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.

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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.

Les récentes avancées technologiques des matériels d’acquisition de données ont permis de réduire le temps d’acquisition d’image en tomographie électrique, ce qui offre des opportunités pour l’étude des écoulements diphasiques transitoires. Parmi les nombreux atouts de cette technique d’imagerie d’écoulements diphasiques, on peut citer son caractère non-intrusif, sa haute fréquence d’acquisition et son faible coût. Un ensemble d’électrodes placées sur le pourtour d’une conduite servent à transmettre une excitation électrique au milieu et à le sonder. Ainsi, la distribution des phases perturbe les champs électriques de manière caractéristique. L’objectif de cette thèse est d’évaluer le potentiel de la tomographie d’impédance électrique rapide. La première étape consiste au développement d’un prototype de capteur et à l’évaluation de sa performance par des essais simplifiés. L’architecture du système utilise un contrôle en potentiel du signal d’excitation et ne nécessite donc pas d’implémenter un module de conversion tension-courant. La seconde étape est la reconstruction de l’image à partir des données mesurées. L’approche qui a été considérée est de supposer une image approchée de la distribution des phases grâce à une identification du régime d’écoulement. Ainsi, le défi de résoudre un problème inverse fortement non-linéaire est simplifié. Une méthode d’identification de régimes d’écoulements horizontaux eau-air a été élaborée avec un module de tomographie de capacitance électrique et une boucle d’essais hydrauliques déjà éprouvés. Cette technique est en cours d’adaptation au prototype de tomographie d’impédance électrique rapide et en amélioration grâce à l’inclusion des régimes d’écoulements verticaux. En parallèle, une méthode de reconstruction d’image a été développée, basée sur l’algorithme NOSER et un postulat pseudo-2D. L’analyse des images reconstruites à partir d’un set d’expériences de référence procure un aperçu des avantages et des défauts de la méthode et du prototype. / Recent developments with data acquisition equipment have reduced the time required for image acquisition with electrical tomography, thereby bringing new opportunities for the study of fast-evolving two-phase flows. Amongst the numerous advantages of this imaging technique for multiphase flow related research are non-intrusiveness, high acquisition rates, low-cost and improved safety. A set of electrodes placed on the periphery of the pipe to be imaged is used to impose an electrical excitation and measure the system response. The distribution of phases inside the study volume distorts the electrical field in a characteristic manner. The objective of this thesis is to assess the potential of electrical impedance tomography at high acquisition rate. The first stage consists in developing a prototype sensor and assessing its performance with simplistic experiments. The system architecture employs voltage control of the excitation and therefore does not require the implementation of the conventional voltage-to-current converter module. A novel data collection method, the full scan strategy, is considered and provides correcting factors for the parasitic impedances in the system. The second stage is the image reconstruction from the measurement data. The approach considered in the thesis is to assume that flow regime identification techniques may provide valuable information on the phase distribution that can be injected in the inverse problem for imaging, thereby tackling the challenge of the non-linearity of the inverse problem. A method for horizontal air-water flow regime identification has been elaborated with an electrical capacitance tomography sensor and multiphase flow rig tried and tested. It is being adapted to the fast electrical impedance tomography prototype and upgraded to include vertical flow regimes. In parallel, an image reconstruction method has been developed based on the NOSER algorithm and a pseudo-2D postulate. The analysis of the reconstructed images for a set of benchmark experiments provide insights on the merits and deficiencies of the algorithm and of the prototype.

We study an inverse problem which seeks to image the internal conductivity map of a body by one measurement of boundary and interior data. In our study the interior data is the magnitude of the current density induced by electrodes. Access to interior measurements has been made possible since the work of M. Joy et al. in early 1990s and couples two physical principles: electromagnetics and magnetic resonance. In 2007 Nachman et al. has shown that it is possible to recover the conductivity from the magnitude of one current density field inside. The method now known as Current Density Impedance Imaging is based on solving boundary value problems for the 1-Laplacian in an appropriate Riemann metric space. We consider two types of methods: the ones based on level sets and a variational approach, which aim to solve specific boundary value problem associated with the 1-Laplacian. We will address the Cauchy and Dirichlet problems with full and partial data, and also the Complete Electrode Model (CEM). The latter model is known to describe most accurately the voltage potential distribution in a conductive body, while taking into account the transition of current from the electrode to the body. For the CEM the problem is non-unique. We characterize the non-uniqueness, and explain which additional measurements fix the solution. Multiple numerical schemes for each of the methods are implemented to demonstrate the computational feasibility.

