O tempo de simulação computacional em planejamento de radioterapia ainda é muito alto. Diversas técnicas de redução de variância têm sido desenvolvidas para o transporte de elétrons a fim de reduzir o tempo de simulação. Destacamos algumas delas: Macro Monte Carlo (MMC), Response History Monte Carlo (RHMC) e Macro Response Monte Carlo (MRMC). Todas es- sas técnicas utilizam base de dados onde as histórias dos elétrons foram previamente simuladas. Tais algoritmos, até o presente momento, foram somente avaliados através da dose absorvida. Neste trabalho, fazemos uma comparação dos espectros dos elétrons utilizando uma implemen- tação própria do MRMC. A base de dados do MRMC consiste de histórias pré-simuladas de elétrons em pequenas esferas de material homogêneo (chamadas de kugel) para diferentes ti- pos de energias e tamanhos de raios. O MRMC usa o kugel de maior raio para transportar o elétron, desde que o mesmo não cruze nenhuma interface entre materiais. Nesta implementa- ção, o transporte do elétron através de uma interface é aproximado por uma linha reta e, ao final, corrige-se sua energia pela perda contínua de energia. A base de dados kugel foi gerada pelo Geant4 versão 8.0 para água, tecido mole e osso compacto, para a faixa de energia de 31,63 MeV até 178 keV, com raios de 0,025 cm a 1,0 cm. Os testes consistem na simulação de um feixe estreito de elétrons em objetos simuladores homogêneos e heterogêneos de forma cilíndrica. Foram obtidos os espectros frontais e laterais pelo MRMC e comparados aos respec- tivos espectros simulados pelo Geant4. Foram simulados 106 histórias em ambos os sistemas, por este motivo não houve a necessidade de normalizar os histogramas. Os espectros avaliados mostram uma boa concordância para energias acima de 5 MeV. A diferença entre as energias dos picos foi menor que 1,7%, para energias acima de 5 MeV em objetos simuladores homo- gêneos. Para o osso compacto as diferenças entre os espectros frontais foram cerca de 5%, e para os laterais menor que 2% para energias acima de 5 MeV. Os tempos de simulação com o MRMC foram de até 15 vezes menores para objetos simuladores homogêneos e cerca de 5 vezes menores para objetos simuladores heterogêneos. / In radiotherapy the computer simulation elapsed time for treatment planning is still a prob- lem. Several techniques for electron transport variance reduction have been developed in order to speed up the calculations. Some of them are: Macro Monte Carlo (MMC), Response History Monte Carlo (RHMC) and Macro Response Monte Carlo (MRMC). All of them use a database where electrons histories were previously simulated. These algorithms have been evaluated only by absorbed dose. This work shows a comparison between electron spectra simulated by our implementation of MRMC. Such algorithm uses a database where electron histories were pre-simulated in small homogeneous spheres (called kugel) for several different initial ener- gies and some different radii. The MRMC transportation code uses the largest kugel size for electron transportation, since it does not cross any material boundary. In this implementation the electron transport through a boundary is done in a straight line and the energy correction is made by continuous slowing down approximation. The kugel database has been generated using Geant4 version 8.0 for water, soft tissue and compact bone, with energy range spanning from 31.63 MeV down to 178 keV and with radius range from 0.025 to 1.0 cm. The MRMC benchmarks consist of an electron pencil beam simulation in homogeneous and heterogeneous cylindrical phantoms. The forward and lateral electron output spectra are computed and com- pared against Geant4 simulations. We have simulated 106 histories in both systems, so the histograms are compared without any normalization factors. The agreement between spectra shapes have been evaluated and show to be good above 5 MeV. The results show an agreement better than 1.7% in the peak energy for energies above 5 MeV, for water and soft tissue homo- geneous phantoms. The agreement for compact bone homogeneous phantom between peaks of forward spectra were around 5% and for side spectra were better than 2% for energies above 5 MeV. The benchmarks have shown that our implementation of MRMC are up to 15 times faster than Geant4 for homogeneous phantoms and 5 times for heterogeneous ones.

