On particle imaging with application to particle radiotherapy

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On particle imaging with application to particle

radiotherapy

Thèse Charles-Antoine Collins-Fekete Doctorat en physique Philosophiæ doctor (Ph.D.) Québec, Canada © Charles-Antoine Collins-Fekete, 2017

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On particle imaging with application to particle

radiotherapy

Thèse

Charles-Antoine Collins-Fekete

Sous la direction de:

Luc Beaulieu, directeur de recherche Joao Seco, codirecteur de recherche

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Résumé

Le but de cette thèse est de développer les techniques et les connaissances en imagerie par par-ticules chargées pour l’application en radiothérapie par hadrons. Dans un premier temps, les techniques d’estimation de parcours sont étudiées de façon phénoménologique et subséquem-ment retrouvée depuis une approache physique théorique, pour chaque ion depuis le proton jusqu’au carbone. Les techniques prenant en compte la connaissance préalable du milieu ont aussi été étudiées pour obtenir l’estimé de parcours le plus précis pour toute particule chargée. À l’aide de cet estimé de parcours précis et rapide, nous nous sommes par la suite penchés sur le problème de la reconstruction tomographique par particules chargées. La première étape de ce processus était l’inclusion de l’algorithme d’estimation de parcours développé précédem-ment dans les techniques conventionnelles de reconstruction itérative tomographique, telle que la reconstruction algébrique itérative, par particules chargées. Nous nous sommes rapidement aperçus de la lenteur du processus de reconstruction itérative et des problèmes de convergence reliés à ce type d’optimisation. Face à ces difficultés, nous avons décidé de développer notre propre algorithme de reconstruction tomographique dont la principale différence est l’optimi-sation individuelle des projections radiographiques. L’idée principale de notre algorithme est de diviser l’objet de la reconstruction en voxels et de retrouver le pouvoir d’arrêt d’une colonne de voxels de façon à ce qu’il maximise la probabilité de l’énergie perdue des protons qui la traversent. Le parcours des protons dans chaque colonne de voxels est calculé par l’algorithme de prédiction de parcours développé au début de la thèse. De cette façon, nous optimisons la résolution spatiale des radiographies individuellement. Les nouvelles radiographies peuvent par la suite être utilisées comme données d’entrée dans un algorithme conventionnel de re-construction tomographique.

La reconstruction tomographique nécessite un grand nombre de projections et celles-ci peuvent être longues à acquérir, ce qui est problématique dans un contexte clinique où le temps de faisceau est précieux et limité. Il existe donc une exigence d’efficacité et d’optimisation de la procédure. Dans cette optique, la prochaine partie de cette thèse s’est concentrée sur l’utili-sation d’un ensemble limité de radiographies pour retrouver les paramètres de pouvoir d’arrêt dans les tissus, et ce de façon spécifique à un patient. La rationnelle de ce projet est que les radiographies peuvent être acquises rapidement, directement avant le traitement. Nous avons

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étudié la possibilité de combiner cet ensemble limité de radiographies avec l’image tomodensi-tométrique à simple énergie acquise lors du diagnostic. Une méthode permettant d’effectuer ce processus à été développée et évaluée sur différents fantômes anthropomorphiques représentant différentes sections du corps humain. Il a été prouvé qu’avec un nombre limité de radiogra-phies, acquérable rapidement avant le traitement, il est possible de retrouver le pouvoir d’arrêt massique dans les tissus spécifiques à un patient avec une grande précision (<1% d’erreur par rapport à la référence).

Pour terminer la thèse, nous avons procédé à l’application expérimentale des différents al-gorithmes développés théoriquement. En collaboration avec le DKFZ (Deutsches Krebsfor-schungszentrum, Heidelberg, Allemagne), le HIT (Heavy Ion Therapy facility, Heidelberg, Allemagne) et la collaboration proton-CT (Loma Linda University, University of California San Francisco, University of California Santa Cruz, University Baylor, États-Unis) nous avons mis en place une expérience de tomographie par particules d’hélium. Nous avons pu utiliser le synchrotron du HIT en combinaison avec le détecteur proton-CT développé par la collabora-tion éponyme pour produire et détecter à la fois en entrée et en sortie un faisceau de particules chargées traversant un médium pré-déterminé. Cette étude nous a permis d’évaluer le bruit et la précision atteignable en imagerie tomographique par particules chargées.

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Abstract

The goal of this thesis is to develop methodology and knowledge in charged particle imaging for application in hadron radiotherapy. First, the various existing algorithm to estimate the path of a charged particle crossing a medium have been studied as a function of their efficiency and accuracy. To find an optimal solution for those two constraints, a phenomenological model has been developed that predict the most likely particle path in a medium. It was subsequently grounded in a solid physical background and extended to every ion up to carbon. Furthermore, prior-knowledge techniques were introduced to obtain the highest accuracy in the path estimate prediction for any ions.

With these techniques in hand, we then approached the problem of tomographic reconstruction of charged particle radiographies. The first step of the work was to introduce the aforemen-tioned path estimate method into a conventional charged particle reconstruction algorithm such as the algebraic reconstruction technique. This process requires a large calculation time that prevents an efficient reconstruction in a clinical work-flow, and suffer from convergence problems that leave the images with a high-noise level. Thus, it was decided to develop our own tomographic reconstruction algorithm in which the main difference resided in the opti-mization of individual projections. In our algorithm, the object was discretized into voxels and the average relative stopping power through voxel columns defined from the source to the detector pixels is optimized such that it maximizes the likelihood of the proton energy loss. The length spent by individual protons in each column is calculated through the path estimate. In this way, the spatial resolution of individual radiographies is optimized. The new radiographies can then be fed into a conventional X-ray tomographic algorithm, such as FDK, for a high resolution pCT reconstruction.

The tomographic reconstruction requires a large number of projections and each can be indi-vidually long to acquire. This might cause problem into a clinical context where the beam time is costly and limited. There is a demand for efficiency in the procedure, which requires opti-mization of the algorithms. In this context, the next part of the thesis consisted on developing a method to utilize a subset of proton radiographies to retrieve stopping power parameters specific to the patient. This was done because a fewer number of radiographies can be acquired rapidly prior to the treatment. We studied the possibility of combining those subset of proton

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radiographies (usually either a single radiography or a pair) with single-energy X-ray tomo-graphic images acquired prior for diagnostic. A new algorithm was develop to combine these two types of images and evaluated against various anthropomorphic phantoms that represents three body sites, the lung, the pelvis and the head. It has been shown that with a limited number of radiographies, it is possible to retrieve stopping power specific to the patient with an RMS error to the ground truth below 1%.

