The impact of electrode area, contact impedance and boundary shape on EIT images

Electrical impedance tomography (EIT) measures the conductivity distribution within an object based on the current applied and voltage measured at surface electrodes. Thus, EIT images are sensitive to electrode properties (i.e. contact impedance, electrode area and boundary shape under the electrode). While some of these electrode properties have been investigated individually, this paper investigates these properties and their interaction using finite element method simulations and the complete electrode model (CEM). The effect of conformal deformations on image reconstruction when using the CEM was of specific interest. Observed artefacts were quantified using a measure that compared an ideal image to the reconstructed image, in this case a no-noise reconstruction that isolated the electrodes' effects. For electrode contact impedance and electrode area, uniform reductions to all electrodes resulted in ringing artefacts in the reconstructed images when the CEM was used, while parameter variations that were not correlated amongst electrodes resulted in artefacts distributed throughout the image. When the boundary shape changed under the electrode, as with non-symmetric conformal deformations, using the CEM resulted in structured distortions within the reconstructed image. Mean electrode contact impedance increases, independent of inter-electrode variation, did not result in artefacts in the reconstructed image.     

Imaging of conductivity changes and electrode movement in EIT

Electrical impedance tomography (EIT) attempts to reconstruct the internal impedance distribution in a medium from electrical measurements at electrodes on the medium surface. One key difficulty with EIT measurements is due to the position uncertainty of the electrodes, especially for medical applications, in which the body surface moves during breathing and posture change. In this paper, we develop a new approach which directly reconstructs both electrode movements and internal conductivity changes for difference EIT. The reconstruction problem is formulated in terms of a regularized inverse, using an augmented Jacobian, sensitive to impedance change and electrode movement. A reconstruction prior term is computed to impose a smoothness constraint on both the spatial distribution of impedance change and electrode movement. A one-step regularized imaging algorithm is then implemented based on the augmented Jacobian and smoothness constraint. Images were reconstructed using the algorithm of this paper with data from simulated 2D and 3D conductivity changes and electrode movements, and from saline phantom measurements. Results showed good reconstruction of the actual electrode movements, as well as a dramatic reduction in image artefacts compared to images from the standard algorithm, which did not account for electrode movement.     

Minimizing EIT image artefacts from mesh variability in finite element models

Electrical impedance tomography (EIT) solves an inverse problem to estimate the conductivity distribution within a body from electrical simulation and measurements at the body surface, where the inverse problem is based on a solution of Laplace's equation in the body. Most commonly, a finite element model (FEM) is used, largely because of its ability to describe irregular body shapes. In this paper, we show that simulated variations in the positions of internal nodes within a FEM can result in serious image artefacts in the reconstructed images. Such variations occur when designing FEM meshes to conform to conductivity targets, but the effects may also be seen in other applications of absolute and difference EIT. We explore the hypothesis that these artefacts result from changes in the projection of the anisotropic conductivity tensor onto the FEM system matrix, which introduces anisotropic components into the simulated voltages, which cannot be reconstructed onto an isotropic image, and appear as artefacts. The magnitude of the anisotropic effect is analysed for a small regular FEM, and shown to be proportional to the relative node movement as a fraction of element size. In order to address this problem, we show that it is possible to incorporate a FEM node movement component into the formulation of the inverse problem. These results suggest that it is important to consider artefacts due to FEM mesh geometry in EIT image reconstruction.     

Temporal image reconstruction in electrical impedance tomography

Electrical impedance tomography (EIT) calculates images of the body from body impedance measurements. While the spatial resolution of these images is relatively low, the temporal resolution of EIT data can be high. Most EIT reconstruction algorithms solve each data frame independently, although Kalman filter algorithms track the image changes across frames. This paper proposes a new approach which directly accounts for correlations between images in successive data frames. Image reconstruction is posed in terms of an augmented image x and measurement vector y, which concatenate the values from the d previous and future frames. Image reconstruction is then based on an augmented regularization matrix R, which accounts for a model of both the spatial and temporal correlations between image elements. Results are compared for reconstruction algorithms based on independent frames, Kalman filters and the proposed approach. For low values of the regularization hyperparameter, the proposed approach performs similarly to independent frames, but for higher hyperparameter values, it uses adjacent frame data to reduce reconstructed image noise.     

