A câmara de ionização é um tipo de dosímetro muito utilizado atualmente para medidas precisas, tais como as necessárias em radioterapia. Existem diferentes tipos de câmaras de ionização para diferentes aplicações, como exemplo, as câmaras tipo lápis utilizadas para dosimetria em tomografia computadorizada (TC) e as câmaras cavitárias de grafite utilizadas como sistemas padrões primários para determinação da taxa de kerma no ar. Neste trabalho, foram caracterizadas duas câmaras de ionização tipo lápis, de diferentes volumes sensíveis e com comprimentos do volume sensível menores que as empregadas em TC, em feixes de 60Co e duas câmaras de ionização de grafite foram desenvolvidas e caracterizadas para constituir um sistema padrão primário para feixes de 60Co. Além destas câmaras de ionização, também foi projetada e avaliada uma câmara de ionização cilíndrica construída utilizando-se cloreto de polivinila (PVC) para estudar inicialmente as configurações geométricas das câmaras de ionização de grafite, já que o PVC é mais facilmente usinado e apresenta um custo relativamente baixo quando comparado ao grafite. O estudo inicial realizado com as câmaras de ionização tipo lápis foi muito importante, principalmente no que se refere à escolha do material para o desenvolvimento das câmaras de ionização, aos parâmetros utilizados nas simulações de Monte Carlo e também na determinação do espectro de radiação que melhor representa a fonte de 60Co do Laboratório de Calibração de Instrumentos (LCI). A partir dos resultados obtidos com as câmaras de ionização tipo lápis e com a câmara de ionização cilíndrica de PVC foram projetadas e caracterizadas experimentalmente e por simulação de Monte Carlo duas câmaras de ionização de grafite. Os resultados obtidos da caracterização destas câmaras de ionização apontaram que elas possuem qualidade metrológica para atuação como padrões primários de referência. Como aplicação do estudo das câmaras de ionização de grafite, o valor da taxa de kerma no ar da fonte de 60Co do LCI foi determinado e comparado com o valor obtido com o padrão de referência do LCI. Os valores determinados com os protótipos desenvolvidos neste projeto (CG1 e CG2) diferiram em apenas 0,17% e 1,7%, respectivamente, do valor calculado com o sistema padrão do IPEN. / Ionization chambers are the most employed dosimeters for precise measurements, as those requested in radiotherapy. There are several different ionization chambers, employed for different applications, such as pencil ionization chambers, used in computed tomography (CT) dosimetry, and cavity ionization chambers, used as primary standard systems for the air kerma determination. In this work two pencil ionization chambers, with sensitive volumes smaller in size and length than those employed in CT, were characterized in 60Co gamma beams, and two graphite ionization chambers were developed and characterized in order to compose a primary standard system for the beam dosimetry of 60Co sources. Besides these ionization chambers, a cylindrical prototype made of polyvinyl chloride (PVC) was developed and characterized, in order to evaluate the geometrical design of the graphite ionization chambers. This step was important, since PVC is easier to use as manufacture material and it presents a lower production cost than graphite. The inicial study, with the pencil ionization chambers, was essential in order to choose the materials and parameters employed for the further ionization chamber models. The determination of the radiation spectra that best fits the 60Co source employed in this work was also carried out with a pencil ionization chamber. From the results with the pencil and the PVC ionization chambers, the graphite dosimeters were projected, developed and characterized, both experimentally and using Monte Carlo simulations. The results obtained with these dosimeters pointed out that they present metrological quality to be used as primary standard systems. As an application of the study concerning the graphite ionization chambers, the air kerma rate of the 60Co source of the Calibration Laboratory was determined and compared with the value obtained with the IPEN standard system. The values obtained with the developed ionization chambers CG1 and CG2 presented differences of only 0.17% and 1.7%, respectively.

