Tesis sobre el tema "Geometrical uncertainties"

This research is devoted to the engineering of a generic, reliable and cost-effective method for the investigation of accuracy in layer based fabrication technologies. It begins with a review of the causes of deviations and uncertainties in component parts, analyses of the existing approaches for accuracy investigation and their limitations and disadvantages. The main focus of the research is the development of an original and convenient methodology capable of defining the dimensional uncertainties and accuracy of the technologies and the distribution of dimensional errors within the entire build area. The Grid Methodology is based on the discretisation of the object to allow the measurement, calculation, visualisation and analysis of part distortion in terms of linear and shear deviations from nominal. A single test piece and routine measurement procedure are utilised to estimate the distribution of the above entities; calculated in a similar way to the geometrical characteristics of strains in solid mechanics. The methodology was applied to research the causes of inaccuracy in the vertical direction of SLS Polystyrene. The presence of a critical dimension in height from where the distortion changes from shrinkage to extension was revealed and explained. The methodology was also utilised to estimate the necessary scaling factors to improve part accuracy, based on the calculated distortions. Implementation of the Grid Method to Micro Projection Stereolithography resulted in the ability to describe and estimate curling distortion in terms of angular deviations from nominal and separate it from linear distortions. - ii - Furthermore the application of the GM to the emerging micro-nano manufacturing sector has been shown to support the assessment of process capability. This provides a means of calculating process tolerances using results obtained from the single test piece. Investigation of the accuracy capabilities of three micro-processes was performed and their compatibility for designing process chains presented.

Le désaccordage intentionnel, plus communément appelé detuning, a été identifié comme une possible technonologie pour réduire la sensibilité du comportement dynamique de roues aubagées soumises au désaccordage involontaire, aussi appelé mistuning, causé par les dispersions matérielle d'une aube à une autre engendrées lors du processus de fabrication et par la variabilité des propriétés mécaniques des matériaux. Le désaccordage intentionnel est mis en place par l'introduction de motifs à partir desquels différents types de secteurs générateurs, ayant des propriétés géométriques et matérielles différentes, sont assemblés. Cependant, les récentes innovations technologiques impliquant l'utilisation d'aubes de plus en plus flexibles et plus légères conduisent à de grands niveaux de déplacements et de déformations, requiérant l'utilisation des équations dynamiques non linéaires tenant compte des non-linéarités géométriques. Ce travail est dédié à l'analyse robuste des effets des non-linéarités géométriques sur la dynamique non linéaire de roues aubagées désacccordées intentionnellement, en rotation, en présence de désaccordage involontaire. Le désaccordage involontaire correspond à des incertitudes dans le modèle numériques et sont prises en compte par une approche probabiliste. Cette thèse de nouveaux résultats concernant la dynamique non linéaire des roues aubagées désaccordées intentionnellement en présense de non-linéarités géométriques et en présence de désaccordage involontaire. Les analyses dynamiques sont effectuées dans le domaine temporel et analysées dans le domaine fréquentiel. L'analyse fréquentielle des réponses non-linéaires mettent en évidence des réponses significatives en dehors de la bande d'excitation. Les intervalles de confiance des réponses stochastiques permettent d'analyser la robustesse du modèle vis-à-vis des incertitudes, c'est-à-dire du niveau de désaccordage involontaire. La roue aubagées utilisée pour les simulations numériques est composée de 24 secteurs pour lesquels différents motifs de roues aubagées désaccordées intentionnellement sont analysés, avec ou sans désaccordage involontaire
The intentional mistuning, also called detuning has been identified as an efficient technological way for reducing the sensitivity of the forced response of bladed disks to unintentional mistuning (simply called mistuning), caused by the manufacturing tolerances and the small variations in the mechanical properties from blade to blade. The intentional mistuning consists in detuning the bladed disk structure by using partial or alternating patterns of different sector types. However, the recent technological improvements that include the use of more flexible and lighter blades can lead to large strains/displacements, which requires the use of nonlinear dynamic equations involving geometric nonlinearities. This work is devoted to the robust analysis of the effects of geometric nonlinearities on the nonlinear dynamic behavior of rotating detuned bladed disks in presence of mistuning. The detuning corresponds to uncertainties in the computational model, and are taken into account by a probabilistic approach. This thesis presents a series of novel results in dynamics of rotating bladed disks with mistuning and detuning in presence of nonlinear geometrical effects. The structural responses are computed in the time domain and are analyzed in the frequency domain. The frequency analysis exhibits responses outside the frequency band of excitation. The confidence region of the stochastic responses allows the robustness to be analyzed with respect to uncertainties, that is to say with respect to the level of mistuning. The bladed disk structure, which is used for the numerical simulations, is made up of 24 blades for which several different detuned patterns are investigated with and without mistuning