Direct reconstruction of tissue parameters from differential multifrequency EIT in vivo

The basic purpose of electrical impedance tomography (EIT) is the reconstruction of conductivity distributions. While multifrequency measurements are of common use, the majority of reconstructed images are still conductivity distributions from one single frequency. More interesting than conductivities at each frequency are electrical tissue parameters, which describe the frequency-dependent conductivity changes of tissue. These parameters give information about physiological or electrical properties of tissues. By using this spectral information, a classification of different tissue types is possible. To get a distribution of tissue parameters, usually a posterior fitting of a tissue model to the conductivity spectra obtained with classical reconstruction algorithms at various frequencies is used. In this work, a single-step reconstruction algorithm for differential imaging was developed for the direct estimation of Cole parameters. This method is termed differential parametric reconstruction. The Cole model was used as the underlying tissue model, where only the relative changes of the two conductivity parameters sigma(0) and sigma(infinity) were reconstructed and the other two parameters of the model which are less identifiable were set to constant values. The reconstruction algorithm was tested with simulated noisy datasets and real measurement data from EIT measurements on the human thorax. These measurements were taken from healthy subjects and from patients with a serious lung injury. The new method yields a good image quality and higher robustness against noise compared to conventional reconstruction methods.     

Accounting for erroneous electrode data in electrical impedance tomography

An unfortunate occurrence in experimental measurements with electrical impedance tomography is electrodes which become detached or poorly connected, such that the measured data cannot be used. This paper develops an image reconstruction methodology which allows use of the remaining valid data. A finite element model of the EIT difference imaging forward problem is linearized as z = Hx, where z represents the change in measurements and x the element log conductivity changes. Image reconstruction is represented in terms of a maximum a posteriori (MAP) estimate as x = inv(Htinv(Rn) + inv(Rx))Htinv(Rn)z, where Rx and Rn represent the a priori estimates of image and measurement noise crosscorrelations, respectively. Using this formulation, missing electrode data can be naturally modelled as infinite noise on all measurements using the affected electrodes. Simulations indicate position error and resolution are close (+/- 10%) to the values calculated without missing electrode data as long as the target was further than 10% of the medium diameter from the affected electrode. Applications of this technique to experimental data show good results in terms of removing artefacts from images.     

Electrode placement configurations for 3D EIT

This paper investigates several configurations for placing electrodes on a 3D cylindrical medium to reconstruct 3D images using 16 electrode EIT equipment intended for use with a 2D adjacent drive protocol. Seven different electrode placement configurations are compared in terms of the following figures of merit: resolution, radial and vertical position error, image magnitude, immunity to noise, immunity to electrode placement errors, and qualitative evaluation of image artefacts. Results show that for ideal conditions, none of the configurations considered performed significantly better than the others. However, when noise and electrode placement errors were considered the planar electrode placement configuration (two rings of vertically aligned electrodes with electrodes placed sequentially in each ring) had the overall best performance. Based on these results, we recommend planar electrode placement configuration for 3D EIT lung imaging of the thorax.     

Numerical modelling errors in electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive technique that aims to reconstruct images of internal impedance values of a volume of interest, based on measurements taken on the external boundary. Since most reconstruction algorithms rely on model-based approximations, it is important to ensure numerical accuracy for the model being used. This work demonstrates and highlights the importance of accurate modelling in terms of model discretization (meshing) and shows that although the predicted boundary data from a forward model may be within an accepted error, the calculated internal field, which is often used for image reconstruction, may contain errors, based on the mesh quality that will result in image artefacts.     

Optical breast shape capture and finite-element mesh generation for electrical impedance tomography

X-ray mammography is the standard for breast cancer screening. The development of alternative imaging modalities is desirable because mammograms expose patients to ionizing radiation. Electrical impedance tomography (EIT) may be used to determine tissue conductivity, a property which is an indicator of cancer presence. EIT is also a low-cost imaging solution and does not involve ionizing radiation. In breast EIT, impedance measurements are made using electrodes placed on the surface of the patient's breast. The complex conductivity of the volume of the breast is estimated by a reconstruction algorithm. EIT reconstruction is a severely ill-posed inverse problem. As a result, noisy instrumentation and incorrect modelling of the electrodes and domain shape produce significant image artefacts. In this paper, we propose a method that has the potential to reduce these errors by accurately modelling the patient breast shape. A 3D hand-held optical scanner is used to acquire the breast geometry and electrode positions. We develop methods for processing the data from the scanner and producing volume meshes accurately matching the breast surface and electrode locations, which can be used for image reconstruction. We demonstrate this method for a plaster breast phantom and a human subject. Using this approach will allow patient-specific finite-element meshes to be generated which has the potential to improve the clinical value of EIT for breast cancer diagnosis.     

