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.

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.

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.

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.

Real-time detection of pneumothorax using electrical impedance tomogyaphy

Objectives: Pneumothorax is a frequent complication during mechanical ventilation. Electrical impedance tomography (EIT) is a noninvasive tool that allows real-time imaging of regional ventilation. The purpose of this study was to 1) identify characteristic changes in the EIT signals associated with pneumothoraces; 2) develop and fine-tune an algorithm for their automatic detection; and 3) prospectively evaluate this algorithm for its sensitivity and specificity in detecting pneumothoraces in real time. Design: Prospective controlled laboratory animal investigation. Setting: Experimental Pulmonology Laboratory of the University of Sao Paulo. Subjects: Thirty-nine anesthetized mechanically ventilated supine pigs (31.0 +/- 3.2 kg, mean +/- SD). Interventions. In a first group of 18 animals monitored by EIT, we either injected progressive amounts of air (from 20 to 500 mL) through chest tubes or applied large positive end-expiratory pressure (PEEP) increments to simulate extreme lung overdistension. This first data set was used to calibrate an EIT-based pneumothorax detection algorithm. Subsequently, we evaluated the real-time performance of the detection algorithm in 21 additional animals (with normal or preinjured lungs), submitted to multiple ventilatory interventions or traumatic punctures of the lung. Measurements and Main Results: Primary EIT relative images were acquired online (50 images/sec) and processed according to a few imaging-analysis routines running automatically and in parallel. Pneumothoraces as small as 20 mL could be detected with a sensitivity of 100% and specificity 95% and could be easily distinguished from parenchymal overdistension induced by PEEP or recruiting maneuvers, Their location was correctly identified in all cases, with a total delay of only three respiratory cycles. Conclusions. We created an EIT-based algorithm capable of detecting early signs of pneumothoraces in high-risk situations, which also identifies its location. It requires that the pneumothorax occurs or enlarges at least minimally during the monitoring period. Such detection was operator-free and in quasi real-time, opening opportunities for improving patient safety during mechanical ventilation.

QUADRANT-SEARCHING: A NEW TECHNIQUE TO REDUCE THE SEARCH SPACE OF THE INVERSE PROBLEM OF EIT USING BEM TO THE DIRECT PROBLEM

The image reconstruction using the EIT (Electrical Impedance Tomography) technique is a nonlinear and ill-posed inverse problem which demands a powerful direct or iterative method. A typical approach for solving the problem is to minimize an error functional using an iterative method. In this case, an initial solution close enough to the global minimum is mandatory to ensure the convergence to the correct minimum in an appropriate time interval. The aim of this paper is to present a new, simple and low cost technique (quadrant-searching) to reduce the search space and consequently to obtain an initial solution of the inverse problem of EIT. This technique calculates the error functional for four different contrast distributions placing a large prospective inclusion in the four quadrants of the domain. Comparing the four values of the error functional it is possible to get conclusions about the internal electric contrast. For this purpose, initially we performed tests to assess the accuracy of the BEM (Boundary Element Method) when applied to the direct problem of the EIT and to verify the behavior of error functional surface in the search space. Finally, numerical tests have been performed to verify the new technique.

On the concept of electrical impedance for an electrolytic cell

The analysis of the electrical impedance of an electrolytic cell in the shape of a slab is performed. We have solved, numerically, the differential equations governing the phenomenon of the redistribution of the ions in the presence of an external electric field, and compared the results with the ones obtained by solving the linear approximation of these equations. The control parameters in our study are the amplitude and the frequency of the applied voltage, assumed a simple harmonic function of the time. We show that for the large amplitudes of the applied voltage, the actual current is no longer harmonic at low frequencies. From this result it follows that the concept of electrical impedance of a cell is a useful quantity only in the case where the linear approximation of the fundamental equations of problem work well.

Can heterogeneity in ventilation be good?

Selection of the optimal positive end-expiratory pressure (PEEP) to avoid ventilator-induced lung injury in patients under mechanical ventilation is still a matter of debate. Many methods are available, but none is considered the gold standard. In the previous issue of Critical Care, Zhao and colleagues applied a method based on electrical impedance tomography to help select the PEEP that minimized ventilation inhomogeneities. Though promising when alveolar collapse and overdistension are present, this method might be misleading in patients with normal lungs.

Persistence of ventilatory defect after resolution of pulmonary interstitial emphysema in a preterm baby

Pulmonary interstitial emphysema is a common complication of mechanical ventilation in preterm babies. We report a case of severe unilateral pulmonary interstitial emphysema in a premature newborn, treated with high-frequency oscillatory ventilation, lateral decubitus positioning and selective intubation. After complete radiological resolution of the pulmonary emphysema in the left lung, the patient was studied by electrical impedance tomography and a marked reduction of ventilation was identified in the left lung despite radiological resolution of the cysts. This finding indicates that functional abnormalities may persist for longer periods after radiologic resolution of such lesions.

