Errors in reconstruction of resistivity images using a linear reconstruction technique

Automated 3D thorax model generation using handheld video-footage

PURPOSE

For the visualization of pulmonary ventilation with Electrical Impedance Tomography (EIT) most devices use standard reconstruction models, featuring common thorax dimensions and predetermined electrode locations. Any discrepancies between the available model and the patient in terms of body shape and electrode position lead to incorrectly displayed impedance distributions. This work addresses that problem by presenting and evaluating a method for 3D model generation of the thorax and any affixed electrodes based on handheld video-footage.

METHODS

Therefore, a process was developed, providing users with the ability to capture a patient's chest and the attached electrodes via smartphone. Once data is collected, extracted images are used to generate a 3D model with a structure from motion approach and locate electrodes with ArUco markers. For the evaluation of the developed method, multiple tests were performed in laboratory environments, which were compared with manually created reference models and differences quantified based on mean distance, standard deviation, and maximum distance.

RESULTS

The implemented workflow allows for automated model reconstruction based on videos or selected images captured with a handheld device. It generates sparse point clouds from which a surface mesh is reconstructed and returns relative coordinates of any identified ArUco marker. The average value for the mean distance error of two model generations was 5.4 mm while the mean standard deviation was 6.0 mm. The average runtime of twelve reconstructions was 5:17 min, with a minimal runtime of 3:22 min and a maximal runtime of 7:29 min.

CONCLUSION

The presented methods and results show that model reconstruction of a patient's thorax and applied electrodes at an emergency site is feasible with already available devices. This is a first step toward the automated generation of patient-specific reconstruction models for Electrical Impedance Tomography based on images recorded with handheld devices.

Feasibility of Temperature Control by Electrical Impedance Tomography in Hyperthermia

We present a simulation study investigating the feasibility of electrical impedance tomography (EIT) as a low cost, noninvasive technique for hyperthermia (HT) treatment monitoring and adaptation. Temperature rise in tissues leads to perfusion and tissue conductivity changes that can be reconstructed in 3D by EIT to noninvasively map temperature and perfusion. In this study, we developed reconstruction methods and investigated the achievable accuracy of EIT by simulating HT treatmentlike scenarios, using detailed anatomical models with heterogeneous conductivity distributions. The impact of the size and location of the heated region, the voltage measurement signal-to-noise ratio, and the reference model personalization and accuracy were studied. Results showed that by introducing an iterative reconstruction approach, combined with adaptive prior regions and tissue-dependent penalties, planning-based reference models, measurement-based reweighting, and physics-based constraints, it is possible to map conductivity-changes throughout the heated domain, with an accuracy of around 5% and cm-scale spatial resolution. An initial exploration of the use of multifrequency EIT to separate temperature and perfusion effects yielded promising results, indicating that temperature reconstruction accuracy can be in the order of 1 ∘C. Our results suggest that EIT can provide valuable real-time HT monitoring capabilities. Experimental confirmation in real-world conditions is the next step.

Measurement-Based Domain Parameter Optimization in Electrical Impedance Tomography Imaging

This paper discusses the optimization of domain parameters in electrical impedance tomography-based imaging. Precise image reconstruction requires accurate, well-correlated physical and numerical finite element method (FEM) models; thus, we employed the Nelder–Mead algorithm and a complete electrode model to evaluate the individual parameters, including the initial conductivity, electrode misplacement, and shape deformation. The optimization process was designed to calculate the parameters of the numerical model before the image reconstruction. The models were verified via simulation and experimental measurement with single source current patterns. The impact of the optimization on the above parameters was reflected in the applied image reconstruction process, where the conductivity error dropped by 6.16% and 11.58% in adjacent and opposite driving, respectively. In the shape deformation, the inhomogeneity area ratio increased by 11.0% and 48.9%; the imprecise placement of the 6th electrode was successfully optimized with adjacent driving; the conductivity error dropped by 12.69%; and the inhomogeneity localization exhibited a rise of 66.7%. The opposite driving option produces undesired duality resulting from the measurement pattern. The designed optimization process proved to be suitable for correlating the numerical and the physical models, and it also enabled us to eliminate imaging uncertainties and artifacts.