A method for modelling and optimizing an electrical impedance tomography system

Electrical impedance tomography (EIT) image reconstruction is an ill-posed problem requiring maximum measurement precision. Recent EIT systems claim 60 to 80 dB precision. Achieving higher values is hard in practice since measurements must be performed at relatively high frequency, on a living subject, while using components whose tolerance is usually higher than 0.1%. To circumvent this difficulty, a method for modelling the electronic circuits of an EIT system was developed in order to optimize the circuits and incorporate the model in the reconstruction algorithms. The proposed approach is based on a matrix method for solving electrical circuits and has been applied to the scan-head which contains the front-end electronic circuits of our system. The method is used to simulate the system characteristic curves which are then optimized with the Levenberg-Marquardt method to find optimal component values. A scan-head was built with the new component values and its simulated performance curves were compared with network analyser measurements. As a result of the optimization, the impedance at the operating frequency was increased to minimize the effects of variations in skin/electrode contact impedance. The transconductance and gain frequency responses were also reshaped to reduce noise sensitivity and unintended signal modulation. Integrating the model in the reconstruction algorithms should further improve overall performance of an EIT system.     

Reconstruction of the shape of conductivity spectra using differential multi-frequency magnetic induction tomography

Magnetic induction tomography (MIT) of biological tissue is used for the reconstruction of the complex conductivity distribution kappa inside the object under investigation. It is based on the perturbation of an alternating magnetic field caused by the object and can be used in all applications of electrical impedance tomography (EIT) such as functional lung monitoring and assessment of tissue fluids. In contrast to EIT, MIT does not require electrodes and magnetic fields can also penetrate non-conducting barriers such as the skull. As in EIT, the reconstruction of absolute conductivity values is very difficult because of the method's sensitivity to numerical errors and noise. To overcome this problem, image reconstruction in EIT is often done differentially. Analogously, this concept has been adopted for MIT. Two different methods for differential imaging are applicable. The first one is state-differential, for example when the conductivity change between inspiration and expiration in the lung regions is being detected. The second one is frequency-differential, which is of high interest in motionless organs like the brain, where a state-differential method cannot be applied. An equation for frequency-differential MIT was derived taking into consideration the frequency dependence of the sensitivity matrix. This formula is valid if we can assume that only small conductivity changes occur. In this way, the non-linear inverse problem of MIT can be approximated by a linear one (depending only on the frequency), similar to in EIT. Keeping this limitation in mind, the conductivity changes between one or more reference frequencies and several measurement frequencies were reconstructed, yielding normalized conductivity spectra. Due to the differential character of the method, these spectra do not provide absolute conductivities but preserve the shape of the spectrum. The validity of the method was tested with artificial data generated with a spherical perturbation within a conducting cylinder as well as for real measurement data. The measurement data were obtained from a potato immersed in saline. The resulting spectra were compared with reference measurements and the preservation of the shape of the spectra was analyzed.     

Excitation patterns in three-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive technique that aims to reconstruct images of internal electrical properties of a domain, based on electrical measurements on the periphery. Improvements in instrumentation and numerical modeling have led to three-dimensional (3D) imaging. The availability of 3D modeling and imaging raises the question of identifying the best possible excitation patterns that will yield to data, which can be used to produce the best image reconstruction of internal properties. In this work, we describe our 3D finite element model of EIT. Through singular value decomposition as well as examples of reconstructed images, we show that for a homogenous female breast model with four layers of electrodes, a driving pattern where each excitation plane is a sinusoidal pattern out-of-phase with its neighboring plane produces better qualitative images. However, in terms of quantitative imaging an excitation pattern where all electrode layers are in phase produces better results.     

