A Tomografia por Impedância Elétrica (EIT) é um método que utiliza estimativas da distribuição de condutividade ou impedância de tecidos orgânicos na obtenção de imagens médicas. O procedimento de obtenção das imagens baseia-se em medições de correntes ou voltagens no contorno da região sob análise e na estimação de parâmetros de um modelo desta região. No caso de pacientes submetidos à respiração artificial, o conhecimento da distribuição absoluta ou das variações de condutividades nos pulmões auxilia na detecção de fenômenos como colapso alveolar ou pneumotórax e permite o ajuste e controle da vazão e pressão do ar fornecido, de modo a evitar a ocorrência de tais anomalias. Este trabalho apresenta algoritmos cujo objetivo é a solução do problema inverso e mal posto de estimar a distribuição absoluta e as variações de condutividades nos pulmões através da EIT para a geração de imagens em duas dimensões. O algoritmo para a estimação da distribuição absoluta de condutividade utiliza o filtro estendido de Kalman. As simulações numéricas mostram que, com medidas incorporando ruído cujo desvio padrão atinge até 12% da máxima voltagem, as estimativas de condutividades convergem para a distribuição esperada com um desvio inferior a 7% do valor da máxima condutividade. Quanto à detecção de variações de condutividades em relação a uma distribuição de condutividades tomada como referência, as simulações numéricas sugerem que a solução do problema depende da utilização de métodos de regularização. / Electrical Impedance Tomography (EIT) is a method that uses estimates of conductivity or impedance distribution in living tissues to generate medical images. The estimation procedure is based on measurements of electrical currents or voltages at the boundary of the region under analysis, and on the processing of these data through a proper algorithm. In patients under artificial ventilation, knowledge of absolute or relative conductivity distribution in the lungs helps detecting the presence of alveolar collapse or pneumothorax, and allows setting and controlling air volume and pressure of the ventilation device. This work presents algorithms that aim at solving the ill-posed inverse problem of estimating absolute and relative conductivity distribution in the lungs through EIT for cross-sectional image reconstruction. The algorithm for absolute conductivity distribution estimation uses the extended Kalman filter. Numerical simulations show that, when the standard deviation of the measurement noise level raises up to 12% of the maximal measured voltage, the conductivity estimates converge to the expected vector within 7% accuracy of the maximal conductivity value. Addressing the estimation of conductivity changes in relation to a conductivity distribution taken as reference, numerical simulations suggest that the problem may be properly solved using regularization methods.

A Tomografia por Impedância Elétrica (EIT) é um método que utiliza estimativas da distribuição de condutividade ou impedância de tecidos orgânicos na obtenção de imagens médicas. O procedimento de obtenção das imagens baseia-se em medições de correntes ou voltagens no contorno da região sob análise e na estimação de parâmetros de um modelo desta região. No caso de pacientes submetidos à respiração artificial, o conhecimento da distribuição absoluta ou das variações de condutividades nos pulmões auxilia na detecção de fenômenos como colapso alveolar ou pneumotórax e permite o ajuste e controle da vazão e pressão do ar fornecido, de modo a evitar a ocorrência de tais anomalias. Este trabalho apresenta algoritmos cujo objetivo é a solução do problema inverso e mal posto de estimar a distribuição absoluta e as variações de condutividades nos pulmões através da EIT para a geração de imagens em duas dimensões. O algoritmo para a estimação da distribuição absoluta de condutividade utiliza o filtro estendido de Kalman. As simulações numéricas mostram que, com medidas incorporando ruído cujo desvio padrão atinge até 12% da máxima voltagem, as estimativas de condutividades convergem para a distribuição esperada com um desvio inferior a 7% do valor da máxima condutividade. Quanto à detecção de variações de condutividades em relação a uma distribuição de condutividades tomada como referência, as simulações numéricas sugerem que a solução do problema depende da utilização de métodos de regularização. / Electrical Impedance Tomography (EIT) is a method that uses estimates of conductivity or impedance distribution in living tissues to generate medical images. The estimation procedure is based on measurements of electrical currents or voltages at the boundary of the region under analysis, and on the processing of these data through a proper algorithm. In patients under artificial ventilation, knowledge of absolute or relative conductivity distribution in the lungs helps detecting the presence of alveolar collapse or pneumothorax, and allows setting and controlling air volume and pressure of the ventilation device. This work presents algorithms that aim at solving the ill-posed inverse problem of estimating absolute and relative conductivity distribution in the lungs through EIT for cross-sectional image reconstruction. The algorithm for absolute conductivity distribution estimation uses the extended Kalman filter. Numerical simulations show that, when the standard deviation of the measurement noise level raises up to 12% of the maximal measured voltage, the conductivity estimates converge to the expected vector within 7% accuracy of the maximal conductivity value. Addressing the estimation of conductivity changes in relation to a conductivity distribution taken as reference, numerical simulations suggest that the problem may be properly solved using regularization methods.