An iterative damped least-squares algorithm for simultaneously monitoring the development of hemorrhagic and secondary ischemic lesions in brain injuries

Electrical impedance tomography (EIT) is a non-invasive and real-time imaging method that has the potential to be used for monitoring intracerebral hemorrhage (ICH). Recent studies have proposed that ischemia secondary to ICH occurs simultaneously in the brain. Real-time monitoring of the development of hemorrhage and risk of secondary ischemia is crucial for clinical intervention. However, few studies have explored the performance of EIT monitoring in cases where hemorrhage and secondary ischemia exist. When these lesions get close to each other, or their conductivity and volume changes differ greatly, it becomes challenging for dynamic EIT algorithms to simultaneously reconstruct subtle injuries. To address this, an iterative damped least-squares (IDLS) algorithm is proposed in this study. The quality of the IDLS algorithm was assessed using blur radius and temporal response during computer simulation and a phantom 3D head-shaped model where bidirectional disturbance targets were simulated. The results showed that the IDLS algorithm enhanced contrast and concurrently reconstructed bidirectional disturbance targets in images. Moreover, it showed superior performance in decreasing the blur radius and was time cost-effective. With further improvement, the IDLS algorithm has the potential to be used for monitoring the development of hemorrhage and risk of ischemia secondary to ICH. Graphical abstract (a) and (b) are simulation images of bidirectional disturbance targets with different change ratios of volume (Vr) and conductivity (σ_r) based on the damped least-squares (DLS) algorithm and iterative damped least-squared (IDLS) algorithm, respectively. (c) shows the performance metrics of blur radius and temporal response with different volume ratio (corresponding to Vr). (d) shows the performance metrics of blur radius and temporal response with different conductivity change percentage (corresponding to σ_r).

A Fidelity-Embedded Regularization Method for Robust Electrical Impedance Tomography

Electrical impedance tomography (EIT) provides functional images of an electrical conductivity distribution inside the human body. Since the 1980s, many potential clinical applications have arisen using inexpensive portable EIT devices. EIT acquires multiple trans-impedance measurements across the body from an array of surface electrodes around a chosen imaging slice. The conductivity image reconstruction from the measured data is a fundamentally ill-posed inverse problem notoriously vulnerable to measurement noise and artifacts. Most available methods invert the ill-conditioned sensitivity or the Jacobian matrix using a regularized least-squares data-fitting technique. Their performances rely on the regularization parameter, which controls the trade-off between fidelity and robustness. For clinical applications of EIT, it would be desirable to develop a method achieving consistent performance over various uncertain data, regardless of the choice of the regularization parameter. Based on the analysis of the structure of the Jacobian matrix, we propose a fidelity-embedded regularization (FER) method and a motion artifact reduction filter. Incorporating the Jacobian matrix in the regularization process, the new FER method with the motion artifact reduction filter offers stable reconstructions of high-fidelity images from noisy data by taking a very large regularization parameter value. The proposed method showed practical merits in experimental studies of chest EIT imaging.

Torso shape detection to improve lung monitoring

OBJECTIVE

Newborns with lung immaturity often require continuous monitoring and treatment of their lung ventilation in intensive care units, especially if born preterm. Recent studies indicate that electrical impedance tomography (EIT) is feasible in newborn infants and children, and can quantitatively identify changes in regional lung aeration and ventilation following alterations to respiratory conditions. Information on the patient-specific shape of the torso and its role in minimizing the artefacts in the reconstructed images can improve the accuracy of the clinical parameters obtained from EIT. Currently, only idealized models or those segmented from CT scans are usually adopted.

APPROACH

This study presents and compares two methodologies that can detect the patient-specific torso shape by means of wearable devices based on (1) previously reported bend sensor technology, and (2) a novel approach based on the use of accelerometers.

MAIN RESULTS

The reconstruction of different phantoms, taking into account anatomical asymmetries and different sizes, are produced for comparison.

