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

Unsupervised sequence-to-sequence learning for automatic signal quality assessment in multi-channel electrical impedance-based hemodynamic monitoring

BACKGROUND AND OBJECTIVE

This study proposes an unsupervised sequence-to-sequence learning approach that automatically assesses the motion-induced reliability degradation of the cardiac volume signal (CVS) in multi-channel electrical impedance-based hemodynamic monitoring. The proposed method attempts to tackle shortcomings in existing learning-based assessment approaches, such as the requirement of manual annotation for motion influence and the lack of explicit mechanisms for realizing motion-induced abnormalities under contextual variations in CVS over time.

METHOD

By utilizing long-short term memory and variational auto-encoder structures, an encoder-decoder model is trained not only to self-reproduce an input sequence of the CVS but also to extrapolate the future in a parallel fashion. By doing so, the model can capture contextual knowledge lying in a temporal CVS sequence while being regularized to explore a general relationship over the entire time-series. A motion-influenced CVS of low-quality is detected, based on the residual between the input sequence and its neural representation with a cut-off value determined from the two-sigma rule of thumb over the training set.

RESULT

Our experimental observations validated two claims: (i) in the learning environment of label-absence, assessment performance is achievable at a competitive level to the supervised setting, and (ii) the contextual information across a time series of CVS is advantageous for effectively realizing motion-induced unrealistic distortions in signal amplitude and morphology. We also investigated the capability as a pseudo-labeling tool to minimize human-craft annotation by preemptively providing strong candidates for motion-induced anomalies. Empirical evidence has shown that machine-guided annotation can reduce inevitable human-errors during manual assessment while minimizing cumbersome and time-consuming processes.

CONCLUSION

The proposed method has a particular significance in the industrial field, where it is unavoidable to gather and utilize a large amount of CVS data to achieve high accuracy and robustness in real-world applications.

Machine learning-based signal quality assessment for cardiac volume monitoring in electrical impedance tomography

Owing to recent advances in thoracic electrical impedance tomography (EIT), a patient’s hemodynamic function can be noninvasively and continuously estimated in real-time by surveilling a cardiac volume signal (CVS) associated with stroke volume and cardiac output. In clinical applications, however, a CVS is often of low quality, mainly because of the patient’s deliberate movements or inevitable motions during clinical interventions. This study aims to develop a signal quality indexing method that assesses the influence of motion artifacts on transient CVSs. The assessment is performed on each cardiac cycle to take advantage of the periodicity and regularity in cardiac volume changes. Time intervals are identified using the synchronized electrocardiography system. We apply divergent machine-learning methods, which can be sorted into discriminative-model and manifold-learning approaches. The use of machine-learning could be suitable for our real-time monitoring application that requires fast inference and automation as well as high accuracy. In the clinical environment, the proposed method can be utilized to provide immediate warnings so that clinicians can minimize confusion regarding patients’ conditions, reduce clinical resource utilization, and improve the confidence level of the monitoring system. Numerous experiments using actual EIT data validate the capability of CVSs degraded by motion artifacts to be accurately and automatically assessed in real-time by machine learning. The best model achieved an accuracy of 0.95, positive and negative predictive values of 0.96 and 0.86, sensitivity of 0.98, specificity of 0.77, and AUC of 0.96.

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.

An efficient Point-Matching Method-of-Moments for 2D and 3D Electrical Impedance Tomography Using Radial Basis functions

AbstractObjective: The inverse problem of computing conductivity distributions in 2D and 3D objects interrogated by low frequency electrical signals, which is called Electrical Impedance Tomography (EIT), is treated using a Method-of-Moment technique.

METHODS

A Point-Matching-Method-of-Moment technique is used to formulate a global integral equation solver. Radial Basis Functions are adopted to express the conductivity distribution. Single-step quadratic-norm (L2) and iterative total variation (L1) regularization techniques are exploited to solve the inverse problem.

RESULTS

Simulation and experimental tests on a circular reconstruction domain show satisfactory performance in deriving conductivity distribution, achieving a Correlation Coefficient (CC) up to 0:863 for 70 dB voltage SNR and 0:842 for 40 dB voltage SNR. The proposed methodology with L2-norm regularization provided better results than traditional iterative Gauss-Newtons approach, whereas with L1-norm regularization it showed promising performance. Moreover, 3D reconstructions on a cylindrical cavity demonstrated superior results near the electrodes planes compared to those of the conventional linearized approach. Finally, application to EIT medical data for dynamic lung imaging successfully revealed the breath-cycle conductivity changes.

CONCLUSION

The results show that the proposed method can be effective for both 2D and 3D EIT and applicable to many applications.

SIGNIFICANCE

Strong conductivity variations are successfully tackled with a very good Correlation Coefficient. In contrast to conventional EIT solutions based on weak-form and linearization on small conductivity changes, the proposed method requires only one step to converge with L2-norm regularization. The proposed method with L1-norm regularization also achieves good reconstruction quality with a low number of iterations.