The aim of this thesis is to determine if the geometric uncertainties that are introduced into the image guided radiotherapy (IGRT) process by Cone Beam CT (CBCT) based IGRT equipment are sufficiently small that they do not pose a significant risk of geometrical error in treatment delivery. This was performed by quantifying and investigating the geometric uncertainties introduced by; (1) calibration of the image geometry, (2) correction of patient position performed by automatic treatment couch systems and (3) automatic image registration of the localisation image with a reference image. In addition, the feasibility of providing user feedback on the likelihood of accurate image registration was investigated. A method was developed using supervised machine learning based on the shape of the image registration algorithm's similarity metric surface. The geometric uncertainties introduced by image calibration and couch positioning were both shown to be less than 1 mm and therefore do not contribute significantly to the overall uncertainties in the IGRT process. Image registration performance for image guidance based on the bony anatomy of the skull was shown to be reproducible, accurate and robust with errors typically less than 1 mm. Moreover, image registration performance did not deteriorate significantly as imaging dose was reduced. For image guidance based on the soft tissues of the prostate, image registration performance was satisfactory for some CBCT images resulting in errors less than 2 mm. However, with the majority of CBCT images, image registration was highly irreproducible with high frequencies of failure. The user feedback of image registration quality was able to correctly classify 84% of image registrations into categories of good, acceptable and unacceptable. No unacceptable classifications were classed as good. CBCT based IGRT equipment does not introduce significant risks into the IGRT process however, appropriate quality assurance measures should be implemented to safeguard against equipment failure and drift since previous system calibration. Automatic image registration of the soft-tissues of the prostate cannot be relied upon for clinical use and therefore it should be used in conjunction with manual methods.

Computer models of the geometry of the real world have a tendency to assume that the shapes and positions of objects can be described exactly. However, real surfaces are subject to irregularities such as bumps and undulations and so do not have perfect, mathematically definable forms. Engineers recognise this fact and so assign tolerance specifications to their designs. This thesis develops a representation of geometric tolerance and uncertainty in assemblies of rigid parts. Geometric tolerances are defined by tolerance zones which are regions in which the real surface must lie. Parts in an assembly can slop about and so their positions are uncertain. Toleranced parts and assemblies of toleranced parts are represented by networks of tolerance zones and datums. Each arc in the network represents a relationship implied by the tolerance specification or by a contact between the parts. It is shown how all geometric constraints can be converted to an algebraic form. Useful results can be obtained from the network of tolerance zones and datums. For example it is possible to determine whether the parts of an assembly can be guaranteed to fit together. It is also possible to determine the maximum slop that could occur in the assembly assuming that the parts satisfy the tolerance specification. Two applications of this work are (1) tolerance checking during design and (2) analysis of uncertainty build-up in a robot assembly plan. I n the former, a designer could check a proposed tolerance specification to make sure that certain design requirements are satisfied. In the latter, knowledge of manufacturing tolerances of parts being manipulated can be used to determine the constraints on the positions of the parts when they are in contact with other parts.

A fundamental challenge in the treatment planning process of multi-fractional external-beam radiation therapy (EBRT) is the tradeoff between tumor control and normal tissue sparing in the presence of geometric uncertainties (GUs). To accommodate GUs, the conventional way is to use an empirical planning treatment volume (PTV) margin on the treatment target. However, it is difficult to determine a near-optimal PTV margin to ensure specified target coverage with as much normal tissue protection as achievable. Coverage optimized planning (COP) avoids this problem by optimizing dose in possible virtual treatment courses with GU models directly incorporated. A near-optimal dosimetric margin generated by COP was reported to savvily accommodate setup errors of target and normal tissues for prostate cancer treatment. This work further develops COP to account for (1) deformable organ motion and (2) delineation uncertainties for high-risk prostate cancer patients. The clinical value of COP is investigated by comparing with two margin-based planning techniques: (i) optimized margin (OM) technique that iteratively modifies PTV margins according to the evaluated target coverage probability and (ii) fixed margin (FM) technique that uses empirically selected constant PTV margins. Without patient-specific coverage probability estimation, FM plans are always less immune to the degraded effect of the modeled GUs than the COP plans or the OM plans. Empirical PTV margins face more risks of undesirable target coverage probability and/or excessive dose to surrounding OAR. The value of COP relative to OM varies with different GUs. As implemented for deformable organ motions, COP has limited clinical benefit. Due to optimization tradeoffs, COP often results in target coverage probability below the prescribed value while OM achieves better target coverage with comparable normal tissue dose. For delineation uncertainties, the clinical value of COP is potentially significant. Compared to OM, COP successfully maintains acceptable target coverage probability by exploiting the slack of normal tissue dose in low dose regions and maximally limiting high dose to normal tissue within tolerance.

