Image monitoring for an intraperitoneal bleeding model of pigs using electrical impedance tomography

Current medical imaging techniques are not effective for timely detection of internal hemorrhage when the bleeding is slow and in small quantities. In this study, electrical impedance tomography (EIT) was applied to monitor the intraperitoneal bleeding of an animal model. Five healthy pigs three months old were used. The process of intraperitoneal bleeding was simulated with the injection of anticoagulated blood which was controlled by an electronic syringe pump. The injected rate was no more than 100 ml h(-1) and the total injection volumes ranged from 300 ml to 500 ml. Sixteen electrodes were attached to the abdomen and used for electrical current excitation and surface voltage measurement. Dynamic changes in impedance distribution within the abdomen were calculated by the back-projection algorithm and a series of EIT images were displayed in a unified range. The monitoring was performed with EIT at a rate of one frame per second and continued for at least 4 h. Intraperitoneal blood volume changes could be identified by inspection of consecutive EIT images during the progression of blood injection. 30 ml of blood in the peritoneum could be detected. EIT was shown to be a promising technique for continuous monitoring of intraperitoneal bleeding over periods of time.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

The spatial resolution improvement of EIT images by GVSPM-FOCUSS algorithm

The focal underdetermined system solver (FOCUSS) algorithm is a recursive algorithm to find the localized energy solution. It is an initialization-dependent algorithm. The generalized vector sample pattern matching (GVSPM) method has been applied to solve the inverse problem of electrical impedance tomography (EIT) and obtain smooth reconstructed images. By combining the GVSPM solution as the initial estimation of the FOCUSS algorithm, an idea termed the GVSPM-FOCUSS method is presented in this paper to improve the spatial resolution and precision of localization for EIT images. The comparisons are carried out between the EIT images reconstructed with the GVSPM-FOCUSS method and the GVSPM method alone. The effectiveness is verified by simulated and tank data for a model of a two-dimensional homogeneous circular disk.     

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.     

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.     

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.     

Static resistivity image of a cubic saline phantom in magnetic resonance electrical impedance tomography (MREIT)

In magnetic resonance electrical impedance tomography (MREIT) we inject currents through electrodes placed on the surface of a subject and try to reconstruct cross-sectional resistivity (or conductivity) images using internal magnetic flux density as well as boundary voltage measurements. In this paper we present a static resistivity image of a cubic saline phantom (50 x 50 x 50 mm3) containing a cylindrical sausage object with an average resistivity value of 123.7 ohms cm. Our current MREIT system is based on an experimental 0.3 T MRI scanner and a current injection apparatus. We captured MR phase images of the phantom while injecting currents of 28 mA through two pairs of surface electrodes. We computed current density images from magnetic flux density images that are proportional to the MR phase images. From the current density images and boundary voltage data we reconstructed a cross-sectional resistivity image within a central region of 38.5 x 38.5 mm2 at the middle of the phantom using the J-substitution algorithm. The spatial resolution of the reconstructed image was 64 x 64 and the reconstructed average resistivity of the sausage was 117.7 ohms cm. Even though the error in the reconstructed average resistivity value was small, the relative L2-error of the reconstructed image was 25.5% due to the noise in measured MR phase images. We expect improvements in the accuracy by utilizing an MRI scanner with higher SNR and increasing the size of voxels scarifying the spatial resolution.     

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.     

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.     

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.     

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.     

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.     

Reducing boundary effects in static EIT imaging

Electrical impedance tomography (EIT) is a non-invasive technique used to image the electrical conductivity and permittivity within a body from measurements taken on the body's surface. High-quality static images are required for many medical imaging applications. Forming such images usually requires an accurate way to calculate the expected voltages on the surface resulting from the application of known currents to that surface. This is described as the forward problem. This paper introduces a new method to improve static images by using an improved forward solution which estimates a different conductivity value for each applied current pattern. This method, creating an automatically adjusting forward solution, can improve the sensitivity of static images under many EIT imaging applications. It does so by reducing the boundary effects caused by electrodes and any layered structures near them such as skin. The drawback of this method is that circularly symmetric structures of interest may be suppressed or eliminated from the images. The performance of this method is illustrated in a 2D circular phantom with simulation data from both a FEM model and experimental data.     

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.