Imaging Conductivity Changes in Monolayer Graphene Using Electrical Impedance Tomography

Recently, graphene has gained a lot of attention in the electronic industry due to its unique properties and has paved the way for realizing novel devices in the field of electronics. For the development of new device applications, it is necessary to grow large wafer-sized monolayer graphene samples. Among the methods to synthesize large graphene films, chemical vapor deposition (CVD) is one of the promising and common techniques. However, during the growth and transfer of the CVD graphene monolayer, defects such as wrinkles, cracks, and holes appear on the graphene surface. These defects can influence the electrical properties and it is of interest to know the quality of graphene samples non-destructively. Electrical impedance tomography (EIT) can be applied as an alternate method to determine conductivity distribution non-destructively. The EIT inverse problem of reconstructing conductivity is highly non-linear and is heavily dependent on measurement accuracy and modeling errors related to an accurate knowledge of electrode location, contact resistances, the exact outer boundary of the graphene wafer, etc. In practical situations, it is difficult to eliminate these modeling errors as complete knowledge of the electrode contact impedance and outer domain boundary is not fully available, and this leads to an undesirable solution. In this paper, a difference imaging approach is proposed to estimate the conductivity change of graphene with respect to the reference distribution from the data sets collected before and after the change. The estimated conductivity change can be used to locate the defects on the graphene surface caused due to the CVD transfer process or environment interaction. Numerical and experimental results with graphene sample of size 2.5 × 2.5 cm are performed to determine the change in conductivity distribution and the results show that the proposed difference imaging approach handles the modeling errors and estimates the conductivity distribution with good accuracy.

Electrical Impedance Tomography for monitoring cardiac radiofrequency ablation: a scoping review of an emerging technology

Arrhythmias are common cardiac diseases which can be treated effectively by the cardiac radiofrequency ablation (CRFA). However, information regarding the lesion growth within the myocardium is critical to the procedure's safety and efficacy but still unavailable in the current catheterisation lab (CathLab). Over the last 20 years, many efforts have been made in order to track the lesion size during the procedure. Unfortunately, all the approaches have their own limitations preventing them from the clinical translation and hence making the lesion size monitoring during a CRFA still an open issue. Electrical Impedance Tomography (EIT) is an impedance imaging modality that might be able to image the thermal-related impedance changes from which the lesion size can be measured. With the availability of the patient's CT scans, for a detailed model, and the catheter-based electrodes for the internal electrodes, EIT accuracy and sensitivity to the ablated sites can be significantly improved and is worth being explored for this application. Though EIT is still new to CRFA with no in-vivo experiments being done according to our up-to-date searching, many related EIT studies and its extensive research in Hyperthermia and other ablations can reveal many hints for a possibility of the CRFA-EIT application. In this paper, we present a review on multiple aspects of EIT in CRFA. First, the expected CRFA-EIT signal range and frequency are discussed based on various measured impedance results obtained from lesions in the past. Second, the possible noise sources that can happen in a clinical CRFA procedure, along with their signal range and frequency compared to the CRFA-EIT signal, and, third, the available current solutions to separate such noises from the CRFA-EIT signal. Finally, we review the progress of EIT in thermal applications over the last two decades in order to identify the developments that EIT can take advantage of and the current drawbacks that need to be solved for a potential CRFA-EIT application.

A Parametric Level Set-Based Approach to Difference Imaging in Electrical Impedance Tomography

This paper presents a novel difference imaging approach based on the recently developed parametric level set (PLS) method for estimating the change in a target conductivity from electrical impedance tomography measurements. As in conventional difference imaging, the reconstruction of conductivity change is based on data sets measured from the surface of a body before and after the change. The key feature of the proposed approach is that the conductivity change to be reconstructed is assumed to be piecewise constant, while the geometry of the anomaly is represented by a shape-based PLS function employing Gaussian radial basis functions (GRBFs). The representation of the PLS function by using GRBF provides flexibility in describing a large class of shapes with fewer unknowns. This feature is advantageous, as it may significantly reduce the overall number of unknowns, improve the condition number of the inverse problem, and enhance the computational efficiency of the technique. To evaluate the proposed PLS-based difference imaging approach, results obtained via simulation, phantom study, and in vivo pig data are studied. We find that the proposed approach tolerates more modeling errors and leads to a significant improvement in image quality compared with the conventional linear approach.

Global and regional degree of obstruction determined by electrical impedance tomography in patients with obstructive ventilatory defect

Background

Electrical impedance tomography is a continuous imaging method capable of measuring lung volume changes. The purpose of this study was to examine whether EIT was capable of evaluating the degree of obstructive ventilatory defect (OVD) on the global and regional level.

