12 research outputs found

    Incorporating a Spatial Prior into Nonlinear D-Bar EIT imaging for Complex Admittivities

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    Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filter to include higher frequency components in the reconstruction, in particular, features that are known with high confidence. This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.Comment: 18 pages, 10 figure

    EIT Imaging of Admittivities with a D-Bar Method and Spatial Prior: Experimental Results for Absolute and Difference Imaging

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    Electrical impedance tomography (EIT) is an emerging imaging modality that uses harmless electrical measurements taken on electrodes at a body\u27s surface to recover information about the internal electrical conductivity and or permittivity. The image reconstruction task of EIT is a highly nonlinear inverse problem that is sensitive to noise and modeling errors making the image reconstruction task challenging. D-bar methods solve the nonlinear problem directly, bypassing the need for detailed and time-intensive forward models, to provide absolute (static) as well as time-difference EIT images. Coupling the D-bar methodology with the inclusion of high confidence a priori data results in a noise-robust regularized image reconstruction method. In this work, the a priori D-bar method for complex admittivities is demonstrated effective on experimental tank data for absolute imaging for the first time. Additionally, the method is adjusted for, and tested on, time-difference imaging scenarios. The ability of the method to be used for conductivity, permittivity, absolute as well as time-difference imaging provides the user with great flexibility without a high computational cost

    A Direct D-Bar Method for Partial Boundary Data Electrical Impedance Tomography With a Priori Information

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    Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that uses surface electrical measurements to determine the internal conductivity of a body. The mathematical formulation of the EIT problem is a nonlinear and severely ill-posed inverse problem for which direct D-bar methods have proved useful in providing noise-robust conductivity reconstructions. Recent advances in D-bar methods allow for conductivity reconstructions using EIT measurement data from only part of the domain (e.g., a patient lying on their back could be imaged using only data gathered on the accessible part of the body). However, D-bar reconstructions suffer from a loss of sharp edges due to a nonlinear low-pass filtering of the measured data, and this problem becomes especially marked in the case of partial boundary data. Including a priori data directly into the D-bar solution method greatly enhances the spatial resolution, allowing for detection of underlying pathologies or defects, even with no assumption of their presence in the prior. This work combines partial data D-bar with a priori data, allowing for noise-robust conductivity reconstructions with greatly improved spatial resolution. The method is demonstrated to be effective on noisy simulated EIT measurement data simulating both medical and industrial imaging scenarios

    Computational advancements in the D-bar reconstruction method for 2-D electrical impedance tomography

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    2016 Spring.Includes bibliographical references.We study the problem of reconstructing 2-D conductivities from boundary voltage and current density measurements, also known as the electrical impedance tomography (EIT) problem, using the D-bar inversion method, based on the 1996 global uniqueness proof by Adrian Nachman. We focus on the computational implementation and efficiency of the D-bar algorithm, its application to finite-precision practical data in human thoracic imaging, and the quality and spatial resolution of the resulting reconstructions. The main contributions of this work are (1) a parallelized computational implementation of the algorithm which has been shown to run in real-time, thus demonstrating the feasibility of the D-bar method for use in real-time bedside imaging, and (2) a modification of the algorithm to include \emph{a priori} data in the form of approximate organ boundaries and (optionally) conductivity estimates, which we show to be effective in improving spatial resolution in the resulting reconstructions. These computational advancements are tested using both numerically simulated data as well as experimental human and tank data collected using the ACE1 EIT machine at CSU. In this work, we provide details regarding the theoretical background and practical implementation for each advancement, we demonstrate the effectiveness of the algorithm modifications through multiple experiments, and we provide discussion and conclusions based on the results

    A parametric level set-based approach to difference imaging in electrical impedance tomography

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    This paper presents a novel difference imaging approach based on the recently developed parametric level set (PLS) method for estimating the change in a target conductivity from electrical impedance tomography measurements. As in conventional difference imaging, the reconstruction of conductivity change is based on data sets measured from the surface of a body before and after the change. The key feature of the proposed approach is that the conductivity change to be reconstructed is assumed to be piecewise constant, while the geometry of the anomaly is represented by a shape-based PLS function employing Gaussian radial basis functions (GRBFs). The representation of the PLS function by using GRBF provides flexibility in describing a large class of shapes with fewer unknowns. This feature is advantageous, as it may significantly reduce the overall number of unknowns, improve the condition number of the inverse problem, and enhance the computational efficiency of the technique. To evaluate the proposed PLS-based difference imaging approach, results obtained via simulation, phantom study, and in vivo pig data are studied. We find that the proposed approach tolerates more modeling errors and leads to a significant improvement in image quality compared with the conventional linear approach