A Tomografia por Impedância Elétrica (TIE) é uma técnica não invasiva usada para produzir imagens que representam a distribuição de resistividade, ou condutividade, de uma seção transversal dentro de um domínio, por vezes o tórax humano, a partir do conhecimento de medidas elétricas feitas através de eletrodos distribuídos na sua fronteira. Correntes injetam-se e medem-se voltagens ou vice-versa. Distribuição de variação de resistividade ou distribuição de valor absoluto de resistividade podem ser estimadas, gerando algoritmos ditos de diferenças ou absolutos. O presente trabalho avalia o desempenho de um algoritmo probabilístico baseado no método Simulated Annealing (SA) para obter distribuições absolutas de resistividade em duas dimensões (2D). O SA difere dos métodos tradicionais de busca, tem a capacidade de escapar de mínimos locais graças ao emprego do critério de Metropolis para a aceitação dos novos pontos no espaço de busca e não precisa da avaliação de derivadas da função objetivo. O algoritmo desenvolvido soluciona o problema inverso da TIE ao resolver iterativamente um problema direto, utilizando distribuições de resistividade obtidas por sorteio aleatório. O sorteio é realizado pelo algoritmo de Metropolis. Na ausência de regularizações, assume-se que a imagem sorteada que minimiza a diferença entre as voltagens medidas na fronteira do domínio e as calculadas é a que mais se aproxima da distribuição de resistividade real. Neste sentido, a imagem final maximiza a verossemelhança. Este trabalho contribui com o desenvolvimento de algoritmos para estimação de imagem aplicados para monitorar a ventilação mecânica dos pulmões. Uma vez que se pretende resolver um problema inverso, não-linear e mal-posto é necessário introduzir informação a priori, na forma de restrições do espaço solução ou de regularizações. São realizados ensaios com dados simulados por meio de um fantoma numérico, dados de bancada experimental e dados provenientes de um tórax humano. Os resultados mostram que a localização, o tamanho e a resistividade do objeto estão dentro da precisão da TIE obtida por métodos clássicos, mas o esforço computacional é grande. Verificam-se, assim, as vantagens e a viabilidade do algoritmo proposto. / The Electrical Impedance Tomography (EIT) is a non-invasive technique used to produce images that represent the cross-sectional electrical resistivity distribution, or conductivity, within a domain, for instance the human thorax, from electrical measurements made through electrodes distributed on its boundary. Currents are injected and voltages measured, or vice-versa. Distributions of resistivity variations or distributions of absolute resistivity can be estimated, producing difference or absolute algorithms. The present work develops and evaluates the performance of a probabilistic algorithm based on the Simulated Annealing method (SA) to obtain absolute resistivity distributions in two dimensions (2D). The SA differs from the traditional search methods, no evaluation of objective function derivatives is required and it is possible to escape from local minima through the use of the Metropolis criterion for acceptance of new points in the search space. The developed algorithm solves the inverse problem of EIT by solving iteratively a direct problem, using random resistivity distributions. The random search is accomplished by the Metropolis algorithm. In the absence of regularizations, it is assumed that the resistivity distribution, an image, that minimizes the difference between the measured electrical potentials on the boundary and computed electrical potentials is the closest to the real resistivity distribution. In this sense, the algorithm maximizes the likelihood. This work contributes to the development of image estimation algorithms applied to lung monitoring, for instance, during mechanical ventilation. To solve this non-linear ill-posed inverse problem it is necessary to introduce prior information in the form of restrictions of the solution space or regularization techniques. The tests are carried out using simulated data obtained from a numerical phantom, an experimental phantom and human thorax data. The results show that the localization of an object, the size of an object and the resistivity of an object are within the accuracy of EIT obtained by classical methods, but the computational effort is large. The advantages and feasibility of the proposed algorithm were investigated.