Methods

41 healthy subjects with no lung diseases and 67 subjects suffering from obstructive lung diseases were examined using EIT and spirometry during forced vital capacity (FVC) maneuver. The subjects were divided into control group (n = 41), early airway obstruction group (n = 26), mild group (n = 17), moderate group (n = 16) and severe group (n = 8) according to the degree of obstruction. Forced expiratory volume in 1 second (FEV₁) and FEV₁/FVC were determined by EIT. The mode index (MI) was proposed to evaluate the degree of global and regional obstruction; the effectiveness of MI was validated by evaluating posture related change of lung emptying capacity in sitting and supine postures; the degree of regional obstruction was determined according to the cut-off values of MI obtained from receiver operating characteristic (ROC) analysis; regional obstruction was located in the four-quadrant region of interest (ROI) and the contour-map ROI with contour lines at the cut-off values of MI.

Results

Significant differences were found between different groups (P<0.05) and the global MI was 0.93±0.03, 0.86±0.05, 0.81±0.09, 0.73±0.09 and 0.60±0.11 (mean ±SD), respectively. The cut-off MI value was 0.90, 0.83, 0.77, and 0.65, respectively.

Conclusion

The results indicated the potential of EIT to evaluate the degree of obstruction in patients with obstructive ventilatory defect on the global and regional level.

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.

Ventilation inhomogeneity in obstructive lung diseases measured by electrical impedance tomography: a simulation study

Electrical impedance tomography (EIT) has mostly been used in the Intensive Care Unit (ICU) to monitor ventilation distribution but is also promising for the diagnosis in spontaneously breathing patients with obstructive lung diseases. Beside tomographic images, several numerical measures have been proposed to quantitatively assess the lung state. In this study two common measures, the 'Global Inhomogeneity Index' and the 'Coefficient of Variation' were compared regarding their capability to reflect the severity of lung obstruction. A three-dimensional simulation model was used to simulate obstructed lungs, whereby images were reconstructed on a two-dimensional domain. Simulations revealed that minor obstructions are not adequately recognized in the reconstructed images and that obstruction above and below the electrode plane may result in misleading values of inhomogeneity measures. EIT measurements on several electrode planes are necessary to apply these measures in patients with obstructive lung diseases in a promising manner.

Impact of four different recumbencies on the distribution of ventilation in conscious or anaesthetized spontaneously breathing beagle dogs: An electrical impedance tomography study

The aim was to examine the effects of recumbency and anaesthesia on distribution of ventilation in beagle dogs using Electrical Impedance Tomography (EIT). Nine healthy beagle dogs, aging 3.7±1.7 (mean±SD) years and weighing 16.3±1.6 kg, received a series of treatments in a fixed order on a single occasion. Conscious dogs were positioned in right lateral recumbency (RLR) and equipped with 32 EIT electrodes around the thorax. Following five minutes of equilibration, two minutes of EIT recordings were made in each recumbency in the following order: RLR, dorsal (DR), left (LLR) and sternal (SR). The dogs were then positioned in RLR, premedicated (medetomidine 0.01, midazolam 0.1, butorphanol 0.1 mg kg^-1 iv) and pre-oxygenated. Fifteen minutes later anaesthesia was induced with 1 mg kg^-1 propofol iv and maintained with propofol infusion (0.1–0.2 mg kg^-1 minute^-1 iv). After induction, the animals were intubated and allowed to breathe spontaneously (FIO₂ = 1). Recordings of EIT were performed again in four recumbencies similarly to conscious state. Centre of ventilation (COV) and global inhomogeneity (GI) index were calculated from the functional EIT images. Repeated-measures ANOVA and Bonferroni tests were used for statistical analysis (p < 0.05). None of the variables changed in the conscious state. During anaesthesia left-to-right COV increased from 46.8±2.8% in DR to 49.8±2.9% in SR indicating a right shift, and ventral-to-dorsal COV increased from 49.8±1.7% in DR to 51.8±1.1% in LLR indicating a dorsal shift in distribution of ventilation. Recumbency affected distribution of ventilation in anaesthetized but not in conscious dogs. This can be related to loss of respiratory muscle tone (e.g. diaphragm) and changes in thoracic shape. Changing position of thoraco-abdominal organs under the EIT belt should be considered as alternative explanation of these findings.

Lobe based image reconstruction in Electrical Impedance Tomography

PURPOSE

Electrical Impedance Tomography (EIT) is an imaging modality used to generate two-dimensional cross-sectional images representing impedance change in the thorax. The impedance of lung tissue changes with change in air content of the lungs; hence, EIT can be used to examine regional lung ventilation in patients with abnormal lungs. In lung EIT, electrodes are attached around the circumference of the thorax to inject small alternating currents and measure resulting voltages. In contrast to X-ray computed tomography (CT), EIT images do not depict a thorax slice of well defined thickness, but instead visualize a lens-shaped region around the electrode plane, which results from diffuse current propagation in the thorax. Usually, this is considered a drawback, since image interpretation is impeded if 'off-plane' conductivity changes are projected onto the reconstructed two-dimensional image. In this paper we describe an approach that takes advantage of current propagation below and above the electrode plane. The approach enables estimation of the individual conductivity change in each lung lobe from boundary voltage measurements. This could be used to monitor disease progression in patients with obstructive lung diseases, such as chronic obstructive pulmonary disease (COPD) or cystic fibrosis (CF) and to obtain a more comprehensive insight into the pathophysiology of the lung.