Electrical impedance tomography (EIT) is a non-destructive, non-invasive, and non-radioactive imaging technique used for reconstructing the internal conductivity distribution of a sensing domain. Performing EIT often requires large, stationary benchtop equipment that can be expensive and impractical. Other researchers have attempted to make portable EIT systems, but they all rely on external computation for image reconstruction/data analysis. This study outlines the development of a low-cost, portable, and wireless EIT data acquisition (DAQ) system that is capable of independently performing image reconstructions on-board. With the proposed system, EIT can be performed on carbon fiber reinforced polymers to spatially locate damages. Since EIT reconstruction algorithms can be extremely computationally intensive, this study has also developed an alternative deep-learning algorithm that leverages the compressed-sensing technique to strategically train a neural network. The proposed neural network has not only achieved comparable results to traditional iterative algorithms, but it can do so in a fraction of the time.

Electrical Impedance Tomography (EIT) is a non linear inverse problem in which the electrical conductivity or resistivity distribution across a closed domain of interest is reconstructed from the surface potentials measured at the domain boundary by injecting a constant sinusoidal current through an array of surface electrodes. Being a non-invasive, non-radiating, non-ionizing, portable and inexpensive methodology, EIT has been extensively studied in medical diagnosis, biomedical engineering, biotechnology, chemical engineering, industrial and process engineering, civil and material engineering, soil and rock science, electronic industry, defense field, nano-technology and many other fields of applied physics. The reconstructed image quality in EIT depends mainly on the boundary data quality and the performance of the reconstruction algorithm used. The boundary data accuracy depends on the design of the practical phantoms, current injection method and boundary data measurement process and precision. On the other hand, the reconstruction algorithm performance is highly influenced by the mathematical modeling of the system, performance of the forward solver and Jacobian computation, inverse solver and the regularization techniques. Hence, for improving the EIT system performance, it is essential to improve the design of practical phantom, instrumentation and image reconstruction algorithm. As the electrical impedance of biological materials is a function of tissue composition and the frequency of applied ac signal, the better assessment of impedance distribution of biological tissues needs multifrequency EIT imaging. In medical EIT, to obtain a better image quality for a complex organ or a body part, accurate domain modelling with a large 3D finite element mesh is preferred and hence, the computation speed becomes very expensive and time consuming. But, the high speed reconstruction with improved image quality at low cost is always preferred in medical EIT. In this direction, a complete multifrequency multifunction EIT (MfMf-EIT) system is developed and multifrequency impedance reconstruction is studied to improve the bioimpedance imaging. The MfMf-EIT system consists of an MfMf-EIT instrumentation (MfMf-EITI), high speed impedance image reconstruction algorithms (IIRA), a Personal Computer (PC) and a number of practical phantoms with EIT sensors or electrodes. MfMf-EIT system and high speed IIRA are studied tested and evaluated with the practical phantoms and the multifrequency impedance imaging is improved with better image quality as well as fast image reconstruction. The MfMf-EIT system is also applied to the human subjects and the impedance imaging is studied for human body imaging and the system is evaluated. MfMf-EIT instrumentation (MfMf-EITI) consists of a multifrequency multifunction constant current injector (MfMf-CCI), multifrequency multifunction data acquisition system (MfMf DAS), a programmable electrode switching module (P-ESM) and a modified signal conditioner blocks (M-SCB) or data processing unit (DPU). MfMf-CCI, MfMf-DAS, P-ESM and M-SCBs are interfaced with a LabVIEW based data acquisition program (LV-DAP) controlled by a LabVIEW based graphical user interface (LV-GUI). LV-GUI controls the current injection and data acquisition with a user friendly, fast, reliable, efficient measurement process. The data acquisition system performance is improved by the high resolution NIDAQ card providing high precision measurement and high signal to noise ratio (SNR). MfMf-EIT system is developed as a versatile data acquisition system with a lot of flexibilities in EIT parameter selection that allows studying the image reconstruction more effectively. MfMf-EIT instrumentation controls the multifrequency and multifunctioned EIT experimentation with a number of system variables such as signal frequency, current amplitude, current signal wave forms and current injection patterns. It also works with either grounded