In magnetic resonance electrical impedance tomography (MR-EIT), crosssectional images of a conductivity distribution are reconstructed. When current is injected to a conductor, it generates a magnetic field, which can be measured by a magnetic resonance imaging (MRI) scanner. MR-EIT reconstruction algorithms can be grouped into two: current density based reconstruction algorithms (Type-I) and magnetic flux density based reconstruction algorithms (Type-II). The aim of this study is to implement a series of reconstruction algorithms for MR-EIT, proposed by several research groups, and compare their performance under the same circumstances. Five direct and one iterative Type-I algorithms, and an iterative Type-II algorithm are investigated. Reconstruction errors and spatial resolution are quantified and compared. Noise levels corresponding to system SNR 60, 30 and 20 are considered. Iterative algorithms provide the lowest errors for the noise- free case. For the noisy cases, the iterative Type-I algorithm yields a lower error than the Type-II, although it can diverge for SNR lower than 20. Both of them suffer significant blurring effects, especially at SNR 20. Another two algorithms make use of integration in the reconstruction, producing intermediate errors, but with high blurring effects. Equipotential lines are calculated for two reconstruction algorithms. These lines may not be found accurately when SNR is lower than 20. Another disadvantage is that some pixels may not be covered and, therefore, cannot be reconstructed. Finally, the algorithm involving the solution of a linear system provides the less blurred images with intermediate error values. It is also very robust against noise.

In this thesis, optimum current injection strategy for Magnetic Resonance Electrical Impedance Tomography (MREIT) is studied. Distinguishability measure based on magnetic flux density is defined for MREIT. Limit of distinguishability is analytically derived for an infinitely long cylinder with concentric and eccentric inhomogeneities. When distinguishability limits of MREIT and Electrical Impedance Tomography (EIT) are compared, it is found that MREIT is capable of detecting smaller perturbations than EIT. When conductivities of inhomogeneity and background object are equal to 0.8S and 1S respectively, MREIT provides improvement of %74 in detection capacity. Optimum current injection pattern is found based on the distinguishability definition. For 2-D cylindrical body with concentric and eccentric inhomogeneities, opposite drive provides best result. As for the 3-D case, a sphere with azimuthal symmetry is considered. Distinguishability limit expression is obtained and optimum current injection pattern is again opposite drive. Based these results, optimum current injection principles are provided and Regional Image Reconstruction (RIR) using optimum currents is proposed. It states that conductivity distribution should be reconstructed for a region rather than for the whole body. Applying current injection principles and RIR provides reasonable improvement in image quality when there is noise in the measurement data. For the square geometry, when SNR is 13dB, RIR provides decrement of nearly %50 in conductivity error rate of small inhomogeneity. Pulse sequence optimization is done for Gradient Echo (GE) and it is compared with Spin Echo (SE) in terms of their capabilities for MREIT.