METHODS

Electrode voltages resulting from different conductivities in each lung lobe were simulated utilizing a realistic 3D finite element model (FEM) of the human thorax and the lungs. Overall 200 different patterns of conductivity change were simulated. A 'lobe reconstruction' algorithm was developed, applying patient-specific anatomical information in the reconstruction process. A standard EIT image reconstruction algorithm and the proposed 'lobe reconstruction' algorithm were used to estimate conductivity change in the lobes. The agreement between simulated and reconstructed conductivity change in particular lobes were compared using Bland-Altman plots, correlation plots and linear regression. To test the applicability of the approach in a realistic scenario, EIT measurements of a patient suffering from cystic fibrosis (CF) were carried out.

RESULTS

Conductivity changes in each lobe generate specific patterns of voltage change. These can be used to estimate the conductivity change in lobes from measured boundary voltage. The correlation coefficient between simulated and reconstructed conductivity change in particular lobes is r > 0.89 for all lobes. Unknown position of the electrode plane leads to over- or underestimation of reconstructed conductivity change. Slight mismatches (± 5% of the forward model height) between the actual position of the electrode plane and the position used in the reconstruction model lead to regression coefficients of 0.7 to 1.3 between simulated and reconstructed conductivity change in the lobes.

CONCLUSION

The presented approach enhances common reconstruction methods by providing information about anatomically assignable units and thus facilitates image interpretation, since impedance change and thus ventilation of each lobe is directly determined in the reconstructions.

Effect of the number of electrodes on the reconstructed lung shape in electrical impedance tomography

Electrical impedance tomography (EIT) is used to monitor the regional distribution of ventilation in a transversal plane of the thorax. In this manuscript we evaluate the impact of different quantities of electrodes used for current injection and voltage measurement on the reconstructed shape of the lungs. Results indicate that the shape of reconstructed impedance changes in the body depends on the number of electrodes. In this manuscript, we demonstrate that a higher number of electrodes do not necessarily increase the image quality. For the used stimulation pattern, utilizing neighboring electrodes for current injection and voltage measurement, we conclude that the shape of the lungs is best reconstructed if 16 electrodes are used.

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.

Regional lung function determined by electrical impedance tomography during bronchodilator reversibility testing in patients with asthma

The measurement of rapid regional lung volume changes by electrical impedance tomography (EIT) could determine regional lung function in patients with obstructive lung diseases during pulmonary function testing (PFT). EIT examinations carried out before and after bronchodilator reversibility testing could detect the presence of spatial and temporal ventilation heterogeneities and analyse their changes in response to inhaled bronchodilator on the regional level. We examined seven patients suffering from chronic asthma (49  ±  19 years, mean age  ±  SD) using EIT at a scan rate of 33 images s(-1) during tidal breathing and PFT with forced full expiration. The patients were studied before and 5, 10 and 20 min after bronchodilator inhalation. Seven age- and sex-matched human subjects with no lung disease history served as a control study group. The spatial heterogeneity of lung function measures was quantified by the global inhomogeneity indices calculated from the pixel values of tidal volume, forced expiratory volume in one second (FEV1), forced vital capacity (FVC), peak flow and forced expiratory flow between 25% and 75% of FVC as well as histograms of pixel FEV1/FVC values. Temporal heterogeneity was assessed using the pixel values of expiration times needed to exhale 75% and 90% of pixel FVC. Regional lung function was more homogeneous in the healthy subjects than in the patients with asthma. Spatial and temporal ventilation distribution improved in the patients with asthma after the bronchodilator administration as evidenced mainly by the histograms of pixel FEV1/FVC values and pixel expiration times. The examination of regional lung function using EIT enables the assessment of spatial and temporal heterogeneity of ventilation distribution during bronchodilator reversibility testing. EIT may become a new tool in PFT, allowing the estimation of the natural disease progression and therapy effects on the regional and not only global level.