The last part of the work was the experimental validation of the various algorithms developed. In collaboration with the (Deutsches Krebsforschungszentrum, Heidelberg), the HIT (Heavy Ion Therapy facility, Heidelberg) and the pCT collaboration (Loma Linda University, Univer-sity of California San Francisco, UniverUniver-sity of California Santa Cruz, UniverUniver-sity Baylor), we designed an experiment to acquire charged particle tomographic images. To do so, we used the HIT’s synchrotron to produce a collimated beam of charged particle combined with the pCT detector to detect the particle before and after having crossed a pre-determined medium. This study allowed us to evaluate the noise, the spatial resolution and the precision achievable with charged particle imaging tomography.

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List of Tables

1.1 Estimated proton range uncertainties and their related clinical sources . . . 5

1.2 Characteristics of crystal scintillators as a detection device for pCT. . . 26

2.1 Gammex RMI-467 material composition . . . 32

2.2 Catphan CTP-404 sensitometry phantom material composition . . . 34

2.3 ICRP material composition for the parametric anthropomorphic phantom . . . 34

2.4 Hounsfield Unit to material composition calibration table . . . 35

3.1 ΛOpt 0,1 Line-pair MTF10% for different entrance energy and WET . . . 56

6.1 Density and atomic composition of the Monte Carlo reference materials. . . 100

7.1 Chemical composition of the Monte Carlo reference materials . . . 119

7.2 Range difference between the MC and the optimization algorithm RSP . . . 127

8.1 Simulated and experimental proton RSP results of the Catphan CTP-404 inserts 144 8.2 Simulated and experimental helium RSP results of the Catphan CTP-404 inserts 145 A.1 I-values of elements, tissue substitutes and water, calculated using the different sources. 157 A.2 Gammex RMI 467 phantom tissue substitute materials. . . 158

A.3 RSP for the Gammex inserts calculated using the individual source formulae. . 162

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List of Figures

1.1 Effect of an heterogeneity for a proton and photon beam . . . 3

1.2 Proton range in water as a function of the entrance energy. . . 8

1.3 Nuclear elastic cross section for human body elements and aluminum. . . 12

1.4 Nuclear inelastic cross section for human body elements and aluminum. . . 13

1.5 Gammex RMI-467 phantom to produce a RSP/HU calibration curve. . . 16

1.6 Example proton radiography of an anthropomorphic head. . . 21

1.7 Schematic representation of the proton radiography system. . . 21

1.8 First proton radiography of an aluminum absorber. . . 22

2.1 Diagram of the Williams’ MLP formalism. . . 28

2.2 Schema of the most likely path χ2 _formalism. _{. . . .} ₃₀

2.3 Radiography of the home-made line pair phantoms . . . 32

2.4 Slanted Edge geometry to calculate the MTF . . . 33

2.5 Representation of the different quality assurance phantoms . . . 33

2.6 Representation of the different parametric body phantoms . . . 34

2.7 Representation of the different anthropomorphic voxel phantoms . . . 35

2.8 Schematic representation of the FDK algorithm . . . 39

2.9 Schematic representation of the oversampling method . . . 43

2.10 Example of the edge-spread function . . . 43

2.11 Example of the line-spread function . . . 44

2.12 Example of the modulation transfer function . . . 45

3.1 Schematic representation of the CSP with varying direction vector magnitude . 50 3.2 Radiographies of the line pair phantom (230 MeV protons). . . 53

3.3 Various proton path estimates compared to the MC path with RMS differences. 54 3.4 ΛOpt _{factor minimizing the RMS error as a function of the WET/WEPL ratio.} ₅₅ 3.5 Relative RMS deviation between MC path and CSP obtained with ΛOpt 0,1 or ΛN orm0,1 . 56 3.6 MTF curve evaluated for various WET computed with ΛOpt _{or Λ}N orm 0,1 . . . 57

4.1 Schema of the Bayesian formalism with two likelihoods . . . 65

4.2 Comparison between the phenomenological and theoretical prediction of Λ0/Λ1. 71 4.3 RMS deviation between the MLP and the MC paths for each ion up to carbon. 72 4.4 Maximal RMS error against the particle charge for a fixed initial energy. . . 73

4.5 Maximal RMS error against the particle charge for a fixed range. . . 74

5.1 Path reconstruction using a hull contour in the abdomen phantom. . . 86

5.2 Parametric and voxelized anthropomorphic abdomen phantom. . . 87

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5.4 Impact of radiation length vs energy loss in MLP accuracy. . . 89

5.5 RMS error as a function of depth for the various path algorithm. . . 90

6.1 Schematic view of the radiography reconstruction algorithm. . . 98

6.2 Representation of the conical beam pRad reconstruction with magnification factor 102 6.3 Single channel projection of the CIRS head WET radiography. . . 103

6.4 Mean and standard deviation proton radiography error . . . 104

6.5 Slanted Edge geometry to calculate the MTF . . . 104

6.6 MTF of the normal/improved pRad with a parallel and conical beam . . . 105

6.7 Comparison of a normal and improved pRad of the head phantom with a DRR 106 6.8 Slanted edge phantom pRad MTF for 200 and 330 MeV protons . . . 106

6.9 FDK reconstructed parallel beam pCT of the Catphan CTP528 module. . . 107

6.10 Three-dimensional MTF of the Catphan CTP-528 for an X-ray CT and a pCT 108 6.11 pCT and X-ray CT of the head phantom with normal and improved pRad . . . 108

7.1 Various path estimates (CSP, SLP and MLP) compared to the MC proton path 122 7.2 Clinical proton beam configurations for the anthropomorphic phantoms . . . . 122

7.3 Gammex RSP precision against MC for various angles. . . 124

7.4 Gammex RSP precision against MC for various energy.. . . 124

7.5 Anthropomorphic RSP precision against MC results yielded by the algorithm . 125 7.6 MC simulated Pristine peak range precision for the various RSP curves. . . 127

8.1 Exposed tracking detector device with two vertical/horizontal layers. . . 134

8.2 Different stages of the assembly of the energy detector. . . 135

8.3 Photo of the calibration phantom for energy output calibration. . . 136

8.4 Schematic representation of the calibration phantom. . . 137

8.5 Overview of the synchrotron accelerator . . . 137

8.6 Photograph of the experimental setup. . . 138

8.7 Catphan CTP-600 with the CTP-528 line pair and CTP-404 sensitometry module 139 8.8 CIRS anthropomorphic pediatric head phantom Model 715 . . . 139

8.9 Initial and improved pRad and HeRad of the CIRS head phantom . . . 140

8.10 Sharp edge experimental setup to acquire pRad/HeRad MTF . . . 141

8.11 Sharp edge profile to calculate the MTF . . . 141

8.12 MTF of the experimental HeRad and pRad using a sharp edge gradient . . . . 142

8.13 Phase II pCT scanner as implemented in the TOPAS simulation . . . 143

8.14 Reconstructed pCT of the CTP-404 and CTP-528 using a reconstruction algo-rithm . . . 143

8.15 Reconstructed HeCT of the CTP-404 and CTP-528 using the CARP algorithm 144 A.1 Calibration curves with RSP values calculated using the various formulae. . . . 159

A.2 Example plan to investigate the range impact within the Gammex phantom.. . 160

A.3 Example dose distributions for the PA and RLat lung double scattering plans. . 160

A.4 Example dose distributions for the AP and Lat prostate double scattering plans 161 A.5 Dose profile for the Bichsel, Janni and ICRU calibration curves . . . 163

A.6 Dose profiles showing the fall offs for the Schneider calibration curves. . . 164

A.7 Errors in the distal R80 of each plan for all calibration curves.. . . 165

A.8 Schneider dose profiles showing the fall offs in the patient cases, . . . 166

A.9 R80 patient errors for each calibration curves against the measurements. . . 166

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À mes frères, ma soeur et mes parents qui m’ont supporté tout au long de ce travail

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So I have just one wish for you–the good luck to be

somewhere where you are free to maintain a scientific integrity, and where you do not feel heed by a need to maintain your position in the organization, or financial support, or so on, to lose your integrity. May you have that freedom.

