area. In the case of the ducial markers, the integrated area was chosen as for the beam prole analysis in section 3.6.3.3. The integration range in y-direction was varied to test the robustness of the chosen window. From the integrated 2D uence map, the cold spots at any position along the beam axis were extracted. To determine the maximum cold spot, the beam proles with and without marker were compared.

Chapter 4

Results & Discussion

In this chapter, the results from the dierent experiments described in the previous chapter are discussed. The performance of the alignment procedure was tested with experimental and simulated data, and the response of Mimosa-28 was investigated for dierent ion species and energies. These preparatory steps were necessary to perform precise measurements for ion-beam therapy applications, like the characterization of beam proles and the evaluation of the uence perturbation induced by ducial markers. The presented results of the alignment procedure and the uence perturbation are published in [START_REF] Reidel | Alignment procedure of silicon pixel detectors for ion-beam therapy applications[END_REF] and [START_REF] Reidel | Fluence perturbation from ducial markers due to edge-scattering measured with pixel sensors for 12 C ion beams[END_REF], respectively.

Alignment procedure performance

The alignment procedure is a mandatory routine, which has to be performed before the data analysis, to be able to reconstruct particle tracks with high resolution. A successful convergence of the algorithm is achieved by the goodness of the alignment parameters, which must be better than the required track resolution. In this section, the results from simulated and experimental data are presented, and the performance of the new alignment procedure is benchmarked against the resulting accuracy of the alignment parameters.

Simulation results

The accuracy and precision of the alignment procedure were tested with Monte Carlo simulations for the setup geometries Geo1 and Geo2 (Table 3.4), beam congurations (Table 3.3), and misalignment scenarios Mis1, Mis2 (Table 3.5) and Mis3 (Table 3.6). The values δx, δy and δφ, listed Table 4.1, represent the mean deviations between the calculated alignment parameters and the set-misalignments, averaged over six beam congurations for each misalignment scenario. These results fulll the alignment procedure requirements for reconstructing tracks with high spatial resolution.

The accuracy and robustness of the results, with average deviations δx, δy < 2 µm and δφ < 0.05 • , dene the good reliability of the algorithm. The uncertainties of the alignment parameters, averaged over the six beam congurations, showed smaller values compared to the ones derived from the elements of the covariance matrix C f m -1 , dened in section 3.2.1.5. Since the results from the covariance matrix are less conservative, the The alignment procedure eciency, in terms of time consumption, for converging to the required values, was evaluated for dierent amount of events given to the algorithm for protons, 4 He and 12 C ions at 150 MeV/u for the setup geometry Geo2. The setup geometry Geo1 was also tested for 150 MeV/u 4 He ions. The average deviations between the calculated alignment parameters and set-misalignments were evaluated, and are shown in Figure 4.1. The average deviations of the translation in x (Figure 4.1 (top)) and y (Figure 4.1 (middle)) are smaller than 2 µm for a minimum of 5000 events. However, the rotational parameter, being more sensitive to the scattering, converges slower (Figure 4.1 (bottom)), and a minimum of 50000 events is required for the convergence of the calculated alignment parameters to the real misalignment values. The heavier the particle is, the faster the algorithm converges because of the stronger angular deections for light particles due to multiple Coulomb scattering. The results of the alignment parameters obtained for the setup geometry Geo1 were very similar to the ones presented for the setup geometry Geo2. In addition, results are independent from the ion optical parameters of the beam (FWHM and divergence) since the results remained the same even when the divergence values of Table 3.3 were increased to larger values up to 20 mrad. The performance of the alignment procedure as a function of the rotational misalignment of the sensors were computed for 150 MeV protons and 300 MeV/u 12 C ions with the setup geometry Geo2. The translations dx and dy were set as the misalignment scenario Mis3 (Table 3.6), and the rotational parameter was varied from 0.5 • up to 10 • compared to the rst sensor. Figure 4.2 depicts the deviations of the translations as a function of the rotational misalignment for 150 MeV protons. For dφ larger than 3 • , the deviations of the translations increase signicantly. The same test was performed for 300 MeV/u 12 C ions and very similar results were obtained. The large deviations of the calculated alignment parameters for dφ > 3 • can be explained by the inaccurate approximation of cos(φ) ≈ 1. However, in practice, the alignment accuracy of ± 3 • for a stable mechanical setup is easily feasible.

Experimental results

To evaluate the performance of the alignment procedure for experimental data, the residuals of the reconstructed tracks were computed, and used as a control of the procedure success. As presented in Table 3.1, the angular distribution from the multiple Coulomb scattering for a set of six sensors is small for therapeutic ion beams. However, the track resolution depends on the setup geometry, inuenced by the distance of the air gaps between the sensors. For particle energies presented in Table 3.1, the track resolution, for a set of six Mimosa-28 placed along the beam axis with air gaps < 3 cm, is better than 10 µm.

When increasing the air gaps, the track resolution becomes worse. Since the procedure developed in this work is based on the clustering, the inuence from the air gaps between the sensors is negligible. Setup geometries with small air gaps (compact geometry) and bigger ones (spread geometry) are presented. The alignment procedure was tested on experimental data, obtained with the setups described in section 3.2. To show the eect of the procedure, the tracking was computed before and after the alignment. The residuals in x and y for 220.51 MeV/u 4 He ions are shown for all sensors in Figure 4.3. The residual distributions prove the success of the alignment procedure. A track resolution of 5.0 µm in x and y, for the presented experimental data, is obtained from the width of the residual distributions (as explained in section 3.1.1.3). Since the accuracy of the alignment procedure is independent from the setup geometry, it is important to verify the robustness of the algorithm for dierent congurations. Each setup geometry was tested with several particle energies: on the one hand proton beams were used with a spread geometry, and on the other hand helium ion beams were used with a compact geometry. The average value of the alignment parameters were computed with the alignment procedure developed in this work (ClusAlign), and compared to the results obtained with the alignment procedure originally implemented in Qapivi (TrackAlign). The procedure was also benchmarked against the state-of-the-art algorithm

Millepede II, used in stand-alone where the input parameters were given after tting the same selection of data used for ClusAlign. In Table 4.2, the average value of the alignment parameter results calculated with the dierent alignment procedures are listed.

Response of Mimosa-28

In this section, the response of the Mimosa-28 sensor, for dierent charged particles and energies, was investigated with respect to the cluster size, which is determined from the number of pixels red by the same particle. The response of two sensor generations of Mimosa-28, mentioned in section 2.2.2, were studied. As explained in section 3.3.1, the experimental setup consisted of six sensors placed along the beam axis, including two sensor generations, without any target for 220.51 MeV/u 4 He ions. Figure 4.5 shows the cluster size distributions for both sensor generations. Cluster size distributions for sensors of Generation 1 (sensor 4 and 6) and Generation 2 (sensor 1 and 3) are shown in the left and right panels, respectively. The distributions from the rst sensor generation describe a double structure where two main cluster sizes are visible, while a single peak is formed for the second sensor generation. It is also important to note that sensor 4 and sensor 6 have dierent distributions even though they belong to the same generation. From one sensor to another, the deposited energy is slightly dierent due to the energy loss in the 50 µm thickness of Mimosa-28 and the air gaps in-between the sensors. However, the impact on the cluster size distribution in negligible for the particle energies used during this experiment. Moreover, the cluster distributions from the second generation (sensor 1 and 3) are in agreement, which conrms the small impact of the energy losses at these energies. The modications performed on the second generation, concerning the noise repartition over the sensor area, manifest a signicant improvement of the response homogeneity of Mimosa-28. Even though this sensor has a low energy resolution due to its binary output, this enhancement contributes to a better cluster denition with respect to the energy loss in the sensor.

Cluster size contributions

As explained in section 2.1.2, the electrons, created by ionizations in the epitaxial layer of the Mimosa-28 sensor, thermally diuse until they are collected by the diode of a pixel.

Since the depleted region of this detector is small, the diusion factor of the produced electrons plays an important role. Therefore, the cluster size depends on the energy deposited by the particle inside the sensitive volume. Additionally to the energy loss, the spatial energy distribution of the particle also contributes to the cluster size. As explained in section 1.4.1, the track structure depends on the particle species and its energy. Even though the particle track has a radial dose distribution smaller than the pixel pitch of 20.7 µm, the response of the detector is a convolution between the track structure, and the diusion of the created electrons. In Figure 4.6, the cluster size is displayed, for all measurements performed at dierent accelerator facilities, for Mimosa-28 Generation 2, as a function of the deposited energy, following the analysis method described in section 3.3.2.

The asymmetric errors of the deposited energy are due to the non-linearity of the energy loss per path length as a function of the primary kinetic energy of the particle (section 1.3.2). The last measurement point shows a larger error than the other measurements since the sensor was positioned close to the Bragg peak region of the primary beam. The empirical model, used to t the data collected with Mimosa-18 by Spririti et al.