Assessment of distribution of ventilation by electrical impedance tomography in standing horses

The aim was to evaluate the feasibility of using electrical impedance tomography (EIT) in horses. Thoracic EIT was used in nine horses. Thoracic and abdominal circumference changes were also measured with respiratory ultrasound plethysmography (RUP). Data were recorded during baseline, rebreathing of CO2 and sedation. Three breaths were selected for analysis from each recording. During baseline breathing, horses regularly took single large breaths (sighs), which were also analysed. Functional EIT images were created using standard deviations (SD) of pixel signals and correlation coefficients (R) of each pixel signal with a reference respiratory signal. Left-to-right ratio, centre-of-ventilation and global-inhomogeneity-index were calculated. RM-ANOVA and Bonferroni tests were used (P < 0.05). Distribution of ventilation shifted towards right during sighs and towards dependent regions during sighs, rebreathing and sedation. Global-inhomogeneity-index did not change for SD but increased for R images during sedation. The sum of SDs for the respiratory EIT signals correlated well with thoracic (r(2) = 0.78) and abdominal (r(2) = 0.82) tidal circumferential changes. Inverse respiratory signals were identified on the images at sternal location and based on reviewing CT images, seemed to correspond to location of gas filled intestines. Application of EIT in standing non-sedated horses is feasible. EIT images may provide physiologically useful information even in situations, such as sighs, that cannot easily be tested by other methods.

Improving image quality in EIT imaging by measurement of thorax excursion

Electrical Impedance Tomography (EIT) is used to visualize the regional ventilation of the lungs using voltage measurements on the surface of the thorax. Unfortunately the image reconstruction process is sensitive to shape deformation. During breathing the inevitable expansion of the thorax influences measured boundary voltages which leads to artifacts in the reconstructed images. A camera based motion-tracking-system was used to measure thorax excursion during breathing and systematically modify measured voltages. Results indicate that image artefacts can be reduced if the measured voltages are modified based on the measured thorax excursion.

Steps towards 3D Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is a promising imaging technique to visualize the dynamics of regional lung ventilation. 2D EIT has shown promise in monitoring ventilation therapy, with the drawback of only displaying a single horizontal slice of the lungs. Until now there are no generally accepted approaches available to generate meaningful 3D images in real-time. This paper describes general problems and first attempts to overcome those that may extend to a hierarchical scheme for 3D EIT imaging.

Functional validation and comparison framework for EIT lung imaging

INTRODUCTION

Electrical impedance tomography (EIT) is an emerging clinical tool for monitoring ventilation distribution in mechanically ventilated patients, for which many image reconstruction algorithms have been suggested. We propose an experimental framework to assess such algorithms with respect to their ability to correctly represent well-defined physiological changes. We defined a set of clinically relevant ventilation conditions and induced them experimentally in 8 pigs by controlling three ventilator settings (tidal volume, positive end-expiratory pressure and the fraction of inspired oxygen). In this way, large and discrete shifts in global and regional lung air content were elicited.

METHODS

We use the framework to compare twelve 2D EIT reconstruction algorithms, including backprojection (the original and still most frequently used algorithm), GREIT (a more recent consensus algorithm for lung imaging), truncated singular value decomposition (TSVD), several variants of the one-step Gauss-Newton approach and two iterative algorithms. We consider the effects of using a 3D finite element model, assuming non-uniform background conductivity, noise modeling, reconstructing for electrode movement, total variation (TV) reconstruction, robust error norms, smoothing priors, and using difference vs. normalized difference data.

RESULTS AND CONCLUSIONS

Our results indicate that, while variation in appearance of images reconstructed from the same data is not negligible, clinically relevant parameters do not vary considerably among the advanced algorithms. Among the analysed algorithms, several advanced algorithms perform well, while some others are significantly worse. Given its vintage and ad-hoc formulation backprojection works surprisingly well, supporting the validity of previous studies in lung EIT.

Variability in EIT Images of Lung Ventilation as a Function of Electrode Planes and Body Positions

This study is aimed at investigating the variability in resistivity changes in the lung region as a function of air volume, electrode plane and body position. Six normal subjects (33.8 ± 4.7 years, range from 26 to 37 years) were studied using the Sheffield Electrical Impedance Tomography (EIT) portable system. Three transverse planes at the level of second intercostal space, the level of the xiphisternal joint, and midway between upper and lower locations were chosen for measurements. For each plane, sixteen electrodes were uniformly positioned around the thorax. Data were collected with the breath held at end expiration and after inspiring 0.5, 1.0, or 1.5 liters of air from end expiration, with the subject in both the supine and sitting position. The average resistivity change in five regions, two 8x8 pixel local regions in the right lung, entire right, entire left and total lung regions, were calculated. The results show the resistivity change averaged over electrode positions and subject positions was 7-9% per liter of air, with a slightly larger resistivity change of 10 % per liter air in the lower electrode plane. There was no significant difference (p>0.05) between supine and sitting. The two 8x8 regions show a larger inter individual variability (coefficient of variation, CV, is from 30% to 382%) compared to the entire left, entire right and total lung (CV is from 11% to 51%). The results for the global regions are more consistent. The large inter individual variability appears to be a problem for clinical applications of EIT, such as regional ventilation. The variability may be mitigated by choosing appropriate electrode plane, body position and region of interest for the analysis.