Les pathologies cardio-vasculaires d’origine athéroscléreuse, premières causes de mortalité dans les pays occidentaux, sont insuffisamment prises en charge par les outils de dépistage et de suivi thérapeutique actuels. La Tomographie par Emission de Positons (TEP) est susceptible d’apporter au clinicien des outils puissants pour le diagnostic et le suivi thérapeutique des patients, en particulier grâce au traceur Fluorodésoxyglucose marqué au fluor 18 ([18F]-FDG). Cependant, l’Effet de Volume Partiel (EVP), dû notamment à la résolution spatiale limitée dans les images (plusieurs millimètres) en regard des faibles dimensions (de l’ordre du millimètre) des VOlumes d’Intérêt (VOIs), et les fluctuations statistiques du signal mesuré présentent des défis pour une quantification fiable.Un modèle original de lésion athéromateuse, paramétré par ses dimensions et sa concentration d’activité, a été développé et des simulations Monte-Carlo d’acquisitions TEP au [18F]-FDG de 36 lésions ont été produites. A partir des acquisitions simulées, nous avons montré que le nombre d’itérations des reconstructions itératives, le post-filtrage appliqué et le moyennage dans le VOI,paramètres relevés comme hautement variables dans une revue de la littérature dédiée, peuvent induire des variations des valeurs de fixation mesurées d’un facteur 1.5 à 4. Nous avons montré qu’une modélisation de la réponse du tomographe pouvait réduire le biais de mesure d’environ 10% par rapport au biais mesuré sur une image reconstruite avec un algorithme itératif standard et pour un niveau de bruit comparable. Sur les images reconstruites, nous avons montré que la fixation mesurée reste très biaisée (sous-estimation de plus de 50% du SUV réel) et dépend fortement des dimensions de la lésion à cause de l’EVP. Un contraste minimum de 4 par rapport à l’activité sanguine est nécessaire pour qu’une lésion soit détectée. Sans correction d’EVP, la mesure présente une corrélation faible avec la concentration d’activité, mais est très corrélée à l’activité totale dans la lésion. L’application d’une correction d’EVP fournit une mesure moins sensible à la géométrie de la lésion et plus corrélée à la concentration d’activité mais réduit la corrélation à l’activité totale dans la lésion.En conclusion, nous avons montré que l’intégralité de la fixation du [18F]-FDG dans les lésions athéromateuses inflammatoires totale peut être caractérisée sur les images TEP. Cette estimée ne requiert pas de correction de l’EVP. Lorsque la concentration d’activité dans la lésion est estimée, les mesures sont très biaisées à cause de l’EVP. Ce biais peut être réduit en mesurant le voxel d’intensité maximale, dans les images reconstruites sans post-filtrage avec au moins 80 itérations incluant un modèle de réponse du détecteur. La mise en œuvre d’une correction d’EVP facilite la détection des changements d’activité métabolique indépendamment de changements de dimensions de la zone siègede l’inflammation. Une quantification absolue exacte de la concentration d’activité dans les lésions ne sera possible que via une amélioration substantielle de la résolution spatiale des détecteurs TEP. / Cardiovascular disease is the leading cause of death in western countries. New strategies and tools for diagnosis and therapeutic monitoring need to be developed to manage patients with atherosclerosis, which is one major cause of cardiovascular disease. Fluorodeoxyglucose Positron Emission Tomography (FDG-PET) is a powerful imaging technique that can detect at early stages plaques prone to rupture. Yet, Partial Volume Effect (PVE), due to the small lesion dimensions (around 1 mm) with respect to the scanner spatial resolution (around 6 mm full width at half maximum), and statistical variations considerably challenge the precise characterization of plaques from PET images. An original model of atheromatous lesion parameterized by its dimensions and activity concentration, was developed. Thirty six Monte Carlo simulations of FDG-PET acquisitions were produced. Based on the simulations, we showed that the number of iterations in iterative reconstructions, the post filtering of reconstructed images and the quantification method in the Volume Of Interests (VOI) varied sharply in an analysis of the dedicated literature. Changes in one of these parameters only could induce variations by a factor of 1.5 to 4 in the quantitative index. Overall, inflammation remained largely underestimated (> 50% of the real uptake). We demonstrated that modeling the detector response could reduce the bias by 10% of its value in comparison to a standard OSEM recontruction and for an identical level of noise. In reconstructed