No description available.

The backprojection method for electrical impedance image reconstruction has been adapted for the opposing current drive configuration implemented in the second generation of Aberdeen impedance imaging systems. The logarithmic conformal transformation is used to solve the Forward problem for a two-dimensional homogeneous medium of circular cross-section. Pixel weights of backprojection are calculated from the normalised distances of the pixel centres from the boundary side of backprojection. An experimental solution to the Forward problem is a homogeneous medium of irregular cross-section and three-dimensional boundary is proposed and implemented. A thorax phantom was built for this purpose using radiotherapy moulding techniques. The potential distribution in this phantom was measured using a tetrapolar inpedance measuring device and the equipotential lines falling on the electrodes were plotted. A reconstruction matrix capable of reconstructing dynamic impedance images of the thorax was formulated. Images representing resistivity change distributions between maximum inspiration and maximum expiration have been reconstructed. These thorax cross-section images show the most faithful representation of the expected resistivity changes due to respiration.

No description available.

Thesis (MEng)--University of South Australia, 1995

Thesis (MEng)--University of South Australia, 1995

In Electrical Impedance Tomography the conductivity of an object is estimated from boundary measurements. An array of electrodes is attached to the surface of the object and current stimuli are applied via these electrodes. The resulting volt ages are measured. The process of estimating the conductivity as a function of space inside the object from voltage measurements at the surface is called reconstruction. Mathematically the ElT reconstruction is a non linear inverse problem, the stable solution of which requires regularisation nwthods. Most common regularisation methods impose that the reconstructed image should be smooth. Such methods confer stability to the reconstruction process, but limit the capability of describing sharp variations in the sought parameter. In this thesis two new methods of regularisation are proposed. The first method, Gallssian anisotropic regularisation, enhances the reconstruction of sharp conductivity changes occurring at the interface between a contrasting object and the background. As such changes are step changes, reconstruction with traditional smoothing regularisation techniques is unsatisfactory. The Gaussian anisotropic filtering works by incorporating prior structural information. The approximate knowledge of the shapes of contrasts allows us to relax the smoothness in the direction normal to the expected boundary. The construction of Gaussian regularisation filters that express such directional properties on the basis of the structural information is discussed, and the results of numerical experiments are analysed. The method gives good results when the actual conductivity distribution is in accordance with the prior information. When the conductivity distribution violates the prior information the method is still capable of properly locating the regions of contrast. The second part of the thesis is concerned with regularisation via the total variation functional. This functional allows the reconstruction of discontinuous parameters. The properties of the functional are briefly introduced, and an application in inverse problems in image denoising is shown. As the functional is non-differentiable, numerical difficulties are encountered in its use. The aim is therefore to propose an efficient numerical implementation for application in ElT. Several well known optimisation methods arc analysed, as possible candidates, by theoretical considerations and by numerical experiments. Such methods are shown to be inefficient. The application of recent optimisation methods called primal- dual interior point methods is analysed be theoretical considerations and by numerical experiments, and an efficient and stable algorithm is developed. Numerical experiments demonstrate the capability of the algorithm in reconstructing sharp conductivity profiles.

No description available.

Electrical impedance tomography is an imaging method with applications to geophysics and medical imaging. A new approximation is presented based on Nachman's 2-dimensional construction for closed domains. It improves upon existing approximations by extending the range of application from resolving 2 times the surface conductivity to imaging perfect conductors and insulators. With perfect knowledge of boundary data, this approximation exactly resolves a single conductive disc embedded in a homogenous domain. The problem, however, is ill-posed, and imaging performance degrades quickly as the distance from the boundary increases. The key to the approximation lies in (a) approximating Fadeev's Green's function (b) pre-processing measured voltages based on a boundary-integral equation (c) solving a linearized inverse problem (d) solving a d-bar equation, and (e) scaling the resulting image based on analytical results for a disc. In the development of the approximation, a new formula for Fadeev's Green's function is presented in terms of the Exponential Integral function. Also, new comparisons are made between reconstructions with and without solving the d-bar equation, showing that the added computational expense of solving the d-bar equation is not justified for radial problems. There is no discernible improvement in image quality. As a result, the approximation converts the inverse conductivity problem into a novel one-step linear problem with pre-conditioning of boundary data and scaling of the resulting image. Several extensions to this work are possible. The approximation is implemented for a circular domain with unit conductivity near the boundary, and extensions to other domains, bounded and unbounded should be possible, with non-constant conductivity near the boundary requiring further approximation. Ultimately, further research is required to ascertain whether it is possible to extend these techniques to imaging problems in three dimensions.