SIGNIFICANCE

As a result, the accelerometers are more versatile than bend sensors, which cannot be used on bigger cross-sections. The computational study estimates the optimal number of accelerometers required in order to generate an image reconstruction comparable to the use of a CT scan as the forward model. Furthermore, since the patient position is crucial to monitoring lung ventilation, the orientation of the phantoms is automatically detected by the accelerometer-based method.

Combing signal processing methods with algorithm priori information to produce synergetic improvements on continuous imaging of brain electrical impedance tomography

Dynamic electrical impedance tomography (EIT) promises to be a valuable technique for monitoring the development of brain injury. But in practical long-term monitoring, noise and interferences may cause insufficient image quality. To help unveil intracranial conductivity changes, signal processing methods were introduced to improve EIT data quality and algorithms were optimized to be more robust. However, gains for EIT image reconstruction can be significantly increased if we combine the two techniques properly. The basic idea is to apply the priori information in algorithm to help de-noise EIT data and use signal processing to optimize algorithm. First, we process EIT data with principal component analysis (PCA) and reconstruct an initial CT-EIT image. Then, as the priori that changes in scalp and skull domains are unwanted, we eliminate their corresponding boundary voltages from data sets. After the two-step denoising process, we finally re-select a local optimal regularization parameter and accomplish the reconstruction. To evaluate performances of the signal processing-priori information based reconstruction (SPR) method, we conducted simulation and in-vivo experiments. The results showed SPR could improve brain EIT image quality and recover the intracranial perturbations from certain bad measurements, while for some measurement data the generic reconstruction method failed.

Compensation for large thorax excursions in EIT imaging

Besides the application of EIT in the intensive care unit it has recently also been used in spontaneously breathing patients suffering from asthma bronchiole, cystic fibrosis (CF) or chronic obstructive pulmonary disease (COPD). In these cases large thorax excursions during deep inspiration, e.g. during lung function testing, lead to artifacts in the reconstructed images. In this paper we introduce a new approach to compensate for image artifacts resulting from excursion induced changes in boundary voltages. It is shown in a simulation study that boundary voltage change due to thorax excursion on a homogeneous model can be used to modify the measured voltages and thus reduce the impact of thorax excursion on the reconstructed images. The applicability of the method on human subjects is demonstrated utilizing a motion-tracking-system. The proposed technique leads to fewer artifacts in the reconstructed images and improves image quality without substantial increase in computational effort, making the approach suitable for real-time imaging of lung ventilation. This might help to establish EIT as a supplemental tool for lung function tests in spontaneously breathing patients to support clinicians in diagnosis and monitoring of disease progression.

A fast time-difference inverse solver for 3D EIT with application to lung imaging

A class of sparse optimization techniques that require solely matrix-vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT.

Impact of model shape mismatch on reconstruction quality in electrical impedance tomography

Electrical impedance tomography (EIT) is a low-cost, noninvasive and radiation free medical imaging modality for monitoring ventilation distribution in the lung. Although such information could be invaluable in preventing ventilator-induced lung injury in mechanically ventilated patients, clinical application of EIT is hindered by difficulties in interpreting the resulting images. One source of this difficulty is the frequent use of simple shapes which do not correspond to the anatomy to reconstruct EIT images. The mismatch between the true body shape and the one used for reconstruction is known to introduce errors, which to date have not been properly characterized. In the present study we, therefore, seek to 1) characterize and quantify the errors resulting from a reconstruction shape mismatch for a number of popular EIT reconstruction algorithms and 2) develop recommendations on the tolerated amount of mismatch for each algorithm. Using real and simulated data, we analyze the performance of four EIT reconstruction algorithms under different degrees of shape mismatch. Results suggest that while slight shape mismatch is well tolerated by all algorithms, using a circular shape severely degrades their performance.

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.

Effect of domain shape modeling and measurement errors on the 2-D D-bar method for EIT

The D-bar algorithm based on Nachman's 2-D global uniqueness proof for the inverse conductivity problem (Nachman, 1996) is implemented on a chest-shaped domain. The scattering transform is computed on this chest-shaped domain using trigonometric and adjacent current patterns and the complete electrode model for the forward problem is computed with the finite element method in order to obtain simulated voltage measurements. The robustness and effectiveness of the method is demonstrated on a simulated chest with errors in input currents, output voltages, electrode placement, and domain modeling.

