This thesis presents the research results on the development of a microwave tomography imaging algorithm capable of reconstructing the dielectric properties of the unknown object. Our focus was on the theoretical aspects of the non-linear tomographic image reconstruction problem with particular emphasis on developing efficient numerical and non-linear optimization for solving the inverse scattering problem. A detailed description of a novel microwave tomography method based on frequency dependent finite difference time domain, a numerical method for solving Maxwell's equations and Genetic Algorithm (GA) as a global optimization technique is given. The proposed technique has the ability to deal with the heterogeneous and dispersive object with complex distribution of dielectric properties and to provide a quantitative image of permittivity and conductivity profile of the object. It is shown that the proposed technique is capable of using the multi-frequency, multi-view, and multi-incident planer techniques which provide useful information for the reconstruction of the dielectric properties profile and improve image quality. In addition, we show that when a-priori information about the object under test is known, it can be easily integrated with the inversion process. This provides realistic regularization of the solution and removes or reduces the possibility of non-true solutions. We further introduced application of the GA such as binary-coded GA, real-coded GA, hybrid binary and real coded GA, and neural-network/GA for solving the inverse scattering problem which improved the quality of the images as well as the conversion rate. The implications and possible advantages of each type of optimization are discussed, and synthetic inversion results are presented. The results showed that the proposed algorithm was capable of providing the quantitative images, although more research is still required to improve the image quality. In the proposed technique the computation time for solution convergence varies from a few hours to several days. Therefore, the parallel implementation of the algorithm was carried out to reduce the runtime. The proposed technique was evaluated for application in microwave breast cancer imaging as well as measurement data from university of Manitoba and Institut Frsenel's microwave tomography systems.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Em radiodiagnósticos, tais como em mamografias, é comum considerar que a radiação espalhada seja um problema, pois degrada o contraste da imagem. Porém, estudos recentes mostraram que é possível identificar a presença de anormalidades num tecido biológico, a partir da distribuição angular dos fótons espalhados (perfil de espalhamento), que fornecem as informações detalhadas sobre a composição estrutural do tecido. No entanto, estudos de base deste tipo tem-se utilizado de simulação computacional, devido à dificuldades e limitações, tanto na obtenção, armazenamento e manipulação das amostras, quanto na instrumentação experimental, além de questões éticas envolvidas. Neste trabalho, foram simulados os perfis de espalhamento elástico, na região de ângulos intermediários, denominado WAXS (do inglês, Wide Angle X-ray Scattering), de tecidos mamários normais e patológicos, bem como de materiais equivalentes a tais tecidos, por fornecer informações sobre as estruturas responsáveis pelo espalhamento em nível molecular. Para a simulação computacional dos perfis de espalhamento foi utilizado o código Monte Carlo, com o auxílio do software MC-GPU. Seu diferencial em relação a outros códigos para simulação de perfis na região de WAXS é a possibilidade de inclusão dos fatores de forma medidos experimentalmente, que englobam a Função de Interferência Molecular, ao invés apenas dos fatores de forma calculados utilizando o Modelo Atômico Independente. Foram construídos dois phantoms virtuais em forma cilíndrica, com inserções cilíndricas internas contendo os seguintes materiais: tecido adiposo, tecido glandular, água, dimetilformamida, etanol, glicerol e nylon, compondo 27 combinações, com simulações específicas em cada uma. Estes materiais foram escolhidos por apresentar características de atenuação similares às dos tecidos mamários normais e patológicos na energia utilizada. Foi utilizado um feixe de fótons monoenergético (Kα-Cu = 8,54 keV) e um detector bidimensional. Os padrões de espalhamento obtidos foram integrados para obtenção dos perfis de espalhamento. Os resultados com os phantoms virtuais foram muito semelhantes aos reportados na literatura para cada um dos materiais puros inseridos nos phantoms. Assim, este trabalho demonstrou à possibilidade de inclusão dos fatores de forma experimentais de cada material, nas simulações dos perfis de espalhamento dos phantom de mama normal e patológica, obtendo resultados mais realísticos e catalogando os resultados de forma que possa ser utilizado como base de dados em trabalhos futuros. Portanto, ainda que preliminares, os resultados deste trabalho corroboram para a exploração de novas técnicas de imagem mamária baseadas no espalhamento elástico de raios X. / In radiodiagnostics, such as mammograms, it is common to consider that scattered radiation is a problem because it degrades the contrast of the image. However, recent studies have