images, we showed that the measured values depended not only on the real uptake but also on the lesion dimensions because of PVE. A minimum contrast of 4 with respect to blood activity was required for the lesion to be observable. Without PVE correction, the measured values exhibited a correlation with activity concentration but were much more correlated with the total uptake in the lesion. Applying a PVE correction leads to an activity estimate that was less sensitive to the geometry of the lesion. The corrected values were more correlated to the activity concentration and less correlated to the total activity. In conclusion, we showed that the total activity in inflammatory lesions could be assessed in FDG-PET images. This estimate did not require PVE correction. Tracer concentration estimates are largely biased due to PVE, and the bias can be reduced by measuring the maximum voxel in the lesion in images reconstructed with at least 80 iterations and by modeling the detector response. Explicit PVE correction is recommended to detect metabolic changes independent of geometric changes. An accurate estimation of plaque uptake will however require the intrinsic spatial resolution of PET scanners to be improved.

Les faisceaux de photons de petites dimensions utilisés en radiothérapie stéréotaxique sont caractérisés par de forts gradients de dose et un manque important d’équilibre électronique latéral, ce qui rend les techniques dosimétriques conventionnelles inadaptées. L’objectif de la thèse est de permettre une meilleure évaluation de la dose délivrée aux patients traités par radiothérapie stéréotaxique. D’une part, les données dosimétriques de base utilisées pour l’étalonnage du système de planification de traitement (TPS) ont été déterminées numériquement. Pour cela, deux installations de radiothérapie de type CyberKnife ont été modélisées avec le code Monte Carlo PENELOPE. Des mesures de rapport d’ouverture du collimateur ont également été réalisées à l’aide de plusieurs détecteurs actifs et de deux dosimètres passifs (film radiochromique et micro-LiF) et comparées aux facteurs d’ouverture du collimateur calculés par simulation. Six détecteurs ont été modélisés afin d’étudier les phénomènes physiques impliqués dans la réponse des détecteurs en petits champs. Parmi les détecteurs étudiés, seuls les films radiochromiques sont en accord avec la simulation, ils peuvent être utilisés sans facteur correctif. La perturbation induite par les autres détecteurs a pu être expliquée, soit par l’effet volume dû à la taille trop importante du volume actif par rapport au diamètre du faisceau, soit par la masse volumique des matériaux utilisés dans la conception du détecteur qui est trop éloignée de celle de l’eau. Les facteurs correctifs, permettant de corriger la non-équivalence-eau et/ou la mauvaise résolution spatiale de chaque détecteur, ont été déterminés pour les deux systèmes CyberKnife.D’autre part, un protocole de mesure de distributions de dose 2D pour les mini-faisceaux, basé sur l’utilisation des films radiochromiques, a été établi et un programme sous MatLab permettant l’analyse entre les distributions de doses mesurées et calculées a été développé. Des plans de traitement stéréotaxique en milieu hétérogène ont ensuite été réalisés pour un fantôme afin d’évaluer les algorithmes de calcul de dose implémentés dans le TPS MultiPlan (TPS associé au système CyberKnife). L’analyse des distributions de dose 2D des plans de traitement a montré que l’algorithme de type « Pencil Beam » implémenté dans MultiPlan est performant en milieu homogène équivalent-eau mais n’est pas adapté pour les milieux à faible densité électronique tels que le poumon. En effet, celui-ci surestime la dose dans le champ (jusqu’à 40%) ce qui peut conduire à diminuer l’efficacité du traitement de la tumeur et la sous-estime hors du champ ce qui risque de sous-évaluer la dose reçue par les organes à risques à proximité. En milieu hétérogène, l’algorithme Monte Carlo implémenté dans MultiPlan est globalement en accord avec la mesure et est par conséquent l’algorithme à privilégier pour estimer la dose délivrée au patient lorsque des milieux à faible densité sont présents. / Dosimetry of small beams is challenging given their small size compared to the detectors, high dose gradient and the lack of lateral electronic equilibrium. The Ph.D. thesis aims to improve the accuracy of the dose delivered to the patient in stereotactic radiotherapy.On the one hand, dosimetric data used to calibrate the treatment planning system (TPS) were determined using numerical simulations. To achieve this, two CyberKnife radiotherapy facilities were modelled