Comparison of methods for optimal choice of the regularization parameter for linear electrical impedance tomography of brain function

Electrical impedance tomography has the potential to provide a portable non-invasive method for imaging brain function. Clinical data collection has largely been undertaken with time difference data and linear image reconstruction methods. The purpose of this work was to determine the best method for selecting the regularization parameter of the inverse procedure, using the specific application of evoked brain activity in neonatal babies as an exemplar. The solution error norm and image SNR for the L-curve (LC), discrepancy principle (DP), generalized cross validation (GCV) and unbiased predictive risk estimator (UPRE) selection methods were evaluated in simulated data using an anatomically accurate finite element method (FEM) of the neonatal head and impedance changes due to blood flow in the visual cortex recorded in vivo. For simulated data, LC, GCV and UPRE were equally best. In human data in four neonatal infants, no significant differences were found among selection methods. We recommend that GCV or LC be employed for reconstruction of human neonatal images, as UPRE requires an empirical estimate of the noise variance.

Electrical impedance tomography guided ventilation therapy

PURPOSE OF REVIEW

Computed tomography (CT) in patients with acute respiratory distress syndrome has shown that intrapulmonary gas is not homogeneously distributed. Although regional ventilation can be studied by isotope and magnetic resonance techniques while aeration of the lungs can be imaged using CT, these techniques are not available at the bedside. Recently, electrical impedance tomography has been introduced as a true bedside technique which provides information on regional ventilation distribution.

RECENT FINDINGS

Electrical impedance tomography can reliably determine regional ventilation in healthy lungs and various models of induced lung injury when compared with CT, electron beam CT, and single photon emission CT. In healthy volunteers and patients with acute lung injury, relative impedance changes on the electrical impedance tomography image demonstrate an excellent correlation with regional changes in lung air content detected by CT. In a limited number of patients with respiratory dysfunction, gas exchange was found to improve when electrical impedance tomography was used to adjust ventilator settings, improving regional ventilation and avoiding tidal alveolar collapse.

SUMMARY

In view of recently published data, it can be concluded that, in critically ill patients, electrical impedance tomography determines reliable regional ventilation. Therefore, this technique has the potential to become a valuable bedside tool.

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.

Reconstructions of conductive and insulating targets using the D-bar method on an elliptical domain

The D-bar algorithm based on A Nachman's 2D global uniqueness proof for the inverse conductivity problem (Nachman 1996 Ann. Math. 143 71-96) is implemented on an elliptical domain. The scattering transform is computed on an ellipse and the complete electrode model (CEM) for the forward problem is computed with the finite element method (FEM) in order to obtain static conductivity reconstructions of conductive and insulating targets in a saline-filled tank. It is demonstrated that the spatial artifacts in the image are significantly reduced when the domain is properly modeled in the reconstruction, as opposed to being modeled as a disk.

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.

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.

Objective selection of hyperparameter for EIT

An algorithm for objectively calculating the hyperparameter for linearized one-step electrical impedance tomography (EIT) image reconstruction algorithms is proposed and compared to existing strategies. EIT is an ill-conditioned problem in which regularization is used to calculate a stable and accurate solution by incorporating some form of prior knowledge into the solution. A hyperparameter is used to control the trade-off between conformance to data and conformance to the prior. A remaining challenge is to develop and validate methods of objectively selecting the hyperparameter. In this paper, we evaluate and compare five different strategies for hyperparameter selection. We propose a calibration-based method of objective hyperparameter selection, called BestRes, that leads to repeatable and stable image reconstructions that are indistinguishable from heuristic selections. Results indicate: (1) heuristic selections of hyperparameter are inconsistent among experts, (2) generalized cross-validation approaches produce under-regularized solutions, (3) L-curve approaches are unreliable for EIT and (4) BestRes produces good solutions comparable to expert selections. Additionally, we show that it is possible to reliably detect an inverse crime based on analysis of these parameters.