Magnetic Resonance Electrical Impedance Tomography (MREIT) algorithms using current density distribution have been proposed in the literature. The current density distribution can be determined by using Magnetic Resonance Current Density Imaging (MRCDI) technique. In MRCDI technique, all three components of magnetic flux density should be measured. Hence, object should be rotated inside the magnet which is not trivial even for small size objects and remains as a strong limitation to clinical applicability of the technique. In this thesis, 2D MRCDI problem is investigated in detail and an analytical relation is found between Bz, Jx and Jy. This study makes it easy to understand the behavior of Bz due to changes in Jx and Jy. Furthermore, a novel 2D MRCDI reconstruction algorithm using one component of B is proposed. Iterative FT-MRCDI algorithm is also implemented. The algorithms are tested with simulation and experimental models. In simulations, error in the reconstructed current density changes between 0.27% - 23.00% using the proposed algorithm and 7.41% - 37.45% using the iterative FT-MRCDI algorithm for various SNR levels. The proposed algorithm is superior to the iterative FT-MRCDI algorithm in reconstruction time comparison. In experimental models, the classical MRCDI algorithm has the best reconstruction performance when the algorithms are compared by evaluating the reconstructed current density images perceptually. However, the J-substitution algorithm reconstructs the best conductivity image by using J obtained from the proposed algorithm. Finally, the iterative FT-MRCDI algorithm shows the best performance when the reconstructed current density images are verified by using divergence theorem.

No description available.

This thesis presents a novel study on Second Generation High Temperature Superconductors, which covers their electromagnetic characteristics and AC loss analysis. Lorentz Force Electrical Impedance Tomography (LFEIT) is one of the most promising hybrid diagnostic scanners with burgeoning potential for biological imaging, particularly in the detection of cancer and internal haemorrhages. The author tried a novel combination of superconducting magnets together with the LFEIT system. The reason is that superconducting magnets can generate a magnetic field with high intensity and homogeneity, which could significantly enhance the electrical signal induced from a sample, thus improving the Signal-to-Noise Ratio (SNR). The author developed four magnet designs for the LEFIT system using the Finite Element Method (FEM) package, COMSOL Multiphysics, and found that a Superconducting Halbach Array magnet can achieve all the requirements (magnetic field properties, geometry, portability, etc.) for the LFEIT system. The optimization study of the superconducting Halbach Array magnet has been carried out on the FEM platform of COMSOL Multiphysics, with 2D models using H-formulation based on B-dependent critical current density and bulk approximation. Optimization focused on the location of the coils, as well as the geometry and number of coils on the premise of maintaining the total amount of superconducting material used in the design. The optimization results showed that the Halbach Array configuration based superconducting magnet is able to generate a magnetic field with an intensity of over 1 Tesla and improved homogeneity. In order to efficiently predict the optimization performance, mathematical formulas were developed for these optimization parameters to determine the intensity and homogeneity of the magnetic field. The mathematical model for the LFEIT system was built based on the theory of the magneto-acousto-electric effect. Then the basic imaging of the electrical signal was developed using Matlab. The magnetic field properties of the magnet design were imported into the LFEIT model. The LFEIT model simulated two samples located in three different magnetic fields with varying magnetic strength and homogeneity. Even if there are no actual alternating currents involved in the DC superconducting magnets mentioned above, they have power dissipation during normal operation (e.g. magnet ramping) and under different background fields. This problem generally goes under the category of “AC loss”. Therefore, the AC loss characteristics of HTS tapes and coils are still fundamentally important for HTS magnet designs, even if they are normally operating in DC conditions. This thesis starts with the AC loss study of HTS tapes. The investigation and comparison of AC losses on Surround Copper Stabilizer (SCS) Tape and Stabilizer-free (SF) Tape have been carried out, which includes AC loss measurement using the electrical method, as well as the real geometry and multi-layer HTS tape simulation using the 2D H formulation by COMSOL Multiphysics. Hysteresis AC losses in the superconducting layer, and eddy current AC losses in the copper stabilizer, silver overlayer and substrate were concerned in this investigation. The measured AC losses were compared to the AC losses from the simulation, using 3 cases of different AC frequency: 10 Hz, 100 Hz, and 1000 Hz. The frequency dependence of AC losses from Stabilizer free Tape and Copper Stabilizer Tape were compared and analysed. A comprehensive AC loss study of a circular HTS coil has been fulfilled. The AC losses from a circular double pancake coil were measured using the electrical method. A 2D axisymmetric H-formulation model using FEM package COMSOL has been