Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D

Electrical impedance tomography (EIT) is a medical imaging technique in which current is applied on electrodes on the surface of the body, the resulting voltage is measured, and an inverse problem is solved to recover the conductivity and/or permittivity in the interior. Images are then formed from the reconstructed conductivity and permittivity distributions. In the 2-D geometry, EIT is clinically useful for chest imaging. In this work, an implementation of a D-bar method for complex admittivities on a general 2-D domain is presented. In particular, reconstructions are computed on a chest-shaped domain for several realistic phantoms including a simulated pneumothorax, hyperinflation, and pleural effusion. The method demonstrates robustness in the presence of noise. Reconstructions from trigonometric and pairwise current injection patterns are included

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D

A direct reconstruction algorithm for complex conductivities in $W^{2,\infty}(\Omega)$, where $\Omega$ is a bounded, simply connected Lipschitz domain in $\mathbb{R}^2$, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.Comment: This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0266-5611/28/9/09500

Comparison of linear and non-linear monotononicity-based shape reconstruction using exact matrix characterizations

Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions, exactly characterize the inhomogeneities based on monotonicity properties of either the Neumann-to-Dirichlet map (non-linear) or its Fr\'echet derivative (linear). We give a comparison of the non-linear and linear approach in the presence of measurement noise, and show numerically that the two methods give essentially the same reconstruction in the unit disk domain. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method in the unit disk geometry.Comment: 18 pages, 5 figures, 1 tabl

Multifrequency methods for Electrical Impedance Tomography

Multifrequency Electrical Impedance Tomography (MFEIT) is an emerging imaging modality which exploits the dependence of tissue impedance on frequency to recover images of conductivity. Given the low cost and portability of EIT scanners, MFEIT could provide emergency diagnosis of pathologies such as acute stroke, brain injury and breast cancer. Whereas time-difference, or dynamic, EIT is an established technique for monitoring lung ventilation, MFEIT has received less attention in the literature, and the imaging methodology is at an early stage of development. MFEIT holds the unique potential to form images from static data, but high sensitivity to noise and modelling errors must be overcome. The subject of this doctoral thesis is the investigation of novel techniques for including spectral information in the image reconstruction process. The aim is to improve the ill-posedness of the inverse problem and deliver the first imaging methodology with sufficient robustness for clinical application. First, a simple linear model for the conductivity is defined and a simultaneous multifrequency method is developed. Second, the method is applied to a realistic numerical model of a human head, and the robustness to modelling errors is investigated. Third, a combined image reconstruction and classification method is developed, which allows for the simultaneous recovery of the conductivity and the spectral information by introducing a Gaussian-mixture model for the conductivity. Finally, a graph-cut image segmentation technique is integrated in the imaging method. In conclusion, this work identifies spectral information as a key resource for producing MFEIT images and points to a new direction for the development of MFEIT algorithms

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

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

Arts of electrical impedance tomographic sensing

This paper reviews governing theorems in electrical impedance sensing for analysing the relationships of boundary voltages obtained from different sensing strategies. It reports that both the boundary voltage values and the associated sensitivity matrix of an alternative sensing strategy can be derived from a set of full independent measurements and sensitivity matrix obtained from other sensing strategy. A new sensing method for regional imaging with limited measurements is reported. It also proves that the sensitivity coefficient back-projection algorithm does not always work for all sensing strategies unless the diagonal elements of the transformed matrix, ATA, have significant values and can be approximate to a diagonal matrix. Imaging capabilities of few sensing strategies were verified with static set-ups, which suggest the adjacent electrode pair sensing strategy displays better performance compared to the diametrically opposite protocol, with both the back-projection and multi-step image reconstruction methods. An application of electrical impedance tomography for sensing gas in water two phase flows is demonstrated

Design and application of a multi-modal process tomography system

This paper presents a design and application study of an integrated multi-modal system designed to support a range of common modalities: electrical resistance, electrical capacitance and ultrasonic tomography. Such a system is designed for use with complex processes that exhibit behaviour changes over time and space, and thus demand equally diverse sensing modalities. A multi-modal process tomography system able to exploit multiple sensor modes must permit the integration of their data, probably centred upon a composite process model. The paper presents an overview of this approach followed by an overview of the systems engineering and integrated design constraints. These include a range of hardware oriented challenges: the complexity and specificity of the front end electronics for each modality; the need for front end data pre-processing and packing; the need to integrate the data to facilitate data fusion; and finally the features to enable successful fusion and interpretation. A range of software aspects are also reviewed: the need to support differing front-end sensors for each modality in a generic fashion; the need to communicate with front end data pre-processing and packing systems; the need to integrate the data to allow data fusion; and finally to enable successful interpretation. The review of the system concepts is illustrated with an application to the study of a complex multi-component process