Assessment of 1-lead and 2-lead electrode patterns in electrical impedance endotomography

Electrical impedance endotomography (EIE) is a modality of impedance imaging where the electrodes are located on an insulating core placed at the centre of the region of interest. The absence of a physical limit to the medium surrounding the probe enables the use of remote electrodes. The present study compares the features of 2-lead measurements, where the two pairs of electrodes are located on the probe, to 1-lead measurements, where one of the two injection electrodes and one of the two sensing electrodes are located at a distance far away from the probe. The methodology was the characterization of the sensitivity matrix under the influence of electrode pattern, reconstruction radius and mesh construction. Three mesh constructions, three values of the reconstruction radius and five electrode patterns were compared. The study was carried out in 2D using calculated data. Measurement noise was simulated by an addition of 5% Gaussian white noise. The images were reconstructed using the Tikhonov method and L-curve technique. The results show that the reconstruction mesh and the radius of the reconstruction domain have less influence on the conditioning of the sensitivity matrix than the electrode pattern. Both 1-lead and 2-lead configurations enabled the reconstruction of images of relatively similar quality. Additional selection criteria are expected from hardware considerations.

Generating accurate finite element meshes for the forward model of the human head in EIT

The use of realistic anatomy in the model used for image reconstruction in EIT of brain function appears to confer significant improvements compared to geometric shapes such as a sphere. Accurate model geometry may be achieved by numerical models based on magnetic resonance images (MRIs) of the head, and this group has elected to use finite element meshing (FEM) as it enables detailed internal anatomy to be modelled and has the capability to incorporate information about tissue anisotropy. In this paper a method for generating accurate FEMs of the human head is presented where MRI images are manually segmented using custom adaptation of industry standard commercial design software packages. This is illustrated with example surface models and meshes from adult epilepsy patients, a neonatal baby and a phantom latex tank incorporating a real skull. Mesh quality is assessed in terms of element stretch and hence distortion.

An averaging two-electrode probe for monitoring changes in myocardial conductivity evoked by ischemia

This paper considers the applicability of effective conductivity measurements for monitoring physiological and/or pathological phenomena induced by ischemia in the myocardium. The sensitivity of a probe, calculated by means of the finite element method, to changes in the conductivity of the tissue examined is defined for this purpose. Probes developed by Schafer and collaborators (1995) and in our own departments have been examined on the basis of this sensitivity. Theoretical results were verified experimentally using a tank, enlarged models of the probes, and a specially developed electronic circuit. It follows from this study that the probe developed by Schafer et al. is characterized by positive and negative sensitivity. This can lead to misinterpretation of the measurements obtained. In contrast, the sensitivity of our probe is dominantly positive. An example of the in vivo result obtained during experimentally induced ischemia in a swine heart is included.

Electrical impedance tomography with compensation for electrode positioning variations

Ideally electrical impedance tomography (EIT) should not be oversensitive to electrode positions, but this conflicts with efforts to produce high-resolution images. Two procedures are presented that balance reducing the sensitivity to electrode position errors with generating practicable EIT images. The first provides a criterion based on electrode sensitivity for regularizing the reconstruction through spectral expansion. The main consequences of this are that smoother images are produced and the number of artefacts and their magnitude are generally reduced. The second modification uses the recorded data to compensate for electrode movements that have occurred after the reference data were measured. Image smoothness is used as the criterion for the readjustment. Computer simulation tests have shown that this modification produces improved image fidelity.