O processo de radioterapia consiste em várias etapas, iniciando na indicação pelo médico. O plano de tratamento passa então por um processo denominado simulação, onde é adquirida uma série de imagens por tomografia computadorizada que são transferidas para o sistema de planejamento, onde a delineação dos volumes alvos e tecidos normais adjacentes serão realizadas. Após a delineação desses volumes, no sistema de planejamento são colocados os campos de irradiação e a dose desejada conforme prescrição médica. O sistema de planejamento calcula então a dose que o volume alvo e os tecidos adjacentes poderão receber. Se estas doses estão dentro dos padrões aceitáveis, o planejamento então é aprovado e enviado ao acelerador linear para a execução do tratamento. Antes da execução do tratamento, é realizada uma imagem, seja através de filme radiográfico ou digitalmente, para avaliar a posição no paciente na mesa de tratamento. Se a localização do paciente está correta, a dose é então liberada. Esse protocolo de aquisição de imagem é denominado como Radioterapia Guiada por Imagem (IGRT). A quantidade de radiografias de posicionamento segue um protocolo definido conforme a região a ser irradiada. Como resultado deste procedimento, sabe-se que uma determinada dose adicional é recebida pelos pacientes, tornando-se um fator importante a ser determinado. Esta avaliação foi realizada através da simulação de Monte Carlo, utilizando o código MCNP. Para isso foi realizada primeiramente toda a caracterização da fonte de raios X com uso de câmaras de ionização e dosimetros TL juntamente com as simulações no MCNP. Após essa caracterização, as imagens e as estruturas do planejamento radioterápico foram convertidas para serem utilizadas no código MCNP. Para que as doses fossem calculadas nos principais órgãos de risco no tratamento de próstata: bexiga, reto e cabeças de fêmur direita e esquerda. / The process of radiotherapy treatment consists of several stages, starting from the statement given by the physician. The treatment planning undergoes a process called simulation, where a series of computed tomography images is acquired and transferred to the treatment planning system, where the delineation of target volumes and adjacent normal tissues will be performed. After the delineation of these volumes, then irradiation fields and dose precribed by the physician are placed in the treatment planning system. It calculates the dose that target volume and surrounding tissues are receiving. If the doses are within acceptable standard values, then the design is approved and submitted to the linear accelerator for the treatment course. Before treatment course, an image is performed, either by radiographic or digital film, in order to evaluate (check) the patient position on the treatment table. If the patient position is correct, the treatment is realized. This image acquisition protocol is called Image-Guided Radiotherapy (IGRT). The amount of radiographic positioning follow a protocol defined for the region to be treated. As a result of this procedure, it is known that a specific additional dose is received by the patient, becoming an important factor to be determined. In this work, this additional dose evaluation was performed by the Monte Carlo simulation using the MCNP algorithm. The characterization of the entire X-ray source was primarily realized with ionization chamber thermoluminescent dosimeters and simulations with the MCNP code. After the X-ray tube characterization, images and the structures for the radiotherapy planning were converted to be used in the MCNP code for dose calculation at the main organs at risk during a prostate treatment: bladder, rectum and femoral heads right and left.

