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This dissertation describes the application of two principled variance reduction strategies to increase the efficiency for two applications within medical physics. The first, called correlated Monte Carlo (CMC) applies to patient-specific, permanent-seed brachytherapy (PSB) dose calculations. The second, called adjoint-biased forward Monte Carlo (ABFMC), is used to compute cone-beam computed tomography (CBCT) scatter projections. CMC was applied for two PSB cases: a clinical post-implant prostate, and a breast with a simulated lumpectomy cavity. CMC computes the dose difference between the highly correlated dose computing homogeneous and heterogeneous geometries. The particle transport in the heterogeneous geometry assumed a purely homogeneous environment, and altered particle weights accounted for bias. Average gains of 37 to 60 are reported from using CMC, relative to un-correlated Monte Carlo (UMC) calculations, for the prostate and breast CTV’s, respectively. To further increase the efficiency up to 1500 fold above UMC, an approximation called interpolated correlated Monte Carlo (ICMC) was applied. ICMC computes using CMC on a low-resolution (LR) spatial grid followed by interpolation to a high-resolution (HR) voxel grid followed. The interpolated, HR is then summed with a HR, pre-computed, homogeneous dose map. ICMC computes an approximate, but accurate, HR heterogeneous dose distribution from LR MC calculations achieving an average 2% standard deviation within the prostate and breast CTV’s in 1.1 sec and 0.39 sec, respectively. Accuracy for 80% of the voxels using ICMC is within 3% for anatomically realistic geometries. Second, for CBCT scatter projections, ABFMC was implemented via weight windowing using a solution to the adjoint Boltzmann transport equation computed either via the discrete ordinates method (DOM), or a MC implemented forward-adjoint importance generator (FAIG). ABFMC, implemented via DOM or FAIG, was tested for a single elliptical water cylinder using a primary point source (PPS) and a phase-space source (PSS). The best gains were found by using the PSS yielding average efficiency gains of 250 relative to non-weight windowed MC utilizing the PPS. Furthermore, computing 360 projections on a 40 by 30 pixel grid requires only 48 min on a single CPU core allowing clinical use via parallel processing techniques.

Depuis quelques années, les codes de calculs Monte Carlo évoluant qui couplent un code Monte Carlo, pour simuler le transport des neutrons, à un solveur déterministe, qui traite l'évolution des milieux dû à l'irradiation sous le flux neutronique, sont apparus. Ces codes permettent de résoudre les équations de Boltzmann et de Bateman dans des configurations complexes en trois dimensions et de s'affranchir des hypothèses multi-groupes utilisées par les solveurs déterministes. En contrepartie, l'utilisation du code Monte Carlo à chaque pas de temps requiert un temps de calcul prohibitif.Dans ce manuscrit, nous présentons une méthodologie originale évitant la répétition des simulations Monte Carlo coûteuses en temps et en les remplaçant par des perturbations. En effet, les différentes simulations Monte Carlo successives peuvent être vues comme des perturbations des concentrations isotopiques de la première simulation. Dans une première partie, nous présenterons donc cette méthode, ainsi que la méthode de perturbation utilisée: l'échantillonnage corrélé. Dans un second temps, nous mettrons en place un modèle théorique permettant d'étudier les caractéristiques de la méthode des échantillons corrélés afin de comprendre ses effets durant les calculs en évolution. Enfin, dans la troisième partie nous discuterons de l'implémentation de cette méthode dans TRIPOLI-4® en apportant quelques précisions sur le schéma de calcul qui apportera une accélération importante aux calculs en évolution. Nous commencerons par valider et optimiser le schéma de perturbation à travers l'étude de l'évolution d'une cellule de combustible de type REP. Puis cette technique sera utilisée sur un calcul d'un assemblage de type REP en début de cycle. Après avoir validé la méthode avec un calcul de référence, nous montrerons qu'elle peut accélérer les codes Monte Carlo évoluant standard de presque un ordre de grandeur. / For several years, Monte Carlo burnup/depletion codes have appeared, which couple Monte Carlo codes to simulate the neutron transport to deterministic methods, which handle the medium depletion due to the neutron flux. Solving Boltzmann and Bateman equations in such a way allows to track fine 3-dimensional effects and to get rid of multi-group hypotheses done by deterministic solvers. The counterpart is the prohibitive calculation time due to the Monte Carlo solver called at each time step.In this document we present an original methodology to avoid the repetitive and time-expensive Monte Carlo simulations, and to replace them by perturbation calculations: indeed the different burnup steps may be seen as perturbations of the isotopic concentration of an initial Monte Carlo simulation. In a first time we will present this method, and provide details on the perturbative technique used, namely the correlated sampling. In a second time we develop a theoretical model to study the features of the correlated sampling method to understand its effects on depletion calculations. In a third time the implementation of this method in the TRIPOLI-4® code will be discussed, as well as the precise calculation scheme a meme to bring important speed-up of the depletion calculation. We will begin to validate and optimize the perturbed depletion scheme with the calculation of a REP-like fuel cell depletion. Then this technique will be used to calculate the depletion of a REP-like assembly, studied at beginning of its cycle. After having validated the method with a reference calculation we will show that it can speed-up by nearly an order of magnitude standard Monte-Carlo depletion codes.