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Glossary

Notation Description

µ X-ray mass attenuation coefficient

c Speed of light in vacuum

β Particle velocity in unit of the speed of light

ρe Electron density

ρe

rel Ratio of medium electron density to water electron density

ρ Mass density

dE/dX Charged particle total stopping power

z Particle atomic charge

Z Medium atomic charge

A Medium atomic number

I Mean excitation energy

X0 Radiation length

E0 Empirical constant in the Highland equation

Ep Proton kinetic energy

mpc2 Proton rest mass energy

mec2 Electron rest mass energy

re Classical electron radius

0 Permittivity of the vacuum

γ Lorentz factor for relativistic particles

α Fine structure constant

C Density correction term to Bethe equation δ Shell correction term to Bethe equation

NA Avogadro Number

Φ Proton beam fluence

Kph _{Photoelectric cross section}

Kcoh _{Coherent scattering cross section}

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Acronyms

AAPM : American Association of Physicists in Medicine RSP : Relative stopping power; the ratio of a

material stopping power to the stopping power of water. OAR : Organ at risk

Geant4 : GEometry ANd Tracking V4

HU : Hounsfield Unit

MC : Monte Carlo

SECT : Single Energy Computed Tomography DECT : Dual Energy Computed Tomography CBCT : Cone-Beam Computed Tomography pCT : Proton Computed Tomography pRad : Proton Radiography

HeCT : Helium Computed Tomography HeRad : Helium Radiography

ICRU : International Commission on Radiation Units & Measurements MCS : Multiple Coulomb Scattering

MLP : Most Likely Path CSP : Cubic Spline Path SLP : Straight Line Path

RMS : Root-mean square

WET : Water equivalent thickness, i.e. the water thickness that produces the same energy loss as the material thickness, to the physical thickness WEPL : Water equivalent path length

TPS : Treatment planning system

ART : Algebraic reconstruction technique DRR : Digitally reconstructed radiography MLE : Maximum Likelihood Estimation

FDK : Feldkamp, Davis, and Kress (inventors of the eponym reconstruction algorithm) CSDA : continuous slowing down approximation

PCA : Principal Component Analysis LBL : Lawrence Berkeley Laboratory

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List of contributions

Peer reviewed journal

1. Collins-Fekete C.A.; Volz, L.; Piersimoni, P.; Bär, E.; Bouchard, H.;Beaulieu, L.; Johnson, R.P.; Schulte, R.; Seco, J., Experimental investigation of the RSP accuracy achievable through diverse particle imaging techniques, 2017 Physics in Medicine and Biology - to be submitted

2. Collins-Fekete C.A.; Bär, E.; Lalonde. A.; Bouchard, H.;Beaulieu, L.; Seco, J., Exten-sion of the Fermi-Eyges most likely path in heterogeneous medium with prior knowledge information, 2017 Physics in Medicine and Biology - to be submitted

3. Collins-Fekete C.A.; Brousmiche S.; C. Hansen D., S.; Beaulieu, L.; Seco, J., Pre-treatment patient-specific stopping-power by combining proton radiography and X-ray CT, 2017 Physics in Medicine and Biology - under review

4. Collins-Fekete C.A.; Volz, L.; K.N. Portillo, S.; Beaulieu, L.; Seco, J., A theoretical framework to predict the most likely hadron path in particle imaging, 2017 Physics in Medicine and Biology - published

5. Collins-Fekete, C.-A.; Brousmiche, S.; K.N. Portillo, S. ; Beaulieu, L.; Seco, J., A maximum likelihood method for high resolution proton radiography/proton CT, 2016, Physics in Medicine and Biology - published

6. Collins-Fekete C.-A.; Doolan, P.; Dias, M.; Beaulieu, L.; Seco, J. Developing a phe-nomenological model of the proton trajectory within a heterogeneous medium required for proton imaging, 2015, Physics in Medicine and Biology - published

7. Dias, M.; Collins-Fekete C.A.; Baroni G.; Riboldi, M.; Seco, J. Investigation of tumor edge detection using multiple Bragg peak detection in carbon therapy, 2016 Physics in Medicine and Biology - under review

8. Doolan, P.; Collins-Fekete, C.-A.; Dias, M.; Ruggieri, T.; D’Souza, D.; Seco, J., Inter-comparison of relative stopping power estimation models for proton therapy, 2016 Physics in Medicine and Biology - published

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International conferences

1. Collins-Fekete C.A.; Schulte, R.; Beaulieu, L.; Seco, J. (Science Council Sym-posium Award), TU-FG-BRB-04: A New Optimization Method for Pre-Treatment Patient-Specific Stopping-Power by Combining Proton Radiography and X-Ray CT. , American Association of Physicist in Medicine (AAPM) Annual Congress (Washington, USA, August 2016)

2. Collins-Fekete C.A.; Volz, L.; K.N. Portillo, S.; Beaulieu, L.; Seco, J. An optimization method for pre-treatment patient-specific stopping-power by combining proton radiog-raphy and X-ray CT, National Physics Laboratory, Proton Physics Research Implemen-tation Group Proton Therapy Physics Workshop (London, UK, December 2016) 3. Collins-Fekete C.A.; Schulte, R.; Beaulieu, L.; Seco, J., SU-C-207A-01: A Novel

Max-imum Likelihood Method for High-Resolution Proton Radiography/proton CT. AAPM Annual Congress (Washington, August 2016)

4. Collins-Fekete C.A.; Beaulieu, L.; Seco, J., Sci-Fri PM: Radiation Therapy, Planning, Imaging, and Special Techniques - 01: On the use of proton radiography to reduce beam range uncertainties and improve patient positioning accuracy in proton therapy. Cana-dian Organization of Medical Physicists (COMP) Annual Congress (St-John, Canada, July 2016)

5. Collins-Fekete C.A.; Brousmiche, S.; Hansen D.; Beaulieu, L.; Seco, J., SU-C-204-04: Patient Specific Proton Stopping Powers Estimation by Combining Proton Radiography and Prior-Knowledge X-Ray CT Information. AAPM Annual Congress (Anaheim, USA, July 2015)

6. Collins-Fekete C.A. Invited speaker, Berkeley, California, University of Berkeley/Lawrence Berkeley National Laboratory (San Francisco, USA, August 2016), From Fermi diffusion equation to hadron imaging : applicability to particle therapy.

