Image Reconstruction Approaches and Circuit Modeling in Electrical Impedance Tomography

Abstract

This PhD thesis presents novel inverse problem formulation and image reconstruction approaches as well as hardware design and simulation methodologies in Electrical Impedance Tomography. Evaluation of the proposed algorithms has been performed via extensive simulations, experimental and invivo data. A simulation interface was also developed to observe the performance of different hardware and electrode configurations. In the first chapter (1), a brief introduction in the definition of Electrical Impedance Tomography as well as a historical review is performed. The second chapter (2) describes the problem’s mathematical formulation, the current and measurement patterns, the forward and the inverse problems. The nonlinear, ill-posed and ill-conditioned inverse problem is treated as a regularized least-square optimization problem. In this chapter, a description of the stateoftheart as well as the more recent approaches on the solution of the inverse problem is performed. It includes linear and nonlinear reqularization approaches, the nonlinear inverse scattering Fourier transformbased D-Bar method, as well as machine learning ones. In the third chapter (3), a novel efficient methodofmoment approach using Green’s functions and modified radial basis functions for the representation of the conductivity logarithm is described. The inverse problem is treated with L1-norm or L2-norm regularization methods. The main advantage of this approach is that it uses a more accurate expression of the relationship between the electrode boundary voltages and the conductivity distribution than the typical weak linearized one. This limits the effects of the problem’s nonlinearity and leads to faster convergence of the solution, even if conductivity perturbations are intense. The approach is also tested in 3D cylindrical setups, while fineremeshing (dual reconstruction) can be also applied. Its effectiveness is verified both qualitatively and quantitatively, through numerous simulation examples with the signal noise considered, as well as experimental and invivo cases. The fourth chapter (4) presents an approach which combines the methodofmoment described in the third chapter with a sparse Bayesian learning algorithm, based on the EM-algorithm. It offers noise robustness and decreases the effect of hyperparameter values to the reconstruction spatial performance. The method is applied on dynamic lung imaging. For its qualitative and quantitative evaluation, a number of three-dimensional thoracic simulated models were built, based on CT images of 3 adult male subjects and considering five breathcycle discrete states: from the expirationend to the inspiration-end. An image registration method for the extraction of the reference (true) images was performed and a number of quantitative metrics was used for the evaluation. Both simulation and invivo results showed improved performance at most of the figures of merit compared to stateoftheart methods. The fifth chapter (5) performs an extensive review of the EIT hardware typical characteristics. Firstly, the basic system’s architecture is described. Secondly, common topologies of current sources for bioimpedance measurement, with their advantages and disadvantages are described. The effect of reduced output impedance, mismatch between source and sink and common signal is discussed. Then, a description of the voltage recording circuitry configuration is performed, followed by SNR estimation models. In addition, the demodulation process and possible digital control methods are described. In the sixth chapter (6) an extensive simulation interface for EIT hardware, developed with MATLAB and LT SPICE is presented. Apart from signal noise, the impact of important effects (common signal, parasitic capacitances, electrode contact impedance, sampling rate and resolution, number of samples per measurement, e.t.c.) in the reconstruction quality is researched. For many of them, accurate mathematical models do not exist, hence a direct simulation approach prior to the design process is essential. The signal noise is added to transient simulations, that are transferred in MATLAB to simulate the digital process. The subject under test is also merged in the simulation setup using frequency-dependent multiport equivalent circuits. In the seventh chapter (7), the content of three research papers about miscellaneous bioimpedance modeling applications is included. In the first part (7.1), a highly tunable twodimensional time-variant thoracic model is presented, focusing on the impact of the boundary and tissues’ movement during the measurement process on the reconstructed image. In second part (7.3), the skin-electrode contact during tetrapolar bioimpedance measurement is simulated using Cole model analog realization. A post-layout implementation and simulation on IC analog circuit evaluates the model’s accuracy. Finally, in the third part (7.4), healthy and cancerous lung cells are realized as Cole model-based analog IC circuits using current feedback amplifiers. In the nineth chapter (8), the conclusions of the research conducted are drawn. Finally, the appendices (9 and 10) include basic parts of the MATLAB code used as well as mathematical proofs for the second Green theorem integral equation formulation and the Neumann Green’s function on a circular domain.