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.

Electrical impedance tomography in extremely prematurely born infants and during high frequency oscillatory ventilation analyzed in the frequency domain

Functional electrical impedance tomography (EIT) measures relative impedance change that occurs in the chest during a distinct observation period and an EIT image describing regional relative impedance change is generated. Analysis of such an EIT image may be erroneous because it is based on an impedance signal that has several components. Most of the change in relative impedance in the chest is caused by air movement but other physiological events such as cardiac activity change in end expiratory level or pressure swings originating from a ventilator circuit can influence the impedance signal. We obtained EIT images and signals in spontaneously breathing healthy adults, in extremely prematurely born infants on continuous positive airway pressure and in ventilated sheep on conventional mechanical or high frequency oscillatory ventilation (HFOV). Data were analyzed in the frequency domain and results presented after band pass filtering within the frequency range of the physiological event of interest. Band pass filtering of EIT data is necessary in premature infants and on HFOV to differentiate and eliminate relative impedance changes caused by physiological events other than the one of interest.

Electrical Impedance Tomography: strategie algoritmiche per il problema inverso

La tomografia ad impedenza elettrica è un metodo di imaging relativamente nuovo che ha suscitato interesse in un ampia gamma di discipline, la sua portabilità, sicurezza e basso costo suggeriscono che potrebbe risolvere diversi problemi clinici. Matematicamente il problema dell'EIT può essere suddiviso in un problema in avanti e uno inverso. Il problema forward, si basa su un'equazione differenziale parziale ellittica, e definisce l'insieme delle tensioni misurate a partire da una distribuzione nota di conducibilità. Il problema inverso è modellato come un problema dei minimi quadrati non lineare, in cui si cerca di ridurre al minimo la differenza tra le tensioni misurate e quelle generate dalla conducibilità ricostruita. Il problema inverso è mal posto e porta ad una soluzione che non dipende con continuità dai dati e quindi le tecniche di ricostruzione richiedono l'introduzione di un termine di regolarizzazione. L'elaborato si concentra sulle strategie algoritmiche per il problema inverso e sulla realizzazione di un'interfaccia grafica in grado di settare i parametri e confrontare velocemente i metodi proposti. Il progetto nella sua visione più ampia vorrebbe utilizzare le strategie algoritmiche proposte per dati ottenuti dal sistema prodotto dall'Università di Bologna nel laboratorio di Ingegneria Cellulare e Molecolare (ICM) di Cesena. I risultati dei test consentono di delineare quali siano gli strumenti migliori per poter arrivare ad una corretta ricostruzione dell'immagine nonché suggerire possibili miglioramenti della configurazione hardware al fine arrivare a risultati sperimentali completi.

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.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Electrical impedance particle size method (Coulter Counter) detects the large fat globules in poorly homogenised UHT processed milk

The large fat globules that can be present in UHT milk due to inadequate homogenisation cause a cream layer to form that limits the shelf life of UHT milk. Four different particle size measurement techniques were used to measure the size of fat globules in poorly homogenised UHT milk processed in a UHT pilot plant. The thickness of the cream layer that formed during storage was negatively correlated with homogenisation pressure. It was positively correlated with the mass mean diameter and the percentage volume of particles between 1.5 and 2 mu m diameter, as determined by laser light scattering using the Malvern Mastersizer. Also, the thickness of the cream layer was positively correlated with the volume mode diameter and the percentage volume of particles between 1.5 and 2 mu m diameter, as determined by electrical impedance using the Coulter Counter. The cream layer thickness did not correlate significantly with the Coulter Counter measurements of volume mean diameter, or volume percentages of particles between 2 and 5 mu m or 5 and 10 mu m diameter. Spectroturbidimetry (Emulsion Quality Analyser) and light microscopy analyses were found to be unsuitable for assessing the size of the fat particles. This study suggests that the fat globule size distribution as determined by the electrical impedance method (Coulter Counter) is the most useful for determining the efficiency of homogenisation and therefore for predicting the stability of the fat emulsion in UHT milk during storage.

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.

Die Faktorisierungsmethode für die elektrische Impedanztomographie im Halbraum

In der vorliegenden Arbeit wird die Faktorisierungsmethode zur Erkennung von Inhomogenitäten der Leitfähigkeit in der elektrischen Impedanztomographie auf unbeschränkten Gebieten - speziell der Halbebene bzw. dem Halbraum - untersucht. Als Lösungsräume für das direkte Problem, d.h. die Bestimmung des elektrischen Potentials zu vorgegebener Leitfähigkeit und zu vorgegebenem Randstrom, führen wir gewichtete Sobolev-Räume ein. In diesen wird die Existenz von schwachen Lösungen des direkten Problems gezeigt und die Gültigkeit einer Integraldarstellung für die Lösung der Laplace-Gleichung, die man bei homogener Leitfähigkeit erhält, bewiesen. Mittels der Faktorisierungsmethode geben wir eine explizite Charakterisierung von Einschlüssen an, die gegenüber dem Hintergrund eine sprunghaft erhöhte oder erniedrigte Leitfähigkeit haben. Damit ist zugleich für diese Klasse von Leitfähigkeiten die eindeutige Rekonstruierbarkeit der Einschlüsse bei Kenntnis der lokalen Neumann-Dirichlet-Abbildung gezeigt. Die mittels der Faktorisierungsmethode erhaltene Charakterisierung der Einschlüsse haben wir in ein numerisches Verfahren umgesetzt und sowohl im zwei- als auch im dreidimensionalen Fall mit simulierten, teilweise gestörten Daten getestet. Im Gegensatz zu anderen bekannten Rekonstruktionsverfahren benötigt das hier vorgestellte keine Vorabinformation über Anzahl und Form der Einschlüsse und hat als nicht-iteratives Verfahren einen vergleichsweise geringen Rechenaufwand.

