Reconstruction of conductivity changes and electrode movements based on EIT temporal sequences

Electrical impedance tomography (EIT) reconstructs a conductivity change image within a body from electrical measurements on the body surface; while it has relatively low spatial resolution, it has a high temporal resolution. One key difficulty with EIT measurements is due to the movement and position uncertainty of the electrodes, especially due to breathing and posture change. In this paper, we develop an approach to reconstruct both the conductivity change image and the electrode movements from the temporal sequence of EIT measurements. Since both the conductivity change and electrode movement are slow with respect to the data frame rate, there are significant temporal correlations which we formulate as priors for the regularized image reconstruction model. Image reconstruction is posed in terms of a regularization matrix and a Jacobian matrix which are augmented for the conductivity change and electrode movement, and then further augmented to concatenate the d previous and future frames. Results are shown for simulation, phantom and human data, and show that the proposed algorithm yields improved resolution and noise performance in comparison to a conventional one-step reconstruction method.     

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.     

Electrical impedance tomography of human brain function using reconstruction algorithms based on the finite element method

Electrical impedance tomography (EIT) is a recently developed technique which enables the internal conductivity of an object to be imaged using rings of external electrodes. In a recent study, EIT during cortical evoked responses showed encouraging changes in the raw impedance measurements, but reconstructed images were noisy. A simplified reconstruction algorithm was used which modelled the head as a homogeneous sphere. In the current study, the development and validation of an improved reconstruction algorithm are described in which realistic geometry and conductivity distributions have been incorporated using the finite element method. Data from computer simulations and spherical or head-shaped saline-filled tank phantoms, in which the skull was represented by a concentric shell of plaster of Paris or a real human skull, have been reconstructed into images. There were significant improvements in image quality as a result of the incorporation of accurate geometry and extracerebral layers in the reconstruction algorithm. Image quality, assessed by blinded subjective expert observers, also improved significantly when data from the previous evoked response study were reanalysed with the new algorithm. In preliminary images collected during epileptic seizures, the new algorithm generated EIT conductivity changes which were consistent with the electrographic ictal activity. Incorporation of realistic geometry and conductivity into the reconstruction algorithm significantly improves the quality of EIT images and lends encouragement to the belief that EIT may provide a low-cost, portable functional neuroimaging system in the foreseeable future.     

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.     

Adjacent stimulation and measurement patterns considered harmful

We characterize the ability of electrical impedance tomography (EIT) to distinguish changes in internal conductivity distributions, and analyze it as a function of stimulation and measurement patterns. A distinguishability measure, z, is proposed which is related to the signal-to-noise ratio of a medium and to the probability of detection of conductivity changes in a region of interest. z is a function of the number of electrodes, the EIT stimulation and measurement protocol, the stimulation amplitude, the measurement noise, and the size and location of the contrasts. Using this measure we analyze various choices of stimulation and measurement patterns under the constraint of medical electrical safety limits (maximum current into the body). Analysis is performed for a planar placement of 16 electrodes for simulated 3D tank and chest shapes, and measurements in a saline tank. Results show that the traditional (and still most common) adjacent stimulation and measurement patterns have by far the poorest performance (by 6.9 ×). Good results are obtained for trigonometric patterns and for pair drive and measurement patterns separated by over 90°. Since the possible improvement over adjacent patterns is so large, we present this result as a call to action: adjacent patterns are harmful, and should be abandoned. We recommend using pair drive and measurement patterns separated by one electrode less than 180°. We describe an approach to modify an adjacent pattern EIT system by adjusting electrode placement.     

Accounting for hardware imperfections in EIT image reconstruction algorithms

Electrical impedance tomography (EIT) is a non-invasive technique for imaging the conductivity distribution of a body section. Different types of EIT images can be reconstructed: absolute, time difference and frequency difference. Reconstruction algorithms are sensitive to many errors which translate into image artefacts. These errors generally result from incorrect modelling or inaccurate measurements. Every reconstruction algorithm incorporates a model of the physical set-up which must be as accurate as possible since any discrepancy with the actual set-up will cause image artefacts. Several methods have been proposed in the literature to improve the model realism, such as creating anatomical-shaped meshes, adding a complete electrode model and tracking changes in electrode contact impedances and positions. Absolute and frequency difference reconstruction algorithms are particularly sensitive to measurement errors and generally assume that measurements are made with an ideal EIT system. Real EIT systems have hardware imperfections that cause measurement errors. These errors translate into image artefacts since the reconstruction algorithm cannot properly discriminate genuine measurement variations produced by the medium under study from those caused by hardware imperfections. We therefore propose a method for eliminating these artefacts by integrating a model of the system hardware imperfections into the reconstruction algorithms. The effectiveness of the method has been evaluated by reconstructing absolute, time difference and frequency difference images with and without the hardware model from data acquired on a resistor mesh phantom. Results have shown that artefacts are smaller for images reconstructed with the model, especially for frequency difference imaging.     

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.     

