Dynamic Imaging in Electrical Impedance Tomography of the Human Chest With Online Transition Matrix Identification

One of the electrical impedance tomography objectives is to estimate the electrical resistivity distribution in a domain based only on electrical potential measurements at its boundary generated by an imposed electrical current distribution into the boundary. One of the methods used in dynamic estimation is the Kalman filter. In biomedical applications, the random walk model is frequently used as evolution model and, under this conditions, poor tracking ability of the extended Kalman filter (EKF) is achieved. An analytically developed evolution model is not feasible at this moment. The paper investigates the identification of the evolution model in parallel to the EKF and updating the evolution model with certain periodicity. The evolution model transition matrix is identified using the history of the estimated resistivity distribution obtained by a sensitivity matrix based algorithm and a Newton-Raphson algorithm. To numerically identify the linear evolution model, the Ibrahim time-domain method is used. The investigation is performed by numerical simulations of a domain with time-varying resistivity and by experimental data collected from the boundary of a human chest during normal breathing. The obtained dynamic resistivity values lie within the expected values for the tissues of a human chest. The EKF results suggest that the tracking ability is significantly improved with this approach.

Recycling Krylov subspaces for efficient large-scale electrical impedance tomography

Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the resulting electric potentials are measured. Then, based on the measurements, an estimation algorithm obtains the three-dimensional internal admittivity distribution that corresponds to the image. One of the main goals of medical EIT is to achieve high resolution and an accurate result at low computational cost. However, when the finite element method (FEM) is employed and the corresponding mesh is refined to increase resolution and accuracy, the computational cost increases substantially, especially in the estimation of absolute admittivity distributions. Therefore, we consider in this work a fast iterative solver for the forward problem, which was previously reported in the context of structural optimization. We propose several improvements to this solver to increase its performance in the EIT context. The solver is based on the recycling of approximate invariant subspaces, and it is applied to reduce the EIT computation time for a constant and high resolution finite element mesh. In addition, we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver. The numerical results show the effectiveness of our approach: the proposed algorithm is faster than the preconditioned conjugate gradient (CG) algorithm. The results also show that even on a standard PC without parallelization, a high mesh resolution (more than 150,000 degrees of freedom) can be used for image estimation at a relatively low computational cost. (C) 2010 Elsevier B.V. All rights reserved.

Bedside estimation of recruitable alveolar collapse and hyperdistension by electrical impedance tomography

To present a novel algorithm for estimating recruitable alveolar collapse and hyperdistension based on electrical impedance tomography (EIT) during a decremental positive end-expiratory pressure (PEEP) titration. Technical note with illustrative case reports. Respiratory intensive care unit. Patients with acute respiratory distress syndrome. Lung recruitment and PEEP titration maneuver. Simultaneous acquisition of EIT and X-ray computerized tomography (CT) data. We found good agreement (in terms of amount and spatial location) between the collapse estimated by EIT and CT for all levels of PEEP. The optimal PEEP values detected by EIT for patients 1 and 2 (keeping lung collapse < 10%) were 19 and 17 cmH(2)O, respectively. Although pointing to the same non-dependent lung regions, EIT estimates of hyperdistension represent the functional deterioration of lung units, instead of their anatomical changes, and could not be compared directly with static CT estimates for hyperinflation. We described an EIT-based method for estimating recruitable alveolar collapse at the bedside, pointing out its regional distribution. Additionally, we proposed a measure of lung hyperdistension based on regional lung mechanics.

Three-dimensional electrical impedance, tomography: A topology optimization approach

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

An Analytic Simplification for the Reconstruction Problem of Electrical Impedance Tomography

This paper introduces a new reconstruction algorithm for electrical impedance tomography. The algorithm assumes that there are two separate regions of conductivity. These regions are represented as eccentric circles. This new algorithm then solves for the location of the eccentric circles. Due to the simple geometry of the forward problem, an analytic technique using conformal mapping and separation of variables has been employed. (C) 2002 John Wiley Sons, Inc.

Use of anisotropic modelling in electrical impedance tomography: description of method and preliminary assessment of utility in imaging brain function in the adult human head.

Electrical Impedance Tomography (EIT) is an imaging method which enables a volume conductivity map of a subject to be produced from multiple impedance measurements. It has the potential to become a portable non-invasive imaging technique of particular use in imaging brain function. Accurate numerical forward models may be used to improve image reconstruction but, until now, have employed an assumption of isotropic tissue conductivity. This may be expected to introduce inaccuracy, as body tissues, especially those such as white matter and the skull in head imaging, are highly anisotropic. The purpose of this study was, for the first time, to develop a method for incorporating anisotropy in a forward numerical model for EIT of the head and assess the resulting improvement in image quality in the case of linear reconstruction of one example of the human head. A realistic Finite Element Model (FEM) of an adult human head with segments for the scalp, skull, CSF, and brain was produced from a structural MRI. Anisotropy of the brain was estimated from a diffusion tensor-MRI of the same subject and anisotropy of the skull was approximated from the structural information. A method for incorporation of anisotropy in the forward model and its use in image reconstruction was produced. The improvement in reconstructed image quality was assessed in computer simulation by producing forward data, and then linear reconstruction using a sensitivity matrix approach. The mean boundary data difference between anisotropic and isotropic forward models for a reference conductivity was 50%. Use of the correct anisotropic FEM in image reconstruction, as opposed to an isotropic one, corrected an error of 24 mm in imaging a 10% conductivity decrease located in the hippocampus, improved localisation for conductivity changes deep in the brain and due to epilepsy by 4-17 mm, and, overall, led to a substantial improvement on image quality. This suggests that incorporation of anisotropy in numerical models used for image reconstruction is likely to improve EIT image quality.