Extraction of electrical characteristics from pixels of multifrequency EIT images

Computer modelling has shown that electrical characteristics of individual pixels may be extracted from within multiple-frequency electrical impedance tomography (MFEIT) images formed using a reference data set obtained from a purely resistive, homogeneous medium. In some applications it is desirable to extract the electrical characteristics of individual pixels from images where a purely resistive, homogeneous reference data set is not available. One such application of the technique of MFEIT is to allow the acquisition of in vivo images using reference data sets obtained from a non-homogeneous medium with a reactive component. However, the reactive component of the reference data set introduces difficulties with the extraction of the true electrical characteristics from the image pixels. This study was a preliminary investigation of a technique to extract electrical parameters from multifrequency images when the reference data set has a reactive component. Unlike the situation in which a homogenous, resistive data set is available, it is not possible to obtain the impedance and phase information directly from the image pixel values of the MFEIT images data set, as the phase of the reactive reference is not known. The method reported here to extract the electrical characteristics (the Cole-Cole plot) initially assumes that this phase angle is zero. With this assumption, an impedance spectrum can be directly extracted from the image set. To obtain the true Cole-Cole plot a correction must be applied to account for the inherent rotation of the extracted impedance spectrum about the origin, which is a result of the assumption. This work shows that the angle of rotation associated with the reactive component of the reference data set may be determined using a priori knowledge of the distribution of frequencies of the Cole-Cole plot. Using this angle of rotation, the true Cole-Cole plot can be obtained from the impedance spectrum extracted from the MFEIT image data set. The method was investigated using simulated data, both with and without noise, and also for image data obtained in vitro. The in vitro studies involved 32 logarithmically spaced frequencies from 4 kHz up to 1 MHz and demonstrated that differences between the true characteristics and those of the impedance spectrum were reduced significantly after application of the correction technique. The differences between the extracted parameters and the true values prior to correction were in the range from 16% to 70%. Following application of the correction technique the differences were reduced to less than 5%. The parameters obtained from the Cole-Cole plot may be useful as a characterization of the nature and health of the imaged tissues.

Bio-electrical impedance analysis for estimation of fat-free mass and muscle mass in cystic fibrosis patients.

The nutritional status of cystic fibrosis (CF) patients has to be regularly evaluated and alimentary support instituted when indicated. Bio-electrical impedance analysis (BIA) is a recent method for determining body composition. The present study evaluates its use in CF patients without any clinical sign of malnutrition. Thirty-nine patients with CF and 39 healthy subjects aged 6-24 years were studied. Body density and mid-arm muscle circumference were determined by anthropometry and skinfold measurements. Fat-free mass was calculated taking into account the body density. Muscle mass was obtained from the urinary creatinine excretion rate. The resistance index was calculated by dividing the square of the subject's height by the body impedance. We show that fat-free mass, mid-arm muscle circumference and muscle mass are each linearly correlated to the resistance index and that the regression equations are similar for both CF patients and healthy subjects.

Measurement of the tree root growth using electrical impedance spectroscopy

Abstract

Probabilistic electrical resistivity tomography of a CO2 sequestration analog

Electrical resistivity tomography (ERT) is a well-established method for geophysical characterization and has shown potential for monitoring geologic CO2 sequestration, due to its sensitivity to electrical resistivity contrasts generated by liquid/gas saturation variability. In contrast to deterministic inversion approaches, probabilistic inversion provides the full posterior probability density function of the saturation field and accounts for the uncertainties inherent in the petrophysical parameters relating the resistivity to saturation. In this study, the data are from benchtop ERT experiments conducted during gas injection into a quasi-2D brine-saturated sand chamber with a packing that mimics a simple anticlinal geological reservoir. The saturation fields are estimated by Markov chain Monte Carlo inversion of the measured data and compared to independent saturation measurements from light transmission through the chamber. Different model parameterizations are evaluated in terms of the recovered saturation and petrophysical parameter values. The saturation field is parameterized (1) in Cartesian coordinates, (2) by means of its discrete cosine transform coefficients, and (3) by fixed saturation values in structural elements whose shape and location is assumed known or represented by an arbitrary Gaussian Bell structure. Results show that the estimated saturation fields are in overall agreement with saturations measured by light transmission, but differ strongly in terms of parameter estimates, parameter uncertainties and computational intensity. Discretization in the frequency domain (as in the discrete cosine transform parameterization) provides more accurate models at a lower computational cost compared to spatially discretized (Cartesian) models. A priori knowledge about the expected geologic structures allows for non-discretized model descriptions with markedly reduced degrees of freedom. Constraining the solutions to the known injected gas volume improved estimates of saturation and parameter values of the petrophysical relationship. (C) 2014 Elsevier B.V. All rights reserved.

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.