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Remerciements

L’étape du doctorat a été une aventure incroyable dans ma vie. J’y ai rencontré des gens formidables et formé des amitiés solides qui dépassent les frontières et les barrières de la langue. J’ai aussi eu la chance de voyager dans plusieurs pays et de vivre dans différentes cultures, tant au niveau social qu’au niveau de la recherche. J’ai passé par toutes les étapes communes aux doctorants, du moment de désespoir en plein milieu d’une longue période aride de recherche, lorsqu’on se pose plusieurs questions sur nos choix, jusqu’au moment de jubilation lorsque nos idées développées sont mises en application et partagées dans des journaux de réputation internationale. Pour cette expérience et cette tranche de vie, j’ai beaucoup de remerciements à adresser. Je commence donc par mes deux superviseurs.

Je tiens à remercier spécialement mes superviseurs Joao Seco et Luc Beaulieu. La liberté de recherche que j’ai eu dans leurs groupes m’a permis de me développer comme individu et comme scientifique. Tout au long de mon doctorat, ils ont su me supporter dans mes idées, autant dans les louanges des bons coups que dans les critiques des mauvais. Leur impartialité m’a permis de développer un esprit critique tout en me sentant soutenu dans mes efforts. Avec les années, ils ont su me donner une autonomie grandissante, jusqu’à me confier des tâches et des responsabilités telle que la supervision d’étudiants, un geste qui témoigne de leur confiance en moi. Je ne me serais pas rendu où je suis sans leur support et sans leur aide et je tiens à les remercier en premier pour m’avoir fait confiance depuis le début de mon doctorat.

J’aimerais aussi remercier spécialement mes colocataires qui ont partagé ma vie quotidienne lorsque j’ai habité à Boston. L’ambiance de la Red House était incroyable, la stimulation scientifique constante accompagnée d’une franche camaraderie. Je n’oublierai jamais toutes les soirées passées devant le tableau (installé au milieu du salon, tenant lieu de télévision) à tenter de résoudre des problèmes de physique de tous les domaines et des intégrales impossibles. Je n’oublierai pas non plus toutes nos nuits de course à pied à travers Boston. Nous courions la nuit parce que c’était le seul moment où la température était supportable et celui que nous avions en commun. Ces courses se sont achevées dans le demi-marathon de Manchester, une expérience mémorable. À mes bon amis Stephen K.N. Portillo, Zachary Slepian et Joseph

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Holden Gibbons, je n’ai pas assez de mots pour vous remercier de m’avoir accueilli dans votre demeure comme un ami et d’avoir fait de mon temps à Boston un moment si agréable. Je tiens à remercier profondément mes amis(amies) et collègues du Cox-8 et de Nashua Street, les deux bureaux que j’ai occupé lors de mon séjour à Boston. Premièrement, je tiens à donner un mot spécial à Marta F. Dias et à Lennart Volz, mes plus proches collaborateurs avec qui j’ai passé la plus grande partie de mes soirées à plancher sur des problèmes physiques ou à descendre une pinte dans un pub adjacent, toujours en discutant physique. J’aimerais aussi remercier profondément Esther Bär, qui a été un roc pour moi dans mes moments les plus difficiles et sur qui je me suis appuyé solidement et m’appuie encore, même à distance. Elle est rapidement devenue pour moi une amie et une conseillère précieuse lorsque je prend des décisions difficiles. Je tiens aussi à ajouter un remerciement spécial à Sébastien Brousmiche, Paul Doolan, Michaela Hoesl, Gizem Cifter et tous les autres avec qui j’ai collaboré et partagé l’ardeur du travail à Boston. Ces amis, des quatre coins du monde, ont partagé mon quotidien de la recherche et notre amitié a été pour moi une bouée à travers les jours où les progrès se faisaient attendre.

Je veux aussi adresser un mot spécial à mes collègues de Québec et du CRCEO: Romain Es-pagnet, Ophélie Piron, Éric Poulin, Marie-Ève Delage, Audrey Cantin et Francois Therriault-Proulx avec qui j’ai fini ma maîtrise et commencé mon doctorat à Québec. Nous avons partagé les difficultés des études graduées et nous nous sommes supporté à travers ces épreuves, même à distance.

Je prend un moment pour remercier très sincèrement ma plus grande supportrice, mon amie de longue date, Émilie Gaudin. Au long du doctorat elle a su m’écouter, me supporter encore et encore et écouter mes histoires de recherche et mes idées farfelues jusqu’à n’être plus capable. Elle est aussi celle qui m’a ramené à la terre et m’a permis de progresser d’un pas rassuré et confiant. Ce doctorat ne serait pas le même sans elle et je tiens à lui assurer que je reconnais tout le support qu’elle m’a offert. Merci du plus profond de mon cœur.

Bien entendu, je ne pourrais terminer ma série de remerciements sans adresser un mot partic-ulier à ma famille qui m’a toujours soutenu et me soutient encore en tout temps et de tous les moyens possible. À chacun de mes frères, Louis-Vincent, David, Philippe et Pierre-François, à ma soeur Catherine et à mes parents Ferenc et Evelyn, je n’ai pas assez de mots pour vous remercier pour tout ce que vous m’avez apporté. Je ne pourrais oublier aussi Audrey-Noémie, Mélanie, Jessie et Sam qui font après tout partie de la famille. Je ne vous remercierai jamais assez.

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J’aimerais rajouter un remerciement aux organismes de subvention provincial et fédéral (CRSNG et FRQNT) qui ont financé mes études. Les subventions que j’ai reçu au cours de mon doctorat m’ont permis de progresser dans ma recherche et de me concentrer sur ce sujet uniquement. Ces subventions ont retiré les soucis financiers et, j’en suis convaincu, sont au cœur même des avancées présentées ici.

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Avant-propos

Les publications

Cette thèse représente le travail combiné du projet de doctorat sur l’imagerie par particule chargée. Cette section présente pour chacun des articles soumis: 1) le titre, 2) la liste d’auteur et de co-auteurs ainsi que leurs instituts reliés, 3) le journal de soumission, 4) l’état actuel de la soumission et 5) la contribution de l’auteur de cette thèse à l’article ainsi que 6) le lien reliant l’article au thème général de la thèse.