load CCI or floating load CCI and collects the boundary data either in grounded potential form or differential form. The MfMf-EITI is futher modified to a battery based MfMf-EIT (BbMfMf-EIT) system to obtain a better patient safety and also to improve the SNR of the boundary data. MfMf-EIT system is having a facility of injecting voltage signal to the objects under test for conducting the applied potential tomography (APT). All the electronic circuit blocks in MfMf-EIT instrumentation are tested, evaluated and calibrated. The frequency response, load response, Fast Fourier Transform (FFT) studies and DSO analysis are conducted for studying the electronic performance and the signal quality of all the circuit blocks. They are all evaluated with both the transformer based power supply (TBPS) and battery based power supply (BBPS). MfMf-DAS, P-ESM and LV-DAP are tested and evaluated with digital data testing module (DDTM) and practical phantoms. A MatLAB-based Virtual Phantom for 2D EIT (MatVP2DEIT) is developed to generate accurate 2D boundary data for assessing the 2D EIT inverse solvers and its image reconstruction accuracy. It is a MATLAB-based computer program which defines a phantom domain and its inhomogeneities to generate the boundary potential data by changing its geometric parameters. In MatVP2DEIT, the phantom diameter, domain discretization, inhomogeneity number, inhomogeneity geometry (shape, size and position), electrode geometry, applied current magnitude, current injection pattern, background medium conductivity, inhomogeneity conductivity all are set as the phantom variables and are chosen indipendently for simulating different phantom configurations. A constant current injection is simulated at the phantom boundary with different current injection protocols and boundary potential data are calculated. A number of boundary data sets are generated with different phantom configurations and the resistivity images are reconstructed using EIDORS (Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software). Resistivity images are evaluated with the resistivity parameters and contrast parameters estimated from the elemental resistivity profiles of the reconstructed impedance images. MfMf-EIT system is studied, tested, evaluated with a number of practical phantoms eveloped with non-biological and biological materials and the multifrequency impedance imaging is improved. A number of saline phantoms with single and multiple inhomogeneities are developed and the boundary data profiles are studied and the phantom geometry is modified. NaCl-insulator phantoms and the NaCl-vegetable phantoms with different inhomogeneity configurations are developed and the multifrequency EIT reconstruction is studied with different current patterns, different current amplitudes and different frequencies using EIDORS as well as the developed IIRAs developed in MATLAB to evaluate the phantoms and MfMf-EIT system. Real tissue phantoms are developed with different chicken tissue backgrounds and high resistive inhomogeneities and the resistivity image reconstruction is studied using MfMf-EIT system. Chicken tissue phantoms are developed with chicken muscle tissue (CMTP) paste or chicken tissue blocks (CMTB) as the background mediums and chicken fat tissue, chicken bone, air hole and nylon cylinders are used as the inhomogeneity to obtained different phantom configurations. Resistivity imaging of all the real tissue phantoms is reconstructed in EIDORS and developed IIRAs with different current patterns, different frequencies and the images are evaluated by the image parameters to assess the phantoms as well as the MfMf-EIT system. Gold electrode phantoms are developed with thin film based flexible gold electrode arrays for improved bioimpedance and biomedical imaging. The thin film based gold electrode arrays of high geometric precision are developed on flexible FR4 sheet using electro-deposition process and used as the EIT sensors. The NaCl phantoms and real tissue phantoms are developed with gold electrode arrays and studied with MfMf-EIT system and and the resiulsts are compared with identical stainless steel electrode phantoms. NaCl phantoms are developed with 0.9% NaCl solution with single and multiple insulator or vegetable tissues as inhomogeneity. Gold electrode real tissue phantoms are also developed with chicken muscle tissues and fat tissues or other high resistive objects. The EIT images are reconstructed for the gold electrode NaCl phantoms and the gold electrode real tissue phantoms with different phantom geometries, different inhomogeneity configurations and different current patterns and the results are compared with identical SS electrode phantoms. High speed IIRAs called High Speed Model Based Iterative Image Reconstruction (HSMoBIIR) algorithms are developed in MATLAB for impedance image reconstruction in Electrical Impedance Tomography (EIT) by implementing high speed Jacobian calculation techniques using “Broyden’s Method (BM)” and “Adjoint Broyden’s Method (ABM)”. Gauss Newton method based EIT inverse solvers repeatitively