Influence of heart motion on cardiac output estimation by means of electrical impedance tomography: a case study.

Electrical impedance tomography (EIT) is a non-invasive imaging technique that can measure cardiac-related intra-thoracic impedance changes. EIT-based cardiac output estimation relies on the assumption that the amplitude of the impedance change in the ventricular region is representative of stroke volume (SV). However, other factors such as heart motion can significantly affect this ventricular impedance change. In the present case study, a magnetic resonance imaging-based dynamic bio-impedance model fitting the morphology of a single male subject was built. Simulations were performed to evaluate the contribution of heart motion and its influence on EIT-based SV estimation. Myocardial deformation was found to be the main contributor to the ventricular impedance change (56%). However, motion-induced impedance changes showed a strong correlation (r = 0.978) with left ventricular volume. We explained this by the quasi-incompressibility of blood and myocardium. As a result, EIT achieved excellent accuracy in estimating a wide range of simulated SV values (error distribution of 0.57 ± 2.19 ml (1.02 ± 2.62%) and correlation of r = 0.996 after a two-point calibration was applied to convert impedance values to millilitres). As the model was based on one single subject, the strong correlation found between motion-induced changes and ventricular volume remains to be verified in larger datasets.

FINITE ELEMENT SIMULATIONS FOR THE COMPREHENSION OF PHYSICAL PHENOMENA INVOLVED IN ELECTRIC IMPEDANCE TOMOGRAPHY OF MASONRY STRUCTURES

The paper describes the preliminary studies of University of Minho on the use of Electric Impedance/Resistance Tomography to assess masonry structures. The study is focused on the analysis of values of current and voltage resulting from the use of an electrical source with voltage and frequency values from a distribution network. The analysis is made from results obtained through computer simulations, using a three-dimensional model of the idealized masonry structures. A finite element program was used for the simulations. Three types of electrodes were used in simulations, and the analysis of the results led to significant conclusions. Later masonry specimens were built and a series of preliminary tests were carried out in the laboratory. The comparative analysis of simulated and experimental results allowed identifying the factors that have influence on the physical results.

Image Reconstruction Using Interval Simulated Annealing in Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an imaging technique that attempts to reconstruct the impedance distribution inside an object from the impedance between electrodes placed on the object surface. The EIT reconstruction problem can be approached as a nonlinear nonconvex optimization problem in which one tries to maximize the matching between a simulated impedance problem and the observed data. This nonlinear optimization problem is often ill-posed, and not very suited to methods that evaluate derivatives of the objective function. It may be approached by simulated annealing (SA), but at a large computational cost due to the expensive evaluation process of the objective function, which involves a full simulation of the impedance problem at each iteration. A variation of SA is proposed in which the objective function is evaluated only partially, while ensuring boundaries on the behavior of the modified algorithm.

Regional lung perfusion estimated by electrical impedance tomography in a piglet model of lung collapse

Borges JB, Suarez-Sipmann F, Bohm SH, Tusman G, Melo A, Maripuu E, Sandstrom M, Park M, Costa EL, Hedenstierna G, Amato M. Regional lung perfusion estimated by electrical impedance tomography in a piglet model of lung collapse. J Appl Physiol 112: 225-236, 2012. First published September 29, 2011; doi: 10.1152/japplphysiol.01090.2010.-The assessment of the regional match between alveolar ventilation and perfusion in critically ill patients requires simultaneous measurements of both parameters. Ideally, assessment of lung perfusion should be performed in real-time with an imaging technology that provides, through fast acquisition of sequential images, information about the regional dynamics or regional kinetics of an appropriate tracer. We present a novel electrical impedance tomography (EIT)-based method that quantitatively estimates regional lung perfusion based on first-pass kinetics of a bolus of hypertonic saline contrast. Pulmonary blood flow was measured in six piglets during control and unilateral or bilateral lung collapse conditions. The first-pass kinetics method showed good agreement with the estimates obtained by single-photon-emission computerized tomography (SPECT). The mean difference (SPECT minus EIT) between fractional blood flow to lung areas suffering atelectasis was -0.6%, with a SD of 2.9%. This method outperformed the estimates of lung perfusion based on impedance pulsatility. In conclusion, we describe a novel method based on EIT for estimating regional lung perfusion at the bedside. In both healthy and injured lung conditions, the distribution of pulmonary blood flow as assessed by EIT agreed well with the one obtained by SPECT. The method proposed in this study has the potential to contribute to a better understanding of the behavior of regional perfusion under different lung and therapeutic conditions.

