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Electrical Impedance Tomography Image Reconstruction Using Iterative Lavrentiev and L Curve Based Regularization Algorithm

Electrical Impedance Tomography Image Reconstruction Using Iterative Lavrentiev and L Curve Based Regularization Algorithm

EIT is a technique used to create images of the electrical properties in the interior of a medium from measurements on its boundary, which is particularly important for medical and industrial applications [26,27]. Usually a set of voltage or current measurements is acquired from the boundaries of a conductive volume. In this paper, we presented an iterative Lavrentiev regularization and L- curve-based algorithm to reconstruct EIT images using knowledge of the noise variance of the measurements and the covariance of the conductivity distribution. The regu- larization parameter should be carefully selected, but it is often heuristically selected in conventional regulariza- tion-based reconstruction algorithms. So, an L-curve- based optimization algorithm is applied to choose the Lavrentiev regularization parameter. The method is vali- dated with numerical analysis and simulation results. Further research efforts are planned to focus on experi- mental investigations [28,29] and other computational electromagnetic-based algorithms [30].
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Adaptive mesh refinement techniques for electrical impedance tomography

Adaptive mesh refinement techniques for electrical impedance tomography

We have developed an algorithm which automatically adapts to the reconstructed image by producing finer meshes in areas where there are sharp gradients in the EIT image. Typically, refinement is required at interfaces between regions with differing conductivities. Although adaptive meshing has not yet been applied to resistance or impedance modelling in a biomedical context, there exists some work on applications of adaptive mesh refinement (AMR) in modelling heart current sources (Johnson and MacLeod 1994)—a topic related to EIT.

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Electrical Impedance Tomography using EIDORS in a Closed Phantom

Electrical Impedance Tomography using EIDORS in a Closed Phantom

Fig 1 shows EIT Experimental set up. It includes signal generator, a voltage to current converter producing a current of 20 mA at 5 KHz, a closed phantom with 16 electrode set up and a multimeter to measure resulting differential voltages [11]. This paper gives description of experiments performed on 16 gold plated silver electrodes, plastic container of 14cm diameter and 7cm height filled with saline solution of 0.9% of sodium chloride having electrical conductivity of 300 ms/m. The low magnitude and low frequency sinusoidal current is applied to the pair of electrodes. Current can be applied in neighboring pattern, opposite pattern, cross pattern and adaptive pattern [12, 13]. The neighboring pattern is also known as adjacent pattern. Brown and Segar (1987) [14] suggested a method where current is applied to a pair of electrodes and voltage is measured from other noncurrent pair of electrodes.
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Boundary Element formulation for Electrical Impedance Tomography

Boundary Element formulation for Electrical Impedance Tomography

Abstract . This paper concerns the modelisation and simulation of the forward problem of Electri- cal Impedance Tomography (EIT), i.e. the computation of an electrical potential due to an applied boundary current. The underlying goal is the estimation of the conductivities of the head tissues, in particular the skull, in order to improve the head models used in Electroencephalography (EEG). In the quasistatic approximation, the problem can be modeled by a Poisson equation with a non-vanishing Neumann boundary condition. We introduce a symmetric boundary integral formulation, which is discretized using mixed finite elements, and show its application to an EIT experiment in view of estimating skull conductivity.
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Recent progress on Frequency Difference Electrical Impedance Tomography

Recent progress on Frequency Difference Electrical Impedance Tomography

Electrical Impedance Tomography(EIT) is a non-invasive imaging technique which aims to provide the cross- sectional distribution of electrical impedance inside the human body. In EIT, we attach surface electrodes (typically 8 to 256) on the boundary of the subject, inject linearly independent patterns of sinusoidal currents in the frequency range of 50Hz to 500kHz, and measure the induced complex voltages. Since the relationship between the applied current and the resulting voltage data provide the electrical propensity of the subject, we use all available distributed current patterns and the measured voltage data set to reconstruct cross-sectional images of the conductivity and/or permittivity distribution inside the subject. This EIT technique has received considerable attention over the past two decades. Several review papers describe numerous aspects of the EIT technique [5, 8, 24, 29, 37], and mathematical theory was developed to support EIT system [1, 10, 16, 23, 26, 27, 34–36].
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A quantitative evaluation of drive pattern selection for optimizing EIT based stretchable sensors