A real-time volumetric visualization system for electrical impedance tomography

Three dimensional (3D) electrical impedance tomography (EIT) presents many additional challenges over and above those associated with two dimensional EIT systems. With present two dimensional (2D) systems, tomographs can be reconstructed and displayed on a PC with a standard computer monitor. In addition, using appropriate data acquisition hardware and simple image reconstruction algorithms, it is possible to collect, reconstruct and display volumetric EIT images in real time using parallel processing architectures. The advantages of this 'real-time' capability are many and include the ability to immediately assess the correct functioning of the system and the ability to track patient events and the effect of procedures in real time. Whilst 3D EIT boundary datasets can be collected in real time, their real-time image reconstruction and display presents some computational challenges. This explains why, to date, no real-time solutions have been presented. In addition the use of a standard computer monitor to display 3D volumes is unsatisfactory since not all depth cues are preserved when using this type of 2D display device. We present a system which is capable of displaying 3D EIT datasets in real time and allows interactive modification of the user's viewpoint. This allows the user to fly around (and through) the EIT volumetric dataset.     

Direct EIT Jacobian calculations for conductivity change and electrode movement

Electrical impedance tomography (EIT) is very sensitive to deformations of the medium boundary shape. For lung imaging, breathing and changes in posture move the electrodes and change the chest shape, resulting in image artefacts. Several approaches have been proposed to improve the reconstructed images; most methods reconstruct both the boundary deformation and conductivity change from the measured data. These techniques require the calculation of the 'movement Jacobian', reflecting measurement changes due to the boundary deformation. Previous papers have calculated this Jacobian using perturbation techniques, which are slow (requiring multiple solutions of the forward problem) and become inaccurate with increasing finite element model size. This effect has limited reconstruction algorithms for deformable media to mostly 2D. To address this problem, we propose a direct method to calculate the Jacobian, based on a formulation of the derivatives of the finite element system matrix with respect to geometry changes. An illustrative example of these calculations is given, as well as a comparison between the proposed method and a perturbation method. Results show this method is approximately 300 times faster; and for larger model sizes, the perturbation method begins to diverge from those from the direct method proposed.     

Systematic errors of EIT systems determined by easily-scalable resistive phantoms

We present a simple method to determine systematic errors that will occur in the measurements by EIT systems. The approach is based on very simple scalable resistive phantoms for EIT systems using a 16 electrode adjacent drive pattern. The output voltage of the phantoms is constant for all combinations of current injection and voltage measurements and the trans-impedance of each phantom is determined by only one component. It can be chosen independently from the input and output impedance, which can be set in order to simulate measurements on the human thorax. Additional serial adapters allow investigation of the influence of the contact impedance at the electrodes on resulting errors. Since real errors depend on the dynamic properties of an EIT system, the following parameters are accessible: crosstalk, the absolute error of each driving/sensing channel and the signal to noise ratio in each channel. Measurements were performed on a Goe-MF II EIT system under four different simulated operational conditions. We found that systematic measurement errors always exceeded the error level of stochastic noise since the Goe-MF II system had been optimized for a sufficient signal to noise ratio but not for accuracy. In time difference imaging and functional EIT (f-EIT) systematic errors are reduced to a minimum by dividing the raw data by reference data. This is not the case in absolute EIT (a-EIT) where the resistivity of the examined object is determined on an absolute scale. We conclude that a reduction of systematic errors has to be one major goal in future system design.     

Development of a neonate lung reconstruction algorithm using a wavelet AMG and estimated boundary form

Objective, non-invasive measures of lung maturity and development, oxygen requirements and lung function, suitable for use in small, unsedated infants, are urgently required to define the nature and severity of persisting lung disease, and to identify risk factors for developing chronic lung problems. Disorders of lung growth, maturation and control of breathing are among the most important problems faced by the neonatologists. At present, no system for continuous monitoring of neonate lung function to reduce the risk of chronic lung disease in infancy in intensive care units exists. We are in the process of developing a new integrated electrical impedance tomography (EIT) system based on wearable technology to integrate measures of the boundary diameter from the boundary form for neonates into the reconstruction algorithm. In principle, this approach could provide a reduction of image artefacts in the reconstructed image associated with incorrect boundary form assumptions. In this paper, we investigate the required accuracy of the boundary form that would be suitable to minimize artefacts in the reconstruction for neonate lung function. The number of data points needed to create the required boundary form is automatically determined using genetic algorithms. The approach presented in this paper is to assist quality of the reconstruction using different approximations to the ideal boundary form. We also investigate the use of a wavelet algebraic multi-grid (WAMG) preconditioner to reduce the reconstruction computation requirements. Results are presented that demonstrate a full 3D model is required to minimize artefact in the reconstructed image and the implementation of a WAMG for EIT.     

