Alistair Boyle

Shape Deformation in Two-Dimensional Electrical Impedance Tomography

Electrical impedance tomography (EIT) uses measurements from surface electrodes to reconstruct an image of the conductivity of the contained medium. However, changes in measurements result from both changes in internal conductivity and changes in the shape of the medium relative to the electrode positions. Failure to account for shape changes results in a conductivity image with significant artifacts. Previous work to address shape changes in EIT has shown that in some cases boundary shape and electrode location can be uniquely determined for isotropic conductivities; however, for geometrically conformal changes, this is not possible. This prior work has shown that the shape change problem can be partially addressed. In this paper, we explore the limits of compensation for boundary movement in EIT using three approaches. First, a theoretical model was developed to separate a deformation vector field into conformal and non-conformal components, from which the reconstruction limits may be determined. Next, finite element models were used to simulate EIT measurements from a domain whose boundary has been deformed. Finally, an experimental phantom was constructed from which boundary deformation measurements were acquired. Results, both in simulation and with experimental data, suggest that some electrode movement and boundary distortions can be reconstructed based on conductivity changes alone while reducing image artifacts in the process.

Addressing the computational cost of large EIT solutions

Electrical impedance tomography (EIT) is a soft field tomography modality based on the application of electric current to a body and measurement of voltages through electrodes at the boundary. The interior conductivity is reconstructed on a discrete representation of the domain using a finite-element method (FEM) mesh and a parametrization of that domain. The reconstruction requires a sequence of numerically intensive calculations. There is strong interest in reducing the cost of these calculations. An improvement in the compute time for current problems would encourage further exploration of computationally challenging problems such as the incorporation of time series data, wide-spread adoption of three-dimensional simulations and correlation of other modalities such as CT and ultrasound. Multicore processors offer an opportunity to reduce EIT computation times but may require some restructuring of the underlying algorithms to maximize the use of available resources. This work profiles two EIT software packages (EIDORS and NDRM) to experimentally determine where the computational costs arise in EIT as problems scale. Sparse matrix solvers, a key component for the FEM forward problem and sensitivity estimates in the inverse problem, are shown to take a considerable portion of the total compute time in these packages. A sparse matrix solver performance measurement tool, Meagre-Crowd, is developed to interface with a variety of solvers and compare their performance over a range of two- and three-dimensional problems of increasing node density. Results show that distributed sparse matrix solvers that operate on multiple cores are advantageous up to a limit that increases as the node density increases. We recommend a selection procedure to find a solver and hardware arrangement matched to the problem and provide guidance and tools to perform that selection.

Electrical Impedance Tomography: Tissue Properties to Image Measures

Electrical impedance tomography (EIT) uses electrical stimulation and measurement at the body surface to image the electrical properties of internal tissues. It has the advantage of noninvasiveness and high temporal resolution but suffers from poor spatial resolution and sensitivity to electrode movement and contact quality. EIT can be useful to applications, where there are conductive contrasts between tissues, fluids, or gasses, such as imaging of cancerous or ischemic tissue or functional monitoring of breathing, blood flow, gastric motility, and neural activity. The past decade has seen clinical application and commercial activity using EIT for ventilation monitoring. Interpretation of EIT-based measures is complex, and this review paper focuses on describing the image interpretation “pathway.” We review this pathway, from Tissue Electrical Properties, EIT Electrodes & Hardware, Sensitivity, Image Reconstruction, Image Processing to EIT Measures. The relationship is discussed between the clinically relevant parameters and the reconstructed properties. An overview is given of areas of EIT application and of our perspectives for research and development.

Electrode models under shape deformation in Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) applies current and measures the resulting voltage on the surface of a target. In biomedical applications, this current is applied, and voltage is measured through electrodes attached to the surface. Electrode models represent these connections in the reconstruction, but changes in the contact impedance or boundary relative to the electrode area can introduce artifacts. Using difference imaging, the effects of boundary deformation and contact impedance variation were investigated. The Complete Electrode Model (CEM) was found to be affected by conformal deformations. Contact impedance variability was found to be a significant source of artifacts in some cases.

Methods for calculating the electrode position Jacobian for impedance imaging

Electrical impedance tomography (EIT) or electrical resistivity tomography (ERT) current and measure voltages at the boundary of a domain through electrodes. SIGNIFICANCE The movement or incorrect placement of electrodes may lead to modelling errors that result in significant reconstructed image artifacts. These errors may be accounted for by allowing for electrode position estimates in the model. Movement may be reconstructed through a first-order approximation, the electrode position Jacobian. A reconstruction that incorporates electrode position estimates and conductivity can significantly reduce image artifacts. Conversely, if electrode position is ignored it can be difficult to distinguish true conductivity changes from reconstruction artifacts which may increase the risk of a flawed interpretation. OBJECTIVE In this work, we aim to determine the fastest, most accurate approach for estimating the electrode position Jacobian. APPROACH Four methods of calculating the electrode position Jacobian were evaluated on a homogeneous halfspace. MAIN RESULTS Results show that Fréchet derivative and rank-one update methods are competitive in computational efficiency but achieve different solutions for certain values of contact impedance and mesh density.

Bioimpedance Spectroscopy Processing and Applications

Bioimpedance spectroscopy (BIS) uses multifrequency impedance measurements of biological tissues to estimate clinically and experimentally relevant parameters. This article reviews the steps involved in measurement, data processing, and applications of BIS data, with an emphasis on managing data quality and sources of errors. Based on a description of error sources, caused by measurement configuration, hardware, and modeling, we describe BIS data denoising. Two classes of modeling, explanatory and descriptive, can be used to reduce data dimensionality to a set of parameters or features. Explanatory models consider the electrical properties of samples and involve fitting data to simplified equivalent electrical circuits. Descriptive models involve reduction of the data to a set of eigenvectors/values which can be studied independently of any assumed electrical characteristics of the sample. Techniques described include fitting and decomposition methods for extraction of explanatory and descriptive model parameters, respectively. Denoising techniques discussed include adjusting measurement configuration, corrective algorithms for removal of artifacts, and use of supervised machine learning for identification of features characteristic of noisy impedance spectra. The article concludes with a discussion of the use of classifiers for labeling BIS data in a range of applications including discrimination of healthy versus pathological tissues.