Localized potentials in electrical impedance tomography

In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a domain and low energy on another. We show that such potentials exist for general L-infinity-conductivities (with positive infima) in almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result for the famous Calderon problem with partial data. We also show how to construct such potentials numerically and use a connection with the factorization method to derive a new non-iterative algorithm for the detection of inclusions in electrical impedance tomography.

Factorization method and irregular inclusions in electrical impedance tomography

In electrical impedance tomography, one tries to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many practically important situations, the investigated object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. Earlier, it has been shown that under suitable regularity conditions positive (or negative) inhomogeneities can be characterized by the factorization technique if the conductivity or one of its higher normal derivatives jumps on the boundaries of the inclusions. In this work, we use a monotonicity argument to generalize these results: We show that the factorization method provides a characterization of an open inclusion (modulo its boundary) if each point inside the inhomogeneity has an open neighbourhood where the perturbation of the conductivity is strictly positive (or negative) definite. In particular, we do not assume any regularity of the inclusion boundary or set any conditions on the behaviour of the perturbed conductivity at the inclusion boundary. Our theoretical findings are verified by two-dimensional numerical experiments.

Measurement of ventilation and cardiac related impedance changes with electrical impedance tomography

Introduction Electrical impedance tomography (EIT) has been shown to be able to distinguish both ventilation and perfusion. With adequate filtering the regional distributions of both ventilation and perfusion and their relationships could be analysed. Several methods of separation have been suggested previously, including breath holding, electrocardiograph (ECG) gating and frequency filtering. Many of these methods require interventions inappropriate in a clinical setting. This study therefore aims to extend a previously reported frequency filtering technique to a spontaneously breathing cohort and assess the regional distributions of ventilation and perfusion and their relationship. Methods Ten healthy adults were measured during a breath hold and while spontaneously breathing in supine, prone, left and right lateral positions. EIT data were analysed with and without filtering at the respiratory and heart rate. Profiles of ventilation, perfusion and ventilation/perfusion related impedance change were generated and regions of ventilation and pulmonary perfusion were identified and compared. Results Analysis of the filtration technique demonstrated its ability to separate the ventilation and cardiac related impedance signals without negative impact. It was, therefore, deemed suitable for use in this spontaneously breathing cohort. Regional distributions of ventilation, perfusion and the combined ΔZV/ΔZQ were calculated along the gravity axis and anatomically in each position. Along the gravity axis, gravity dependence was seen only in the lateral positions in ventilation distribution, with the dependent lung being better ventilated regardless of position. This gravity dependence was not seen in perfusion. When looking anatomically, differences were only apparent in the lateral positions. The lateral position ventilation distributions showed a difference in the left lung, with the right lung maintaining a similar distribution in both lateral positions. This is likely caused by more pronounced anatomical changes in the left lung when changing positions. Conclusions The modified filtration technique was demonstrated to be effective in separating the ventilation and perfusion signals in spontaneously breathing subjects. Gravity dependence was seen only in ventilation distribution in the left lung in lateral positions, suggesting gravity based shifts in anatomical structures. Gravity dependence was not seen in any perfusion distributions.

Determination of respiratory gas flow by electrical impedance tomography in an animal model of mechanical ventilation

Background A recent method determines regional gas flow of the lung by electrical impedance tomography (EIT). The aim of this study is to show the applicability of this method in a porcine model of mechanical ventilation in healthy and diseased lungs. Our primary hypothesis is that global gas flow measured by EIT can be correlated with spirometry. Our secondary hypothesis is that regional analysis of respiratory gas flow delivers physiologically meaningful results. Methods In two sets of experiments n = 7 healthy pigs and n = 6 pigs before and after induction of lavage lung injury were investigated. EIT of the lung and spirometry were registered synchronously during ongoing mechanical ventilation. In-vivo aeration of the lung was analysed in four regions-of-interest (ROI) by EIT: 1) global, 2) ventral (non-dependent), 3) middle and 4) dorsal (dependent) ROI. Respiratory gas flow was calculated by the first derivative of the regional aeration curve. Four phases of the respiratory cycle were discriminated. They delivered peak and late inspiratory and expiratory gas flow (PIF, LIF, PEF, LEF) characterizing early or late inspiration or expiration. Results Linear regression analysis of EIT and spirometry in healthy pigs revealed a very good correlation measuring peak flow and a good correlation detecting late flow. PIFEIT = 0.702 · PIFspiro + 117.4, r2 = 0.809; PEFEIT = 0.690 · PEFspiro-124.2, r2 = 0.760; LIFEIT = 0.909 · LIFspiro + 27.32, r2 = 0.572 and LEFEIT = 0.858 · LEFspiro-10.94, r2 = 0.647. EIT derived absolute gas flow was generally smaller than data from spirometry. Regional gas flow was distributed heterogeneously during different phases of the respiratory cycle. But, the regional distribution of gas flow stayed stable during different ventilator settings. Moderate lung injury changed the regional pattern of gas flow. Conclusions We conclude that the presented method is able to determine global respiratory gas flow of the lung in different phases of the respiratory cycle. Additionally, it delivers meaningful insight into regional pulmonary characteristics, i.e. the regional ability of the lung to take up and to release air.