using the PENELOPE Monte Carlo code. Output ratios measurements were performed with several active detectors and with two passive dosimeters (radiochromic film and micro-LiF) and compared with output factors calculated by simulation. Six detectors were modeled in order to study the detectors response in small beams. Among the detectors studied, only the radiochromic films were in agreement with the simulations, they can be used without correction factors. The disturbance of the detectors response in small beams was explained either by the volume effect induced by the active volume, which is too high compared to the beam size, or by the mass density effect induced by the detector body materials which are too far from water mass density. The correction factors, required to correct the disturbance caused by the non-water-equivalence and/or the low spatial resolution of each detector, were calculated for the two CyberKnife systems.On the other hand, a 2D dose measurement protocol using radiographic films and a MatLab program were developed. Stereotactic treatment plans were then performed for a phantom in order to assess the calculation algorithms implemented in the MultiPlan TPS (associated with the CyberKnife system). The analysis of the 2D dose distributions related to the stereotactic treatment plans has shown that the “Pencil Beam” based algorithm implemented in MultiPlan is suitable for dose calculation in homogeneous water-equivalent media but not in low electronic density media such as the lung. Indeed, the dose is overestimated (up to 40%) inside the field and may lead to reduce the tumor treatment efficiency while it is underestimated outside the field which can underestimate the dose to critical organs within proximity of the tumor. Regarding the Monte Carlo algorithm implemented in MultiPlan, calculated and measured dose distributions are consistent and, as a consequence, it is the most suitable algorithm available in MultiPlan to estimate the dose received by a patient when low density media are involved.

Ces dernières années, la multiplication du nombre d’actes d’imagerie scanographique a eu pour conséquence l’augmentation de la dose collective due aux examens d’imagerie médicale. La dose au patient en imagerie scanographique est donc devenue un enjeu de santé publique majeur impliquant l’optimisation des protocoles d’examen, ces derniers devant tenir compte de la qualité image, indispensable aux radiologues pour poser leur diagnostic. En pratique clinique, l’optimisation est réalisée à partir d’indicateurs empiriques ne donnant pas accès à la dose aux organes et la qualité image est mesurée sur des fantômes spécifiques, tel que le fantôme CATPHAN®. Sans aucune information sur la dose aux organes et aucun outil pour prendre en compte l’avis du praticien, il est difficile d’optimiser correctement les protocoles. Le but de ce travail de thèse est de développer un outil qui permettra l’optimisation de la dose au patient tout en préservant la qualité image nécessaire au diagnostic. Ce travail est scindé en deux parties : (i) le développement d’un simulateur de dose Monte Carlo (MC) à partir du code PENELOPE, et (ii) l’estimation d’un critère de qualité image objectif. Dans ce but, le scanner GE VCT Lightspeed 64 a été modélisé à partir des informations fournies dans la note technique du constructeur et en adaptant la méthode proposée par Turner et al (Med. Phys. 36:2154-2164). Les mouvements axial et hélicoïdal du tube ont été implémentés dans l’outil MC. Pour améliorer l’efficacité de la simulation, les techniques de réduction de variance dites de splitting circulaire et longitudinal ont été utilisées. Ces deux réductions de variances permettent de reproduire le mouvement uniforme du tube le long de l’axe du scanner de manière discrète. La validation expérimentale de l’outil MC a été réalisée dans un premier temps en conditions homogènes avec un fantôme fabriqué au laboratoire et le fantôme CTDI, habituellement utilisé en routine clinique pour les contrôles qualité. Puis, la distribution de la dose absorbée dans le fantôme anthropomorphe CIRS ATOM, a été mesurée avec des détecteurs OSL et des films Gafchromic® XR-QA2. Ensuite, la dose aux organes a été simulée pour différentes acquisitions dans le fantôme femme de la CIPR 110 afin de créer une base de données utilisable en clinique. En parallèle, la qualité image a été étudiée en utilisant le fantôme CATPHAN® 600. A partir du module CTP 404, le rapport signal sur bruit (SNR pour signal to noise ratio) a été calculé en utilisant le modèle développé par Rose (J. Opt. Soc. Am. A 16:633-645). Un grand nombre d’images, correspondant à différents