evaluate the Jacobian (J) which consumes a lot of computation time for reconstruction, whereas, the HSMoBIIR with Broyden’s Methods (BM)-based accelerated Jacobian Matrix Calculators (JMCs) provides the high speed schemes for Jacobian (J) computation which is integrated with conjugate gradient scheme (CGS) for fast impedance reconstruction. The Broyden’s method based HSMoBIIR (BM-HSMoBIIR) and Adjoint Broyden’s method based HSMoBIIR (ABM-HSMoBIIR) algorithm are developed for high speed improved impedance imaging using BM based JMC (BM-JMC) and ABM-based JMC (ABM-JMC) respectively. Broyden’s Method based HSMoBIIR algorithms make explicit use of secant and adjoint information that can be obtained from the forward solution of the EIT governing equation and hence both the BM-HSMoBIIR and ABM-HSMoBIIR algorithms reduce the computational time remarkably by approximating the system Jacobian (J) successively through low-rank updates. The impedance image reconstruction is studied with BM-HSMoBIIR and ABM-HSMoBIIR algorithms using the simulated and practical phantom data and results are compared with a Gauss-Newton method based MoBIIR (GNMoBIIR) algorithm. The GNMoBIIR algorithm is developed with a Finite Element Method (FEM) based flexible forward solver (FFS) and Gauss-Newton method based inverse solver (GNIS) working with a modified Newton-Raphson iterative technique (NRIT). FFS solves the forward problem (FP) to obtain the computer estimated boundary potential data (Vc) data and NRIT based GNIS solve the inverse problem (IP) and the conductivity update vector [Δσ] is calculated by conjugate gradient search by comparing Vc measured boundary potential data (Vm) and using the Jacobian (J) matrix computed by the adjoint method. The conductivity reconstruction is studied with GNMoBIIR, BM-HSMoBIIR and ABM-HSMoBIIR algorithms using simulated data a practical phantom data and the results are compared. The reconstruction time, projection error norm (EV) and the solution error norm (Eσ) produced in HSMoBIIR algorithms are calculated and compared with GNMoBIIR algorithm. Results show that both the BM-HSMoBIIR and ABM-HSMoBIIR algorithms successfully reconstructs the conductivity distribution of the domain under test with its proper inhomogeneity and background conductivities for simulation as well as experimental studies. Simulated and practical phantom studies demonstrate that both the BM-HSMoBIIR and ABM-HSMoBIIR algorithms accelerate the impedance reconstruction by more than five times. It is also observed that EV and Eσ are reduced in both the HSMoBIIR algorithms and hence the image quality is improved. Noise analysis and convergence studies show that both the BM-HSMoBIIR and ABM-HSMoBIIR algorithms works faster and better in noisy conditions compared to GNMoBIIR. In low noise conditions, BM-HSMoBIIR is faster than to ABM-HSMoBIIR algorithm. But, in higher noisy environment, the ABM-HSMoBIIR is found faster and better than BM-HSMoBIIR. Two novel regularization methods called Projection Error Propagation-based Regularization (PEPR) and Block Matrix based Multiple Regularization (BMMR) are proposed to improve the image quality in Electrical Impedance Tomography (EIT). PEPR method defines the regularization parameter as a function of the projection error contributed by the mismatch (difference) between the data obtained from the experimental measurements (Vm) and calculated data (Vc). The regularization parameter in the reconstruction algorithm gets modified automatically according to the noise level in measured data and ill-posedness of the Hessian matrix. The L-2 norm of the projection error is calculated using the voltage difference and it is used to find the regularization parameter in each iteration in the reconstruction algorithm. In BMMR method, the response matrix (JTJ) obtained from the Jacobian matrix (J) has been partitioned into several sub-block matrices and the highest eigenvalue of each sub-block matrices has been chosen as regularization parameter for the nodes contained by that sub-block. The BMMR method preserved the local physiological information through the multiple regularization process which is then integrated to the ill-posed inverse problem to make the regularization more effective and optimum for all over the domain. Impedance imaging with simulated data and the practical phantom data is studied with PEPR and BMMR techniques in GNMoBIIR and EIDORS and the reconstructed images are compared with the single step regularization (STR) and Modified Levenberg Regularization (LMR). The projection error and the solution error norms are estimated in the reconstructions processes with PEPR and the BMMR methods and the results are compared with the errors estimated in STR and modified LMR techniques. Reconstructed images obtained with PEPR and BMMR are also studied with image parameters and contrast parameters and the reconstruction performance with PEPR and BMMR are evaluated by comparing the results with STR and modified LMR. PEPR and BMMR techniques are successfully implemented in the GNMoBIIR and EIDORS algorithms to