(2017) [START_REF] Spiriti | CMOS active pixel sensors response to low energy light ions[END_REF], can not reproduce the trend of the experimental data from this work, properly. For a deposited energy < 1 MeV in 14 µm silicon layer, the model can be used to estimate the cluster size as a function of the energy loss. However, for a higher deposited energy, signicant discrepancies are observed between the model and the experimental data.

In Figure 4.6, the model from Spiriti et al. was extended by a linear term, and thus ts better the number of pixels per cluster n p for a deposited energy ∆E as: In Figure 4.7, radial dose distributions of dierent ion beams crossing a silicon volume equivalent to the one of Mimosa-28 sensor, are displayed. The radial dose distributions were computed with the Monte Carlo code Trax [START_REF] Krämer | Calculations of heavy-ion track structure[END_REF] for several ion species and energies, similar to the ones used in the experimental measurements. This study shows that the cluster size depends on the deposited energy of the primary particle. The results in Figure 4.6, do not show a dependence on the ion species. For instance, the high energy 56 Fe ions and the low energy 12 C ions with a similar energy loss in the sensor of around 4 MeV have a comparable cluster size, even though the radial dose distribution depends on the particle species (Figure 4.7). Other experiments could be performed in the future, to fully characterize Mimosa-28, such as a threshold scan, and the study of the cluster size for other ion species and energies. The results from this work can be used for a better understanding of such a sensor. The FOOT experiment uses Mimosa-28 as vertex detectors, and the simulation of the sensor is based on the experimental data presented in Figure 4.6. In addition, a future analog sensor based on Mimosa-28 is intended to be produced within the STRONG project.

n p =

Response to dierent fragments

In this analysis, the mean cluster size was computed, following the method described in section 3.3.2. In Figure 4.8, the mean cluster size distribution, obtained with the tracker vttrack consisting of three Mimosa-28 sensors placed behind a water phantom of 4 cm thickness for 287.50 MeV/u carbon ions, is depicted. The same analysis was performed with the tracker bmtrack, placed in front of the water phantom. In Figure 4.9, the 2D histogram denes the mean cluster size of vttrack as a function of the mean cluster size of bmtrack, for 287.50 MeV/u carbon ions. From this analysis, it is possible to evaluate the correlation between the tracks in front and behind the target, similar to a ∆E∆E telescope. Figures 4.8 and 4.9 illustrate the response of Mimosa-28 to a complex eld composed of primary ions and the dierent emitted frag-ments. The particle identication can not be performed precisely due to the low energy resolution of such sensor. However, the pronounced peak delivers reliable information to separate primary ions and lighter fragments. This study revealed the dependence of the cluster size as a function of the energy loss in the Mimosa-28 sensor. Even though the energy resolution of this sensor is low, the cluster size can be used as an information to separate the primary ions from the lighter fragments, and hence, improve the tracking. This is useful, especially, for larger and more complex multi detector experimental setups like FOOT [START_REF] Valle | FOOT: a new experiment to measure nuclear fragmentation at intermediate energies[END_REF].

Lateral beam spread along the longitudinal axis

In this section, the lateral beam spread was investigated for dierent proton beams at several therapeutic energies. The beam proles, measured with a set of Mimosa-28 sensors, are presented and compared to the predictions of the transport code Scattman [START_REF] Schardt | Heavy-ion tumor therapy: Physical and radiobiological benets[END_REF][START_REF] Weber | Volumenkonforme Bestrahlung mit Kohlensto-Ionen zur Vorbereitung einer Strahlentherapie[END_REF].

Beam proles from Mimosa-28 sensors

The beam proles were measured along the beam axis with the experimental setup described in Figure 3.2 (top panel). The proles have a width of around 5 and 2.7 mm for 125.3 and 219.8 MeV protons, respectively. The larger width at lower energy is due to the increase of the angular distribution that can be estimated by the Highland formula (equation 1.4). The Gaussian t can reproduce the measured data, but could be improved by its convolution with more complex functions to better t the prole tails. Several studies were performed with a description of dierent parametrization models [START_REF] Parodi | The inuence of lateral beam prole modications in scanned proton and carbon ion therapy: a Monte Carlo study[END_REF][START_REF] Bellinzona | On the parametrization of lateral dose proles in proton radiation therapy[END_REF]. However, a simple Gaussian t was used in this work since the prole tails were not well measured due to the size of the sensor.

Particle transport

The particle transport code Scattman, described in section 3.4.2, was compared to the measured data obtained with the experimental setup described in Figure 3.2 (top panel).

The beam proles, measured with the Mimosa-28 sensors at dierent positions along the beam axis, were projected in x and y and tted with a Gaussian function, as shown in Figure 4.10. In Figure 4.11, the beam widths σ x and σ y , obtained from the Gaussian t of each sensor prole, are displayed as a function of the distance from the exit window, for 125.3, 188.8 and 219.8 MeV proton beams. In the same gure, the lateral beam spread along the longitudinal axis, which was determined from Scattman, is shown. The initial ion optical parameters obtained from the t optimization for the corresponding proton beams are listed in Table 4.4. The initial ion optical parameters obtained from Scattman vary in x and y for each particle beam. With the presented method, the beam width along the z-axis was determined with only six measured points. However, the robustness of the results could be improved in case that the beam prole would be measured with more spread distances along the z-axis, especially with measurement points closer to the exit window. In particle therapy, the beam width should be well known at the isocenter in the therapy room, due to the regular QA. In Table 4.5, the beam widths σ x and σ y obtained in this work were computed at isocenter position (120 cm from the exit window), and compared to the ones obtained one year earlier by [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF] [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF]. The latter used the Lynx detector [START_REF] Russo | Dosimetric characterization of a commercial 2-D scintillation detector for quality assurance tests in scanned proton and carbon ion beams[END_REF], which couples a scintillating screen with a charge couple device. 4.5: Beam widths in x and y obtained from the measurements performed in this work with Mimosa-28 sensors for dierent energies proton beams at isocenter position.

The measurements by [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF] [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF] are also listed for the same z-position.

Energy (MeV)

σ x (mm) σ x (mm) [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF] σ y (mm) σ y (mm) [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF] 90 The values in Table 4.5 show deviations between the measured beam widths with Mimosa-28 and the ones in [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF]. These deviations can be explained by the fact that the measurements were performed in the experimental room in the Trento Therapy Center, which means that the regular QA is not performed as for a patient treatment room. This can lead to deviations on the beam proles from one day to another. In addition, the beam widths measured in this work are systematically larger than the ones from [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF]. This could also be explained by the additional multiple Coulomb scattering caused by the sensors placed in front of the isocenter position while for the work in [START_REF] Tommasino | Proton beam characterization in the experimental room of the Trento Proton Therapy facility[END_REF], the detector was placed only at the isocenter position.

Fluence perturbation due to ducial markers

In this work, the results of the uence perturbations due to ducial markers are presented.

In the rst part, the edge-scattering eects are described with a proof-of-concept of the new measurement method, using a tracker system of six CMOS pixel sensors. In the second part, the uence perturbation results from inhomogeneous scattering due to ducial markers are reported, and are published in [START_REF] Reidel | Fluence perturbation from ducial markers due to edge-scattering measured with pixel sensors for 12 C ion beams[END_REF]. The measurements aimed to quantify the uence perturbation caused by these markers used in particle therapy, detailed in section 1.6.

Edge-scattering eects

As explained in section 1.3.5, a particle beam passing through a target with sharp edges and strong density gradients suers inhomogeneous scattering, creating uence perturbations. In this section, the results from the experiment described in section 3.6.1 are presented.

Beam proles of Mimosa-28 sensors

The 2D cluster maps were computed following the method described in section 3.6.4 for the bone and the gold hammer targets, described in Table 3.8. The cluster map and its projection in x, from the rst sensor placed behind the target of the experimental setup (Figure 3.4), are displayed in Figures 4.12 and 4.13 for the bone and the hammer targets, respectively. In both cases, the uence perturbations can be observed for a proton beam impinging on the target edge. For the bone target, one overshoot and one undershoot are produced from the round edge of the target placed around zero along the x-axis. In the case of the hammer target, the beam covered the full target area, and several perturbations were induced by the dierent edges of the triangular shaped target. These proles in Figures 4.12 and 4.13 illustrate the uence perturbations at the rst sensor position placed behind the target along the z-axis.

Fluence distribution

The reconstructed uence maps were computed by following the analysis method assessed in section 3.6.4, based on all single reconstructed tracks. The uence maps are presented in The propagation of the perturbation due to edge-scattering can be evaluated with uence maps presented in Figures 4.14 and 4.15. Even though the thickness of the gold hammer is much smaller than the one of the bone target (see Table 3.8), the perturbations from both targets are similar along the beam axis. The strength of the perturbation can be correlated to the angular deection, estimated by the Highland approximation (equation 1.4). Since the density of gold is around 10 times bigger than the one of cortical bone, the created perturbation of gold is much larger than from lighter materials for a given thickness. The presented method is able to determine the propagation of the perturbation induced from edge-scattering eects. Both targets, evaluated above, produced a signicant eect on the uence since their dimensions and materials are relatively large.