paramètres d’acquisition et de reconstruction, ont été analysées afin d’étudier les variations du SNR. Les acquisitions avec un SNR proche du critère de Rose ont été sélectionnées pour permettre des nouvelles acquisitions avec un fantôme préclinique contenant des petites structures suspectes en PMMA de différents diamètres. Ces images ont été analysées par deux radiologues expérimentés. Sur chaque image, ils devaient déterminer si une anomalie était présente ou non et indiquer leur niveau de confiance sur leur choix. Deux courbes ROC ont ainsi été obtenues : une pour les anomalies dites « détectables » par le critère de Rose (SNR > 5), et une pour les anomalies dites « non-détectables ». L’analyse des courbes montre que les deux radiologues détectent plus facilement les lésions suspectes lorsque que le critère de Rose est satisfait, démontrant le potentiel du modèle de Rose dans l’évaluation de la qualité image pour les tâches cliniques de détection. En conclusion, à partir des paramètres d’acquisition, la dose aux organes a été corrélée à des valeurs de SNR. Les premiers résultats prouvent qu’il est possible d’optimiser les protocoles en utilisant la dose aux organes et le critère de Rose, avec une réduction de la dose pouvant aller jusqu’à un facteur 6. / Due to the significant rise of computed tomography (CT) exams in the past few years and the increase of the collective dose due to medical exams, dose estimation in CT imaging has become a major public health issue. However dose optimization cannot be considered without taking into account the image quality which has to be good enough for radiologists. In clinical practice, optimization is obtained through empirical index and image quality using measurements performed on specific phantoms like the CATPHAN®. Based on this kind of information, it is thus difficult to correctly optimize protocols regarding organ doses and radiologist criteria. Therefore our goal is to develop a tool allowing the optimization of the patient dose while preserving the image quality needed for diagnosis. The work is divided into two main parts: (i) the development of a Monte Carlo dose simulator based on the PENELOPE code, and (ii) the assessment of an objective image quality criterion. For that purpose, the GE Lightspeed VCT 64 CT tube was modelled with information provided by the manufacturer technical note and by adapting the method proposed by Turner et al (Med. Phys. 36: 2154-2164). The axial and helical movements of the X-ray tube were then implemented into the MC tool. To improve the efficiency of the simulation, two variance reduction techniques were used: a circular and a translational splitting. The splitting algorithms allow a uniform particle distribution along the gantry path to simulate the continuous gantry motion in a discrete way. Validations were performed in homogeneous conditions using a home-made phantom and the well-known CTDI phantoms. Then, dose values were measured in CIRS ATOM anthropomorphic phantom using both optically stimulated luminescence dosimeters for point doses and XR-QA Gafchromic® films for relative dose maps. Comparisons between measured and simulated values enabled us to validate the MC tool used for dosimetric purposes. Finally, organ doses for several acquisition parameters into the ICRP 110 numerical female phantoms were simulated in order to build a dosimetric data base which could be used in clinical practice. In parallel to this work, image quality was first studied using the CATPHAN® 600. From the CTP 404 inserts, the signal-to-noise ratio (SNR) was then computed by using the classical Rose model (J. Opt. Soc. Am. A 16:633-645). An extensive number of images, linked to several acquisitions setups, were analyzed and SNR variations studied. Acquisitions with a SNR closed to the Rose criterion were selected. New acquisitions, based on those selected, were performed with a pre-clinical phantom containing suspect structures in PMMA. These images were presented to two senior radiologists. Both of them reviewed all images and indicated if they were able to locate the structures or not using a 5 confidence levels scale. Two ROC curves were plotted to compare the detection ability if the bead was detectable (SNR > 5) or not. Results revealed a significant difference between the two types of image and thus demonstrated the Rose criterion potential for image quality quantification in CT. Ultimately, organ dose estimations were linked to SNR values through acquisition parameters. Preliminary results proved that an optimization can be performed using the Rose criterion and organ dose estimation, leading to a dose reduction by a factor up to 6.