Choice of reconstructed tissue properties affects interpretation of lung EIT images

Electrical impedance tomography (EIT) estimates an image of change in electrical properties within a body from stimulations and measurements at surface electrodes. There is significant interest in EIT as a tool to monitor and guide ventilation therapy in mechanically ventilated patients. In lung EIT, the EIT inverse problem is commonly linearized and only changes in electrical properties are reconstructed. Early algorithms reconstructed changes in resistivity, while most recent work using the finite element method reconstructs conductivity. Recently, we demonstrated that EIT images of ventilation can be misleading if the electrical contrasts within the thorax are not taken into account during the image reconstruction process. In this paper, we explore the effect of the choice of the reconstructed electrical properties (resistivity or conductivity) on the resulting EIT images. We show in simulation and experimental data that EIT images reconstructed with the same algorithm but with different parametrizations lead to large and clinically significant differences in the resulting images, which persist even after attempts to eliminate the impact of the parameter choice by recovering volume changes from the EIT images. Since there is no consensus among the most popular reconstruction algorithms and devices regarding the parametrization, this finding has implications for potential clinical use of EIT. We propose a program of research to develop reconstruction techniques that account for both the relationship between air volume and electrical properties of the lung and artefacts introduced by the linearization.

Mutual information as a measure of image quality for 3D dynamic lung imaging with EIT

We report on a pilot study of dynamic lung electrical impedance tomography (EIT) at the University of Manchester. Low-noise EIT data at 100 frames per second were obtained from healthy male subjects during controlled breathing, followed by magnetic resonance imaging (MRI) subsequently used for spatial validation of the EIT reconstruction. The torso surface in the MR image and electrode positions obtained using MRI fiducial markers informed the construction of a 3D finite element model extruded along the caudal-distal axis of the subject. Small changes in the boundary that occur during respiration were accounted for by incorporating the sensitivity with respect to boundary shape into a robust temporal difference reconstruction algorithm. EIT and MRI images were co-registered using the open source medical imaging software, 3D Slicer. A quantitative comparison of quality of different EIT reconstructions was achieved through calculation of the mutual information with a lung-segmented MR image. EIT reconstructions using a linear shape correction algorithm reduced boundary image artefacts, yielding better contrast of the lungs, and had 10% greater mutual information compared with a standard linear EIT reconstruction.

Human CT Measurements of Structure/Electrode Position Changes During Respiration with Electrical Impedance Tomography

For pulmonary applications of Electrical Impedance Tomography (EIT) systems, the electrodes are placed around the chest in a 2D ring, and the images are reconstructed based on the assumptions that the object is rigid and the measured resistivity change in EIT images is only caused by the actual resistivity change of tissue. Structural changes are rarely considered. Previous studies have shown that structural changes which result in tissue/organ and electrode position changes tend to introduce artefacts to EIT images of the thorax. Since EIT reconstruction is an ill-posed inverse problem, any small inaccurate assumptions of object may cause large artefacts in reconstructed images. Accurate information on structure/electrode position changes is a need to understand factors contributing to the measured resistivity changes and to improve EIT reconstruction algorithm. Our previous study using MRI technique showed that chest expansion leads to electrode and tissue/organ movements but not significant as proposed. The accuracy of the measurements by MRI may be limited by its relatively low temporal and spatial resolution. In this study, structure/electrode position changes during respiration cycle in patients who underwent chest CT scans are further investigated. For each patient, sixteen fiduciary markers are equally spaced around the surface, the same as the electrode placement for EIT measurements. A CT scanner with respiration-gated ability is used to acquire images of the thorax. CT thoracic images are retrospectively reconstructed corresponding temporally to specific time periods within respiration cycle (from 0% to 90%, every 10%). The average chest expansions are 2 mm in anterior-posterior and -1.6 mm in lateral directions. Inside tissue/organ move down 9.0±2.5 mm with inspiration of tidal volume (0.54±0.14 liters), ranging from 6 mm to 12 mm. During normal quiet respiration, electrode position changes are smaller than expected. No general patterns of electrode position changes are observed. The results in this study provide guidelines for accommodating the motion that may introduce artefacts to EIT images.

Shape deformation in two-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) uses measurements from surface electrodes to reconstruct an image of the conductivity of the contained medium. However, changes in measurements result from both changes in internal conductivity and changes in the shape of the medium relative to the electrode positions. Failure to account for shape changes results in a conductivity image with significant artifacts. Previous work to address shape changes in EIT has shown that in some cases boundary shape and electrode location can be uniquely determined for isotropic conductivities; however, for geometrically conformal changes, this is not possible. This prior work has shown that the shape change problem can be partially addressed. In this paper, we explore the limits of compensation for boundary movement in EIT using three approaches. First, a theoretical model was developed to separate a deformation vector field into conformal and nonconformal components, from which the reconstruction limits may be determined. Next, finite element models were used to simulate EIT measurements from a domain whose boundary has been deformed. Finally, an experimental phantom was constructed from which boundary deformation measurements were acquired. Results, both in simulation and with experimental data, suggest that some electrode movement and boundary distortions can be reconstructed based on conductivity changes alone while reducing image artifacts in the process.