Fiducial markers

The ducial markers studied in this work are in use for image guidance in case of interfractional motions of the tumor during particle therapy. The markers need to follow several criteria: good visibility on X-ray projections or on CBCT images, low artifact production on the treatment planning CT, and low dose perturbations during the treatment. The latter criteria was evaluated with carbon ion beams of dierent energies for dierent small ducial markers (e.g., 0.280 mm diameter for the gold Anchor) that were designed to produce low dose perturbations. The new measurement concept using six high resolution pixel sensors was applied to detect these small perturbations, and then compute a 3D image of the uence reconstructed from all single tracks. With this method, the maximum perturbation from four dierent ducial markers (Table 3.9) was evaluated for three energies of 12 C ion beams (Table 3.10).

Beam proles: Mimosa-28 vs. radiochromic lms

The beam proles measured with Mimosa-28 and the radiochromic lms were rst compared without any perturbation. For this, the analysis method explained in section 3.6.3.3 was followed, and the beam proles in x and y were computed at dierent positions along the z-axis. In Figure 4.16, the beam proles in x and y are presented in front of the PE block, behind the PE block and behind the water aquarium from the CMOS measurements (S1b, S2b and S3a), superimposed with the lm measurements (F1, F2 and F3), respectively (experimental setups in Figures 3.5 and 3.6). The mean value and RMS of each prole were computed after integration over a range of -8000 to +8000 µm, and are listed in Table 4.6. The resulting beam prole parameters, measured without any perturbation, of the radiochromic lms and the Mimosa-28 sensors are in agreement. The mean value and RMS dierences, in x and y, of the two experiments are smaller than 50 and 150 µm, respectively. The deviations between the two measurement methods can be explained by the dierent detector resolutions, and by the few months in-between the two measurements. Since the radiochromic lms are used to measure the deposited dose, while Mimosa-28 sensors deliver a uence information, the output from the two detectors diers.

Even though the beam proles measured with the pixel sensors were adjusted by applying a weighting factor, as explained in section 3.6.3.3, the correction is not precise since the energy resolution of the sensors is low. As observed in Figure 4.16, the deviation increases behind the PE block and the water aquarium. The production of lighter fragments increases through these layers, and the resulting eld becomes more complex, which also enlarges the deviation between the two measurement methods. In addition, the produced light fragments, such as protons, are emitted at larger angles than the heavier ones and deposit less energy. Therefore, the tail of the beam proles from the lm measurements is smaller than the one from the CMOS sensors before applying a correction factor. With the latter measurement concept, the deposited energy from the particles passing through the detectors and their charge can be correlated to the cluster size, as studied in section 4.2.1.2. Due to the digital output of the Mimosa-28 [START_REF] Spiriti | CMOS active pixel sensors response to low energy light ions[END_REF], it is not possible to separate the dierent produced fragments clearly.

However, the primary 12 C ions could be distinguished from the lighter fragments due to its well dened cluster size.

In the second part, the beam proles from the Mimosa-28 were benchmarked against the radiochromic lm measurements when the particle beam suers perturbations due to ducial markers. The analysis method described in section 3.6.3.3 was followed again, where the length of the integrated area along the y-axis was 8 mm for the Gold Anchor #1 and the Visicoil markers, and 2.5 mm for the Gold Anchor #2 and the carbon-coated ZrO 2 markers. The selected area for the data analysis was identical for both experiments. Since the perturbation is determined compared to the beam proles without any perturbation, the latter proles were also analyzed by selecting the same area. In Figure 4.17, the beam proles from the sensor S3a and the lm F3 with the Gold Anchor #1 are presented. The observed perturbation induced by this marker shows a cold spot of 2.4% from the Mimosa-28 sensor and 2.5% from the radiochromic lm, for measurements performed with 294.97 MeV/u 12 C ions. The results obtained from both measurement techniques are in good agreement with and without a ducial marker placed inside the water aquarium. Therefore, the new measurement concept with the use of high resolution tracker for the determination of uence perturbations induced by ducial markers is validated.

-

Fluence perturbation from Mimosa-28 sensor measurements

Since the uence perturbation from the ducial markers is induced by multiple Coulomb scattering, the perturbation varies along the beam axis. A maximum cold spot is present at a certain position z, which is dicult to precisely predict before the analysis of the experimental data. In this section, the results of the maximum perturbation due to the ducial markers are computed from the uence map of all reconstructed tracks, as explained in section 3.6.4. The uence maps were integrated over a determined area as for the analysis in section 4.4.2.1. To determine the maximum cold spot, the beam prole with the marker was compared to the beam prole without marker for the same integrated area at the same position along the beam axis. In Figures 4.18,4.19 and 4.20, the uence maps and the corresponding beam proles for the maximum induced cold spots are shown for the Gold Anchor #1, the Visicoil and the carbon-coated ZrO 2 ducial markers, for every carbon ion beam listed in Table 3.10. The zero positions in x and z are the coordinates of the ducial marker position. A summary of the maximum cold spot values from the ducial markers and their corresponding position along the beam axis are listed in Table 4.7. The uncertainties on the maximum cold spot values were calculated as the quadratic sum of the uncertainty on the beam proles, with and without marker. The relative uncertainty on a single beam prole was calculated as a function of the integrated entries at the position x, where the maximum cold spot was determined. The uncertainty on the position z, where the maximum cold spot is present, was considered as 3 mm, comprising the uncertainty of the sensor positioning and the uncertainty on the reconstructed track. The left panels show the uence maps reconstructed from all tracks, and the right panels show their corresponding prole at the position z, where the perturbation is maximum for 278.84 (top panels), 294.97 (middle panels) and 310.61 MeV/u (bottom panels) carbon ion beams from the experimental measurements. The black vertical dash-dotted line on the uence map represents the corresponding position along the beam axis where the cold spot is maximum. In the right panels, the red line shows the prole at this position when the marker is placed inside the water aquarium, while the blue line shows the prole when there is no perturbation for the same position z. In the same panels, the vertical dotted line indicates the position in x of the maximum perturbation, while the dotted horizontal lines quantify the cold spot from the proles with and without perturbation at this position. The integration range in y-direction was varied to benchmark the robustness of the chosen window. The results obtained with the dierent integration ranges showed a good agreement. The values from Table 4.7 demonstrate that the maximum cold spots and their position in z vary as a function of the marker type, and the primary beam energy. The smaller the energy is, the stronger is the eect induced by the marker on the particle beam. Fiducial markers with high density and high atomic number create stronger and larger cold spots.

In this work, the Gold Anchor #2, described in Table 3.9, was also analyzed. In Figure 4.21, the uence map and the beam prole at the maximum cold spot position is shown for 310.61 MeV/u carbon ions. The cold spot created by the Gold Anchor #2 is observed to be about 4.4%. However, the precise quantication of the cold spot induced by this ducial marker was not possible, due to a lack of statistics and its more complex shape. The integrated area selected for this folded marker was relatively small compared to the Gold Anchor #1. The previous results show that the new measurement concept for evaluating uence perturbations due to ducial markers could be successfully applied to evaluate the resulting cold spots. The hot spots were not reported in this work even though they can also be identied. In general, a slight overdosage in a small part of the target volume is considered much less critical than a local underdosage that can potentially cause a recurrence of the tumor. A good rule of thumb is that the magnitude of the two hot spots is roughly 50% of the enclosed cold spot, as observed in Figures 4.184.20. However, this also depends on the orientation of the marker compared to the primary beam. It is important to note that, for all measurements, the beam prole was integrated, and the total area of the proles with and without markers was found to be the same. The cold spot increases with the density and the atomic number of the marker material. The maximum cold spot created along the beam axis and its position dier for all markers since it depends on several factors such as the density, the orientation and the thickness of the marker. The beam energy also inuences the perturbation since multiple Coulomb scattering depends on the projectile energy. All markers were measured in vertical position and the Gold Anchor was also measured when folded. This study shows that the Viscoil marker, which has a diameter of 0.5 mm, induces a stronger uence perturbation than the Gold Anchor #1 of 0.28 mm diameter. The carbon-coated ZrO 2 is thicker, but induces less perturbation since it is less dense. The maximum cold spots, measured in this work for a 278.84 MeV/u carbon ion beam, were about 6.6 and 9.2% for the Gold Anchor #1 and the Viscoil, and their position downstream of the ducial marker were 13 and 15 mm, respectively. For the carbon-coated ZrO 2 marker, the perturbation was found to be < 3% for all energies. Therefore, it could be a good candidate for image guidance during carbon ion therapy treatments. However, since it has a lower density than gold markers, it can be dicult to see it on X-ray projections. For instance, at HIT in Germany, the Gold Anchor is used for proton therapy treatments of prostate cancer. In contrast to the gold markers, the carbon-coated ZrO 2 marker is not visible on the daily X-ray imaging at HIT. The measurements presented in this work were performed with a setup where the pixel sensors were placed in a short distance behind the water aquarium (see Figure 3.5). In general, the distance of the cold spot is larger for markers that induce smaller scattering angles, and the magnitude is then smaller. Therefore, the maximum cold spots for the ZrO 2 marker appear behind the water aquarium (compare Table 4.7 and Figure 3.5). The water equivalent path length of the sensors and the air gaps in-between were estimated to be < 1 mm in total, which has little inuence on the results. If the air gap in front of the sensor would be replaced by water, the magnitude of the cold spot would be slightly but not signicantly suppressed, and its distance from the marker would also decrease slightly. For the Gold Anchor and the Visicoil markers, the positions of the cold spots were found to be inside the water aquarium, and therefore, would not be dierent if the water aquarium would be larger. The cold spots, evaluated with radiochromic lms in previous studies for protons [START_REF] Cheung | Dose perturbations and image artifacts caused by carbon-coated ceramic and stainless steel ducials used in proton therapy for prostate cancer[END_REF][START_REF] Huang | Investigation of dose perturbations and the radiographic visibility of potential ducials for proton radiation therapy of the prostate[END_REF], were bigger than the ones found in this work. This was expected since the multiple Coulomb scattering of protons is stronger than for 12 C ions. In addition, the gold markers investigated by [START_REF] Cheung | Dose perturbations and image artifacts caused by carbon-coated ceramic and stainless steel ducials used in proton therapy for prostate cancer[END_REF] [START_REF] Cheung | Dose perturbations and image artifacts caused by carbon-coated ceramic and stainless steel ducials used in proton therapy for prostate cancer[END_REF] had a diameter of 0.8 mm, which is bigger compared to the ones studied in this work, with a maximum diameter of 0.5 mm.