Chapitre 3: Developing a phenomenological model of the proton trajectory within a hetero-geneous medium required for proton imaging

Charles-Antoine Collins-Fekete1,2,3_{, Paul Doolan}4_{, Marta F. Dias}3−5_{, Luc Beaulieu}1,2_{, Joao}

Seco3,6,7

1_{Département de physique, de génie physique et d’optique et Centre de recherche sur le cancer,}

Université Laval, Québec, Canada

2_{Département de radio-oncologie et CRCHU de Québec, CHU de Québec, QC, Canada} 3_{Department of Radiation Oncology, Francis H. Burr Proton Therapy Center Massachusetts}

General Hospital (MGH), Boston, MA, USA

4_{Department of Medical Physics and Bioengineering, University College London, London,}

U.K.

5_{Dipartamento di Elettronica, Informazione e Bioingegneria - DEIB, Politecnico di Milano,}

Italy

6_{Deutsches Krebsforschungszentrum Heidelberg, Baden-Württemberg, DE}

7_{University of Heidelberg, Department of Physics and Astronomy Heidelberg, Baden-Württemberg,}

DE

Journal de soumission : Physics in Medicine and Biology État de la soumission : Publié

Contribution de l’auteur : J’ai développé le concept avec mes superviseurs, effectué les simulations nécessaires pour le valider, analysé les résultats et rédigé l’article. Les autres co-auteurs ont étudié l’idée originale, apporté des suggestions au concept et révisé l’article.

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Lien avec la thèse: L’article présente une méthode rapide pour estimer la trajectoire d’une particule dans un médium. La vitesse de cette méthode permet d’améliorer le temps de re-construction tomographique, la lenteur du calcul de trajectoire de particules étant une des lacunes en imagerie en proton.

Chapitre 4: A theoretical framework to predict the most likely ion path in particle imaging Charles-Antoine Collins-Fekete1,2,3_{, Lennart Volz}4,5_{, Stephen K. N. Portillo}6_{, Luc Beaulieu}1,2_,

Joao Seco3,4,5

DE

6_{Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA}

Contribution de l’auteur : J’ai développé le concept de la statistique de Bayes pour cet article avec les co-auteurs. L’extension aux particules chargées à été faite par la suite et j’en suis venu à l’idée fondamentale derrière l’article. Les autres co-auteurs ont étudié l’idée origi-nale, apporté des suggestions au concept et révisé l’article.

Lien avec la thèse: Cet article permet de rattacher à la physique fondamentale les procé-dures d’estimé de parcours qui seront utiles pour la reconstruction d’image en tomographie par particules chargées. La conclusion est que l’hélium est la particule la plus précise pour la reconstruction tomographique en particules chargées et ceci orientera la recherche future et la section expérimentale.

Chapitre 5: Extension of the Fermi-Eyges most likely path in heterogeneous medium with prior knowledge information

Charles-Antoine Collins-Fekete1,2,3,4_{, Esther Bär}5,6_{, Arthur Lalonde}5,6_{, Hugo Bouchard}5,6_{, Luc}

Beaulieu1,2_{, Joao Seco}3,4

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2_{Département de radio-oncologie et CRCHU de Québec, CHU de Québec, QC, Canada} 3_{Deutsches Krebsforschungszentrum Heidelberg, Baden-Württemberg, DE}

DE

5 _{Département de Physique, Université de Montréal, Pavillon Roger-Gaudry, 2900 Boulevard}

Édouard-Montpetit, Montréal, Québec H3T 1J4, Canada

6 _{Acoustics and Ionising Radiation Team, National Physical Laboratory, Hampton Road,}

Ted-dington,TW11 0LW, UK

Journal de soumission : Physics in Medicine and Biology État de la soumission : Soumis

Contribution de l’auteur : Cet article est à l’origine d’une nouvelle collaboration avec le groupe de recherche de Hugo Bouchard. De façon commune, nous sommes arrivés à l’idée de combiner l’expertise du groupe en imagerie photonique double énergie et notre expertise en imagerie protonique pour améliorer la précision des estimés de parcours. J’ai effectué les simulations nécessaires ainsi que la rédaction du manuscrit. Les autres co-auteurs ont étudié l’idée originale, apporté des suggestions au concept et révisé l’article.

Lien avec la thèse: Cet article finalise le travail d’amélioration de l’estimé de parcours dans le patient en étudiant l’introduction de connaissance préalables dans l’estimé et la prise en compte d’hétérogénéité. Il permettra d’effectuer les reconstructions tomographiques de la plus haute qualité.

Chapitre 6: A maximum likelihood method for high resolution proton radiography/proton CT Charles-Antoine Collins-Fekete1,2,3_{, Sébastien Brousmiche}4_{, Stephen K. N. Portillo}5_{, Luc}

Beaulieu1,2_{, Joao Seco}3,6,7

4_{Ion Beams Application - IBA, Louvain-la-Neuve, Belgique}

5_{Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA} 6_{Deutsches Krebsforschungszentrum Heidelberg, Baden-Württemberg, DE}

DE

Contribution de l’auteur : Je suis à l’origine du concept de reconstruction tomographique derrière cet article. L’idée nous est venu en discutant avec les co-auteurs. J’ai effectué les

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sim-ulations nécessaires pour valider le concept et j’ai développé l’analyse mathématique nécessaire permettant de bien présenter l’algorithme. Les autres co-auteurs ont étudié l’idée originale, apporté des suggestions au concept et révisé l’article.

Lien avec la thèse : La reconstruction tomographique par particules chargées est la pierre angulaire de ce projet de doctorat. Cet article jette les bases de l’algorithme utilisé pour faire ce processus, combiné avec les algorithmes d’estimé de parcours présentés précédemment. Chapitre 7: Pre-treatment patient-specific stopping-power by combining list-mode proton ra-diography and X-ray CT

Charles-Antoine Collins-Fekete1,2,3_{, Sébastien Brousmiche}4_{, David C. Hansen}5_{, Luc Beaulieu}1,2_,

Joao Seco3,6,7

General Hospital (MGH), Boston, Massachusetts

4_{Ion Beams Application - IBA, Louvain-la-Neuve}

5_{Department of Medical Physics, Aarhus University Hospital, Aarhus} 6_{Deutsches Krebsforschungszentrum Heidelberg, Baden-Württemberg, DE}

DE

Journal de soumission : Physics in Medicine and Biology État de la soumission : Accepté

Contribution de l’auteur: En collaboration avec les auteurs, nous avons développé le con-cept de l’article. J’ai par la suite programmé l’algorithme, simulé les données nécessaires pour valider le concept et écrit l’article. Les autres co-auteurs ont étudié l’idée originale, apporté des suggestions au concept et révisé l’article.

Lien avec la thèse : La lacune de la tomographie par particules chargées est le long temps d’acquisition ainsi que le long temps de reconstruction de l’image en trois dimensions. Cette méthode permet d’approximer rapidement, à partir de 2 projections orthogonales, le même type d’information que l’on retrouve dans l’imagerie par particules chargées.