shown that it is possible to identify the presence of abnormalities in a biological tissue, from the angular distribution of scattered photons (scattering profile), which provide detailed information on the structural composition of the tissue. Basic studies of this type have been used for computational simulation, due to the difficulties and limitations, both in obtaining, storing and manipulating the samples, as well as in the experimental instrumentation, besides the ethical issues involved. In this work, the elastic scattering profiles of normal and pathological mammary tissues, and the materials equivalent to these tissues, were simulated in the region of intermediate angles, called WAXS (Wide Angle X-ray Scattering). This structure responsible for scattering at the molecular level. For the computational simulation of the scattering profiles was used the Monte Carlo code, with the aid of the MC-GPU software. Its differential in relation to other codes for simulation of profiles in the WAXS region is the possibility of including experimentally measured form factors, which encompass the Molecular Interference Function, instead of only the form factors calculated using the Independent Atomic Model. Two cylindrical virtual phantoms were constructed with internal cylindrical inserts filled with the following materials: adipose tissue, glandular tissue, water, dimethylformamide, ethanol, glycerol and nylon, composing 27 combinations, with specific simulations in each one. These materials were chosen because they presented attenuation characteristics similar to the normal and pathological mammary tissues in the energy used. A monoenergetic photon beam (Kα-Cu = 8.54 keV) and a two-dimensional detector were used. The scattering patterns obtained were integrated to obtain the scattering profiles. The results with the virtual phantoms were very similar to those reported in the literature for each of the pure materials inserted in the phantoms. Thus, this work demonstrated the possibility of including the experimental form factors of each material in the simulations of the scattering profiles of the normal and pathological breast phantom, obtaining more realistic results and cataloging the results in a way that can be used as a database in future work. Therefore, although preliminary, the results of this work corroborate the exploration of new breast imaging techniques based on elastic X-ray scattering.

New advances in computational modeling and instrumentation in the past decade has enabled the use of electromagnetic radiation for non-invasive monitoring of the physio-logical state of biological tissues. The near infrared (NIR) light having the wavelength range of 600 nm -1000 nm has been the main contender in these emerging molecular imaging modalities. Assessment of accurate pathological condition of the tissue under investigation relies on the contrast in the molecular images, where the endogenous contrast may not be sufficient in these scenarios. The fluorescence (exogenous) contrast agents have been deployed to overcome these difficulties, where the preferential uptake by the tumor vasculature leads to high contrast,making this modality one of the biggest contenders in small-animal and soft-tissue molecular imaging modalities. In Fluorescence diffuse optical spectroscopy/imaging, this exogenous drug is excited by NIR laser light causing the emission of the fluorescence light. The emitted fluorescence light is typically dependent on the life time and concentration of the exogenous drug coupled with physiology associated with the tissue under investigation. As there is an excitation and emission of the light,the underlying physics of the problem is described by a coupled diffusion equations. These coupled diffusion equations are typically solved by advanced numerical methods, which tend to be computationally demanding. In this work, analytical solutions for these coupled partial differential equations (PDEs) for the regular geometries for both time-domain and frequency-domain cases were developed. Till now, the existing literature has not dealt with all regular geometries and derived analytical solutions were only for couple of geometries. Here a universally acceptable generic solution was developed based on Green’s function approach that is applicable to any regular geometry. Using this, the analytical solutions for the regular geometries that is encountered in diffuse fluorescence spectroscopy/imaging were obtained. These solutions can play an important role in determining the bulk fluorescence properties of the tissue, which could act as good initial guesses for the advanced image reconstruction techniques and/or can also facilitate the calibration of experimental fluorescence data by removing biases and source-detector variations. In the second part of this work, the developed analytical models for regular geometries were validated through comparison with the established numerical models that are traditionally used in the diffuse fluorescence spectroscopy/imaging. This comparison not only validated the developed analytical models, but also showed that analytical models are capable of providing bulk fluorescence properties with at least one order of magnitude less computational cost compared to the highly optimized traditional numerical models.