For the lm measurements, the beam intensities are generally in the order of 10 7 10 8 particles/s, which means that after some seconds, a measurement is done. In the case of the Mimosa-28 sensors, the beam intensity needs to be decreased to 10 3 10 4 particles/s to avoid pile-up in the detectors, leading to longer measurement times. Each measurement took about 1 hour, and the low particle rates can lead in some cases to a lack of statistics. For instance, precisely quantifying the cold spot of the Gold Anchor #2, which has a complex geometry and a smaller integrated area, was dicult within the measurement time. However, as shown in Figure 4.21, the structure of this ducial marker creates several cold spots. As investigated in this work, the perturbation is more important for lower energy beams since the scattering is stronger. The absorbed dose is proportional to the uence and the LET. The latter varies along the particle path and is higher for low energies. This implies that the dose perturbation is stronger if the created cold spot appears to be in the Bragg peak region. For heavy ions (e.g., carbon ions), fragments of lower Z than the primary beam are produced, forming a fragmentation tail behind the Bragg peak. These fragments are also scattered by the markers, and contribute to the dose perturbation. However, they do not have a major impact compared to the primary ions. The perturbations in this work were measured with markers positioned in a perpendicular orientation with respect to the beam axis, and showed cold spots ranging from less than 3% up to 9%. As studied by [START_REF] Newhauser | Monte Carlo simulations of the dosimetric impact of radiopaque ducial markers for proton radiotherapy of the prostate[END_REF] [START_REF] Newhauser | Monte Carlo simulations of the dosimetric impact of radiopaque ducial markers for proton radiotherapy of the prostate[END_REF], the orientation of the marker has an impact on the dose perturbation. The magnitude of the perturbation is stronger for a parallel orientation of the marker with respect to the beam axis, resulting in a larger thickness of the scattering material. On the other hand, the volume of the perturbation becomes smaller. Within the available beam time of the presented measurement campaign, the work was focused more likely where the markers are not parallel to the beam. In a future work, the eect of dierent marker orientations could also be examined with the presented setup. From a clinical point of view, perturbations should be considered if the markers, used for image guidance, have a high atomic number and a diameter > 0.5 mm. However, for a clear statement about the clinical impact, it is necessary to include all parameters contributing to the dose perturbations. They depend on the type of markers used, their position inside the tumor, the type of particle and its energy, as well as the irradiation elds used for the patient treatment. In addition, it is very dicult to assess the clinical impact of the dose perturbations that also depends on complicated tissue eects, and is highly patient specic. However, there is a potential risk from the cold spots for a locale recurrence of the tumor. Therefore, it was one goal of this work to quantify and compare the eect on the dose for dierent markers in a sense that there is less or more risk. It is also important to note that the perturbations measured in this work are due to an edge-scattering eect from the markers, and not to a range shift from dierent stopping powers. The hot spots were not investigated in this study, but could be measured as well as their position in order to verify that they are not produced inside healthy tissues, such as organs at risk. In a future work, the setup could be improved where the sensors would be placed inside the water aquarium, and using a scanned beam to have a homogeneous eld instead of a Gaussian beam spot.

Conclusions & Outlook

The aim of this PhD thesis was to optimize and test measurement methods for ion-beam therapy applications, using CMOS pixel sensors. For this, Mimosa-28 sensors, which are high spatial resolution pixel detectors, were implemented in a series of several setups and experiments at dierent accelerator facilities.

In order to perform high precision measurements with Mimosa-28 sensors, mechanical accuracy and robustness of the setup are necessary. In this work, the setup was mechanically improved by placing each sensor proximity board in a robust holder, designed with CATIA V5, for a precise tting. The experimental setup was also optimized by tting several electronics boards inside a 19-inch rack drawer with all cables and interconnections, ameliorating the handling of the experimental setup and reducing the setup time. For a proper stability during the experiments, the sensors were attached to an optical bench, and all cables are clamped to avoid any sensor movement due to the cable strain. The changes to the experimental setup were successfully implemented and used for all experiments, demonstrating the good mechanical properties achieved in this work, and enabling a mobile setup that can be easily transported to dierent accelerator facilities.

Additionally, the sensor alignment is a crucial step in order to reach the micrometer precision of the sensors. With such purpose, an alignment procedure was developed, in the frame of this work, to correct the mechanical misalignment of a set of sensors placed along the beam axis. The procedure is based on a global χ 2 minimization and matrix operations for all events at the same time. Its performance was evaluated with simulated and experimental data, resulting in uncertainties < 3 µm for the translations and < 0.1 • for the rotation. This alignment procedure was used for all experimental data recorded during this work, and demonstrated its low time consumption and its reliability with a proper convergence, leading to a spatial resolution better than 10 µm on the reconstructed tracks. The new alignment procedure can be used for all linear CMOS tracker with an ecient, easy-to-implement and robust algorithm.

Since the response of the Mimosa-28 sensor to dierent ion species was not fully understood, the characterization of Mimosa-28 was performed by evaluating the response of the sensor, dened as the cluster size, against dierent particle species and energies. The study of two sensor generations showed the improved results of the second generation due to electronics upgrade of the sensor, resulting in a more homogeneous noise repartition over the full sensor area. This generation was then evaluated with dierent particle species and energies, demonstrating an energy loss dependence from the cluster size. Further tests would be required to completely characterize the sensor performance, such as noise threshold scan and recording data with other ion species and energies than the ones used. The data collected in this work can be used for the FOOT experiment [START_REF] Valle | FOOT: a new experiment to measure nuclear fragmentation at intermediate energies[END_REF] that integrates several Mimosa-28 sensors, and for the STRONG project that intends to develop an analog sensor based on the characteristics of Mimosa-28. In order to exploit the Mimosa-28 sensors for characterization of beam envelope at low intensities, the proles of therapeutic particle beams were measured for dierent ion beams in several facilities. The position and width of the beam were extracted from the Gaussian t of the beam proles. By placing a set of sensors along the beam axis, the lateral beam spread along the longitudinal axis, was determined with the transport code Scattman.

With this method, the initial ion optical parameters of the beam were extracted, and the beam width at any position along the beam axis could be determined. An online tool for beam monitoring was also developed in order to obtain the beam information for experiments requiring low beam intensities. This tool was successfully used during several experiments to adjust the beam as needed, and can also be used in the future for various experiments to monitor the proles of particle beams at low intensity.

The Mimosa-28 was also successfully used for the evaluation of uence perturbations due to edge-scattering eects induced by ducial markers that were evaluated with a new measurement method, using a set of Mimosa-28 sensors. The 3D uence distributions were computed with all reconstructed tracks, and the propagation of the perturbation along the beam axis was established after calculating the 2D uence maps. The uence perturbations were then quantied for several small ducial markers, used in ion-beam therapy for patient positioning verication in case of interfractional motions of the tumor. The studied markers were composed of dierent materials and had dierent geometries. The maximum cold spots, created behind the ducial markers, were quantied as well as their longitudinal position after computing the 2D uence maps. This measurement method was validated against the standard measurement method, using radiochromic lms. The measurements showed that the uence perturbations due to edge-scattering eects can be signicantly reduced when low density and low atomic number materials are used, such as the carboncoated ZrO 2 marker instead of the gold ones. Therefore, such markers should be preferred for carbon ion treatments if the imaging method used for positioning can recognize them. With the use of a tracker system, the maximum cold spots from ducial markers could be determined without knowing their position along the beam axis in advance, which makes this measurement concept superior compared to radiochromic lms. The measurement of uence perturbations with this new method should also be done for other therapy beams, especially for light ions such as protons or helium ions since they scatter dierently compared to carbon beams. Additionally, the experimental data from this study can be useful for the benchmarking of Monte Carlo codes or other dose calculation algorithms.