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Foreword

Publications

This thesis represents the cumulated work done throughout the doctoral project on charged particle imaging. This section will present for each article 1) the title, 2) the list of authors with their respective institutions, 3) the journal where the manuscript has been submitted, 4) the actual state of the submission, 5) the author’s contribution to the project presented in the article and 6) the link between the article and the thesis general subject.

Chapter 3: Developing a phenomenological model of the proton trajectory within a heteroge-neous medium required for proton imaging

Charles-Antoine Collins-Fekete1,2,3_{, Paul Doolan}4_{, Marta F. Dias}3−5_{, Luc Beaulieu}1,2_{, Joao}

Seco3,6,7

4_{Department of Medical Physics and Bioengineering, University College London, London,}

U.K.

5_{Dipartamento di Elettronica, Informazione e Bioingegneria - DEIB, Politecnico di Milano,}

Italy

DE

Journal : Physics in Medicine and Biology State of the submission : Published

Author’s contribution: I developed the concept in collaboration with both my supervisors. I then performed the required simulations to validate it, analyze the results and wrote the manuscript.The other co-authors studied the original idea, came with suggestions to

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amelio-rate the project and revised the final manuscript.

Link with the doctoral thesis: The project presents a rapid and efficient method to es-timate the most likely path of a proton through a medium. The speed of this method helps greatly in reducing reconstruction times. It is a major step towards creating new reconstruc-tion algorithm as it allows for quick development and thorough testing of various methods. Chapter 4: A theoretical framework to predict the most likely ion path in particle imaging Charles-Antoine Collins-Fekete1,2,3_{, Lennart Volz}4,5_{, Stephen K. N. Portillo}6_{, Luc Beaulieu}1,2_,

Joao Seco3,4,5

DE

6_{Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA}

Author’s contribution : I developed the concept of the Bayesian statistic with the co-authors. The extension towards heavier ions was subsequently done by me and I came with the key conclusion that helium was the best particle to perform charged particle imaging. The other co-authors studied the original idea, came with suggestions to ameliorate the project and revised the final manuscript.

Link with the doctoral thesis: This article derive the path estimate of the charged particle from theoretical foundations. It will be subsequently used in the reconstruction algorithm. The conclusion that helium provides the best path estimate will help to lead future research in the field.

Chapter 5: Extension of the Fermi-Eyges most likely path in heterogeneous medium with prior knowledge information

Charles-Antoine Collins-Fekete1,2,3,4_{, Esther Bär}5,6_{, Arthur Lalonde}5,6_{, Hugo Bouchard}5,6_{, Luc}

Beaulieu1,2_{, Joao Seco}3,4

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2_{Département de radio-oncologie et CRCHU de Québec, CHU de Québec, QC, Canada} 3_{Deutsches Krebsforschungszentrum Heidelberg, Baden-Württemberg, DE}

DE

5 _{Département de Physique, Université de Montréal, Pavillon Roger-Gaudry, 2900 Boulevard}

Édouard-Montpetit, Montréal, Québec H3T 1J4, Canada

6 _{Acoustics and Ionising Radiation Team, National Physical Laboratory, Hampton Road,}

Ted-dington,TW11 0LW, UK

Journal : Physics in Medicine and Biology State of the submission : Submitted

Author’s contribution: This article was the outcome of a newly established collaboration with the research group of Hugo Bouchard. Together with his student, we joined together their expertise on DECT and our knowledge of particle imaging to come up with a new way to ameliorate path estimate. For this project, I performed the required simulation and wrote the manuscript. The other co-authors studied the original idea, came with suggestions to ameliorate the project and revised the final manuscript.

Link with the doctoral thesis: This article achieve the work done in the doctoral thesis in trying to ameliorate the charged particle path estimate when crossing a medium. To do so, we introduced prior knowledge in the developed equation which lead to better path estimate which directly improved the spatial resolution of the reconstructed images.

Chapter 6: A maximum likelihood method for high resolution proton radiography/proton CT Charles-Antoine Collins-Fekete1,2,3_{, Sébastien Brousmiche}4_{, Stephen K. N. Portillo}5_{, Luc}

Beaulieu1,2_{, Joao Seco}3,6,7

4_{Ion Beams Application - IBA, Louvain-la-Neuve, Belgique}

5_{Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA} 6_{Deutsches Krebsforschungszentrum Heidelberg, Baden-Württemberg, DE}

DE

Author’s contribution : I came with the idea of this novel tomographic reconstruction algorithm whilst discussing with the co-authors. I then performed the required simulation to

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validate the mathematics and assess the performance of the algorithm. Subsequently, I defined the mathematics to correctly represent the algorithm. The other co-authors studied the orig-inal idea, came with suggestions to ameliorate the project and revised the forig-inal manuscript. Link with the doctoral thesis : The charged particle tomographic reconstruction is the step stone of this doctoral project. This article lays the groundwork to do so, by producing a new algorithm that perform this task efficiently and with high accuracy when combined with the previously developed path estimate algorithm.

Chapter 7: Pre-treatment patient-specific stopping-power by combining list-mode proton ra-diography and X-ray CT

Charles-Antoine Collins-Fekete1,2,3_{, Sébastien Brousmiche}4_{, David C. Hansen}5_{, Luc Beaulieu}1,2_,

Joao Seco3,6,7

General Hospital (MGH), Boston, Massachusetts

4_{Ion Beams Application - IBA, Louvain-la-Neuve}

5_{Department of Medical Physics, Aarhus University Hospital, Aarhus} 6_{Deutsches Krebsforschungszentrum Heidelberg, Baden-Württemberg, DE}

DE

Journal : Physics in Medicine and Biology State of the submission : Accepted

Author’s contribution : In collaboration with all the co-authors, we developed the theory behind this manuscript. I programmed the algorithm, simulated the necessary data and vali-dated the concept. I then drafted the manuscript. The other co-authors studied the original idea, came with suggestions to ameliorate the project and revised the final manuscript. Link with the doctoral thesis : The most prominent flaw of charged particle tomog-raphy is the long acquisition and reconstruction time to acquire the stopping power maps. The method developed in this project allows to approximate quickly, from only two orthogo-nals projections, the same information. It is aimed to be used in clinics prior to the treatment.

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Chapter 1

Introduction

1.1 Proton radiotherapy treatment

1.1.1 History and clinical rationale

The first medical application of ionizing radiation happened in 1895 with the use of X-ray radiography by Röntgen [1]. X-ray radiography opened the door to many advances in medical diagnostic. Only a few months after Röntgen’s announcements, Victor Despeignes, a French physician, presented the first treatment of stomach cancer with X-rays. The results were encouraging: a week-long treatment was followed by a diminution of pain and reduction in the size of the tumour [2]. As research and case treatment progressed, the observation was made that increased dose to cancerous tissues would lead to a higher cure rate, but soon followed by normal tissue complications. Thus, subsequent research aimed to modulate the dose delivery to spare healthy tissue while maintaining prescribed dose to the target [3]. The use of computers in treatment planning, X-ray imaging such as radiography and computed tomography, and the introduction of reproducible patient positioning setups are few examples of subsequent developments that intended to fulfill this goal. In this line of ideas, the use of charged particle radiation therapy was first proposed by Wilson [4] in 1946. In his paper, he introduced the concept of utilizing the finite range of the proton beam to treat deep-seated tumors while minimizing the dose to the surrounding healthy tissues.