Electrical impedance tomography is an imaging method with applications to geophysics and medical imaging. A new approximation is presented based on Nachman's 2-dimensional construction for closed domains. It improves upon existing approximations by extending the range of application from resolving 2 times the surface conductivity to imaging perfect conductors and insulators. With perfect knowledge of boundary data, this approximation exactly resolves a single conductive disc embedded in a homogenous domain. The problem, however, is ill-posed, and imaging performance degrades quickly as the distance from the boundary increases. The key to the approximation lies in (a) approximating Fadeev's Green's function (b) pre-processing measured voltages based on a boundary-integral equation (c) solving a linearized inverse problem (d) solving a d-bar equation, and (e) scaling the resulting image based on analytical results for a disc. In the development of the approximation, a new formula for Fadeev's Green's function is presented in terms of the Exponential Integral function. Also, new comparisons are made between reconstructions with and without solving the d-bar equation, showing that the added computational expense of solving the d-bar equation is not justified for radial problems. There is no discernible improvement in image quality. As a result, the approximation converts the inverse conductivity problem into a novel one-step linear problem with pre-conditioning of boundary data and scaling of the resulting image. Several extensions to this work are possible. The approximation is implemented for a circular domain with unit conductivity near the boundary, and extensions to other domains, bounded and unbounded should be possible, with non-constant conductivity near the boundary requiring further approximation. Ultimately, further research is required to ascertain whether it is possible to extend these techniques to imaging problems in three dimensions.

Introduction: Electrical Impedance Tomography (EIT) is an emerging clinical imaging technique. Functional EIT by Evoked Response (fEITER) was developed at the University of Manchester as a high-speed, functional brain imaging device for use at the bedside. This 32-electrode EIT system applies an injection frequency of 10kHz and captures data using a 10ms temporal resolution. This thesis reports on the first volunteer and patient trials undertaken using fEITER for the following conditions: (a) flashing visual sequence - 14 awake volunteers; (b) a voluntary Valsalva manoeuvre (VM) - 15 awake volunteers and (c) during the induction of anaesthesia - 16 elective surgical patients. Aims: The research presented in this thesis was undertaken to differentiate between noise and physiological changes in raw fEITER data signals. Methods: SNR was determined for fEITER. Raw fEITER signals were pre-processed to reduce noise and dominant trends before multiple comparisons between reference and stimulus data were undertaken. Histograms and ROC curves were produced to illustrate the difference between reference and stimulus fEITER data. AUC values for single-subject and pooled ROC curves were calculated to determine whether fEITER data can be reliably differentiated between reference and stimulus conditions. Approximate Entropy (ApEn) was applied to evaluate the regularity of high frequency components within fEITER data for each trial condition. Results: Average SNR values for fEITER acquired using mesh and physical phantoms ranged from 62.94dB to 63.58dB, and 28.29dB to 31.45dB respectively. The following AUC values were acquired: Visual stimulus-frontal electrode pairs and electrode pairs overlying the visual cortex 0.520 and 0.505 respectively; VM: 0.658; and induction of anaesthesia: 0.547. The VM induced the greatest difference between pooled reference and stimulus data. Visual stimulation and induction of anaesthesia data showed poor distinction between pooled reference and stimulus data, although some single subject data did show a significant response. No significant differences were acquired for the comparison of ApEn-reference and ApEn-stimulus data for all trial conditions using a Wilcoxon's signed ranks test (visual stimulus-frontal electrode pairs: upper p = 0.998, visual stimulus-electrode overlying the visual cortex: upper p = 0.980; the VM: upper p = 0.976, and induction of anaesthesia: p = 0.912). Discussion: Although single-subject and pooled fEITER data recorded during the VM produced the greatest differences between reference and stimulus measurements, stimuli such as visual flashes and induction of anaesthesia may not be large enough to induce quantifiable changes between reference and stimulus data recorded from single electrode pairs. Collectively, these results provide little evidence to show that pre-processing of raw fEITER data amplifies features in fEITER waveforms which may be representative of physiological changes induced by an applied stimulus.