El CMC, tamaño y forma de micelas son características importantes en la determinación de sus principales propiedades y campos de aplicación. Esta tesis tiene dos partes, las transiciones de forma de las micelas que se trata con "Single chain Field Theory, /SCMFT)" y simulaciones de Monte Carlo. El SCMFT reveló todas las características esenciales de las transiciones de forma esférica a cilíndrica y esférica a disco de las micelas. MC muestra que las transiciones esfera a cilindro se produce a través de una región en que esferas y cilindros coexisten junto con otras formas intermedias.

Hadron Therapy is an advanced radiotherapy technique for cancer treatment. It offers a better irradiation ballistic than conventional techniques and therefore requires appropriate quality assurance procedures. In this work, we upgraded the GEANT4-based GATE Monte Carlo platform in order to recalculate the TPS dose distributions in view of further benchmarking. In a first step, we selected an appropriate simulation environment (physics models and parameters) in order to produce accurate and efficient simulations. GATE simulations were validated using measurements and other Monte Carlo codes for depth-dose and transverse profiles. While a good agreement was found for depth-dose profiles, larger discrepancies were pointed out for transverse profiles. In a second step, we developed a modeling method to simulate active scanning beam delivery systems, which does not require to simulate the components of the treatment nozzle. The method has been successfully applied to an IBA proton therapy system and validated against measurements for complex treatment plans. Interfaces have also been developed in order to link DICOM RT ION PLAN and DICOM RT DOSE with GATE. Finally, we compared in a third step the TPS and Monte Carlo dose distributions in homogeneous and heterogeneous configurations. The beam models of both dose engines were in satisfactory agreement, allowing further evaluation of clinical treatment plans. A two-field prostate plan has been evaluated, showing a satisfactory agreement between the TPS and Monte Carlo, and demonstrating the novel capabilities of the platform for the evaluation of the TPS. To summarize, we selected an appropriate simulation environment for proton therapy, proposed a modeling method for active scanning systems and presented a method to compare the TPS and Monte Carlo dose distributions. All tools developed in GATE were or will be publicly released. A detailed validation stage of the system including absolute dosimetry is still necessary, in order to quantitatively evaluate its accuracy in various homogeneous and heterogeneous configurations. In this thesis, we have demonstrated that the GATE Monte Carlo platform is a good candidate for the simulation of active scanning delivery systems, allowing further TPS benchmarking. Moreover, the GATE platform also handles imaging applications, such as PET or prompt-gamma imaging towards online treatment monitoring and paves the way of interdisciplinary research advances.

The thesis studies the martingale properties, probabilistic methods and efficient unbiased Monte Carlo simulation methods for various time-homogeneous diffusion models commonly used in mathematical finance. Some of the popular stochastic volatility models such as the Heston model, the Hull-White model and the 3/2 model are special cases. The thesis consists of the following three parts: Part I: Martingale properties in time-homogeneous diffusion models: Part I of the thesis studies martingale properties of stock prices in stochastic volatility models driven by time-homogeneous diffusions. We find necessary and sufficient conditions for the martingale properties. The conditions are based on the local integrability of certain deterministic test functions. Part II: Analytical pricing methods in time-homogeneous diffusion models: Part II of the thesis studies probabilistic methods for determining the Laplace transform of the first hitting time of an integral functional of a time-homogeneous diffusion, and pricing an arithmetic Asian option when the stock price is modeled by a time-homogeneous diffusion. We also consider the pricing of discrete variance swaps and discrete gamma swaps in stochastic volatility models based on time-homogeneous diffusions. Part III: Nearly Unbiased Monte Carlo Simulation: Part III of the thesis studies the unbiased Monte Carlo simulation of option prices when the characteristic function of the stock price is known but its density function is unknown or complicated.

The goal of radiotherapy is to operate within the therapeutic window - delivering doses of ionizing radiation to achieve locoregional tumour control, while minimizing normal tissue toxicity. A greater therapeutic ratio can be achieved by utilizing radiosensitizing agents designed to enhance the effects of radiation at the tumour. Gold nanoparticles (AuNP) represent a novel radiosensitizer with unique and attractive properties. AuNPs enhance local photon interactions, thereby converting photons into localized damaging electrons. Experimental reports of AuNP radiosensitization reveal this enhancement effect to be highly sensitive to irradiation source energy, cell line, and AuNP size, concentration and intracellular localization. This thesis explored the physics and some of the underlying mechanisms behind AuNP radiosensitization. A Monte Carlo simulation approach was developed to investigate the enhanced photoelectric absorption within AuNPs, and to characterize the escaping energy and range of the photoelectric products. Simulations revealed a 10^3 fold increase in the rate of photoelectric absorption using low-energy brachytherapy sources compared to megavolt sources. For low-energy sources, AuNPs released electrons with ranges of only a few microns in the surrounding tissue. For higher energy sources, longer ranged photoelectric products travelled orders of magnitude farther. A novel radiobiological model called the AuNP radiosensitization predictive (ARP) model was developed based on the unique nanoscale energy deposition pattern around AuNPs. The ARP model incorporated detailed Monte Carlo simulations with experimentally determined parameters to predict AuNP radiosensitization. This model compared well to in vitro experiments involving two cancer cell lines (PC-3 and SK-BR-3), two AuNP sizes (5 and 30 nm) and two source energies (100 and 300 kVp). The ARP model was then used to explore the effects of AuNP intracellular localization using 1.9 and 100 nm AuNPs, and 100 and 300 kVp source energies. The impact of AuNP localization was most significant for low-energy sources. At equal mass concentrations, AuNP size did not impact radiosensitization unless the AuNPs were localized in the nucleus. This novel predictive model of AuNP radiosensitization could help define the optimal use of AuNPs in potential clinical strategies by determining therapeutic AuNP concentrations, and recommending when active approaches to cellular accumulation are most beneficial.