Three-dimensional electrical impedance tomography of human brain activity

Regional cerebral blood flow and blood volume changes that occur during human brain activity will change the local impedance of that cortical area, as blood has a lower impedance than that of brain. Theoretically, such impedance changes could be measured from scalp electrodes and reconstructed into images of the internal impedance of the head. Electrical Impedance Tomography (EIT) is a newly developed technique by which impedance measurements from the surface of an object are reconstructed into impedance images. It is fast, portable, inexpensive, and noninvasive, but has a relatively low spatial resolution. EIT images were recorded with scalp electrodes and an EIT system, specially optimized for recording brain function, in 39 adult human subjects during visual, somatosensory, or motor activity. Reproducible impedance changes of about 0.5% occurred in 51/52 recordings, which lasted from 6 s after the stimulus onset to 41 s after stimulus cessation. When these changes were reconstructed into impedance images, using a novel 3-D reconstruction algorithm, 19 data sets demonstrated significant impedance changes in the appropriate cortical region. This demonstrates, for the first time, that significant impedance changes, which could form the basis for a novel neuroimaging technology, may be recorded in human subjects with scalp electrodes. The final images contained spatial noise and strategies to reduce this in future work are presented.     

A high-precision voltage source for EIT

Electrical impedance tomography (EIT) utilizes electrodes placed on the surface of a body to determine the complex conductivity distribution within the body. EIT can be performed by applying currents through the electrodes and measuring the electrode voltages or by applying electrode voltages and measuring the currents. Techniques have also been developed for applying the desired currents using voltage sources. This paper describes a voltage source for use in applied-voltage EIT that includes the capability of measuring both the applied voltage and applied current. A calibration circuit and calibration algorithm are described which enables all voltage sources in an EIT system to be calibrated to a common standard. The calibration minimizes the impact of stray shunt impedance, passive component variability and active component non-ideality. Simulation data obtained using PSpice are used to demonstrate the effectiveness of the circuits and calibration algorithm.     

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.     

Experimental justification for using 3D conductivity reconstructions in electrical impedance tomography

Conductivity imaging of the breast using electrical impedance tomography (EIT) is a three-dimensional (3D) problem since the induced currents are free to travel through the entire tissue volume. It is therefore necessary to determine the effect this 3D current flow has on the image reconstruction problem and to ascertain how much benefit is gained by using a more appropriate 3D model to estimate the conductivity distribution. In addition, it is important to consider how much is gained if measurements are collected from multiple circular arrays of electrodes positioned around the breast as opposed to just a single plane of electrodes. We used a 64 electrode EIT system to collect data from a series of high contrast saline phantoms to determine the benefits gained by using a 3D model and the incorporation of out-of-plane measurements. We found that it is preferable to use a 3D mesh even when looking only at a single plane through the object of interest and that this 3D mesh should extend in the axial direction at least one radius away from the plane of interest. Further, out-of-plane measurements enhance axial information and improve the quantification of reconstructed inclusions by a factor of 2.2 in the particular case presented here. These findings should ultimately be incorporated to clinical imaging with EIT when circular electrode arrays are employed.     

Magnetic resonance electrical impedance tomography (MREIT) for high-resolution conductivity imaging

Cross-sectional imaging of an electrical conductivity distribution inside the human body has been an active research goal in impedance imaging. By injecting current into an electrically conducting object through surface electrodes, we induce current density and voltage distributions. Based on the fact that these are determined by the conductivity distribution as well as the geometry of the object and the adopted electrode configuration, electrical impedance tomography (EIT) reconstructs cross-sectional conductivity images using measured current-voltage data on the surface. Unfortunately, there exist inherent technical difficulties in EIT. First, the relationship between the boundary current-voltage data and the internal conductivity distribution bears a nonlinearity and low sensitivity, and hence the inverse problem of recovering the conductivity distribution is ill posed. Second, it is difficult to obtain accurate information on the boundary geometry and electrode positions in practice, and the inverse problem is sensitive to these modeling errors as well as measurement artifacts and noise. These result in EIT images with a poor spatial resolution. In order to produce high-resolution conductivity images, magnetic resonance electrical impedance tomography (MREIT) has been lately developed. Noting that injection current produces a magnetic as well as electric field inside the imaging object, we can measure the induced internal magnetic flux density data using an MRI scanner. Utilization of the internal magnetic flux density is the key idea of MREIT to overcome the technical difficulties in EIT. Following original ideas on MREIT in early 1990s, there has been a rapid progress in its theory, algorithm and experimental techniques. The technique has now advanced to the stage of human experiments. Though it is still a few steps away from routine clinical use, its potential is high as a new impedance imaging modality providing conductivity images with a spatial resolution of a few millimeters or less. This paper reviews MREIT from the basics to the most recent research outcomes. Focusing on measurement techniques and experimental methods rather than mathematical issues, we summarize what has been done and what needs to be done. Suggestions for future research directions, possible applications in biomedicine, biology, chemistry and material science are discussed.     

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.     