Although Wilson’s home institution was Harvard University, the first experiment that aimed to assess the physical and radio-biological properties of proton beams was done in 1948 at the Lawrence Berkeley Laboratory in California. Tobias, Anger, and Lawrence [5] first pub-lished their work on biological studies on mice using protons, deuterons, and helium beams. The first patient was subsequently treated in 1954. Proton radiotherapy was then introduced slowly throughout the world. Briefly, the Gustav Werner Institute in Uppsala opened first a treatment center in Sweden (1955), followed by the Harvard University Cyclotron Labo-ratory, Cambridge, USA (1959), the Institute of Theoretical and Experimental Physics in

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Moscow (1968), the National Institute of Radiological Sciences in Chiba, Japan (1979), the Paul Scherrer Institute in Switzerland (1984), the Institute of Clatterbridge, U.K. (1989), the Orsay’s Institute, France (1991), and the iThemba Laboratory for Accelerator Based Sciences in South Africa (1993). As of 2015, 154203 patients were treated with charged particle therapy. Out of those, 2054 were treated with Helium, 1100 with pions, 19376 with carbons ions, 433 with others heavier ions and the remaining 131240 patients were treated with protons (data collected by the Particle Therapy Co-Operative Group) [6].

Proton radiotherapy offers sizable advantages over conventional X-ray radiotherapy due to the physical characteristics of the proton beam, which contains a narrow dose peak (known as the Bragg peak), at a defined position along the depth dose curve. Conformal treatment is achieved by positioning the Bragg peak to hit the tumor volume, either by varying the incident proton energy or by placing range shifters along the beam line before the patient. Multiple pristine peaks are cumulated, and the total dose is adjusted by modulating both the proton beam fluence and energy to create a dose-constant region known as the spread-out Bragg peak. The procedure is shown briefly in Figure1.1. The absence of dose after the distal edge of the spread-out Bragg peak theoretically allows the proton beam to be directed toward a critical structure without irradiating it, providing a huge advantage in comparison with traditional X-ray beams. Furthermore, Paganetti et al. [7] have demonstrated that normal tissue sparing is systematically better with protons and ions. This tissue sparing seems to indicate that proton/ion therapy is a better treatment choice for deep-seated tumors and tumors close to critical structures, e.g. head-and-neck treatments. The small dose to healthy tissues also reduces the risk of developing secondary cancer [8]. In addition, pediatric patients benefits from this procedure as it could limit the radiation exposure to healthy and developing tissues [9,10].

Despite the promising potential of particle therapy in cancer treatment, initial benefits were not reached. This is mainly caused by the uncertainties introduced during the patient imaging process as well as the modelling of the particle beam out of the delivery system. These uncertainties reduced greatly the ability to deliver a precise plan within the tumour region. Large margins were necessary to account for the potential variations in beam range caused by these uncertainties. These margins were crucial to obtain a robust plan since the impact of a failed treatment on the dose to the organ at risk is more severe in particle therapy than in X-ray radiotherapy. Furthermore, the significant cost associated with building proton accelerators reduced its widespread clinical application. Nevertheless, in the past 15 years, hospitals around the world have slowly started to adopt this technology to treat cancer patients. This is mainly due to the advancements in accelerator technology that reduce the operational costs of a proton facility. Extending on the idea of proton therapy, individual centers around the world (HIMAC, HIT, CNAO, MedAustron) have proposed the use of heavier ions such as carbon ions for radiotherapy. Indeed, carbon ions provide superior physical dose distributions due to reduced

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Figure 1.1 – Range uncertainty introduce by on a depth dose curve in water with (red line) and without (black line) an unaccounted tissue heterogeneity of higher density for a proton (dashed line) and a photon beam (full line). The proton beam energy is adjusted to match the pristine peaks in a spread-out Bragg peak over the target area. Figure adapted from Levin et al [11].

lateral scattering, reduced range straggling and increased entrance-to-peak ratio. Furthermore, enhanced biological effects are expected for heavy ion treatments, including greater cell killing effectiveness and decreased radiation resistance of hypoxic cells in tumors [8, 12]. Moreover, carbon ions have a higher linear energy transfer than protons and photons. Because of this, carbon ions have been shown to be more efficient in killing oxygen-deficient tumors that are radio-resistant to protons [8]. On the other hand, carbon ions show a higher dose on the distal front of the Bragg peak due to the presence of nuclear fragments that travels a longer range than the initial carbon particle. Despite the potential physical and biological advantages of carbon ions over protons, proton facilities are usually preferred, mostly due to the operational and construction costs of heavier ion facilities. Another reason is that the sharper Bragg peak shown in carbon therapy increases the tumor sensibility to range uncertainty compared to the proton, which could cause severe over-dosage effects in the patient [13]. Unlike the distal fallout of protons at the end of the range, the depth-dose curve of carbon ions is characterized by a nuclear tail consisting of secondary particles produced by the fragmentation of carbon ions [14]. Finally, despite the theoretical advantage regarding biological and physical characteristics of carbon ions over protons, clinical evidence of the benefits is still lacking [15].

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1.1.2 Range uncertainties and related impact in clinical treatment

As mentioned above, the high sensitivity of the Bragg peak position to uncertainties encoun-tered in the planning and treatment process reduces the flexibility of proton therapy and hinder its full potential. Margins of 3.5 % + 1 mm [16] are used to account for range uncer-tainties in the Bragg peak position, reducing the applicability of proton therapy and increasing normal tissue dose. Furthermore, errors in the estimate of the Bragg peak range may cause severe irradiation of organs at risks (OARs). For example, the margins mentioned above imply a potential 8 mm overshot in a beam crossing 20 cm of soft tissue, a common distance for treatments in chest cases [16].

Figure 1.1demonstrates the effects of an unplanned heterogeneity of higher density on a pro-ton beam treatment compared to a conventional phopro-ton treatment. While the phopro-ton beam intensity is more attenuated, degrading the maximal dose past the heterogeneity, the proton beam Bragg peak is shifted, resulting in a full undershooting of the target tumor. In general, target under dosing will occur if the heterogeneity has a higher stopping power than what planned. On the other hand, organs at risk overdosing will happen if the heterogeneity has a lower stopping power than what was planned, with the beam propagating deeper in the patient. Proton range uncertainties can also be caused by deficient modelling of multiple Coulomb scattering [17], uncertainties in the estimate of the mean excitation energy [18], in-adequate reproduction of the treatment setup [19], uncertainties in the computed tomography (CT) conversion to relative stopping power (RSP) [20], CT grid resolution and partial volume effects [21], biological effects [22], uncertainties in the patient placement [23], and motion dur-ing treatment [24]. The various range uncertainties and their estimated impact on the total uncertainty on the patient treatment have been tabulated by Paganetti [16] and are shown in Table 1.1.

