Electrical Impedance Tomography (ElT) is an emerging imaging technique with applications in the medical field and in the field of industrial process tomography (lPT). Until recently, data acquisition and image reconstruction schemes have been constructed with the assumption that the object being imaged is two-dimensional. In recent years, some research groups have started to address the third dimensional aspects of ElT by both building three dimensional enabled data acquisition systems and solving the three dimensional Forward Problem numerically since this allows the possibility of modelling complex shapes. However, solving the Forward Problem analytically is still very attractive as an analytical solution does not depend on the way the domain has been meshed. Furthermore, if dynamic images are reconstructed which are less sensitive to the model of the electrodes employed, the shape of the object being imaged and the position of the electrodes, an analytical solution to the Forward Problem can be used to reconstruct dynamic three dimensional images. This thesis will start by describing how a full analytical solution for a finite right circular cylinder (which approximately models the human thorax) on which two electrodes have been placed, is derived. It will be shown that the analytical solution has two different forms. Results will be presented detailing the convergence performance of the two different forms as well as comparisons between the analytical solution and experimentally obtained data. Finally three dimensional images reconstructed using these methods will be presented. In order to better approximate the shape of the human thorax, the above work has been extended to provide an analytical solution for an elliptical cylinder and this is presented in this thesis for the first time together with some simulation results. Today in Multi-frequency Electrical Impedance Tomography (MEIT), new hardware for recording measurements operating above 1MHz is now available. This high operating frequency raises the question of the validity of the employed quasi-static conditions used in the associated Forward Problem modelling. It is important to be able to determine when the quasi-static conditions fail and to investigate the differences between a solution to the Forward Problem based on quasi-static conditions and the one based on non quasistatic conditions at these frequencies. This thesis details the derivation of a new analytical solution based on non quasi-static conditions for a finite right circular cylinder having two electrodes placed on its boundary. Some comparisons between the new analytical solution and data obtained from in-vitro experiments will be presented in this thesis. A comparison between the new analytical solution and the analytical solution derived earlier in this thesis (which is based on quasi-static conditions) is also conducted. Whilst these results are preliminary results, they reveal that for situations associated with imaging the human thorax the quasi-static assumption appear violated when most modern MEIT systems are employed. This frequency dependent three dimensional analytical Forward Problem work has wide ranging implications for the future of MEIT. The thesis will conclude with some initial thoughts on how to incorporate anisotropy into three dimensional Forward Problem solutions.

The objective of this study is to develop a finite element model of the human thorax with a protective body armor system so that the model can adequately determine the thorax's biodynamical response from a projectile impact. The finite element model of the human thorax consists of the thoracic skeleton, heart, lungs, major arteries, major veins, trachea, and bronchi. The finite element model of the human thorax is validated by comparing the model's results to experimental data obtained from cadavers wearing a protective body armor system undergoing a projectile impact. When the model is deemed valid, a parametric study is performed to determine the components of the model that have the greatest effect on its biodynamical response to a projectile impact.

Depuis plusieurs décennies, l’évaluation des armes à létalité réduite (ALR) et des gilets pare-balles suscite l’intérêt majeur des forces de l’ordre autour du globe. En effet, ces armes présumées à létalité réduite ou non létales sont tenues d’occasionner uniquement une douleur suffisamment importante à un individu afin d’assurer sa neutralisation. Les gilets pare-balles, quant à eux, doivent garantir un certain niveau de protection pour réduire le risque de traumatismes lié à leur déformation dynamique. Le Centre de Recherche, d’Expertise et d’appui Logistique (CREL) du Ministère de l’Intérieur français a ainsi pour objectif le développement d’un outil de prédiction du risque lésionnel thoracique lors d’impacts balistiques non pénétrants. Cela permettrait alors d’évaluer les performances des ALR et des gilets pare-balles avant leur déploiement en théâtre d’opérations. Plus précisément, cette méthode doit uniquement être fondée sur la mesure directe du processus dynamique de déformation d’un bloc de gel synthétique soumis à un impact balistique. Pour répondre à ce besoin, l’approche numérique est considérée dans ces travaux de thèse par l’emploi du mannequin numérique du thorax humain HUByx comme un outil intermédiaire permettant la détermination de fonctions de transfert entre les mesures expérimentales sur un bloc de gel et le risque lésionnel. La reproduction de conditions d’impact réelles sur HUByx nécessite la caractérisation et la modélisation de projectiles ALR ainsi que de projectiles d’armes à feu et de gilets pare-balles. Elles reposent sur une procédure d’identification par méthode inverse appliquée à l’essai de Taylor pour la modélisation des ALR et à l’essai du cône dynamique d’enfoncement sur le bloc de gel pour celle du couple projectile/gilet pare-balles. Des travaux sont dédiés à la caractérisation mécanique et à la modélisation du gel synthétique sous sollicitations dynamiques. Enfin, une approche statistique basée sur des analyses de corrélation est introduite exploitant à la fois les mesures expérimentales, les données numériques ainsi que les rapports de cas de la littérature. Une cartographie du thorax associée au risque de fractures costales est établie et est uniquement fonction d’une mesure expérimentale. / For decades, the assessment of less-lethal weapons (LLW) and bulletproof vests has generated major interest from law enforcement agencies around the world. Indeed, these presumed less-lethal or non-lethal weapons are required to cause only significant pain to an individual to ensure their neutralization. Bulletproof vests, in turn, must provide a certain level of protection to reduce the risk of trauma related to their dynamic deformation. The Center for Research, Expertise and Logistics Support (CREL) of the French Ministry of the Interior aims to develop a tool to predict thoracic injury risk during non-penetrating ballistic impacts. It would therefore be possible to evaluate the performance of LLW and bulletproof vests before their deployment in operations. More precisely, this method must only be based on the direct measurement of the dynamic process of deformation of a synthetic gel block subjected to a ballistic impact. To address that issue, the numerical approach is considered in this thesis by the use of the human thorax dummy HUByx as an intermediate tool for the determination of transfer functions between experimental metrics on a gel block and the risk of injury. The reproduction of real impact conditions on HUByx thus requires the characterization and modeling of less-lethal projectiles as well as projectiles of firearms and bulletproof vests. They rely on an inverse method identification procedure applied to the Taylor test for modeling LLW and on the analysis of blunt impacts on the gel block for projectiles/bulletproof vests. Work is then dedicated to the mechanical characterization and modeling of the synthetic gel under dynamic loadings. Finally, a statistical approach based on correlation analyses is introduced using both experimental measurements, numerical data as well as case reports from the literature. A thorax mapping associated with the risk of rib fractures is established and only depends on an experimental metric.