High fidelity imaging and high performance computing in nonlinear EIT

We show that nonlinear EIT provides images with well defined characteristics when smoothness of the image is used as a constraint in the reconstruction process. We use the gradient of the logarithm of resistivity as an effective measure of image smoothness, which has the advantage that resistivity and conductivity are treated with equal weight. We suggest that a measure of the fidelity of the image to the object requires the explicit definition and application of such a constraint. The algorithm is applied to the simulation of intra-ventricular haemorrhaging (IVH) in a simple head model. The results indicate that a 5% increase in the blood content of the ventricles would be easily detectable with the noise performance of contemporary instrumentation. The possible implementation of the algorithm in real time via high performance computing is discussed.     

A novel approach for EIT regularization via spatial and spectral principal component analysis

Electrical impedance tomography, EIT, is an imaging modality in which the internal conductivity distribution of an object is reconstructed based on voltage measurements on the boundary. This reconstruction problem is a nonlinear and ill-posed inverse problem, which requires regularization to ensure a stable solution. Most popular regularization approaches enforce smoothness in the inverse solution. In this paper, we propose a novel approach to build a subspace for regularization using a spectral and spatial multi-frequency analysis approach. The approach is based on the construction of a subspace for the expected conductivity distributions using principal component analysis. It is shown via simulations that the reconstructed images obtained with the proposed method are better than with the standard regularization approach. Using this approach, the percentage of misclassified finite elements was reduced up to twelve fold from the initial percentages after five iterations. The advantage of this technique is that prior information is extracted from the characteristic response of an object at different frequencies and spatially across the finite elements.     

The complete electrode model for EIT in a mammography geometry

We have developed an EIT system for simultaneous use in a mammography examination, allowing for highly accurate co-registration between the two modalities. In this pre-clinical study, we investigate the importance of properly modeling the interface between the electrodes and the medium being imaged. We have implemented the complete electrode model for a parallel-plane mammography geometry, in which currents are injected into the medium through two planar sets of electrodes above and below the medium. We make use of the ACT4 device to conduct saline-tank experiments showing the improvement of the complete model over an ave-gap model, which ignores both the conductivity of the electrodes and the surface impedance. The experimental results show an improvement in both forward modeling accuracy and in the quality of the resulting reconstructed images using the complete electrode model, as compared to the ave-gap model.     

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.     

Flexible electrode belt for EIT using nanofiber web dry electrodes

Efficient connection of multiple electrodes to the body for impedance measurement and voltage monitoring applications is of critical importance to measurement quality and practicality. Electrical impedance tomography (EIT) experiments have generally required a cumbersome procedure to attach the multiple electrodes needed in EIT. Once placed, these electrodes must then maintain good contact with the skin during measurements that may last several hours. There is usually also the need to manage the wires that run between the electrodes and the EIT system. These problems become more severe as the number of electrodes increases, and may limit the practicality and portability of this imaging method. There have been several trials describing human-electrode interfaces using configurations such as electrode belts, helmets or rings. In this paper, we describe an electrode belt we developed for long-term EIT monitoring of human lung ventilation. The belt included 16 embossed electrodes that were designed to make good contact with the skin. The electrodes were fabricated using an Ag-plated PVDF nanofiber web and metallic threads. A large contact area and padding were used behind each electrode to improve subject comfort and reduce contact impedances. The electrodes were incorporated, equally spaced, into an elasticated fabric belt. We tested the electrode belt in conjunction with the KHU Mark1 multi-frequency EIT system, and demonstrate time-difference images of phantoms and human subjects during normal breathing and running. We found that the Ag-plated PVDF nanofiber web electrodes were suitable for long-term measurement because of their flexibility and durability. Moreover, the contact impedance and stability of the Ag-plated PVDF nanofiber web electrodes were found to be comparable to similarly tested Ag/AgCl electrodes.     

Breast EIT using a new projected image reconstruction method with multi-frequency measurements

We propose a new method to produce admittivity images of the breast for the diagnosis of breast cancer using electrical impedance tomography(EIT). Considering the anatomical structure of the breast, we designed an electrode configuration where current-injection and voltage-sensing electrodes are separated in such a way that internal current pathways are approximately along the tangential direction of an array of voltage-sensing electrodes. Unlike conventional EIT imaging methods where the number of injected currents is maximized to increase the total amount of measured data, current is injected only twice between two pairs of current-injection electrodes attached along the circumferential side of the breast. For each current injection, the induced voltages are measured from the front surface of the breast using as many voltage-sensing electrodes as possible. Although this electrode configurational lows us to measure induced voltages only on the front surface of the breast,they are more sensitive to an anomaly inside the breast since such an injected current tends to produce a more uniform internal current density distribution. Furthermore, the sensitivity of a measured boundary voltage between two equipotential lines on the front surface of the breast is improved since those equipotential lines are perpendicular to the primary direction of internal current streamlines. One should note that this novel data collection method is different from those of other frontal plane techniques such as the x-ray projection and T-scan imaging methods because we do not get any data on the plane that is perpendicular to the current flow. To reconstruct admittivity images using two measured voltage data sets, a new projected image reconstruction algorithm is developed. Numerical simulations demonstrate the frequency-difference EIT imaging of the breast. The results show that the new method is promising to accurately detect and localize small anomalies inside the breast.     

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.