Ce travail de thèse porte sur la quantification et la prise en compte des variations anatomiques en cours de radiothérapie guidée par l'image pour le cancer de la prostate. Nous proposons tout d'abord une approche basée population pour quantifier et analyser les incertitudes géométriques, notamment à travers des matrices de probabilité de présence de la cible en cours de traitement. Nous proposons ensuite une méthode d'optimisation des marges suivant des critères de couverture géométrique de la cible tumorale. Cette méthode permet d'obtenir des marges objectives associées aux différents types d'incertitudes géométriques et aux différentes modalités de repositionnement du patient. Dans un second temps, nous proposons une méthode d'estimation de la dose cumulée reçue localement par les tissus pendant un traitement de radiothérapie de la prostate. Cette méthode repose notamment sur une étape de recalage d'images de façon à estimer les déformations des organes entre les séances de traitement et la planification. Différentes méthodes de recalage sont proposées, suivant les informations disponibles (délinéations ou points homologues) pour contraindre la déformation estimée. De façon à évaluer les méthodes proposées au regard de l'objectif de cumul de dose, nous proposons ensuite la génération et l'utilisation d'un fantôme numérique reposant sur un modèle biomécanique des organes considérés. Les résultats de l'approche sont présentés sur ce fantôme numérique et sur données réelles. Nous montrons ainsi que l'apport de contraintes géométriques permet d'améliorer significativement la précision du cumul et que la méthode reposant sur la sélection de contraintes ponctuelles présente un bon compromis entre niveau d'interaction et précision du résultat. Enfin, nous abordons la question de l'analyse de données de populations de patients dans le but de mieux comprendre les relations entre dose délivrée localement et effets cliniques. Grâce au recalage déformable d'une population de patients sur une référence anatomique, les régions dont la dose est significativement liée aux événements de récidive sont identifiées. Il s'agit d'une étude exploratoire visant à terme à mieux exploiter l'information portée par l'intégralité de la distribution de dose, et ce en fonction du profil du cancer.