Granger (1980) found that the aggregation of m short-memory AR(1) processes yields a long-memory process. Thereby he assumed m -> ∞, Gaussian shape and betadistributed AR(1) parameters over (0; 1). To test hypotheses that long memory in climate time series comes from aggregation, the finding of Granger (1980) cannot be directly applied. First, the number of \"microclimatic\" processes to be aggregated is finite. Second, climatic processes often produce right-skewed data. Third, the AR(1) parameters of the microclimatic processes could be restricted to a narrower interval than (0; 1). We therefore perform Monte Carlo simulations to study aggregation in climate time series under realistic conditions. The long-memory parameter, H, is estimated by fitting an ARFIMA model to various types of aggregations. Our results are as follows. First, for m above a few hundred, H approaches saturation. Second, the distributional shape has little influence, as noted by Granger (1980). Third, the upper limit of the interval for the AR(1) parameter has a strong influence on the saturation value of H, as noted by Granger (1980). / Granger (1980) fand heraus, dass die Summe von m schwach seriell abhängigen AR(1)-Prozessen einen stark seriell abhängigen Prozess ergibt. Er nahm dabei an, dass m -> ∞ geht, die Verteilungen Gaußsch sind und die AR(1)-Parameter beta-verteilt über (0; 1) sind. Um die Hypothese zu testen, daß starke serielle Abhängigkeit in Klimazeitreihen von dieser \"Aggregation\" rührt, kann das Ergebnis von Granger (1980) jedoch nicht direkt angewendet werden. Erstens: die Anzahl \"mikroklimatischer\", zu summierender Prozesse is endlich. Zweitens: Klimaprozesse erzeugen oft rechtsschief verteilte Daten. Drittens: die AR(1)-Parameter der mikroklimatischen Prozesse mögen auf ein engeres Intervall begrenzt sein als (0; 1). Wir f¨uhren deshalb Monte-Carlo-Simulationen durch, um die Aggregation in Klimazeitreihen für realistische Bedingungen zu studieren. Der Parameter H, der die starke serielle Abhängigkeit beschreibt, wird geschätzt durch die Anpassung eines ARFIMA-Modelles an unterschiedliche Aggregations-Typen. Unsere Ergebnisse sind wie folgt. Erstens: für m oberhalb einiger hundert erreicht H S¨attigung. Zweitens: die Verteilungsform hat geringen Einfluß, wie von Granger (1980) bemerkt. Drittens: die obere Grenze des Intervalles für den AR(1)-Parameter hat einen starken Einfluß auf den Sättigungwert von H, wie von Granger (1980) bemerkt.

Depuis le début du XX siècle, la thématique de transport a concentré l’attentionde nombreux chercheurs. L’objectif étant alors d’identifier et de comprendre lesdifférentes sources de diffusions prenant part à la résistivité de la matière. Les deuxpremières sources diffusives mises en évidence ont été les phonons dépendant de latempérature, et les défauts du réseau cristallin. Dans les années 1950, l’étude des semiconducteursa fait émerger une troisième source de diffusion, la diffusion magnétique.Dès la mise en évidence du rôle joué par le magnétisme sur la résistivité de certainsmatériaux, il a rapidement été établi que la résistivité magnétique R est tributaire dela stabilité de l’ordre magnétique du réseau. A basse température T, la diffusion desélectrons s’ opère par l e biais des ondes de spins. A haute température, R est proportionnelleaux corrélations spin-spin. Cependant, les mécanismes de diffusion ayant lieuau voisinage de la température de transition ordre/désordre magnétique restent encoremal comprise. L’objectif de cette thèse a consisté à étudier ce problème à l’aide d’uneapproche nouvelle basée sur la simulation Monte Carlo. En effet, les théories existantessont toutes construites avec des hypothèses sur les mécanismes à l’origine du comportementde résistance tels que : fonction corrélation spin-spin, longueur de localisation.Elles utilisent beaucoup d’approximations au cours du calcul telles que théorie du champmoyen, approximation du temps de relaxation, la portée des fonctions de corrélation. Lesprincipaux handicaps de ces théories sont de n’être valables que pour certaines gammesde températures, et d’être tributaires du type de magnétisme porté par les réseaux cristallins.Notre approche offre quant à elle une procédure unifiée concernant l’étude desrésistivités magnétiques fonction de la température. Cette méthode peut s’appliquer `atout type de matériaux, tout ordre magnétique (ferromagnétique, antiferromagnétique,ferrimagnétique, verre de spin, ...), tout type de modèle de spins (Ising, Heisenberg, XY,...), enfin tout type de réseau cristallin. Seule la