Electrical impedance tomography can monitor dynamic hyperinflation in dogs

We assessed in eight dogs the accuracy with which electrical impedance tomography (EIT) can monitor changes in lung volume by comparing the changes in mean lung conductivity obtained with EIT to changes in esophageal pressure (Pes) and to airway opening pressure (Pao) measured after airway occlusion. The average volume measurement errors were determined: 26 ml for EIT; 35 ml for Pao; and 54 ml for Pes. Subsequently, lung inflation due to applied positive end-expiratory pressure was measured by EIT (delta VEIT) and Pao (delta VPAO) under both inflation and deflation conditions. Whereas delta VPAO was equal under both conditions, delta VEIT was 28 ml greater during deflation than inflation, indicating that EIT is sensitive to lung volume history. The average inflation delta VEIT was 67.7 +/- 78 ml greater than delta VPAO, for an average volume increase of 418 ml. Lung inflation due to external expiratory resistance was measured during ventilation by EIT (delta VEIT,vent) and Pes (delta VPes,vent) and at occlusion by EIT (delta VEIT,occl), Pes, and Pao. The average differences between EIT estimates and delta VEIT,occl were 5.8 +/- 44 ml for delta VEIT,vent and 49.5 +/- 34 ml for delta VEIT,occl. The average volume increase for all dogs was 442.2 ml. These results show that EIT can provide usefully accurate estimates of changes in lung volume over an extended time period and that the technique has promise as a means of conveniently and noninvasively monitoring lung hyperinflation.

Assessment of errors in static electrical impedance tomography with adjacent and trigonometric current patterns

In electrical impedance tomography (EIT), difference imaging is often preferred over static imaging. This is because of the many unknowns in the forward modelling which make it difficult to obtain reliable absolute resistivity estimates. However, static imaging and absolute resistivity values are needed in some potential applications of EIT. In this paper we demonstrate by simulation the effects of different error components that are included in the reconstruction of static EIT images. All simulations are carried out in two dimensions with the so-called complete electrode model. Errors that are considered are the modelling error in the boundary shape of an object, errors in the electrode sizes and localizations and errors in the contact impedances under the electrodes. Results using both adjacent and trigonometric current patterns are given.

An interleaved drive electrical impedance tomography image reconstruction algorithm

In this study, a reconstruction algorithm for a 16-electrode interleaved-drive electrical impedance tomography (EIT) system is developed, based on inversion of an analytically calculated sensitivity matrix. The sensitivity matrix is calculated using Geselowitz's lead-sensitivity theorem. Eight interleaved electrodes out of 16 (equally spaced) electrodes are designated as current injection electrodes and the remaining eight electrodes are designated as measurement electrodes. The sensitivity matrix is singular, therefore singular value decomposition (SVD) of the sensitivity matrix, followed by pseudoinversion-with and without truncation-is used to reconstruct images. The algorithm is a single-pass algorithm. Data from a saline filled tank and in vivo data during respiration and the cardiac cycle, acquired by using a Sheffield multifrequency system, are used to reconstruct images. The effect of different truncation levels on the reconstructed images is investigated.

Impedance imaging of lung ventilation: do we need to account for chest expansion?

Electrical impedance tomography (EIT) uses surface electrical measurements to image changes in the conductivity distribution within a medium. When used to measure lung ventilation, however, measurements depend both on conductivity changes in the thorax and on rib cage movement. Given that currently available reconstruction techniques assume that only conductivity changes are present, certain errors are introduced. A finite element model (FEM) is used to calculate the effect of chest expansion on the reconstructed conductivity images. Results indicate that thorax expansion accounts for up to 20% of the reconstructed image amplitude and introduces an artifact in the center of the image tending to "move" the reconstructed lungs closer together. Although this contribution varies depending on anatomical factors, it is relatively independent of inspiration depth. For certain applications in which one is only interested in changes in the level of physiological activity, the effect of the expansion can be neglected because it varies linearly with impedance changes. We conclude that chest expansion can contribute significantly to the conductivity images of lung ventilation and should be taken into account in the interpretation of these images.

Electrical impedance tomography: regularized imaging and contrast detection

Dynamic electrical impedance tomography (EIT) images changes in the conductivity distribution of a medium from low frequency electrical measurements made at electrodes on the medium surface. Reconstruction of the conductivity distribution is an under-determined and ill-posed problem, typically requiring either simplifying assumptions or regularization based on a priori knowledge. This paper presents a maximum a posteriori (MAP) approach to linearized image reconstruction using knowledge of the noise variance of the measurements and the covariance of the conductivity distribution. This approach has the advantage of an intuitive interpretation of the algorithm parameters as well as fast (near real time) image reconstruction. In order to compare this approach to existing algorithms, the authors develop figures of merit to measure the reconstructed image resolution, the noise amplification of the image reconstruction, and the fidelity of positioning in the image. Finally, the authors develop a communications systems approach to calculate the probability of detection of a conductivity contrast in the reconstructed image as a function of the measurement noise and the reconstruction algorithm used.