Geometric uncertainties are inevitable in radiotherapy. These uncertainties in tumour position are classified as systematic (Ε) and random (δ) errors. To account for these uncertainties, a margin is added to the clinical target volume (CTV) to create the planning target volume (PTV). The size of the PTV is critical for obtaining an optimal treatment plan. Dose-based (i.e., physical) margin recipes as a function of systematic and random errors based on coverage probability of a certain level of dose (90% or 95% of the prescription dose) have been published and widely used. However, with a TCP-based margin it is possible to consider fractionation and the radiobiological characteristics, especially the dose-response slope (50) of the tumour. Studies have shown that the density of the clonogens decrease from the boundary of the gross tumour volume (GTV). In such a scenario, dose that is lower than in the GTV should be sufficient to eradicate these clonogens. Thus a smaller PTV margin with a gradual dose fall off can be used if the clonogen density in the GTV-CTV region is found to be lower than in GTV. Studies have reported tiny tumour islets outside the CTV region. These tiny tumour islets can be eradicated in some cases by the incidental dose outside the PTV due to the nature of the photon beam irradiation, but if they are not in the beam path the treatment outcome is compromised. In this thesis, a Monte Carlo approach is used to simulate the effect of geometric uncertainties, number of fractions and dose-response slope (gamma50) using the 'enhanced Marsden' TCP model on the treatment outcome. Systematic and random errors were drawn from a pseudo-random number generator. The dose variations caused by tumour displacements due to geometric uncertainties in the CTV are accumulated each fraction on a voxel-by-voxel basis. Required margins for ≤ 1% mean population TCP (TCPpop) for four-field (4F) brick and a highly conformal spherical dose distribution for varying number of fractions, different γ50 and different combinations of Ε and δ are investigated. It is found that TCP-based margins are considerably smaller than dose-based recipes in most cases except for tumours with a steep dose-response slope (high γ50) and a small number of fractions for both 4F and spherical dose distributions. For smaller geometric uncertainties (Ε = δ = 1 mm) margins can be close to zero for the 4F technique due to high incidental dose outside the PTV. It is evident from the analyses that margins depend on the number of fractions, γ50, the degree of dose conformality in addition to Ε and δ. Ideally margins should be anisotropic and individualized, taking into account γ50, number of fractions, and the dose distribution, as well as estimates of Ε and γ. No single 'recipe' can adequately account for all these variables. Using an exponential clonogen distribution in the GTV-CTV region, possible PTV margin reduction is demonstrated. Moreover, the effect of extra-CTV tumour islets is studied using a prostate IMRT plan. The islets were randomly distributed around the CTV with in a radius of 3 cm to represent different patients. The doses were rescaled up to 102 Gy to obtain the dose-response curve (DRC). Interestingly, the obtained DRC showed a biphasic response where 100% TCP could not be achieved just by escalating the dose. Another potential problem encountered in intensity-modulated radiotherapy (IMRT) is the problems caused by the 'interplay' effect between the respiration-induced tumour motion and the multileaf collimator (MLC) leaves movement during treatment. Several dosimetric studies in the literature have shown that 'interplay' effects blur the dose distribution by producing 'hot' and 'cold' dose inside the tumour. Most of these studies were done in a phantom with ion chambers or films, which provide only 1D or 2D dose information. If 3D dose information is available, a TCP based analysis would provide a direct estimate of interplay on the clinical outcome. In this thesis, an in-house developed dose model enabled us to calculate the 3D time-resolved dose contribution to each voxel in the target volume considering the change in segment shapes and position of the target volume. Using the model, delivered dose is accumulated in a voxel-by-voxel basis inclusive of tumour motion over the course of treatment. The effect of interplay on dose and TCP is studied for conventionally and hypofractionated treatments using DICOM datasets. Moreover, the effect of dose rate on interplay is also studied for single-fraction treatments. Simulations were repeated several times to obtain mean population TCP (TCPpop) for each plan. The average variation observed in mean dose to the target volumes were -0.76 ± 0.36% for the 20 fraction treatment and -0.26 ± 0.68%, -1.05 ± 0.98% for the 3- and single-fraction treatments respectively. For the 20-fraction treatment, the drop in TCPpop was -1.05 ± 0.39%, whereas for the 3 and single fraction treatments it was -2.8 ± 1.68% and -4.0 ± 2.84% respectively. By reducing the dose rate from 600 to 300 MU/min for the single-fraction treatments, the drop in TCPpop was reduced by ~ 1:5%. In summary, the effect of interplay on treatment outcome is negligible for conventionally fractionated treatments, whereas a considerable drop in TCP is observed for the 3- and single-fraction treatments. Where no motion management techniques such as tracking or gating are available for hypo-fractionated treatments, reduced dose rate could be used to reduce the interplay effect.

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.