In a future work, Mimosa-28 could be used to detect strong gradients edges for monitoring intrafractional motions of a tumor during ion-beam therapy. The vertex distributions can be reconstructed to verify the treatment delivery in the case of moving targets. Preliminary tests have been performed at GSI, with the detection of prompt particles, showing promising results.

Claire-Anne REIDEL Applications for CMOS pixel sensors in ion-beam therapy Résumé : En hadronthérapie, des mesures de haute précision sont essentielles pour avoir une base de données robuste et délivrer le traitement prescrit au patient. Dans ce travail, un système de trajectométrie, composé de capteurs à pixels Mimosa-28, a été utilisé pour diérentes applications cliniques. Plusieurs améliorations ont été implémentées au niveau matériel et logiciel résultant à une résolution spatiale de trace 10 µm. Les expériences ont été menées avec succès dans diérents centres médicaux et de recherche. Les prols de faisceaux ont été mesurés et la largeur du faisceau le long de l'axe a pu être calculée grâce à un code de transport basé sur la diusion. Un outil en ligne de suivi de faisceau a été développé pour avoir une information rapide de son prol. D'autre part, les perturbations de la uence dues à des marqueurs de repères pour un faisceau 12 C ont été évaluées. Après reconstruction et extrapolation de chaque trace, une distribution 3D de la uence a pu être établie et la perturbation maximale de la uence et sa position ont pu être quantiées. Les points froids mesurés varient entre moins de 3% à 9.2% pour un marqueur et une énergie de faisceau dénis.

Mots clés : Hadronthérapie, Mimosa-28, Capteur à pixels CMOS, Prol de faisceau, Marqueurs de repère Abstract: In ion-beam therapy, high precision measurements are essential for having robust basic data to deliver the prescribed treatment to the patient. In this study, Mimosa-28 pixel sensors were used as a tracker system for dierent medical applications. Several hardware and software improvements were implemented leading to a spatial track resolution 10 µm. The experiments were conducted with success in dierent medical and research facilities. In this work, beam proles were measured along the beam axis and the width of the beam along the axis could be calculated with a transportation code based on multiple Coulomb scattering. Moreover, an online beam monitoring was developed in order to have fast information about the beam prole. In another study, the uence perturbation of 12 C ion beams due to small ducial markers was investigated. After reconstruction and extrapolation of single track, a 3D uence distribution could be performed and the maximum perturbation and its position along the beam axis could be quantied. In this work, the measured cold spot varied between less than 3% up to 9.2% for a dened marker and a dened primary energy beam.

Keywords: Ion-beam therapy, Mimosa-28, CMOS pixel sensor, Beam prole, Fiducial marker

List of Tables 1 . 1 4 . 7

 1147 Parameters used in the Bethe-Bloch formula. . . . . . . . . . . . . . . . . . 3.1 Accumulated angular distribution due to multiple Coulomb scattering, calculated with the Highland approximation, for a set of six Mimosa-28 sensors. 3.2 Energy and FWHM of the proton and helium ion beams dedicated to the alignment runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Particle, energy and ion optical beam parameters, used for the Monte Carlo simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Sensor positions along the beam axis for a compact geometry and a spread geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Misalignment scenarios for a set of six sensors with small misalignment values and larger ones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Translational and rotational misalignment scenario for a set of six sensors. . 3.7 Particle species and beam energies used for the cluster size study of Mimosa-28 sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Characteristics of the targets used for the edge-scattering experiment. . . . 3.9 Characteristics of the ducial markers used for the uence perturbation measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 Characteristics of the carbon ion beams used for the experimental measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Average deviations between the calculated alignment parameters and the set-misalignments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Average value of the alignment parameter results for dierent alignment algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Parameters used to t the experimental data in Figure 4.6. . . . . . . . . . 4.4 Ion optical parameters obtained from Scattman for dierent proton beams. 4.5 Beam widths obtained from the measurements with Mimosa-28 sensors for dierent proton beams at isocenter position. . . . . . . . . . . . . . . . . . . 4.6 Mean and RMS values of the beam proles in x and y from the Mimosa-28 sensors and the radiochromic lms. . . . . . . . . . . . . . . . . . . . . . . . vi Summary of the cold spot values where the perturbation is maximum, and its position along the z-axis for the dierent ducial markers measured with Mimosa-28 sensors for carbon ion beams. . . . . . . . . . . . . . . . . . . . 86 vii List of Figures 1.1 Depth-dose proles of photons, protons and carbon ions in water. . . . . . . 1.2 SOBP created with carbon ions in water, covering 5 cm in depth. . . . . . . 1.3 Interaction mechanisms relevant for particle therapy with the example of a 12 C projectile interacting with a 12 C target. . . . . . . . . . . . . . . . . . . 1.4 Stopping power as a function of the energy for dierent ion beams. . . . . . 1.5 CSDA range in water as a function of the energy for dierent ion beams. . . 1.6 Lateral beam width as a function of the depth for protons and carbon ions at dierent energies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Inhomogeneous scattering of a beam particle passing through strong density gradients and sharp edges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Track structure of a proton and a carbon ion at 10 MeV/u in water. . . . . 1.9 Survival curves for photons and heavy ions. RBE as a function of the LET for dierent ion beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4. 6

 6 Cluster size as a function of the deposited energy for Mimosa-28. . . . . . . 4.7 Radial dose distributions for dierent ion species and energies. . . . . . . . . 4.8 Mean cluster size distribution for a set of Mimosa-28 sensors placed behind a water phantom for 287.50 MeV/u carbon ions. . . . . . . . . . . . . . . . . 4.9 Mean cluster size distribution of vttrack as a function of bmtrack for 287.50 MeV/u carbon ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 Beam proles in x and y computed from the 2D cluster maps for 125.3 and 219.8 MeV proton beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.11 Lateral beam prole measurements of Mimosa-28 sensors and tted with Scattman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Beam prole from Mimosa-28 sensor for 150.14 MeV proton beam with the bone target placed along the beam axis. . . . . . . . . . . . . . . . . . . . . 4.13 Beam prole from Mimosa-28 sensor for 150.14 MeV proton beam with the gold hammer target placed along the beam axis. . . . . . . . . . . . . . . . . 4.14 Fluence map computed from Mimosa-28 sensor for 150.14 MeV proton beam with the bone target placed along the beam axis. . . . . . . . . . . . . 4.15 Fluence map computed from Mimosa-28 sensor for 150.14 MeV proton beam with the gold hammer target placed along the beam axis. . . . . . . . 4.16 Beam proles from Mimosa-28 sensors and EBT3 radiochromic lms irradiated with 294.97 MeV/u carbon ion beam. . . . . . . . . . . . . . . . . . . 4.17 Beam proles in x from Mimosa-28 sensor and EBT3 radiochromic lm for the Gold Anchor ducial marker. . . . . . . . . . . . . . . . . . . . . . . . . 4.18 Reconstructed uence maps and beam proles of carbon ions at three different energies through the Gold Anchor #1 marker placed at position zero in (x,z) coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1 . 1 :

 11 Figure 1.1: Depth-dose proles of 6 MV photons (black dashed line), 170 MeV protons (red line) and 325 MeV/u carbon ions (blue line) in water simulated with the Geant4 version 10.05 Monte Carlo code.For the photon curve, an energy-uence spectrum was simulated using the data set from a 6 MV Varian Linac[START_REF] Sheikh-Bagheri | Monte Carlo calculation of nine megavoltage photon beam spectra using the BEAM code[END_REF].

Figure 1 . 2 :

 12 Figure 1.2: Spread out Bragg peak (SOBP) created with carbon ions in water, covering 5 cm in depth. The pristine Bragg curves (black dashed lines) are superimposed to obtain

Figure 1 . 3 :

 13 Figure 1.3: Interaction mechanisms relevant for particle therapy with the example of a 12 C projectile interacting with a 12 C target. The elastic and inelastic Coulomb interactions are represented in panels (a) and (b), while the inelastic nuclear interaction is illustrated in panel (c). Figure inspired by [42].

Figure 1 . 4 :

 14 Figure 1.4: Stopping power as a function of the energy for protons (red line), 4 He (magenta line), 12 C (blue line), 16 O (green line) and 20 Ne (black line) ions in water. The energy loss values were calculated using Lise++ [50].

Figure 1 . 5 :

 15 Figure 1.5: CSDA range in water as a function of the energy for protons (red line), 4 He (red line), 12 C (blue line), 16 O (green line) and 20 Ne (black line) ions. The range values were calculated with Lise++ [50].