improve the impedance image reconstruction by regularizing the solution domain in EIT reconstruction process. As the multifrequency EIT is always preferred in biological object imaging for better assessments of the frequency dependent bioimpedance response, multifrequency impedance imaging is studied with MfMf-EIT system developed for biomedical applications. MfMf-EIT system is studied, tested and evaluated with practical phantoms suitably developed for multifrequency impedance imaging within a wide range of frequency. Different biological materials are studied with electrical impedance spectroscopy (EIS) and a number of practical biological phantoms suitable for multifrequency EIT imaging are developed. The MfMf-EIT system is studied, tested and evaluated at different frequency levels with different current patterns using a number of NaCl phantoms with single, multiple and hybrid vegetable tissue phantoms as well as with chicken tissue phantoms. BbMfMf-EIT system is also studied and evaluated with the multifrequency EIT imaging using the developed biological phantoms. The developed MfMf-EIT system is applied on human body for impedance imaging of human anatomy. Impedance imaging of human leg and thigh is studied to visualize the muscle and bone tissues using different current patterns and different relative electrode positions. Ag/AgCl electrodes are attached to the leg and thigh using ECG gel and the boundary data are collected with MfMf-EIT EIT system by injecting a 1 mA and 50 kHz sinusoidal constant current with neighbouring and opposite current injection patterns. Impedance images of the femur bone of the human thigh and the tibia and fibula bones of the human leg along with the muscle tissue backgrounds are reconstructed in EIDORS and GNMoBIIR algorithms. Reconstructed resistivity profiles of bone and muscles are compared with the resistivity data profiles reported in the published literature. Impedance imaging of leg and thigh is studied with MfMf-EIT system for different current patterns, relative electrode positions and the images are evaluated to assess the system reliability. Battery based MfMf-EIT system (BbMfMf-EIT) is also studied for human leg and thigh imaging and it is observed that MfMf-EIT system and BbMfMf-EIT system are suitable for impedance imaging of human body imaging though the BbMfMf-EIT system increases the patiet safety. Therefore, the developed MfMf-EIT and BbMfMf-EIT systems are found quite suitable to improve the bio-impedance imaging in medical, biomedical and clinical applications as well as to study the anatomical and physiological status of the human body to diagnose, detect and monitor the tumors, lesions and a number of diseases or anatomical abnormalities in human subjects.

<div> <p>Fiber reinforced polymer composites are widely used in manufacturing advanced light weight structures for the aerospace, automotive, and energy sectors owing to their superior stiffness and strength. With the increasing use of composites, there is an increasing need to monitor the health of these structures during their lifetime. Currently, health monitoring in filament wound composites is facilitated by embedding piezoelectrics and optical fibers in the composite during the manufacturing process. However, the incorporation of these sensing elements introduces sites of stress concentration which could lead to progressive damage accumulation. In addition to introducing weak spots in the structure, they also make the manufacturing procedure difficult. </p> <p> </p> <p>Alternatively, nanofiller modification of the matrix imparts conductivity which can be leveraged for real time health monitoring with fewer changes to the manufacturing method. Well dispersed nanofillers act as an integrated sensing network. Damage or strain severs the well-connected nanofiller network thereby causing a local change in conductivity. The self-sensing capabilities of these modified composites can be combined with low cost, minimally invasive imaging modalities such as electrical impedance tomography (EIT) for damage detection. To date, however, EIT has exclusively been used for damage detection in planar coupons. These simple plate-like structures are not representative of real-world complex geometries. This thesis advances the state of the art in conductivity-based structural health monitoring (SHM) and nondestructive evaluation (NDE) by addressing this limitation of EIT. The current study will look into damage detection of a non-planar multiply connected domain – a filament-wound glass fiber/epoxy tube modified by carbon black (CB) filler. The results show that EIT is able to detect through holes as small as 7.94 mm in a tube with length-to-diameter ratio of 132.4 mm-to-66.2 mm (aspect ratio of 2:1). Further, the sensitivity of EIT to damage improved with decreasing tube aspect ratio. EIT was also successful in detecting sub-surface damage induced by low velocity impacts. These results indicate that EIT has much greater potential for composite SHM and NDE than prevailing work limited to planar geometries suggest.</p> </div> <br>