Dans cette thèse, on s’intéresse à la modélisation et à la simulation numérique de systèmes couplés fluide-structure, constitués d'une structure élastique partiellement remplie d'un liquide avec une surface libre, tenant compte des effets de ballottement et de capillarité. Le fluide interne est considéré comme linéaire, acoustique, dissipatif et la structure, à comportement élastique linéaire, est soumise à de grands déplacements induisant des non-linéarités géométriques. Le travail présenté dans ce manuscrit s'intéresse tout d’abord à l’étude théorique de ce type de système couplé fluide-structure et s'attache à la construction et à l’implémentation du modèle numérique en utilisant un modèle réduit non linéaire adapté. Ce modèle réduit permet d'effectuer les calculs dynamiques non linéaires et permet également de mieux comprendre les phénomènes liés à chaque partie du système couplé. Plusieurs applications numériques sont ensuite développées permettant l’analyse de divers phénomènes liés aux différents couplages et transferts d’énergie dans le système. Le premier axe de développement consiste en la quantification et en la réduction du temps de calcul nécessaire à la construction de la base de projection du modèle réduit pour des modèles numériques de systèmes couplés fluide-structure de très grande dimension. Une nouvelle méthodologie est présentée permettant de réduire les coûts numériques induits par la résolution de trois problèmes généralisés aux valeurs propres ne pouvant être résolus sur les ordinateurs de puissance intermédiaire. Un second axe de développement concerne la quantification de l’influence de l'opérateur de couplage entre la structure et la surface libre du liquide interne permettant de prendre en compte la condition d’angle de contact capillaire au niveau de la ligne triple tout en considérant une structure déformable. Le troisième axe est basé sur des travaux expérimentaux publiés en 1962, dans le cadre de développements de la NASA pour les lanceurs, qui ont mis en évidence un phénomène inattendu de ballottement de grande amplitude en basses-fréquences pour le liquide interne lors de l’excitation moyenne-fréquence du réservoir. On propose de revisiter et d'expliquer les causes de ce phénomène inattendu au travers d’une simulation numérique prenant en compte les non-linéarités géométriques de la structure. Enfin, un dernier axe de développement est consacré à la propagation des incertitudes non paramétriques de la structure dans le système par les différents mécanismes de couplages. La modélisation stochastique non paramétrique est celle de l'approche probabiliste non paramétrique qui utilise la théorie des matrices aléatoires. Une méthodologie permettant l’identification de l'hyperparamètre est présentée, basée sur un ensemble de données expérimentales et sur la résolution d'un problème statistique inverse. Une validation numérique de cette méthode sur un ensemble de données expérimentales simulées est présentée
In this thesis, we are interested in computationally modeling and simulating coupled fluid-structure systems constituted of an elastic structure partially filled with a fluid with a free surface, considering the effects of sloshing and capillarity. The internal fluid is linear, acoustic, dissipative, and the linear elastic structure is submitted to large displacements inducing geometrical nonlinearities. The work presented in this manuscript first details the theoretical study regarding such coupled fluid-structure systems and focuses on the construction and implementation of the computational model using an adapted nonlinear reduced-order model. This reduced-order model allows for performing the nonlinear dynamical simulations and for better understanding the phenomena related to each subset of the coupled system. Several numerical applications are then presented to analyze various phenomena related to the different coupling mechanisms and energy transfers in such fluid-structure system. The first development axis consists in quantifying and reducing the computational resources required for the construction of the projection basis of the reduced-order model when dealing with very-large dimension fluid-structure computational models. A new methodology is presented, which allows for reducing the computational costs required for solving three generalized eigenvalue problems that cannot be solved on medium-power computers. A second development axis is devoted to the quantification of the influence of the coupling operator between the structure and the free surface of the internal liquid allowing for taking into account the capillary contact angle condition on the triple line while considering a deformable structure. The third axis is based on experimental research published in 1962 in the framework of NASA researches for orbital launchers, which highlighted an unexpected phenomenon of large amplitude and low-frequency sloshing of an internal liquid for a medium-frequency excitation of the tank. We propose to revisit these experimental results and to explain the causes of such unexpected phenomenon through a numerical simulation taking into account the geometrical nonlinearities of the structure. Finally, the last development axis is devoted to the propagation of nonparametric uncertainties of the structure in the system by the different coupling mechanisms. The nonparametric stochastic model is the nonparametric probabilistic approach using the random matrix theory. A methodology for identifying the hyperparameter is presented, based on an experimental data set and on an inverse statistical problem. A numerical validation of this method on a simulated experimental data set is presented