established, which was able to make consistency with the real circular coil used in the experiment. To model a circular HTS coil, a 2D axisymmetric model provided better accuracy than a general 2D model, and was also more efficient than a 3D model. Three scenarios were analysed: (1) AC transport current and DC magnetic field, (2) DC transport current and AC magnetic field, (3) AC transport current and AC magnetic field. The angular dependence analysis on the coil under the magnetic field with the different orientation angle  was carried out for all three scenarios. For scenario (3), the effect of the relative phase difference ∆ between the AC current and the AC field on the total AC loss of the coil was investigated. To summarise, a current/field/angle/phase dependent AC loss (I, B, , ∆) study of circular HTS coil has been carried out, which could potentially benefit the future design and research of HTS AC systems. The AC losses of horizontally parallel HTS tapes have been investigated. The AC losses of the middle and end tape of three parallel tapes have been measured using the electrical method, and compared to those of an individual isolated tape. The effect of the interaction between tapes on AC losses has been analysed, and compared with finite element method (FEM) simulations using the 2D H formulation implemented in COMSOL Multiphysics. The electromagnetic induction around the three parallel tapes was monitored using COMSOL simulation. The electromagnetic induction and AC losses generated by a conventional three turn coil were simulated as well, and then compared to the case of three parallel tapes with the same AC transport current. The analysis demonstrated that HTS parallel tapes could be potentially used in wireless power transfer systems, which could have lower total AC losses than conventional HTS coils. By using FEM simulations, cases of increasing number of parallel tapes was considered, and the normalised ratio between the total average AC losses per tape and the AC losses of an individual single tape have been calculated for different gap distances. A new parameter is proposed, Ns, a turning point the for number of tapes, to divide Stage 1 and Stage 2 for the AC loss study of horizontally parallel tapes. For Stage 1, N < Ns, the total average losses per tape increased with the increasing number of tapes. For Stage 2, N > Ns, the total average losses per tape started to decrease with the increasing number of tapes. The analysis demonstrates that horizontally parallel HTS tapes could be potentially used in superconducting devices like HTS transformers, which could retain or even reduce the total average AC losses per tape with large numbers of parallel tapes.

A Tomografia por Impedância elétrica (TIE) tem como objetivo gerar imagens da distribuição de resistividade dentro de um domínio. A TIE injeta correntes em eletrodos alocados na fronteira do domínio e mede potenciais elétricos através dos mesmos eletrodos. A TIE é considerada um problema inverso, não-linear e mal posto. Atualmente, para gerar uma solução do problema inverso, existem duas classes de algoritmos para estimar a distribuição de resistividade no interior do domínio, os que estimam variações da distribuição de resistividade do domínio e os absolutos, que estimam a distribuição de resistividade. Variações da distribuição de resistividade são o resultado da solução de um sistema linear do tipo Ax = b. O objetivo do presente trabalho é avaliar o desempenho da Programação Linear (PL) na solução do sistema linear, avaliar o algoritmo quanto a propaga- ção de erros numéricos e avaliar os efeitos de restringir o espaço solução através de restrições de PL. Os efeitos do uso de Programação Linear é avaliado tanto em métodos que geram imagens de diferenças, como o Matriz de Sensibilidade, como em métodos absolutos, como o Gauss-Newton. Mostra-se neste trabalho que o uso da PL diminui o erro numérico propagado quando comparado ao uso do algoritmo LU Decomposition. Resulta também que reduzir o espaço solução, diretamente através de restrições de PL, melhora a resolução em resistividade e a resolução espacial da imagem quando comparado com o uso de LU Decomposition. / Electrical impedance tomography (EIT) generates images of the resistivity distribution of a domain. The EIT method inject currents through electrodes placed on the boundary of the domain and measures electric potentials through the same electrodes. EIT is considered an inverse problem, non-linear and ill-conditioned. There are two classes of algorithms to estimate the resistivity distribution inside the domain, difference images algorithms, which estimate resistivity distribution variations, and absolute images algorithms, which estimate the resistivity distribution. Resistivity distribution variations are the solution of a linear system, say Ax = b. In this work, the main objective is to evaluate the performance of Linear Programming (LP) solving an EIT linear system from the point of view of the numerical error propagation and the ability to constrain the solution space. The impact of using LP to solve an EIT linear system is evaluated on a difference image algorithm and on an absolute algorithm. This work shows that the use of LP diminishes the numerical error propagation compared to LU Decomposition. It is also shown that constraining the solution space through LP improves the resistivity resolution and the spatial resolution of the images when compared to LU Decomposition.