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Radiation therapy is continuously increasing in complexity due to technological innovation in delivery techniques, necessitating thorough dosimetric verification. Comparing accurately predicted portal dose images to measured images obtained during patient treatment can determine if a particular treatment was delivered correctly. The goal of this thesis was to create a method to predict portal dose images that was versatile and accurate enough to use in a clinical setting. All measured images in this work were obtained with an amorphous silicon electronic portal imaging device (a-Si EPID), but the technique is applicable to any planar imager. A detailed, physics-motivated fluence model was developed to characterize fluence exiting the linear accelerator head. The model was further refined using results from Monte Carlo simulations and schematics of the linear accelerator. The fluence incident on the EPID was converted to a portal dose image through a superposition of Monte Carlo-generated, monoenergetic dose kernels specific to the a-Si EPID. Predictions of clinical IMRT fields with no patient present agreed with measured portal dose images within 3% and 3 mm. The dose kernels were applied ignoring the geometrically divergent nature of incident fluence on the EPID. A computational investigation into this parallel dose kernel assumption determined its validity under clinically relevant situations. Introducing a patient or phantom into the beam required the portal image prediction algorithm to account for patient scatter and attenuation. Primary fluence was calculated by attenuating raylines cast through the patient CT dataset, while scatter fluence was determined through the superposition of pre-calculated scatter fluence kernels. Total dose in the EPID was calculated by convolving the total predicted incident fluence with the EPID-specific dose kernels. The algorithm was tested on water slabs with square fields, agreeing with measurement within 3% and 3 mm. The method was then applied to five prostate and six head-and-neck IMRT treatment courses (~1900 clinical images). Deviations between the predicted and measured images were quantified. The portal dose image prediction model developed in this thesis work has been shown to be accurate, and it was demonstrated to be able to verify patients’ delivered radiation treatments.

Introduction Monte-Carlo simulations can be used to assess isotope production on small medical cyclotrons. These simulations calculate the particle interactions with electric and magnetic fields, as well as the nuclear reactions. The results can be used to predict both yields and isotopic contaminations and can aid in the optimum design of target material and target geometry [1,2]. FLUKA is a general-purpose tool widely used in many applications from accelerator shielding to target design, calorimetry, activation, dosimetry, detector design, neutrino physics, or radiotherapy [3,4]. In this work, we applied the Monte-Carlo code FLUKA to determine the accuracy of predicting yields of various isotopes as compared to experimental yields. Material and Methods The proton beam collimation system, as well as the liquid and solid target of the TR13 cyclotron at TRIUMF, has been modeled in FLUKA. The proton beam parameters were initially taken from the cyclotron design specifications and were optimized against experimental measurements from the TR13. Data from irradiations of different targets and with different beam currents were collected in order to account for average behavior, see FIG. 1. Yields for a pencil proton beam as well as a beam spread out in direction and energy have been calculated and have been compared to experimental results obtained with the TR13. Results and Conclusion The reactions listed in TABLE 1 were assessed. For most reactions a good agreement was found in the comparison between experimental and simulated saturation yield. TABLE 1 only shows the yields simulated with a proton beam with a spread in both direction and energy. In most cases, the simulated yield is slightly larger or comparable. Only the calculated yield for 55Co was significantly lower by a factor of 4.2. This is still a good agreement considering that FLUKA was originally a high-energy physics code. It may indicate that the FLUKA internal cross-section calculation for this isotope production needs some optimization. In summary, we conclude that FLUKA can be used as a tool for the prediction of isotope production as well as for target design.

In order to reduce the unnecessary radiation exposure for the clinical personnel, the optimization of procedures in the quality control test of gamma camera was investigated. A significant component of the radiation dose in performing the quality control testing is handling phantoms of radioactivity, especially the mixing to get a uniform activity concentration. Improving the phantom mixing techniques appeared to be a means of reducing radiation dose to personnel. However, this is difficult to perform without a continuous dynamic tomographic acquisition system to study mixing the phantom. In the first part of this study a computational fluid dynamics model was investigated to simulate the mixing procedure. Mixing techniques of shaking and spinning were simulated using the computational fluid dynamics tool FLUENT. In the second part of this study a Siemens E.Cam gamma camera was simulated using the Monte Carlo software SIMIND. A series of validation experiments demonstrated the reliability of the Monte Carlo simulation. In the third part of this study the simulated the mixing data from FLUENT was used as the source distribution in SIMIND to simulate a tomographic acquisition of the phantom. The planar data from the simulation was reconstructed using filtered back projection to produce a tomographic data set for the activity distribution in the phantom. This completed the simulation routine for phantom mixing and verified the Proof-in-Concept that the phantom mixing problem can be studied using a combination of computational fluid dynamics and nuclear medicine radiation transport simulations.