connaissance du Hamiltonien permet defaire la simulation, et de reproduire des mesures expérimentales avec la possibilité d’unecomparaison quantitative.Dans un premier temps, nous traitons de structures ferromagnétiques et interprétons les différents mécanismes de diffusion en fonction de la température. Nousétendons ensuite l´étude aux systèmes antiferromagnétiques, frustrés et non-frustrés. Cessystèmes n’ont fait l’objet que de peu d’études. Dans le cas des systèmes antiferromagnétiques non-frustrés, nous sommes en mesure de contredire une prédiction théoriquefaite par Haas en 1968, concernant la forme de la résistance magnétique à la transition dephase . Dès lors, nous nous consacrerons à l’étude des mécanismes de transport dansdes systèmes antiferromagnétiques frustrés. Ces travaux ont permis de mettre en évidencedes comportements nouveaux des transitions de phases des résistances magnétiques : nousmontrons que ces résistances subissent une transition du premier ordre , mais qu’ilest également possible par le contrôle d’un paramètre du modèle, de choisir le sens de latransition : des hautes résistances vers les basses résistances ou inversement .Pour finir, nous confrontons nos résultats de simulations avec des mesures expérimentalesen réalisant une étude de transport sur un matériau semiconducteur antiferromagnétique :MnTe. Il résulte de cette étude un bon accord entre nos résultats de simulations et lesmesures expérimentales . / ....

Les protocoles de traitement du cancer par Radiothérapie Conformationnelle par Modulation d'Intensité (RCMI) ciblent avec une précision de plus en plus grande la tumeur. Pour cela, ils nécessitent des informations anatomiques précises du patient juste avant le traitement, qui peuvent d'être obtenues à l'aide de systèmes d'imagerie embarqués sur l'accélérateur linéaire médical délivrant le faisceau de traitement. Ces systèmes, composés d'un tube à rayons X et d'un détecteur 2D planaire, sont appelés kV-Cone Beam CT (kV-CBCT). Aujourd'hui, leur usage est très fortement répandu dans le cadre des traitements par RCMI. Cependant, ces examens kV-CBCT sont responsables d'une dose de rayonnements ionisants additionnelle qui est loin d'être négligeable et pouvant d'être à l'origine de l'apparition d'effets secondaires, tels que des cancers radio-induits chez les patients traités. Au cours de cette thèse, un simulateur basé sur la méthode de Monte-Carlo a été développé permettant ainsi d'estimer avec précision les doses délivrées aux organes lors des examens d'imagerie kV-CBCT. Cet outil a ensuite été utilisé afin d'étudier différentes stratégies de prise en compte clinique de ces doses additionnelles. L'étude présentée dans ce manuscrit propose notamment une méthode rapide d'estimation des niveaux de doses délivrés aux organes prenant en compte la morphologie de chaque patient. Cette stratégie a été développée à partir d'une cohorte de 50 patients incluant 40 enfants et 10 adultes. Ces travaux ont été réalisés en collaboration avec l'unité de physique médicale du Centre Eugène Marquis à Rennes qui a fourni les données cliniques nécessaires à l'étude. / Protocols for cancer treatment using intensity-modulated radiation therapy (IMRT) allow to target the tumor with an increased precision. They require accurate anatomical information of the patient just before the treatment, which can be obtained using on-board imaging systems mounted on the medical linear accelerator delivering the treatment beam. These systems, composed of an X-ray tube and a 2D planar detector, are called kV-Cone Beam CT (kV-CBCT). Nowadays, they are widely used in the context of IMRT treatments. However, these kV-CBCT examinations are also responsible for an additional dose of ionizing radiations which is far to be negligible and could be the cause for secondary effects, such as radiation-induced second cancers for treated patients. During this PhD work, a simulator based on the Monte Carlo method was developed in order to calculate accurately the doses delivered to organs during kV-CBCT examinations. Then, this tool was used to study several strategies to take in account for the imaging additional doses in clinical environment. The study reported here includes, in particular, a fast and personalized method to estimate the doses delivered to organs. This strategy was developed using a cohort of 50 patients including 40 children and 10 adults. This work has been done in collaboration with the medical physics unit of the Eugène Marquis medical center in Rennes, which has collected the clinical data used for this study.