博士
國立中央大學
土木工程學系
106
This study proposes analytical and numerical solutions for the uncertainties of volumetric fraction (Vf), fracture intensity (FI), and mechanical properties in heterogeneous media and discontinuous rock masses, respectively. In addition, the relationship of the uncertainties of geometries estimates and mechanical properties can be also obtained via statistical theorem. The uncertainties induced by Vf or FI can be obtained by addressing the solutions of geometric uncertainty. For a heterogeneous media (bimrock, concrete…), the representative volume element (RVE) is employed for a statistical derivation model. The circle-squared RVE is used for 2D isotropic (or randomly orientated) heterogeneous rock features, the ellipse-parallelogram RVE is used for 2D anisotropic (or preferred orientation) heterogeneous medium features, and the sphere-cubic RVE is used for 3D heterogeneous medium features. To validate the analytical solutions, this study develops numerical heterogeneous media codes in 2D and 3D to demonstrate 1D and 2D Vf measurements, respectively. These codes employ periodic boundaries to eliminate the boundary effect and to control the volumetric fraction of the model more precisely. For a discontinuous rock mass (fractured rock), the Poisson distribution model is used for a mathematical derivation model for 1D, 2D, and 3D fracture intensity (P10, P21, and P32, respectively) measurements. This study also develops a discrete fracture network (DFN) code to simulate P10 and P21 measurements. In addition, the commercial DFN code, FracMan, is employed to simulate P21 and P32 measurements. Similarly, these simulations are used to validate the analytical solutions of fractured rock. The uncertainty of the mechanical properties induced by Vf or FI can be obtained by substituting the results for the uncertainty of Vf or FI into a normal random variable from a correlative model of that property. In the correlative model analysis, the mechanical properties of a heterogeneous rock mass can be determined using micro-mechanical models or Particle Flow Code (PFC) simulations, and the mechanical properties of a discontinuous rock mass can be determined via simulations of a synthetic rock mass (SRM, which combines DFN and PFC models). Several systematic parametric studies are carried out to investigate the mechanical properties and their uncertainties and obtain those of a heterogeneous or discontinuous rock induced by assemblages (block, fracture, or particle). According to the statistical analysis, the uncertainties of the mechanical properties of site samplings can be calculated from the uncertainties induced by the Vf or FI and the uncertainties induced by assemblages of blocks, fractures, and particles. This relation can be confirmed through numerical simulations. One or two illustrations of how to use the proposed solutions are given at the end of each chapter.

Radiation therapy is afflicted by a multitude of geometric uncertainties, which must be compensated to ensure treatment success. Such mitigation is currently achieved by enlarging the apparent target volume by various safety margins. This thesis investigated uncertainty sources relating to target position and extent in oesophageal carcinoma, both static and dynamic, and evaluated their impact in a combined model. The first were errors inherent to delineation of the gross tumour volume (GTV), where computed tomography (CT) imaging, the overall modality of choice for target volume delineation (TVD), has a tendency to overestimate target extent. Two rival modalities, [18F]-fluorodeoxyglucose positron emission tomography (FDG-PET) and endoscopic ultrasound (EUS), are generally expected to yield more accurate assessments. EUS has previously suffered from a difficulty in transferring its findings to the spatial domain in which TVD is undertaken. This limitation was overcome here through the use of endoscopically implanted fiducial markers visible on the planning CT. This has enabled their inclusion in TVD and allowed a direct comparison of FDG-PET and EUS based target extents, which were found to agree quite well on average, but showed occasional discrepancies on the order of a few cm. Recently published reports on inter-observer variability (IOV) in TVD of oesophageal carcinoma were summarised with a particular focus on its reduction afforded by the use of fiducial markers. The influence of IOV was investigated more widely in other tumour entities, where it was shown to increase during the course of treatment, mostly due to differing adaptation practices. Microscopic disease extension (MDE), undetectable prior to treatment with current imaging techniques, constituted the second uncertainty source. Reports on histopathological measurements of MDE incidence and its distance from the main tumour were reviewed and spatial measurements extracted to derive a combined estimate of the distribution of extension distances. The overall incidence was estimated as 14.6%, with individual studies reporting widely differing values. Conventional margin widths to compensate for MDE were extracted from the pooled distribution and found to largely agree with the common clinical choice of 3–5 cm, but associated with broad confidence intervals. The addition of such margins to the GTV defines the clinical target volume (CTV). Most studies acknowledged tissue deformations as a major problem, but not all implemented means to prevent or correct it. Preliminary measurements on oesophageal resection specimens were presented, wherein fiducial markers were used to measure tissue deformations, and might ultimately be used to correct spatial measurements of MDE. Fiducial markers also facilitated the study of inter-fractional target mobility in a cohort (n=23) receiving daily orthogonal X-ray imaging for target positioning verification. Markers were found capable of detecting target misalignments, which were a common occurrence with 54% and 15% of analysed markers and treatment fractions showing displacements from their planned position in excess of 5 and 10mm, respectively. Mobility amplitudes were highest in the longitudinal direction and a dependence on tumour location was hinted at, with motion more restricted for proximally located lesions. Measures of systematic and random mobility components were extracted to derive safety margins, which are added to the CTV to form the planning target volume (PTV). A radiobiological model of tumour control probability (TCP) was then evaluated under different uncertainty scenarios. It simplified the tumour system to its longitudinal dimension, which is most affected by the aforementioned phenomena, and simulated positional uncertainties, as well as MDE. The differential impact of systematic and random mobility components on TCP was demonstrated and margin widths sufficient to limit TCP reduction to 1% could best be described by a quadratic combination of their magnitudes. This composition was still applicable when MDE was introduced and mitigated by a conventional margin, but the relative impact of both components shifted. The addition of a PTV margin to the CTV afforded the MDE-positive subpopulation similar protection against positional uncertainties as the same margin achieved without consideration of MDE. The MDE-negative subpopulation attained a much improved tolerance to positional uncertainties through the CTV margin, which also propagated to the overall population. An alternative mitigation of MDE was attempted by optimising the applied dose distribution to an assumed tumour cell density distribution motivated by the literature, which decreases towards the target edge. The optimisation maximised TCP while preserving the integral dose delivered with a conventional margin, under the assumption that this translates into a similar likelihood of normal tissue toxicity. Reduced doses could be delivered to lower cell density regions without sacrificing overall TCP, but this reduction was modest despite vastly diminished cell densities. When this spared dose was redistributed so as to enlarge the treated area, negligible TCP change was observed, but redistribution to the central target did result in appreciably improved TCP in both subpopulations. These effects persisted when positional uncertainties were added and when MDE incidence was increased to the most extreme value reported in the literature.