Figure 1 . 6 :

 16 Figure 1.6: Lateral beam width as a function of the depth for protons (red lines) and carbon ions (blue lines) at dierent energies (top panel) for a setup representing a clinical case (bottom panel). The initial FWHM was set to 5 mm and the position 0 mm represents the exit window position. The calculations were performed with the transport code

Figure 1 . 7 :

 17 Figure 1.7: Inhomogeneous scattering of a beam particle passing through strong density gradients and sharp edges. The uence perturbation from edge-scattering eects creates an under-and overshoot behind the target.

Figure 1 . 8 :

 18 Figure 1.8: Track structure of a proton (left panel) and a carbon ion (right panel) at 10 MeV/u in water. The red points describe the ionizations due to the primary particle while the blue points are the ionizations created by the secondary δ-electrons. The simu-

Figure 1 . 9 :

 19 PhotonsHeavy Ions

Figure 1 . 10 :

 110 Figure 1.10: Treatment plan delivering a homogeneous dose to a head and neck tumor with the use of photons (left panel) and carbon ions (right panel). The blue arrows indicate the eld orientations, with the use of seven elds in the case of photons and four elds in the case of carbon ions. The white contour lines mark the OARs with two parotids and the spinal cord. Both plans were computed with the software matRad [75]. Image courtesy of Dr. Athena Paz.

Figure 2 . 1 :

 21 Figure 2.1: Schematic cross-section of a monolithic active pixel sensor for charged particle detection. Ionization processes occur after the passage of a charged particle inside the epitaxial layer. The produced electrons diuse thermally (red dotted lines), and are collected by the N-well diode. Figure redrawn from [93].

Figure 2 . 2 :

 22 Figure 2.2: Functional block diagram of Mimosa-28 pixel sensor (left panel). Figure redrawn from [7]. Picture of Mimosa-28 pixel sensor (right panel).

Figure 2 . 2 (

 22 Figure 2.2 (left panel) represents the functional block diagram of Mimosa-28 sensor and

Figure 2 . 2 (

 22 Figure 2.2 (right panel) shows a picture of the sensor. This sensor has a total thickness of 50 µm with a high resistivity epitaxial layer (> 400 Ω•cm) of 14 µm. Each pixel integrates an amplier and a CDS, improving the SNR. Mimosa-28 is read out line by line in rolling shutter mode with column-level discrimination delivering a binary signal, and has an integration time of 186.5 µs. The output signal is then processed by zero suppression, where only signals from the red pixels are registered. The performance of Mimosa-28

Figure 2 . 3 :

 23 Figure 2.3: Schematics of the pixel architecture (left panel) and the connections of the pixel column to the discriminator (right panel) for Mimosa-28.Figure redrawn from [7].

  Figure redrawn from [7].

Figure 2 . 4 :

 24 Figure 2.4: Schematics of the discriminator architecture (top panel) and the corresponding time diagram (bottom panel) of Mimosa-28.Figure redrawn from [7].

FakeFigure 2 . 5 :

 25 Figure 2.5: Performance of Mimosa-28 as a function of the noise threshold measured at 30 • C with minimum ionizing particles. The detection eciency is shown in black, the single point resolution of the sensor is represented in red and the number of fake hits per pixel per readout frame is sketched in blue. Figure redrawn from [7].

Figure 2 . 6 :

 26 Figure 2.6: Coding of the binary data for Mimosa-28 sensor. The top panel illustrates a sequence example of red pixels from a line of one block. The middle panel describes the coding of a status, while the bottom panel describes the coding of a state.

Figure 2 . 7 :

 27 Figure 2.7: Temporal noise (left panel) and xed pattern noise (right panel) distributions obtained from the characterization of Mimosa-28. The red dotted line represents the Gaussian t of the distribution.

Figure 2 . 8 :

 28 Figure 2.8: Schematic of the data acquisition system used for operating several Mimosa-28 sensors.

Figure 2 . 10 :

 210 Figure 2.10: Photo of the pre-cabled 19-inch rack drawer for Mimosa-28 setup. In the front of the box, RJ45 feed-through connectors are xed.

Figure 2 . 11 :

 211 Figure 2.11: Photo of the Mimosa-28 setup during an experiment performed at the Marburg Ion-beam Therapy Center, where six sensors are placed along an optical bench. All cables, connected to the sensor proximity boards, are clamped to a cage made from aluminum proles.

Figure 3 . 1 (

 31 middle panel) and (right panel) illustrate a reconstructed track before and after the alignment procedure, respectively.

Figure 3 . 1 :

 31 Figure 3.1:The left panel illustrates a reconstructed track with six sensors placed along the beam axis for an optimal scenario. The middle and right panels sketch a reconstructed track before and after the alignment procedure with six sensors placed along the beam axis. The particle positions are dened by the red circles, while the track is represented by the blue line.

Figure 3 . 2 :

 32 Figure 3.2: Experimental setups dedicated to test the performance of the alignment procedure. In both cases, the setup consisted of six Mimosa-28 sensors placed along the beam axis. The top panel illustrates the setup with a spread geometry tested with protons at the Proton Therapy Center in Trento. The bottom panel sketches the setup with a compact geometry tested with helium ions at the HIT facility.

Figure 3 . 3 :

 33 Figure 3.3: Targets used for the edge-scattering experiment: hammer target (left panel) and bone target (right panel).

Figure 3 . 4 :

 34 Figure 3.4: Experimental setup dedicated for the edge-scattering experiment with six

Figure 3 . 5 :

 35 Figure 3.5: Experimental congurations used to measure the uence perturbation of several carbon ion beams due to ducial markers with six Mimosa-28 pixel sensors placed along the beam axis.

Figure 3 . 6 :

 36 Figure 3.6: Experimental setup dedicated to measure the dose perturbation due to ducial markers with EBT3 radiochromic lms.

Figure 4 . 1 :

 41 Figure 4.1: Average deviations δx (top), δy (middle) and δφ (bottom) between the calculated alignment parameters and set-misalignments, for the Monte Carlo simulations, as a function of the number of events, for 150 MeV/u protons, 4 He and 12 C ions with the scenario Geo2 Mis3. The δ-values are averaged over all sensors, and the error bars represent the range (minmax) of the δ-values.

Figure 4 . 2 :

 42 Figure 4.2: Deviation δx as a function of the rotational set-misalignments of dierent sensors for 150 MeV protons with the setup geometry Geo2.

Figure 4 . 3 :

 43 Figure 4.3: Histograms of the residuals in x (top panels) and y (bottom panels), before (left panels) and after (right panels) the alignment procedure ClusAlign for 220.51 MeV/u 4 He ions, for all sensors and all tracks (from the experimental data recorded at HIT). The red dotted line denes the Gaussian t of the residuals.

Table 4 . 2 :

 42 Average value of the alignment parameter results over six energies, in the range of 80220 MeV protons (from the experimental data recorded at the Proton Center Therapy in Trento), calculated with ClusAlign, TrackAlign and Millepede II. The standard deviation of the average value of the alignment parameters is given in parentheses. Sensor dx (µm) dy (µm) dφ (

  The alignment parameter results of ClusAlign and Millepede II are in agreement. The average values of TrackAlign, originally implemented in Qapivi, dier from the ones obtained with ClusAlign and Millepede II, with discrepancies up to 25 µm for the translations and 0.4 • for the rotation. All alignment parameter results obtained with ClusAlign showed uncertainties < 3 µm for the translations and < 0.1 • for the rotation, concerning the experimental data. As explained in section 4.1.1, the deviation of the rotational parameter increases proportionally with the z-distance. To verify the inuence of the rotational parameter on the track resolution, the rst and the last rotations were xed during the alignment procedure. As for the simulated data, the small error on the rotational parameter has no relevant inuence on the track residuals. The residuals in x and y for all sensors were computed after the alignment procedure of the dierent algorithms (ClusAlign, TrackAlign and Millepede II) with a compact setup geometry for 220.51 MeV/u 4 He ions, and are depicted in Figure 4.4. The residual distributions from ClusAlign illustrate the signicant improvement of the procedure implemented in this work compared to TrackAlign. The residuals computed after performing the alignment procedures ClusAlign and Millepede II are comparable and result in a track resolution of 5.0 µm.

Figure 4 . 4 :

 44 Figure 4.4: Histograms of the residuals in x (left panel) and y (right panel) after the alignment procedure with ClusAlign (black dots), TrackAlign (blue dots) and Millepede II (red dots) for 220.51 MeV/u 4 He ions (from the experimental data recorded at HIT), for all sensors and all tracks.

4. 2 . 1

 21 Cluster size 4.2.1.1 Generation 1 vs. Generation 2

Figure 4 . 5 :

 45 Figure 4.5: Cluster size distributions from the sensors of Generation 1 (left panel) and Generation 2 (right panel) for 220.51 MeV/u 4 He ions.