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Bayesian analysis is definitely different from the classic statistical methods. Although, both of them use subjective ideas, it is used in the selection of models in the classic statistical methods, rather than as an explicit part in Bayesian models, which allows the combination of subjective ideas with the data collected, update the prior information and improve inferences. Drastic growth of Bayesian applications indicates it becomes more and more popular, because the advent of computational methods (e.g., MCMC) renders sophisticated analysis. In Bayesian framework, the flexibility and generality allows it to cope with very complex problems. One big obstacle in earlier Bayesian analysis is how to sample from the usually complex posterior distribution. With modern techniques and fast-developed computation capacity, we now have tools to solve this problem. We discuss Acceptance-Rejection sampling, importance sampling and then the MCMC methods. Metropolis-Hasting algorithm, as a very versatile, efficient and powerful simulation technique to construct a Markov Chain, borrows the idea from the well-known acceptance-rejection sampling to generate candidates that are either accepted or rejected, but then retains the current values when rejection takes place (1). A special case of Metropolis-Hasting algorithm is Gibbs Sampler. When dealing with high dimensional problems, Gibbs Sampler doesn’t require a decent proposal distribution. It generates the Markov Chain through univariate conditional probability distribution, which greatly simplifies problems. We illustrate the use of those approaches with examples (with R codes) to provide a thorough review. Those basic methods have variants to deal with different situations. And they are building blocks for more advanced problems. This report is not a tutorial for statistics or the software R. The author assumes that readers are familiar with basic statistical concepts and common R statements. If needed, a detailed instruction of R programming can be found in the Comprehensive R Archive Network (CRAN): http://cran.R-project.org / text

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In structural equation models, researchers often examine two types of causal effects: direct and indirect effects. Direct effects involve variables that "directly" influence other variables, whereas indirect effects are transmitted via intervening variables. While researchers have paid considerable attention to the distribution of sample direct effects, the distribution of sample indirect effects has only recently been considered. Using the (delta) method (Rao, 1973), Sobel (1982) derived the asymptotic distribution for estimators of indirect effects in recursive systems. Sobel (1986) then derived the asymptotic distribution for estimators of total indirect effects in the Joreskog covariance structure model (Joreskog, 1977). This study examined the applicability of the large sample theory described by Sobel (1986) in small samples. Monte Carlo methods were used to evaluate the behavior of estimated total indirect effects in sample sizes of 50, 100, 200, 400, and 800. Two models were used in the analysis. Model 1 was a nonrecursive model with latent variables, feedback, and functional constraints among the effects (Duncan, Haller, & Portes, 1968; Sobel, 1986). Model 2 was a recursive model with observable variables (Duncan, Featherman, & Duncan, 1972). In addition, variations in these models were studied by randomly increasing and decreasing model parameters. The principal findings of the study suggest certain guidelines for researchers who use Sobel's procedures to evaluate total indirect effects in structural equation models. In order for the behavior of the estimates to approximate the asymptotic properties, sample sizes of 400 or more are indicated for nonrecursive systems similar to Model 1, and for recursive systems such as Model 2, sample sizes of 200 or more are suggested. At these sample sizes, researchers can expect sample indirect effects to be accurate point estimators, and confidence intervals for the effects to behave as theory predicts. A caveat to the above guidelines is that, when the total indirect effects are "small" in magnitude, relative to the scale of the model, convergence to the asymptotic properties appears to be very slow. Under these conditions, sampling distributions for the "smaller" valued estimates were positively skewed. This caused estimates to be significantly different from true values, and confidence intervals to behave contrary to theoretical expectations.

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