Comparison of frequency difference reconstruction algorithms for the detection of acute stroke using EIT in a realistic head-shaped tank

Imaging of acute stroke might be possible using multi-frequency electrical impedance tomography (MFEIT) but requires absolute or frequency difference imaging. Simple linear frequency difference reconstruction has been shown to be ineffective in imaging with a frequency-dependant background conductivity; this has been overcome with a weighted frequency difference approach with correction for the background but this has only been validated for a cylindrical and hemispherical tank. The feasibility of MFEIT for imaging of acute stroke in a realistic head geometry was examined by imaging a potato perturbation against a saline background and a carrot-saline frequency-dependant background conductivity, in a head-shaped tank with the UCLH Mk2.5 MFEIT system. Reconstruction was performed with time difference (TD), frequency difference (FD), FD adjacent (FDA), weighted FD (WFD) and weighted FDA (WFDA) linear algorithms. The perturbation in reconstructed images corresponded to the true position to <9.5% of image diameter with an image SNR of >5.4 for all algorithms in saline but only for TD, WFDA and WFD in the carrot-saline background. No reliable imaging was possible with FD and FDA. This indicates that the WFD approach is also effective for a realistic head geometry and supports its use for human imaging in the future.     

A motion-compensated cone-beam CT using electrical impedance tomography imaging

Cone-beam CT (CBCT) is an imaging technique used in conjunction with radiation therapy. For example CBCT is used to verify the position of lung cancer tumours just prior to radiation treatment. The accuracy of the radiation treatment of thoracic and upper abdominal structures is heavily affected by respiratory movement. Such movement typically blurs the CBCT reconstruction and ideally should be removed. Hence motion-compensated CBCT has recently been researched for correcting image artefacts due to breathing motion. This paper presents a new dual-modality approach where CBCT is aided by using electrical impedance tomography (EIT) for motion compensation. EIT can generate images of contrasts in electrical properties. The main advantage of using EIT is its high temporal resolution. In this paper motion information is extracted from EIT images and incorporated directly in the CBCT reconstruction. In this study synthetic moving data are generated using simulated and experimental phantoms. The paper demonstrates that image blur, created as a result of motion, can be reduced through motion compensation with EIT.     

Validation of weighted frequency-difference EIT using a three-dimensional hemisphere model and phantom

Frequency-difference (FD) electrical impedance tomography (EIT) using a weighted voltage difference has recently been proposed for imaging haemorrhagic stroke, abdominal bleeding and tumors. Although its feasibility was demonstrated through two-dimensional numerical simulations and phantom experiments, we should validate the method in three-dimensional imaging objects. At the same time, we need to investigate its robustness against geometrical modeling errors in boundary shapes and electrode positions. We performed a validation study of the weighted FD method through three-dimensional numerical simulations and phantom experiments. Adopting hemispherical models and phantoms whose admittivity distributions change with frequency, we investigated the performance of the method to detect an anomaly. We found that the simple FD method fails to detect the anomaly, whereas reconstructed images using the weighted FD method clearly visualize the anomaly. The weighted FD method is robust against modeling errors of boundary-shape deformations and displaced electrode positions. We also found that the method is capable of detecting an anomaly surrounded by a shell-shaped obstacle simulating the skull. We propose the weighted FD method for future studies of animal and human experiments.     

Evaluation of EIT system performance

An electrical impedance tomography (EIT) system images internal conductivity from surface electrical stimulation and measurement. Such systems necessarily comprise multiple design choices from cables and hardware design to calibration and image reconstruction. In order to compare EIT systems and study the consequences of changes in system performance, this paper describes a systematic approach to evaluate the performance of the EIT systems. The system to be tested is connected to a saline phantom in which calibrated contrasting test objects are systematically positioned using a position controller. A set of evaluation parameters are proposed which characterize (i) data and image noise, (ii) data accuracy, (iii) detectability of single contrasts and distinguishability of multiple contrasts, and (iv) accuracy of reconstructed image (amplitude, resolution, position and ringing). Using this approach, we evaluate three different EIT systems and illustrate the use of these tools to evaluate and compare performance. In order to facilitate the use of this approach, all details of the phantom, test objects and position controller design are made publicly available including the source code of the evaluation and reporting software.