Evaluation of different stimulation and measurement patterns based on internal electrode: application in cardiac impedance tomography

The conductivity distribution around the thorax is altered during the cardiac cycle due to the blood perfusion, heart contraction and lung inflation. Previous studies showed that these bio-impedance changes are appropriate for non-invasive cardiac function imaging using Electrical Impedance Tomography (EIT) techniques. However, the spatial resolution is presently low. One of the main obstacles in cardiac imaging at the heart location is the large impedance variation of the lungs by respiration and muscles on the dorsal and posterior side of the body. In critical care units there is a potential to insert an internal electrode inside the esophagus directly behind the heart in the same plane of the external electrodes. The aim of the present study is to evaluate different current stimulation and measurement patterns with both external and internal electrodes. Analysis is performed with planar arrangement of 16 electrodes for a simulated 3D cylindrical tank and pig thorax model. In our study we evaluated current injection patterns consisting of adjacent, diagonal, trigonometric, and radial to the internal electrode. The performance of these arrangements was assessed using quantitative methods based on distinguishability, sensitivity and GREIT (Graz consensus Reconstruction algorithm for Electrical Impedance Tomography). Our evaluation shows that an internal electrode configuration based on the trigonometric injection patterns has better performance and improves pixel intensity of the small conductivity changes related to heart near 1.7 times in reconstructed images and also shows more stability with different levels of added noise. For the internal electrode, when we combined radial or adjacent injection with trigonometric injection pattern, we found an improvement in amplitude response. However, the combination of diagonal with trigonometric injection pattern deteriorated the shape deformation (correlation coefficient r=0.344) more than combination of radial and trigonometric injection (correlation coefficient r=0.836) for the perturbations in the area close to the center of the cylinder. We also find that trigonometric stimulation pattern performance is degraded in a realistic thorax model with anatomical asymmetry. For that reason we recommend using internal electrodes only for voltage measurements and as a reference electrode during trigonometric stimulation patterns in practical measurements.

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.

Positive end-expiratory pressure-induced changes in end-expiratory lung volume measured by spirometry and electric impedance tomography

BACKGROUND

A bedside tool for monitoring changes in end-expiratory lung volume (ΔEELV) would be helpful to set optimal positive end-expiratory pressure (PEEP) in acute lung injury/acute respiratory distress syndrome patients. The hypothesis of this study was that the cumulative difference of the inspiratory and expiratory tidal volumes of the first 10 breaths after a PEEP change accurately reflects the change in lung volume following a PEEP alteration.

METHODS

Changing PEEP induces lung volume changes, which are reflected in differences between inspiratory and expiratory tidal volumes measured by spirometry. By adding these differences with correction for offset, for the first 10 breaths after PEEP change, cumulative tidal volume difference was calculated to estimate ΔEELV(VT) ((i-e)) . This method was evaluated in a lung model and in patients with acute respiratory failure during a PEEP trial. In patients, ΔEELV(VT) ((i-e)) were compared with simultaneously measured changes in lung impedance, by electric impedance tomography (EIT), using calibration vs. tidal volume to estimate changes in ΔEELV(EIT) .

RESULTS

In the lung model, there was close correlation (R(2)  = 0.99) between ΔEELV(VT) ((i-e)) and known lung model volume difference, with a bias of -4 ml and limits of agreement of 42 and -50 ml. In 12 patients, ΔEELV(EIT) was closely correlated to ΔEELV(VT) ((i-e)) (R(2)  = 0.92), with mean bias of 50 ml and limits of agreement of 131 and -31 ml. Changes in EELV estimated by EIT (ΔEELV(EIT) ) exceeded measurements by spirometry (ΔEELV(VT) ((i-e)) ), with 15 (±15)%.

CONCLUSIONS

We conclude that spirometric measurements of inspiratory-expiratory tidal volumes agree well with impedance changes monitored by EIT and can be used bedside to estimate PEEP-induced changes in EELV.

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.

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.

Compensation of modelling errors due to unknown domain boundary in electrical impedance tomography

Electrical impedance tomography is a highly unstable problem with respect to measurement and modeling errors. This instability is especially severe when absolute imaging is considered. With clinical measurements, accurate knowledge about the body shape is usually not available, and therefore an approximate model domain has to be used in the computational model. It has earlier been shown that large reconstruction artefacts result if the geometry of the model domain is incorrect. In this paper, we adapt the so-called approximation error approach to compensate for the modeling errors caused by inaccurately known body shape. This approach has previously been shown to be applicable to a variety of modeling errors, such as coarse discretization in the numerical approximation of the forward model and domain truncation. We evaluate the approach with a simulated example of thorax imaging, and also with experimental data from a laboratory setting, with absolute imaging considered in both cases. We show that the related modeling errors can be efficiently compensated for by the approximation error approach. We also show that recovery from simultaneous discretization related errors is feasible, allowing the use of computationally efficient reduced order models.