Figure 4 . 6 :

 46 Figure 4.6: Measured cluster size as a function of the deposited energy in the active silicon layer of Mimosa-28.

  u 12 C ions 10 MeV/u 12 C ions 285 MeV/u 12 C ions 216 MeV/u 40 Ar ions 994 MeV/u 56 Fe ions

Figure 4 . 7 :

 47 Figure 4.7: Radial dose distributions for 126 MeV protons (red line), 128 MeV/u 4 He ions (magenta line), 5 MeV/u 12 C ions (yellow line), 10 MeV/u 12 C ions (blue line), 285 MeV/u 12 C ions (cyan line), 216 MeV/u 40 Ar ions (green line) and 994 MeV/u 56 Fe ions (black line). These distributions were computed with the Monte Carlo code Trax [67]. Data courtesy of Dr. Daria Boscolo.

Figure 4 . 8 :

 48 Figure 4.8: Mean cluster size distribution computed with a set of three Mimosa-28 sensors placed behind a water phantom of 4 cm thickness, for 287.50 MeV/u carbon ions.

Figure 4 . 9 :

 49 Figure 4.9: 2D histogram of the mean cluster size of vttrack as a function of bmtrack from the two sets of Mimosa-28 sensors placed in front and behind a water phantom of 4 cm thickness, for 287.50 MeV/u carbon ions.

Figure 4 .Figure 4 . 10 :

 4410 Figure 4.10: Beam proles in x (middle panels) and y (bottom panels), computed from the 2D cluster maps (top panels), for 125.3 MeV (left panels) and 219.8 MeV (right panels) proton beams. The data, measured in the experimental room of the Proton Therapy Center in Trento, were obtained with sensor 1 from the experimental setup in Figure 3.2 (top panel). The red dotted line represents the Gaussian t.

Figure 4 . 11 :

 411 Figure 4.11: Lateral beam prole measurements of Mimosa-28 sensors in x and y, and tted with the transport code Scattman for 125.3 MeV (top panel), 188.8 MeV (middle panel) and 219.8 MeV (bottom panel) proton beams. The data from the Mimosa-28 sensors were recorded in the experimental room at the Proton Therapy Center in Trento.

Figure 4 . 12 :

 412 Figure 4.12: Two dimensional beam prole from Mimosa-28 sensor (left panel), and its projection in x (right panel), for 150.14 MeV proton beam from the experimental measurements performed at MIT with the bone target placed along the beam axis.

Figure 4 . 13 :

 413 Figure 4.13: Two dimensional beam prole from Mimosa-28 sensor (left panel), and its projection in x (right panel), for 150.14 MeV proton beam from the experimental measurements performed at MIT with the gold hammer target placed along the beam axis.

Figure 4 .

 4 [START_REF] Lederman | The early history of radiotherapy: 18951939[END_REF] and Figure4.15 for the bone target and the gold hammer, respectively.

Figure 4 . 14 :

 414 Figure 4.14: Reconstructed uence map for 150.14 MeV proton beam passing through the bone target placed at position zero in (x,z) coordinates. The uence map was computed from all tracks reconstructed with Mimosa-28 sensors. The vertical dotted line shows the position of the rst sensor placed behind the target.

Figure 4 . 15 :

 415 Figure 4.15: Reconstructed uence map for 150.14 MeV proton beam passing through the gold hammer target placed at position zero in (x,z) coordinates. The uence map was computed from all tracks reconstructed with Mimosa-28 sensors. The vertical dotted line shows the position of the rst sensor placed behind the target.

Figure 4 . 16 :

 416 Figure 4.16: Beam proles from Mimosa-28 sensors and EBT3 radiochromic lms irradiated with 294.97 MeV/u carbon ion beam. The left panels show the proles in x, while the right panels show the proles in y for the Mimosa-28 sensors (blue line) and EBT3radiochromic lms (red line). Results at three dierent positions were compared: in front of the PE block with sensor S1b and lm F1 (top panels), behind the PE block with sensor S2b and lm F2 (middle panels), and behind the water aquarium with sensor S3a and lm F3 (bottom panels).

Figure 4 . 17 :

 417 Figure 4.17: Experimental measurements of the beam proles in x for 294.97 MeV/u carbon ion beam taken from Mimosa-28 sensor S3a (left panel) and EBT3 radiochromic lm F3 (right panel). The perturbation induced by the Gold Anchor #1 placed inside the aquarium (red line) is compared to the system without any perturbation (dashed blue line).

Figure 4 . 18 :

 418 Figure 4.18: Reconstructed uence maps and beam proles of carbon ions at three dierent energies through the Gold Anchor #1 marker placed at position zero in (x,z) coordinates.The left panels show the uence maps reconstructed from all tracks, and the right panels show their corresponding prole at the position z, where the perturbation is maximum for 278.84 (top panels), 294.97 (middle panels) and 310.61 MeV/u (bottom panels) carbon ion beams from the experimental measurements. The black vertical dash-dotted line on the uence map represents the corresponding position along the beam axis where the cold spot is maximum. In the right panels, the red line shows the prole at this position when the marker is placed inside the water aquarium, while the blue line shows the prole when there is no perturbation for the same position z. In the same panels, the vertical dotted line indicates the position in x of the maximum perturbation, while the dotted horizontal lines quantify the cold spot from the proles with and without perturbation at this position.

Figure 4 . 19 :

 419 Figure 4.19: Reconstructed uence maps and beam proles of carbon ions at three dierent energies through the Visicoil marker placed at position zero in (x,z) coordinates. The panels description is the same as Figure 4.18.

Figure 4 . 20 :

 420 Figure 4.20: Reconstructed uence maps and beam proles of carbon ions at three different energies through the carbon-coated ZrO 2 marker placed at position zero in (x,z) coordinates. The panels description is the same as Figure 4.18.

Figure 4 . 21 :

 421 Figure 4.21: Reconstructed uence map and beam prole for 310.61 MeV/u carbon ion beam through the Gold Anchor #2 marker placed at position zero in (x,z) coordinates. The panels description is the same as Figure 4.18.

  Pixel architecture of Mimosa-28. . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Discriminator architecture of Mimosa-28. . . . . . . . . . . . . . . . . . . . 2.5 Performance of Mimosa-28 as a function of the noise threshold. . . . . . . . 2.6 Coding of the binary data for Mimosa-28. . . . . . . . . . . . . . . . . . . . 2.7 Noise distributions evaluated for Mimosa-28. . . . . . . . . . . . . . . . . . 2.8 Schematic of the DAQ system used for Mimosa-28. . . . . . . . . . . . . . . 2.9 Holder designed for Mimosa-28 sensor. . . . . . . . . . . . . . . . . . . . . . 2.10 Photo of the pre-cabled 19-inch rack drawer for Mimosa-28 sensor setup. . 2.11 Photo of an experimental setup using six Mimosa-28 sensors. . . . . . . . . Experimental setups dedicated to the alignment runs with six Mimosa-28 sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Targets used for the edge-scattering experiment. . . . . . . . . . . . . . . . . 3.4 Experimental setup dedicated for the edge-scattering experiment with six Mimosa-28 sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Experimental setup dedicated for uence perturbation measurements due to ducial markers with six Mimosa-28 sensors. . . . . . . . . . . . . . . . . . 3.6 Experimental setup dedicated for dose perturbation measurements due to ducial markers with EBT3 radiochromic lms. . . . . . . . . . . . . . . . . 4.1 Average deviations between the calculated alignment parameters and setmisalignments as a function of the number of events. . . . . . . . . . . . . .

	LIST OF FIGURES
	3.2
	viii

1.10 Treatment plan comparison for a head and neck tumor using photons and carbon ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Schematic cross-section of a monolithic active pixel sensor for charged particle detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Functional block diagram and picture of Mimosa-28. . . . . . . . . . . . . . 2.3 3.1 Reconstructed track with six sensors before and after the alignment procedure. 4.2 Deviation δx as a function of the rotational set-misalignments. . . . . . . . 4.3 Residuals in x and y before and after the alignment procedure. . . . . . . . 4.4 Residuals in x and y for dierent alignment algorithms. . . . . . . . . . . . 4.5 Cluster size distributions from the sensors of Generation 1 and Generation 2.

Table 1 .

 1 1: Variables used in the Bethe-Bloch formula.

	Symbol	Denition

  2.1.2, the sensor is divided in four groups, where the discriminator level of each group can be adjusted independently. With this purpose, the temporal and xed pattern noise, resulting from the pixels combined with the discriminators, are measured for each group. In this work, the characterization of 12 Mimosa-28 was performed at IPHC in Strasbourg. In Figure2.7, the noise distributions are shown for one group of one sensor, resulting in a temporal noise of 1.02 mV, mainly coming from the pixel behavior, and determined by the mean value of

	2.2. MIMOSA-28
	Counts (a.u.)	15000 20000 25000					Mean Std Dev Constant Mean Sigma Mean Std Dev Constant Mean Sigma Mean: Std Dev: Constant: Mean: Sigma:	1.024 0.09903 2.372e+04 1.023 0.09272 1.024 0.09903 2.372e+04 1.023 0.09272 1.024 0.09903 2.372e+04 1.023 0.09272	Counts (a.u.)	15000 20000 25000				Mean Std Dev Constant Mean Mean Std Dev Constant Mean Mean: Std Dev: Constant: Mean: Sigma Sigma Sigma:	0.05784 -0.5421 2.082e+04 0.06265 -0.05784 -0.5421 2.082e+04 0.06265 --0.05784 0.5421 2.082e+04 -0.06265 0.5224 0.5224 0.5224
		10000								10000
		5000								5000
		0	0	0.5	1	1.5	2	2.5	3	0	-4	-2	0	2	4
						Noise distribution (mV)				Threshold distribution (mV)

the noise distribution (Figure

2

.7 (a)). The xed pattern noise of 0.54 mV is dominated by the discriminator dispersion, dened by the width of the threshold distribution (Figure

2

.7 (b)). The threshold levels of all groups can be later set via a join test action group (JTAG).