    B-spline based sharp feature preserving shape reconstruction approach for electrical impedance tomography

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    This paper presents a B-spline based shape reconstruction approach for electrical impedance tomography (EIT). In the proposed approach, the conductivity distribution to be reconstructed is assumed to be piecewise constant. The geometry of the inclusions is parameterized using B-spline curves, and the EIT forward solver is modified as a set of control points representing the inclusions’ boundary to the data on the domain boundary. The low order representation decreases the computational demand and reduces the ill-posedness of the EIT reconstruction problem. The performance of the proposed B-spline based approach is tested with simulations which demonstrate the most popular biomedical application of EIT: lung imaging. The approach is experimentally validated using water tank data. In addition, robustness studies of the proposed approach considering varying initial guesses, inaccurately known contact impedances, differing numbers of control points, and degree of B-spline are performed. The simulation and experimental results show that the B-spline based approach offers improvements in image quality in comparison to the traditional Fourier series based reconstruction approach, as measured by quantitative metrics such as relative size coverage ratio and relative contrast. Inasmuch, the proposed approach is demonstrated to offer clear improvement in the ability to preserve the sharp properties of the inclusions to be imaged

    Advanced digital electrical impedance tomography system for biomedical imaging

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    Electrical Impedance Tomography (EIT) images the spatial conductivity distribution in an electrode-bounded sensing domain by non-intrusively generating an electric field and measuring the induced boundary voltage. Since its emergence, it has attracted ample interest in the field of biomedical imaging owing to its fast, cost efficient, label-free and non-intrusive sensing ability. Well-investigated biomedical applications of the EIT include lung ventilation monitoring, breast cancer imaging, and brain function imaging. This thesis probes an emerging biomedical application of EIT in three dimensional (3D) cell culture imaging to study non-destructively the biological behaviour of a 3D cell culture system, on which occasion real-time qualitative and quantitative imaging are becoming increasingly desirable. Focused on this topic, the contribution of the thesis can be summarised from the perspectives of biomedical-designed EIT system, fast and effective image reconstruction algorithms, miniature EIT sensors and experimental studies on cell imaging and cell-drug response monitoring, as follows. First of all, in order to facilitate fast, broadband and real-time 3D conductivity imaging for biomedical applications, the design and evaluation of a novel multi-frequency EIT (mfEIT) system was presented. The system integrated 32 electrode interfaces and its working frequency ranged from 10 kHz to 1 MHz. Novel features of the system included: a) a fully adjustable multi-frequency current source with current monitoring function was designed; b) a flexible switching scheme together with a semi-parallel data acquisition architecture was developed for high-frame-rate data acquisition; c) multi-frequency simultaneous digital quadrature demodulation was accomplished, and d) a 3D imaging software, i.e. Visual Tomography, was developed to perform real-time two dimensional (2D) and 3D image reconstruction, visualisation and analysis. The mfEIT system was systematically tested and evaluated on the basis of the Signal to Noise Ratio (SNR), frame rate, and 2D and 3D multi-frequency phantom imaging. The highest SNR achieved by the system was 82.82 dB on a 16-electrode EIT sensor. The frame rate was up to 546 frames per second (fps) at serial mode and 1014 fps at semi-parallel mode. The evaluation results indicate that the presented mfEIT system is a powerful tool for real-time 2D and 3D biomedical imaging. The quality of tomographic images is of great significance for performing qualitative or quantitative analysis in biomedical applications. To realise high quality conductivity imaging, two novel image reconstruction algorithms using adaptive group sparsity constraint were proposed. The proposed algorithms considered both the underlying structure of the conductivity distribution and sparsity priors in order to reduce the degree of freedom and pursue solutions with the group sparsity structure. The global characteristic of inclusion boundaries was studied as well by imposing the total variation constraint on the whole image. In addition, two adaptive pixel grouping methods were also presented to extract the structure information without requiring any a priori knowledge. The proposed algorithms were evaluated comparatively through numerical simulation and phantom experiments. Compared with the state-of-the-art algorithms such as l1 regularisation, the proposed algorithms demonstrated superior spatial resolution and preferable noise reduction performance in the reconstructed images. These features were demanded urgently in biomedical imaging. Further, a planar miniature EIT sensor amenable to the standard 3D cell culture format was designed and a 3D forward model was developed for 3D imaging. A novel 3D-Laplacian and sparsity joint regularisation algorithm was proposed for enhanced 3D image reconstruction. Simulated phantoms with spheres located at different vertical and horizontal positions were imaged for 3D imaging performance evaluation. Image reconstructions of MCF-7 human breast cancer cell spheroids and triangular breast cancer cell pellets were carried out for experimental verification. The results confirmed that robust impedance measurement on the highly conductive cell culture medium was feasible and, greatly improved image quality was obtained by using the proposed regularisation method. Finally, a series of cancer cell spheroid imaging tests and real-time cell-drug response monitoring experiments by using the developed mfEIT system (Chapter 3), the designed miniature EIT sensors (Chapter 6) and the proposed image reconstruction algorithms (Chapter 4, 5 and 6) were carried out followed by comparative analysis. The stability of long-term impedance measurement on the highly conductive cell culture medium was verified firstly. Subsequently, by using the proposed algorithms in Chapter 4 and Chapter 5, high quality cancer cell spheroid imaging on a miniature sensor with 2D electrode configuration was achieved. Further, preliminary experiments on real-time monitoring of human breast cancer cell and anti-cancer drug response were performed and analysed. Promising results were obtained from these experiments. In summary, the work demonstrated in this thesis validated the feasibility of using the developed mfEIT system, the proposed image reconstruction algorithms, as well as the designed miniature EIT sensors to visualise 3D cell culture systems such as cell spheroids or artificial tissues and organs. The established work would expedite the real-time qualitative and quantitative imaging of 3D cell culture systems for the rapid assessment of cellular dynamics