Data processing techniques for serial EIT spectroscopy images: a review of some preliminary results

Mutlifrequency EIT imaging should allow specific organs within the body to be identified by their impedance spectrum, and the use of parametric imaging should lead to a much greater freedom from movement artefacts. This will make EIT more attractive as a monitoring technique, but the data rate will require automated processing of the images. The application of dynamic regions of interest, generated on a frame by frame basis, is described, with examples from the imaging of neonatal lungs and adult stomach. The lung can be objectively identified on a single frame from the fRSC, SC and RC images, but the stomach could only be identified on the dynamic images.

A real-time electrical impedance tomography system for clinical use--design and preliminary results

An instrument is described which produces images of the electrical impedance distribution within the body at a rate of 25 frames per second, allowing lung ventilation and lung perfusion to be observed in real time. The instrument makes impedance measurements using an array of 16 electrodes on the surface of the body, and reconstructs the images using a weighted backprojection technique. The design of the data acquisition electronics and the reconstruction and display processor are described. Some preliminary in vitro and in vivo results from the system are presented.

A method of reducing the error caused by boundary shape and electrode positions in electrical impedance tomography

This paper describes a method of reducing the influence of the data error caused by non-ideal boundary shape and electrode placement on reconstructed images. A data calibration and a modified Newton-Raphson reconstruction are combined in the method to ensure rapid convergence and small reconstruction error. The method is verified by the simulated data of a 2D software phantom and the practical measurements of a cylindrical saline tank.

A neural network image reconstruction technique for electrical impedance tomography

Reconstruction of images in electrical impedance tomography requires the solution of a nonlinear inverse problem on noisy data. This problem is typically ill-conditioned and requires either simplifying assumptions or regularization based on a priori knowledge. The authors present a reconstruction algorithm using neural network techniques which calculates a linear approximation of the inverse problem directly from finite element simulations of the forward problem. This inverse is adapted to the geometry of the medium and the signal-to-noise ratio (SNR) used during network training. Results show good conductivity reconstruction where measurement SNR is similar to the training conditions. The advantages of this method are its conceptual simplicity and ease of implementation, and the ability to control the compromise between the noise performance and resolution of the image reconstruction.

Estimation of tissue resistivities from multiple-electrode impedance measurements

In order to measure in vivo resistivity of tissues in the thorax, the possibility of combining anatomical data extracted from high-resolution images with multiple-electrode impedance measurements, a priori knowledge of the range of tissue resistivities, and a priori data on the instrumentation noise is assessed in this study. A statistically constrained minimum-mean-square error estimator (MIMSEE) that minimizes the effects of linearization errors and instrumentation noise is developed and compared to the conventional least-squares error estimator (LSEE). The MIMSEE requires a priori signal and noise information. The statistical constraint signal information was obtained from a priori knowledge of the physiologically allowed range of regional resistivities. The noise constraint information was obtained from a priori knowledge of the linearization error and the instrumentation noise. The torso potentials were simulated by employing a three-dimensional canine torso model. The model consists of four different conductivity regions: heart, right lung, left lung, and body. It is demonstrated that the statistically constrained MIMSEE performs significantly better than the LSEE in determining resistivities. The results based on the torso model indicate that regional resistivities can be estimated to within 40% accuracy of their true values by utilizing a statistically constrained MIMSEE, even if the instrumentation noise is comparable to the measured torso potentials. The errors obtained using the LSEE with the same linearized transfer function and level of instrumentation noise were about five times larger than those obtained using the MIMSEE. For larger measurement errors the MIMSEE performs even better when compared to the LSEE.