Table 3 .

 3 1: Accumulated angular distribution due to multiple Coulomb scattering for a set of six Mimosa-28 sensors, for 150 and 300 MeV/u protons, 4 He and 12 C ions.

		Protons	Helium ions	Carbon ions
	Energy (MeV/u)	150	300	150	300	150	300
	σ α (mrad)	2.1	1.1	1.1	0.6	1.0	0.5

Table 3 .

 3 2: Energy and FWHM of the proton beams from the Proton Therapy Center in Trento and helium ion beams from the HIT facility.

	Protons

Table 3 .

 3 3: Particle, energy and ion optical beam parameters (FWHM and divergence) at the vacuum window, used for the Monte Carlo simulations.

		Protons	Helium ions	Carbon ions
	Energy (MeV/u)	150.0	300.0	150.0		300.0	150.0	300.0
	FWHM (mm)	7.1	7.1	7.1		5.9	5.9	4.7
	Divergence (mrad)	5.0	3.0	3.0		2.5	2.5	2.0
	Table 3.4: Sensor positions along the beam axis for a compact geometry (Geo1), and a
	spread geometry (Geo2).
		Sensor	1	2	3	4	5	6
	Position (cm)	Geo1	-1.25 -0.75 -0.25	0.25	0.75	1.25
		Geo2	-12.50 -7.50 -2.50	2.50	7.50	12.50

Table 3 .

 3 5: Two misalignment scenarios for a set of six sensors. Mis1 describes a scenario with small misalignment values, whereas Mis2 contains larger misalignment values. Rotational misalignments are set to zero in both cases.

Table 3 .

 3 6: Translational and rotational misalignment scenario Mis3, for a set of six sensors.

		Sensor	1	2	3	4	5	6
		dx (µm)	0.0	438.0	-349.0	-913.0	166.0	0.0
	Mis3	dy (µm)	0.0	-225.0	574.0	-682.0	751.0	0.0
		dφ ( • )	0.00	0.823	-0.150	-1.730	-0.340	1.228

Table 3 .

 3 7: Particle species and beam energies used for the cluster size study of Mimosa-

	28 sensor. The accelerator facilities where these measurements were conducted are also
	indicated.
	Particle	Energy (MeV/u)	Facility
	1 H 1+ ions	150.14	MIT a
		80.64	HIT b
	4 He 2+ ions	130.25	HIT b
		220.51	HIT b
		11.4	GSI c
		180	GSI c
		278.84	MIT a
	12 C 6+ ions	287.50	MIT a
		294.97	MIT a
		310.64	MIT a
	40 Ar 18+ ions	225	GSI c
	56 Fe 25+ ions	1000	GSI c

a Ion-beam Therapy Center in Marburg (Germany) b Ion-beam Therapy Center in Heidelberg (Germany) c Helmholtzzentrum für Schwerionenforschung GmbH in Darmstadt (Germany)

Table 3 . 8 :

 38 Characteristics of the targets used for the edge-scattering experiment.

	Name	Shape	Material	ρ (g/cm 3 )	Thickness (mm)
	Bone	Block (round edge)	Cortical bone	1.82	30
	Hammer	Triangle	Gold	19.3	0.5

Table 3 .

 3 9: Characteristics of the dierent ducial markers used for the uence perturbation measurements.

	Name	Manufacturer	Material	Shape	Length Diameter (mm) (mm)	Mass (mg)
	Visicoil	IBA	Gold	coil-shaped	20	0.5	24
	Gold Anchor #1	Naslund Medical AB	Gold	straight	11 b	0.28	9 c
	Gold Anchor #2	Naslund Medical AB	Gold	folded	2.5 d	0.28	14 e
	Acculoc Carbon marker Technologies Carbon Medical	ZrO 2	a	bone-shaped	3	1	5.5

a carbon-coated b nominal length: 10 mm c nominal mass: 8 mg d unfolded: 17.5 mm, nominal length: 20 mm e nominal mass: 17 mg

Table 3 .

 3 10: Beam energy, FWHM at the isocenter and range in water (calculated with Lise++) of the carbon ion beams used for the experimental measurements.

	Energy (MeV/u)	FWHM (mm)	Range in water (mm)
	278.84	5.6	150.4
	294.97	5.5	165.1
	310.61	5.4	179.9
	3.6.3.1 Mimosa-28 sensor measurements

  = 3.6 eV for silicon, and the values of r s , T s , δ, a and b are listed in Table4.3.

		2πr s ln	∆E 2πE g T s	+ δ	+ a∆E + b	,	(4.1)
			Spriti et al.		Linear term
	where E g Table 4.3: Parameters used to t the experimental data in Figure 4.6 from Spiriti et al.
	(2017) [9] and from equation 4.1.
		r s	T s		δ	a (keV -1 )	b
	Spririti et al.	3.61	4261.15		1.27		-	-
	Equation 4.1	1.39	858.61		0.45		0.02	4.81

Table 4 .

 4 4: Initial ion optical parameters obtained from Scattman for dierent proton beams illustrated in Figure 4.11, and measured at the Proton Therapy Center in Trento.

			σ 0 (mm)	σ α,0 (mrad)	k 0 (mm)
	125 MeV	x-axis y-axis	3.8 3.5	3.1 6.6	-770 -820
	189 MeV	x-axis y-axis	2.0 2.2	1.0 3.8	460 -790
	220 MeV	x-axis y-axis	1.4 1.7	1.3 3.2	67 -620

Table 4 .

 4 6: Mean and RMS values of the beam proles in x and y from the Mimosa-28 sensors and the radiochromic lms, at equal positions along the beam axis for 294.97 MeV/u carbon ion beam.

		In front of PE	Behind PE	Behind aquarium
		S1b	F1	S2b	F2	S3a	F3
	Mean in x (µm)	181.3	188.8	172.3	156.7	104.4	157.2
	RMS in x (µm)	2409	2372	2706	2674	2903	2973
	Mean in y (µm)	-61.8	28.0	1.8	39.4	-41.3	1.0
	RMS in y (µm)	2509	2551	2753	2837	2968	3090

Table 4 . 7 :

 47 Summary of the cold spot values where the perturbation is maximum, and its position along the z-axis for the dierent ducial markers measured with Mimosa-28 sensors for carbon ions at three dierent energies.

		Maximum cold spot (%)		Position in z (mm)
	Energy (MeV/u)	ZrO 2	Gold Anchor #1	Visicoil	ZrO 2	Gold Anchor #1	Visicoil
	278.84	2.8 ± 0.7	6.6 ± 0.4	9.2 ± 0.4	23 ± 3	12 ± 3	15 ± 3
	294.97	2.9 ± 0.7	4.4 ± 0.4	8.0 ± 0.4	31 ± 3	13 ± 3	17 ± 3
	310.61	2.9 ± 0.6	4.2 ± 0.4	7.2 ± 0.4	40 ± 3	15 ± 3	21 ± 3

Acknowledgments

deviations from the averaged parameters of the dierent congurations are presented in Table 4.1. It can be observed that the uncertainty of the rotational parameter increases proportionally with the sensor distance along the beam axis. This systematic can be induced by dierent parameters, such as the socalled weak mode [START_REF] Blobel | A New Method for the High-Precision Alignment of Track Detectors[END_REF][START_REF]Physics at the Terascale, Millepede II[END_REF] (e.g., torsion of the tracker) and the initial constraints. Since the rotation of the rst plane is xed, and the rotational parameter has a weak correlation with the other translational parameters, small errors can be induced on the rotational alignment parameter results with an increase proportional to the z-distance. The inuence of the rotation constraint was tested after performing the tracking for the case that the rotation of the rst plane was xed vs. the case that the rotations of the rst and last planes were xed during the alignment procedure. Even though the deviations δ on the rotational alignment parameters were smaller in the second case, the resulting residuals of the tracks were the same in both cases. In this work, only the rst rotational parameter was xed in order to correct the initial torsion of the setup. The CPU time for performing the complete alignment procedure was ∼ 50 s in single-threaded mode for 50000 events. Table 4.1: Average deviations between the calculated alignment parameters and the setmisalignments for all sensors [START_REF] Coolidge | A powerful Röntgen ray tube with a pure electron discharge[END_REF]. The deviations were averaged over six beam congurations, listed in Table 3