Traditionally, uncertainties are handled by expanding the irradiated volume to ensure target dose coverage to a certain probability. The uncertainties arise from e.g. the uncertainty in positioning of the patient at every fraction, organ motion and in defining the region of interests on the acquired images. The applied margins are inherently population based and do not exploit the geometry of the individual patient. Probabilistic planning on the other hand incorporates the uncertainties directly into the treatment optimization and therefore has more degrees of freedom to tailor the dose distribution to the individual patient. The aim of this thesis is to create a framework for probabilistic evaluation and optimization based on the concept of dose coverage probabilities. Several computational challenges for this purpose are addressed in this thesis. The accuracy of the fraction by fraction accumulated dose depends directly on the accuracy of the deformable image registration (DIR). Using the simulation framework, we could quantify the requirements on the DIR to 2 mm or less for a 3% uncertainty in the target dose coverage. Probabilistic planning is computationally intensive since many hundred treatments must be simulated for sufficient statistical accuracy in the calculated treatment outcome. A fast dose calculation algorithm was developed based on the perturbation of a pre-calculated dose distribution with the local ratio of the simulated treatment’s fluence and the fluence of the pre-calculated dose. A speedup factor of ~1000 compared to full dose calculation was achieved with near identical dose coverage probabilities for a prostate treatment. For some body sites, such as the cervix dataset in this work, organ motion must be included for realistic treatment simulation. A statistical shape model (SSM) based on principal component analysis (PCA) provided the samples of deformation. Seven eigenmodes from the PCA was sufficient to model the dosimetric impact of the interfraction deformation. A probabilistic optimization method was developed using constructs from risk management of stock portfolios that enabled the dose planner to request a target dose coverage probability. Probabilistic optimization was for the first time applied to dataset from cervical cancer patients where the SSM provided samples of deformation. The average dose coverage probability of all patients in the dataset was within 1% of the requested.

O objetivo deste trabalho é analisar a distribuição das tensões residuais que resultam da combinação das variações volumétricas resultantes dos gradientes térmicos e das transformações de fase que ocorrem durante a têmpera de cilindros de aço AISI/SAE 1045, 4140 e 4340. O modelo matemático usado para este objetivo utiliza o programa AC3 de modelagem de tratamentos térmicos (curvas de transformação, curvas de resfriamento, microestrutura e a dureza do material), para alimentar um modelo de elementos finitos, considerando acoplamento termo-mecânico e comportamento não linear elasto-plástico, para previsão de tensões residuais em cilindros de aço AISI/SAE 1045, 4140 e 4340 temperados em água. São apresentados, também, os resultados de observações metalográficas e perfis de dureza que confirmam qualitativamente as previsões do programa AC3. A verificação do modelo numérico por elementos finitos foi efetuada através da medição das tensões residuais nos cilindros de aço com o emprego da técnica de difração de raios X. A simulação numérica, através do método dos elementos finitos comprova, nos três casos estudados, a existência de tensões residuais de compressão na região superficial após o processo de têmpera e indica de maneira quantitativa e qualitativa que as tensões mais significativas são as tangenciais. Os resultados obtidos a partir do modelo numérico mostraram uma aderência significativa em comparação com os resultados experimentais. / The aim of this work is to analyze the distribution of residual stresses resulting from combination of volumetric changes due to heat gradients and phase changes occurring during the quenching process of AISI/SAE 1045, 4140 and 4340 steel cylinders. The mathematical model used for this objective uses the AC3 program for modeling thermal treatments (transformation curves, cooling curves, microstructure and material hardness), whose results were fed into a finite element model, considering thermal-mechanical coupling and non-linear elastic-plastic behavior for forecasting of residual stresses in AISI/SAE 1045, 4140 and 4340 steel cylinders quenched in water. The observed microstructures and measured hardness confirmed qualitatively the previsions of the AC3 program. The results of finite element modeling were compared to experimental measurements of residual stresses measured at the surface, using X-Ray diffraction techniques. The finite element numerical simulation shows, for the three studied cases, the presence of compressive residual stresses in the surface region after a quenching process and indicates qualitatively and quantitatively that the most significant stresses are the tangential ones. The results obtained from the numerical model showed a significant adherence in comparison with the experimental results.

O objetivo deste trabalho é analisar a distribuição das tensões residuais que resultam da combinação das variações volumétricas resultantes dos gradientes térmicos e das transformações de fase que ocorrem durante a têmpera de cilindros de aço AISI/SAE 1045, 4140 e 4340. O modelo matemático usado para este objetivo utiliza o programa AC3 de modelagem de tratamentos térmicos (curvas de transformação, curvas de resfriamento, microestrutura e a dureza do material), para alimentar um modelo de elementos finitos, considerando acoplamento termo-mecânico e comportamento não linear elasto-plástico, para previsão de tensões residuais em cilindros de aço AISI/SAE 1045, 4140 e 4340 temperados em água. São apresentados, também, os resultados de observações metalográficas e perfis de dureza que confirmam qualitativamente as previsões do programa AC3. A verificação do modelo numérico por elementos finitos foi efetuada através da medição das tensões residuais nos cilindros de aço com o emprego da técnica de difração de raios X. A simulação numérica, através do método dos elementos finitos comprova, nos três casos estudados, a existência de tensões residuais de compressão na região superficial após o processo de têmpera e indica de maneira quantitativa e qualitativa que as tensões mais significativas são as tangenciais. Os resultados obtidos a partir do modelo numérico mostraram uma aderência significativa em comparação com os resultados experimentais. / The aim of this work is to analyze the distribution of residual stresses resulting from combination of volumetric changes due to heat gradients and phase changes occurring during the quenching process of AISI/SAE 1045, 4140 and 4340 steel cylinders. The mathematical model used for this objective uses the AC3 program for modeling thermal treatments (transformation curves, cooling curves, microstructure and material hardness), whose results were fed into a finite element model, considering thermal-mechanical coupling and non-linear elastic-plastic behavior for forecasting of residual stresses in AISI/SAE 1045, 4140 and 4340 steel cylinders quenched in water. The observed microstructures and measured hardness confirmed qualitatively the previsions of the AC3 program. The results of finite element modeling were compared to experimental measurements of residual stresses measured at the surface, using X-Ray diffraction techniques. The finite element numerical simulation shows, for the three studied cases, the presence of compressive residual stresses in the surface region after a quenching process and indicates qualitatively and quantitatively that the most significant stresses are the tangential ones. The results obtained from the numerical model showed a significant adherence in comparison with the experimental results.