Dosímetros Luminescentes Opticamente Estimulados (OSL) vêm sendo testados como alternativa dosimétrica no controle da qualidade e verificação de tratamentos por possuir características adequadas para esse fim, como elevada sensibilidade à radiação ionizante, alta resolução espacial e facilidade de leitura. Neste trabalho, o óxido de alumínio, dopado com diferentes concentrações de carbono (Al2O3:C), foi estudado como material dosimétrico OSL. Nanotubos de carbono de paredes simples também foi avaliado como dopante, associados ao mesmo material, Al2O3:NTC, em alguns testes preliminares de resposta em função da dose em feixes de fótons de 50 kVp. O presente trabalho apresenta o processo de fabricação do dosímetro OSL, além de testes dosimétricos envolvendo metodologia experimental e por simulação Monte Carlo com o código PENELOPE para avaliação da resposta dosimétrica do Al2O3:C em função da concentração do carbono dopante. Neste trabalho foi investigada a resposta do dosímetro OSL para doses entre 50 cGy e 1000 cGy, em um amplo intervalo de energia de feixes de fótons. Foi analisada também, a interferência do uso do dosímetro OSL de Al2O3:C nas doses superficial e profunda em tratamentos radioterápicos. O dosímetro Al2O3:C(1%) apresentou diferença percentual máxima de 12% na homogeneidade de resposta em um grupo de 100 dosímetros e linearidade de resposta entre as doses de 50 cGy e 800 cGy para feixes de fótons de alta energia de 1,25 MV, 6 MV e 15 MV. Já para feixes de fótons de baixas energias, de 50 kVp, 120 kVp e 200 kVp, o dosímetro apresentou diferença significativa entre as respostas, evidenciando dependência com a energia. Além disso, foi investigada a estabilidade do sinal OSL em função do tempo e estipulado um tempo mínimo de armazenamento do dosímetro, entre a exposição e a leitura. O dosímetro Al2O3:NTC apresentou um aumento de sensibilidade de até 30% em relação ao dosímetro Al2O3:C(1%). Os resultados encontrados neste trabalho sugerem o uso do material dosimétrico OSL estudado como ferramenta em controle da qualidade em procedimentos clínicos de rotina na Radioterapia. / Optically Stimulated Luminescent dosimeters (OSL) have been tested as a dosimetric alternative in quality control and treatment verification since they have suitable characteristics for this purpose, such as high sensitivity to ionizing radiation, high spatial resolution and readability. In this work the aluminum oxide, doped with different concentrations of carbon (Al2O3:C), was studied as OSL dosimetric material. Single-walled carbon nanotubes were also evaluated as a dopant associated with the same material, Al2O3:NTC, and preliminary tests of response to dose in photon beams of 50 kVp were performed. This work presents the fabrication process of the OSL dosimeter, and dosimetric tests involving experimental methodology and Monte Carlo simulation with PENELOPE code to evaluate the response of the dosimetric Al2O3:C as a function of the concentration of carbon dopant. In this study we investigated the response of the OSL dosimeter for doses ranging from 50 cGy to 1000 cGy in a wide range of energy of photon beams. The interference of the OSL dosimeter Al2O3:C in superficial and deep doses in Radiotherapy treatments was also analyzed. The dosimeter Al2O3:C (1%) had a maximum percentage difference of 12% in the homogeneity of a group of 100 dosimeters and presented linearity of response in a dose range of 50 cGy and 800 cGy for photon beams of high energy of 1.25 MV, 6 MV and 15 MV. As for photon beams of low energies of 50 kVp, 120 kVp and 200 kVp, the dosimeter showed a significant difference between responses, indicationg dependence on energy. In addition, we investigated the stability of the OSL signal as a function of time and set a minimum time of storage of the dosimeter, between exposure and reading. The dosimeter Al2O3:NTC showed an increased sensitivity of up to 30% over the dosimeter Al2O3:C (1%). The findings on this study suggest the use of the material studied as OSL dosimeter as a tool in quality control in routine clinical procedures in Radiotherapy.