A significant fraction of these uncertainties come from the estimate of the tissue stopping power within the patient (which consist of the CT and mean excitation energy related uncertain-ties) [16,18,25]. Pre-treatment X-ray CTs are routinely used for diagnostic, positioning, and treatment planning purposes. In the clinical routine, an X-ray CT of the patient is acquired and converted to RSP using a tissue substitution calibration curve. However, no bijection exists between HU number and RSP [18]. Furthermore, the calibration curve is created by scanning plastic materials which poorly represents the human tissues in the patient. In this method, considering the various outlined uncertainties, a mean error of 3.5% was measured for tissue RSP’s [18], going as high as 5% in the lung. Dual energy X-ray CT is seen as a promising venue to reduce range uncertainty. A novel material decomposition technique [26] allowed to predict the RSP with higher accuracy. Furthermore, recent literature on DECT reconstruction method [26–29] quoted an uncertainty of ≈1.0% over all the human body tis-sues that are currently tabulated [30–32]. The standard deviation of the RSP error is however still high, up to 7% for high-density materials [25]. Furthermore, DECT conversion technique

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Table 1.1 – Estimated proton range uncertainties and their sources and the potential of Monte Carlo for reducing the uncertainty [16]. The estimations are average numbers based on 1.5 standard deviations.

Range uncertainty Range uncertainty

Source of range uncertainty in the patient without Monte Carlo with Monte Carlo

Independent of dose calculation

Measurement uncertainty in water for commissioning ±0.3 mm ±0.3 mm

Compensator design ±0.2 mm ±0.2 mm

Beam reproducibility ±0.2 mm ±0.2 mm

Patient setup ±0.7 mm ±0.7 mm

Dose calculation

Biology (always positive)1 +≈0.8% +≈0.8%

CT imaging and calibration ±0.5% ±0.5%

CT conversion to tissue (excluding I-values) ±0.5% ±0.2%

CT grid size ±0.3% ±0.3%

Mean excitation energy (I-values) in tissue ±1.5% ±1.5%

Range degradation; complex inhomogeneities -0.7% ±0.1%

Range degradation; local lateral inhomogeneities2 _±2.5% _±0.1%

Total (excluding1 ,2) 2.7% ±1.2 mm 2.4% ±1.2 mm

Total (excluding,1₎ _{4.6% ±1.2 mm} _{2.4% ±1.2 mm}

may suffer from low-dose noise associated with the dose-reduction technique present in those methods. This noise may increase the quoted standard deviation [33].

Proton imaging is a new and promising branch of proton therapy that has generated many in-terests in recent literature [34–48]. Energy loss proton computed tomographic directly yields the stopping power in a phantom. Furthermore, the acquisition in the patient setup be-fore treatment presents advantages for patient positioning and treatment reproducibility [49]. However, the technique has considerable challenges both in the tomographic reconstruction algorithms [17, 29] and in the conceptual design of the detector [38, 50]. To deal with the poor resolution due to multiple Coulomb scattering, actual proton tomographic reconstruction algorithms require single event proton entrance and exit information (position and direction vector, and energy) to estimate a most-likely proton path [17, 50] through the patient. Sin-gle event processing requires a severe reduction of the beam flux which induces considerable delay. Furthermore, the gantry scan can only be done at slow speed which would further decrease the acquisition speed. Proton radiography represents a modality that may be easier to implement in the clinical environment in the short term. Nonetheless, to achieve reasonable acquisition time while keeping a good image quality, detectors with low dead-time and high spatial resolution are required.

The combination of imaging modalities was suggested to help reduce proton therapy uncer-tainties. Hansen et al. [51] used a kilo-voltage cone-beam CT (CBCT) as prior information to accelerate the convergence of the iterative algorithm in proton computed tomography (pCT). Furthermore, Schneider et al. [52] investigated the feasibility of combining proton radiography and X-ray CT imaging modalities to obtain patient specific stopping power. However, their

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work used a straight-line approximation, which is known to represent proton paths poorly for a clinical energy loss [17,39].

This thesis focuses on trying to improve the estimate of the patient relative stopping power to improve the proton radiotherapy treatment accuracy. It will first investigates the different current proton path estimate approaches and aims to introduce a new path estimate that is both of high precision and time-efficient. Then, we will focus on the tomographic reconstruc-tion algorithms, outlining their limitareconstruc-tions, and we will propose a new approach to improve the quality as well as the rapidity of the reconstructions. Finally, as combined imaging system has been proposed recently as a new research direction, this thesis investigates whether it is possible to combine X-ray and proton imaging to obtain a more precise path estimate/stopping power map. This introduction briefly covers the proton interactions with matter which are relevant to this work (Section 1.2). Subsequently, the different existing algorithms to map the single or dual energy X-ray CT and their Hounsfield Unit products to tissue stopping powers are discussed (Section1.3and Section1.4). Finally, we discuss the proton imaging system his-tory and state of the art (Section1.5). Chapter2provides a deeper explanation of the methods commonly used in the thesis, e.g. the Monte Carlo algorithms, the tomographic reconstruc-tion techniques, and the proton path estimate. Chapter 3 focuses on our initial development of a phenomenological proton path. Chapter 4 starts from a physics perspective and bridges the gap between the phenomenological path and the theoretical background, presenting a unified most likely path algorithm for every light ion up to carbon. Chapter 5 then extends the most likely path algorithm to various heterogeneous materials. Chapter 6 introduces a newly proposed radiography reconstruction method, using a dimension reduction combined with the conventional photon FDK algorithm. Chapter 7 focuses on multi-modality imaging by combining X-Ray CT imaging techniques with particles radiographs. Finally, Chapter 8

demonstrates the experimental work done trying to validate the algorithms developed in the previous chapters.

1.2 Proton interaction with matter

In this section, basic concepts that describe proton interactions with matter are presented briefly, and relevant references are indicated for the reader who wishes to deepen their under-standing. A charged particle interacts with matter 1) by losing energy with the atomic elec-trons, described by the stopping power, 2) by deflecting against atomic nuclei which produce the lateral deviation and the related scattering power and 3) by suffering a head-on collision with an atomic nuclei, setting secondary particles in motion through nuclear reactions. Each of these aspects is treated separately.

On particle imaging with application to particle radiotherapy

On particle imaging with application to particle

radiotherapy

On particle imaging with application to particle

radiotherapy

Résumé

Abstract

Contents

List of Tables

List of Figures

Glossary

Acronyms

List of contributions

Peer reviewed journal

International conferences

Remerciements

Avant-propos

Foreword

Chapter 1

Introduction

1.1

Proton radiotherapy treatment

1.2

Proton interaction with matter