    Advanced electrode models and numerical modelling for high frequency Electrical Impedance Tomography systems

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    The thesis discusses various electrode models and finite element analysis methods for Electrical Impedance Tomography (EIT) systems. EIT is a technique for determining the distribution of the conductivity or admittivity in a volume by injecting electrical currents into the volume and measuring the corresponding potentials on the surface of the volume. Various electrode models were investigated for operating EIT systems at higher frequencies in the beta-dispersion band. Research has shown that EIT is potentially capable to distinguish malignant and benign tumours in this frequency band. My study concludes that instrumental effects of the electrodes and full Maxwell effects of EIT systems are the major issues, and they have to be addressed when the operating frequency increases. In the thesis, I proposed 1) an Instrumental Electrode Model (IEM) for the quasi-static EIT formula, based on the analysis of the hardware structures attached to electrodes; 2) a Complete Electrode Model based on Impedance Boundary Conditions (CEM-IBC) that introduces the contact impedances into the full Maxwell EIT formula; 3) a Transmission line Port Model (TPM) for electrode pairs with the instrumental effects, the contact impedance, and the full Maxwell effects considered for EIT systems. Circuit analysis, Partial Differential Equations (PDE) analysis, numerical analysis and finite element methods were used to develop the models. The results obtained by the proposed models are compared with widely used Commercial PDE solvers. This thesis addresses the two major problems (instrumental effects of the electrodes and full Maxwell effects of EIT systems) with the proposed advanced electrode models. Numerical experiments show that the proposed models are more accurate in the high frequency range of EIT systems. The proposed electrode models can be also applicable to inverse problems, and the results show promising. Simple hardware circuits for verifying the results experimentally have been also designed

    Active complex electrode (ACE1) electrical impedance tomography system & anatomically inspired modeling of electrode-skin contact impedance, The

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    Includes bibliographical references.2016 Summer.Electrical Impedance Tomography (EIT) is a technique used to image the varying electrical properties of biological tissues or tissue conductivity and permittivity. There are many clinical uses of EIT, but as a newer imaging modality, there is interest in improving hardware to acquire EIT data, creating models of the system and generating high quality images. The two main contributions of this work include: (1) EIT hardware advancements and (2) software modeling to simulate measured human subject data. Specifically, this dissertation includes the design and testing of Colorado State University's first EIT system, the pairwise current injection active complex electrode (ACE1) system for phasic voltage measurement. The ACE1 system was primarily designed for thoracic EIT applications, and its performance and limitations were tested through a variety of experiments. Additionally, the EIT forward problem was used to investigate electrode-skin contact impedance
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