In financial markets, spread option is a derivative security with two underlying assets and the payoff of the spread option depends on the difference of these assets. We consider American style spread option which allows the owners to exercise it at any time before the maturity. The complexity of pricing American spread option is that the boundary of the corresponding partial differential equation which determines the option price is unknown and the model for the underlying assets is two-dimensional.In this dissertation, we incorporate the stochasticity to the interest rate and assume that it satisfies the Vasicek model or the CIR model. We derive the partial differential equations with terminal and boundary conditions which determine the American spread option with stochastic interest rate and formulate the associated free boundary problem. We convert the free boundary problem to the linear complimentarity conditions for the American spread option, so that we can go around the free boundary and compute the option price numerically. Alternatively, we approximate the option price using methods based on the Monte Carlo simulation, including the regression-based method, the Lonstaff and Schwartz method and the dual method. We make the comparisons among the option prices derived by the partial differential equation method and Monte Carlo methods to show the accuracy of the result.

[pt] O modelo implementado neste trabalho, proposto em Barone-Adesi, Engle e Mancini (2008), utiliza o método da Simulação Histórica Filtrada em conjunto com a simulação de Monte Carlo para calibração de parâmetros de um modelo GARCH a partir do qual opções do mercado brasileiro são apreçadas. Os retornos da simulação são gerados a partir das inovações empíricas obtidas no modelo GARCH assimétrico ajustado aos retornos diários das ações. Os resultados obtidos apontam para ajustes satisfatórios dentro da amostra, quando comparado ao modelo de Black E Scholes. No entanto, fora da amostra, resultados similares foram verificados para ambos os modelos de apreçamento. / [en] The model implemented in this work, proposed by Barone-Adesi, Engle, and Mancini (2008), applies the Filtered Historical Simulation method based on Monte Carlo simulation to calibrate the parameters of a GARCH model in which options from Brazilian market are priced. The simulated returns are generated from empirical innovations obtained by an asymmetric GARCH model adjusted for daily stock returns. The results suggest a satisfactory in-sample fit when compared to the Black E Scholes model. However, similar results were observed out-of-sample for both pricing models.