In vivo impedance imaging with total variation regularization

We show that electrical impedance tomography (EIT) image reconstruction algorithms with regularization based on the total variation (TV) functional are suitable for in vivo imaging of physiological data. This reconstruction approach helps to preserve discontinuities in reconstructed profiles, such as step changes in electrical properties at interorgan boundaries, which are typically smoothed by traditional reconstruction algorithms. The use of the TV functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation. This cannot be efficiently solved with traditional optimization techniques such as the Newton method. We explore two implementations methods for regularization with the TV functional: the lagged diffusivity method and the primal dual-interior point method (PD-IPM). First we clarify the implementation details of these algorithms for EIT reconstruction. Next, we analyze the performance of these algorithms on noisy simulated data. Finally, we show reconstructed EIT images of in vivo data for ventilation and gastric emptying studies. In comparison to traditional quadratic regularization, TV regularization shows improved ability to reconstruct sharp contrasts.

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.

Patient-specific finite element modeling of respiratory lung motion using 4D CT image data

Development and optimization of methods for adequately accounting for respiratory motion in radiation therapy of thoracic tumors require detailed knowledge of respiratory dynamics and its impact on corresponding dose distributions. Thus, computer aided modeling and simulation of respiratory motion have become increasingly important. In this article a biophysical approach for modeling respiratory lung motion is described: Major aspects of the process of lung ventilation are formulated as a contact problem of elasticity theory which is solved by finite element methods; lung tissue is assumed to be isotropic, homogeneous, and linearly elastic. A main focus of the article is to assess the impact of biomechanical parameters (values of elastic constants) on the modeling process and to evaluate modeling accuracy. Patient-specific models are generated based on 4D CT data of 12 lung tumor patients. Simulated motion patterns of inner lung landmarks are compared with corresponding motion patterns observed in the 4D CT data. Mean absolute differences between model-based predicted landmark motion and corresponding breathing-induced landmark displacements as observed in the CT data sets are in the order of 3 mm (end expiration to end inspiration) and 2 mm (end expiration to midrespiration). Modeling accuracy decreases with increasing tumor size both locally (landmarks close to tumor) and globally (landmarks in other parts of the lung). The impact of the values of the elastic constants appears to be small. Outcomes show that the modeling approach is an adequate strategy in predicting lung dynamics due to lung ventilation. Nevertheless, the decreased prediction quality in cases of large tumors demands further study of the influence of lung tumors on global and local lung elasticity properties.

Electrical impedance tomography problem with inaccurately known boundary and contact impedances

In electrical impedance tomography (EIT) electric currents are injected into a body with unknown electromagnetic properties through a set of contact electrodes at the boundary of the body. The resulting voltages are measured on the same electrodes and the objective is to reconstruct the unknown conductivity function inside the body based on these data. All the traditional approaches to the reconstruction problem assume that the boundary of the body and the electrode-skin contact impedances are known a priori. However, in clinical experiments one usually lacks the exact knowledge of the boundary and contact impedances, and therefore, approximate model domain and contact impedances have to be used in the image reconstruction. However, it has been noticed that even small errors in the shape of the computation domain or contact impedances can cause large systematic artefacts in the reconstructed images, leading to loss of diagnostically relevant information. In a recent paper (Kolehmainen , 2006), we showed how in the 2-D case the errors induced by the inaccurately known boundary can be eliminated as part of the image reconstruction and introduced a novel method for finding a deformed image of the original isotropic conductivity using the theory of TeichmUller mappings. In this paper, the theory and reconstruction method are extended to include the estimation of unknown contact impedances. The method is implemented numerically and tested with experimental EIT data. The results show that the systematic errors caused by inaccurately known boundary and contact impedances can efficiently be eliminated by the reconstruction method.

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.

Arbitrary geometry patient interfaces for breast cancer detection and monitoring with electrical impedance tomography

Electrical impedance tomography (EIT) is a promising technology enabling the detection or observation of many biological processes. This is typically accomplished by applying currents at known locations on an outer surface (in this case skin) and measuring voltages at other locations. This information is then used to determine electrical properties of tissue found between the electrodes by solving the associated Laplace equation. Such problems depend upon knowing the exact boundary conditions (BC). Unfortunately BCs are not always easily determined and approximations are accepted out of necessity due to problem complexity or time constraints. The EIT group at Dartmouth College has developed two new patient interfaces for breast cancer detection and monitoring both of which speed acquisition time and allow for precision BC information in natural and arbitrary geometries. Preliminary experimental results are presented.

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.