A Tomografia por Impedância Elétrica (TIE) é uma técnica não invasiva usada para produzir imagens que representam a distribuição de resistividade, ou condutividade, de uma seção transversal dentro de um domínio, por vezes o tórax humano, a partir do conhecimento de medidas elétricas feitas através de eletrodos distribuídos na sua fronteira. Correntes injetam-se e medem-se voltagens ou vice-versa. Distribuição de variação de resistividade ou distribuição de valor absoluto de resistividade podem ser estimadas, gerando algoritmos ditos de diferenças ou absolutos. O presente trabalho avalia o desempenho de um algoritmo probabilístico baseado no método Simulated Annealing (SA) para obter distribuições absolutas de resistividade em duas dimensões (2D). O SA difere dos métodos tradicionais de busca, tem a capacidade de escapar de mínimos locais graças ao emprego do critério de Metropolis para a aceitação dos novos pontos no espaço de busca e não precisa da avaliação de derivadas da função objetivo. O algoritmo desenvolvido soluciona o problema inverso da TIE ao resolver iterativamente um problema direto, utilizando distribuições de resistividade obtidas por sorteio aleatório. O sorteio é realizado pelo algoritmo de Metropolis. Na ausência de regularizações, assume-se que a imagem sorteada que minimiza a diferença entre as voltagens medidas na fronteira do domínio e as calculadas é a que mais se aproxima da distribuição de resistividade real. Neste sentido, a imagem final maximiza a verossemelhança. Este trabalho contribui com o desenvolvimento de algoritmos para estimação de imagem aplicados para monitorar a ventilação mecânica dos pulmões. Uma vez que se pretende resolver um problema inverso, não-linear e mal-posto é necessário introduzir informação a priori, na forma de restrições do espaço solução ou de regularizações. São realizados ensaios com dados simulados por meio de um fantoma numérico, dados de bancada experimental e dados provenientes de um tórax humano. Os resultados mostram que a localização, o tamanho e a resistividade do objeto estão dentro da precisão da TIE obtida por métodos clássicos, mas o esforço computacional é grande. Verificam-se, assim, as vantagens e a viabilidade do algoritmo proposto. / The Electrical Impedance Tomography (EIT) is a non-invasive technique used to produce images that represent the cross-sectional electrical resistivity distribution, or conductivity, within a domain, for instance the human thorax, from electrical measurements made through electrodes distributed on its boundary. Currents are injected and voltages measured, or vice-versa. Distributions of resistivity variations or distributions of absolute resistivity can be estimated, producing difference or absolute algorithms. The present work develops and evaluates the performance of a probabilistic algorithm based on the Simulated Annealing method (SA) to obtain absolute resistivity distributions in two dimensions (2D). The SA differs from the traditional search methods, no evaluation of objective function derivatives is required and it is possible to escape from local minima through the use of the Metropolis criterion for acceptance of new points in the search space. The developed algorithm solves the inverse problem of EIT by solving iteratively a direct problem, using random resistivity distributions. The random search is accomplished by the Metropolis algorithm. In the absence of regularizations, it is assumed that the resistivity distribution, an image, that minimizes the difference between the measured electrical potentials on the boundary and computed electrical potentials is the closest to the real resistivity distribution. In this sense, the algorithm maximizes the likelihood. This work contributes to the development of image estimation algorithms applied to lung monitoring, for instance, during mechanical ventilation. To solve this non-linear ill-posed inverse problem it is necessary to introduce prior information in the form of restrictions of the solution space or regularization techniques. The tests are carried out using simulated data obtained from a numerical phantom, an experimental phantom and human thorax data. The results show that the localization of an object, the size of an object and the resistivity of an object are within the accuracy of EIT obtained by classical methods, but the computational effort is large. The advantages and feasibility of the proposed algorithm were investigated.