[pt] O apreçamento de opções é um dos temas mais importantes da economia financeira. Este estudo introduz uma versão não paramétrica da Transformada de Esscher para o apreçamento neutro ao risco de opções financeiras. Os tradicionais métodos paramétricos exigem a formulação de um modelo neutro ao risco explícito e são operacionalmente apenas para poucas funções densidade de probabilidade. Em nossa proposta, com simples suposições, evitamos a necessidade da formulação de um modelo neutro ao risco para os retornos. Primeiro, simulamos uma amostra de trajetórias de retornos sob a distribuição original P. Então, baseado na Transformada de Esscher, a amostra é reponderada, dando origem a uma amostra com risco neutralizado. Em seguida, os preços dos derivativos são obtidos através de uma simples média dos payoffs de cada trajetória da opção. Comparamos nossa proposta com alguns métodos de apreçamento tradicionais, aplicando quatro exercícios em situações diferentes, para destacar as diferenças e as semelhanças entre os métodos. Sob as mesmas condições e em situações similares, o método proposto reproduz os resultados dos métodos de apreçamento estabelecidos na literatura, o modelo de Black e Scholes (1973) e o método de Duan (1995). Quando as condições são diferentes, o método proposto indica que há mais risco do que outros métodos podem capturar. / [en] Option valuation is one of the most important topics in financial economics. This study introduces a nonparametric version of the Esscher transform for risk neutral option pricing. Traditional parametric methods require the formulation of an explicit risk-neutral model and are operational only for a few probability density functions. In our proposal, we make only mild assumptions on the price kernel and there is no need for the formulation of the risk-neutral model for the returns. First, we simulate sample paths for the returns under the historical distribution P. Then, based on the Esscher transform, the sample is reweighted, giving rise to a risk-neutralized sample from which derivative prices can be obtained by a simple average of the pay-offs of the option to each path. We compare our proposal with some traditional pricing methods, applying four exercises under different situations, which seek to highlight the differences and similarities between the methods. Under the same conditions and in similar situations, the option pricing method proposed reproduces the results of pricing methods fully established in the literature, the Black and Scholes [3] model and the Duan [13] method. When the conditions are different, the results show that the method proposed indicates that there is more risk than the other methods can capture.

Diffusion magnetic resonance imaging (dMRI) has made a significant breakthrough in neurological disorders and brain research thanks to its exquisite sensitivity to tissue cytoarchitecture. However, as the water diffusion process in neuronal tissues is a complex biophysical phenomena at molecular scale, it is difficult to infer tissue microscopic characteristics on a voxel scale from dMRI data. The major methodological contribution of this thesis is the development of an integrated and generic Monte Carlo simulation framework, 'Diffusion Microscopist Simulator' (DMS), which has the capacity to create 3D biological tissue models of various shapes and properties, as well as to synthesize dMRI data for a large variety of MRI methods, pulse sequence design and parameters. DMS aims at bridging the gap between the elementary diffusion processes occurring at a micrometric scale and the resulting diffusion signal measured at millimetric scale, providing better insights into the features observed in dMRI, as well as offering ground-truth information for optimization and validation of dMRI acquisition protocols for different applications.We have verified the performance and validity of DMS through various benchmark experiments, and applied to address particular research topics in dMRI. Based on DMS, there are two major application contributions in this thesis. First, we use DMS to investigate the impact of finite diffusion gradient pulse duration (delta) on fibre orientation estimation in dMRI. We propose that current practice of using long delta, which is enforced by the hardware limitation of clinical MRI scanners, is actually beneficial for mapping fibre orientations, even though it violates the underlying assumption made in q-space theory. Second, we employ DMS to investigate the feasibility of estimating axon radius using a clinical MRI system. The results suggest that the algorithm for mapping the direct microstructures is applicable to dMRI data acquired from standard MRI scanners.

<p>Reference radiation fields for x-ray qualities are described by the International Organization of Standards (ISO). This study describes the procedure to establish nine different low energy X-ray qualities at the national metrology laboratory, Swedish Radiation Protection Authority, following the document ISO 4037. Measurements of tube voltage, half-value layer, mean energy and spectral resolution have been performed for qualities N-15, N-20, N-25, N-30, N-40, L-20, L-30, L-35 and L-55. Furthermore, dose equivalent conversion coefficients for operational quantities ambient dose equivalent, personal dose equivalent and directional dose equivalent have been calculated by folding the mono-energetic conversion factors with measured spectral distributions of the x-ray qualities. The spectral distributions were unfolded from pulse-height distributions to photon distributions using simulated data of the semi-conductor detector used for measurements, generated with the Monte Carlo code PENELOPE.</p>