Pulmonary lesion induced by low and high positive end-expiratory pressure levels during protective ventilation in experimental acute lung injury

Objective: To investigate the effects of low and high levels of positive end-expiratory pressure (PEEP), without recruitment maneuvers, during lung protective ventilation in an experimental model of acute lung injury (ALI). Design: Prospective, randomized, and controlled experimental study. Setting: University research laboratory. Subjects: Wistar rats were randomly assigned to control (C) [saline (0.1 ml), intraperitoneally] and ALI [paraquat (15 mg/kg), intra peritoneally] groups. Measurements and Main Results: After 24 hours, each group was further randomized into four groups (six rats each) at different PEEP levels = 1.5, 3, 4.5, or 6 cm H(2)O and ventilated with a constant tidal volume (6 mL/kg) and open thorax. Lung mechanics [static elastance (Est, L) and viscoelastic pressure (Delta P2, L)] and arterial blood gases were measured before (Pre) and at the end of 1-hour mechanical ventilation (Post). Pulmonary histology (light and electron microscopy) and type III procollagen (PCIII) messenger RNA (mRNA) expression were measured after 1 hour of mechanical ventilation. In ALI group, low and high PEEP levels induced a greater percentage of increase in Est, L (44% and 50%) and Delta P2, L (56% and 36%) in Post values related to Pre. Low PEEP yielded alveolar collapse whereas high PEEP caused overdistension and atelectasis, with both levels worsening oxygenation and increasing PCIII mRNA expression. Conclusions: In the present nonrecruited ALI model, protective mechanical ventilation with lower and higher PEEP levels than required for better oxygenation increased Est, L and Delta P2, L, the amount of atelectasis, and PCIII mRNA expression. PEEP selection titrated for a minimum elastance and maximum oxygenation may prevent lung injury while deviation from these settings may be harmful. (Crit Care Med 2009; 37:1011-1017)

Detecção de contaminação de solo por vinhaça através de análise de dados de eletrorresistividade

The vinasse, awaste produced in the proportion of 13 liters for each liter of alcohol. It has a high potential of polluting groundwater and superficial water resources, changes the soil behaviour and can also develop sanilization problems. This work aims to evaluate the efficiency of the DC-resistivity method in detecting and mapping anomalies caused by inappropriate disposal of vinasse in an inactive infiltration tank located at Sepé-Tiarajú settlement of landless agricultural laborers in the Ribeirão Preto region. Besides, as secondary goals, this work aims to characterize the type of anomaly residue as well as to diagnose its influence inside and outside of the limits of the tank. Eleven electrical resistivity tomography profiles were carried out with the dipole-dipole array, 10m of dipoles length and 5 leveis of investigation The geophysical survey enabled us to conclude that the DC-resistivity method is appropriate for mapping the contamination plume caused by intense vinasse disposal and its influence. It enabled also to conclude that the contamination exceeds the tank limits. The vinasse influence can be characterized by low resistivity values between 10 Ohm.m and 90 Ohm.m and its behavior can be compared with the one of the chorume, which is also conductive.

Theory of small-signal ac response of a dielectric liquid containing two groups of ions

The analysis of Macdonald for electrolytes is generalized to the case in which two groups of ions are present. We assume that the electrolyte can be considered as a dispersion of ions in a dielectric liquid, and that the ionic recombination can be neglected. We present the differential equations governing the ionic redistribution when the liquid is subjected to an external electric field, describing the simultaneous diffusion of the two groups of ions in the presence of their own space charge fields. We investigate the influence of the ions on the impedance spectroscopy of an electrolytic cell. In the analysis, we assume that each group of ions have equal mobility, the electrodes perfectly block and that the adsorption phenomena can be neglected. In this framework, it is shown that the real part of the electrical impedance of the cell has a frequency dependence presenting two plateaux, related to a type of ambipolar and free diffusion coefficients. The importance of the considered problem on the ionic characterization performed by means of the impedance spectroscopy technique was discussed. (c) 2008 American Institute of Physics.

Power imbalance application region method for distributed synchronous generator anti-islanding protection design and evaluation

This paper presents a novel graphical approach to adjust and evaluate frequency-based relays employed in anti-islanding protection schemes of distributed synchronous generators, in order to meet the anti-islanding and abnormal frequency variation requirements, simultaneously. The proposed method defines a region in the power mismatch space, inside which the relay non-detection zone should be located, if the above-mentioned requirements must be met. Such region is called power imbalance application region. Results show that this method can help protection engineers to adjust frequency-based relays to improve the anti-islanding capability and to minimize false operation occurrences, keeping the abnormal frequency variation utility requirements satisfied. Moreover, the proposed method can be employed to coordinate different types of frequency-based relays, aiming at improving overall performance of the distributed generator frequency protection scheme. (C) 2011 Elsevier B.V. All rights reserved.

Power Factor Calculation by the Finite Element Method

The use of finite element analysis (FEA) to design electrical motors has increased significantly in the past few years due the increasingly better performance of modern computers. Even though the analytical software remains the most used tool, the FEA is widely used to refine the analysis and gives the final design to be prototyped. The power factor, a standard data of motor manufactures data sheet is important because it shows how much reactive power is consumed by the motor. This data becomes important when the motor is connected to network. However, the calculation of power factor is not an easy task. Due to the saturation phenomena the input motor current has a high level of harmonics that cannot be neglected. In this work the FEA is used to evaluate a proposed (not limitative) methodology to estimate the power factor or displacement factor of a small single-phase induction motor. Results of simulations and test are compared.

Analysis of a Three-Phase LSPMM by Numerical Method

Line-start permanent magnet motor (LSPMM) is a very attractive alternative to replace induction motors due to its very high efficiency and constant speed operation with load variations. However, designing this kind of hybrid motor is hard work and requires a good understanding of motor behavior. The calculation of load angle is an important step in motor design and can not be neglected. This paper uses the finite element method to show a simple methodology to calculate the load angle of a three-phase LSPMM combining the dynamic and steady-state simulations. The methodology is used to analyze a three-phase LSPMM.