IMRT uses non-uniform beam intensities within a radiation field to provide patient-specific dose shaping, resulting in a dose distribution that conforms tightly to the planning target volume (PTV). Unavoidable geometric uncertainty arising from patient repositioning and internal organ motion can lead to lower conformality index (CI), a decrease in tumor control probability (TCP) and an increase in normal tissue complication probability (NTCP). The CI of the IMRT plan depends heavily on steep dose gradients between the PTV and organ at risk (OAR). Geometric uncertainties reduce the planned dose gradients and result in a less steep or “blurred” dose gradient. The blurred dose gradients can be maximized by constraining the dose objective function in the static IMRT plan or by reducing geometric uncertainty during treatment with corrective verification imaging. Internal organ motion and setup error were evaluated simultaneously for 118 individual patients with implanted fiducials and MV electronic portal imaging (EPI). The Gaussian PDF is patient specific and group standard deviation (SD) should not be used for accurate treatment planning for individual patients. Frequent verification imaging should be employed in situations where geometric uncertainties are expected. The dose distribution including geometric uncertainties was determined from integration of the convolution of the static dose gradient with the PDF. Local maximum dose gradient (LMDG) was determined via optimization of dose objective function by manually adjusting DVH control points or selecting beam numbers and directions during IMRT treatment planning. EUDf is a useful QA parameter for interpreting the biological impact of geometric uncertainties on the static dose distribution. The EUDf has been used as the basis for the time-course NTCP evaluation in the thesis. Relative NTCP values are useful for comparative QA checking by normalizing known complications (e.g. reported in the RTOG studies) to specific DVH control points. For prostate cancer patients, rectal complications were evaluated from specific RTOG clinical trials and detailed evaluation of the treatment techniques. Treatment plans that did not meet DVH constraints represented additional complication risk. Geometric uncertainties improved or worsened rectal NTCP depending on individual internal organ motion within patient.

This work addresses the application of Isogeometric Analysis to the simulation of particle accelerator cavities and other electromagnetic devices whose performance is mainly determined by their geometry. By exploiting the properties of B-Spline and Non-Uniform B-Spline basis functions, the Isogeometric approximation allows for the correct discretisation of the spaces arising from Maxwell's equations and for the exact representation of the computational domain. This choice leads to substantial improvements in both the overall accuracy and computational effort. The suggested framework is applied to the evaluation of the sensitivity of these devices with respect to geometrical changes using Uncertainty Quantification methods and to shape optimisation processes. The particular choice of basis functions simplifies the construction of the geometry deformations significantly. Finally, substructuring methods are proposed to further reduce the computational cost due to matrix assembly and to allow for hybrid coupling of Isogeometric Analysis and more classical Finite Element Methods. Considerations regarding the stability of such methods are addressed. The methods are illustrated by simple numerical tests and real world device simulations with particular emphasis on particle accelerator cavities.