A quantitative evaluation of drive pattern selection for optimizing EIT based stretchable sensors

Abstract: Electrical Impedance Tomography (EIT) is a medical imaging technique that has been recently used to realize stretchable pressure sensors. In this method, voltage measurements are taken at electrodes placed at the boundary of the sensor and are used to reconstruct an image of the applied touch pressure points. The drawback with EIT-based sensors, however, is their low spatial resolution due to the ill-posed nature of the EIT reconstruction. In this paper, we show our performance evaluation of different EIT drive patterns, specifically strategies for electrode selection when performing current injection and voltage measurements. We compare voltage data with Signal-to-Noise Ratio (SNR) and Boundary Voltage Changes (BVC), and study image quality with Size Error (SE), Position Error (PE) and Ringing (RNG) parameters, in the case of one-point and two-point simultaneous contact locations. The study shows that, in order to improve the performance of EIT based sensors, the electrode selection strategies should dynamically change correspondingly to the location of the input stimuli. In fact, the selection of one drive pattern over another can improve the target size detection and position accuracy up to 4.7% and 18%, respectively.
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Development of a high speed current injection and voltage measurement system for electrical impedance tomography based stretchable sensors

Development of a high speed current injection and voltage measurement system for electrical impedance tomography based stretchable sensors

Figure 6 shows an example of the voltage data set acquired through the first DAQ differential channel, namely the difference between electrodes 1 and 2 at each current injection step. The profile of the boundary data potentials indicates the effective multiplexers’ channel switching with a precise conveyance of the control digital bits. Additionally, the image shows that choosing a number of samples for each channel equal to 800 is a good compromise between reaching the static conditions at each time step and having a fast data set update rate. In fact, it is visible that the effects of transients are negligible after just 25 samples. For each current injection time step, the mean value of the samples is calculated after the static conditions are reached. This is then used as the final value for calculating the 208 voltage data set, as seen in Figure 7. In order to qualitatively demonstrate the quality of the hardware setup and the voltage data, Figure 8 shows the reconstructed images when a pressure input is applied in different positions over the sensor. In the reconstructed figures, a red colour indicates a positive change in the conductivity, while a blue colour represents the ringing artefacts, which are bands or "ghosts" near the edges, typical of linear filters such as EIT systems.
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Design and Development of a Microscopic Electrical Impedance Tomography System

Design and Development of a Microscopic Electrical Impedance Tomography System

In EIT, the current source is the essential part of EIT Microscopic. Many studies have been carried out using multiple constant current sources and alternative current sources to be excited through the electrodes [6]. In order to reconstruct the cross-sectional images, the measuring boundary voltage data is collected, processed and analyzed to obtain the image of the conductivity distribution. One of the limitations faced previously is the current source performance of the EIT system, where this factor determines the accuracy of the measurement. When several current sources are applied, calibration is very important to make the sum of all currents is always at zero. In this paper, we propose using multiple current sources to maximize the accuracy of the system and fast multi-channel voltmeters have been suggested in order to reduce the time of data acquisition. Usually, the current source consists of a voltage-to-current converter.
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Comparison of total variation algorithms for electrical impedance tomography

Comparison of total variation algorithms for electrical impedance tomography

A Perspex cylindrical tank study was designed to validate the simulations and test the performance of these TV algorithms in 2D. A tank with the same properties as described for the simulations was used. Electrodes were stainless steel discs, 1 cm in diameter. A current of peak amplitude 133 A  and frequency 1 kHz was injected and boundary voltages were measured according to the polar protocol. To mimic the properties of living tissues, biological objects were used as a background. The background medium was a mixture of 0.1% concentration NaCl solution and carrot cubes of approximately 4 mm diameter. The cylindrical potato perturbation of diameter 4.6cm and height 10 cm was placed at (x: -4cm y: 0cm) in the saline-carrot mixture (figure 6). The conductivities of the saline-carrot mixture and potato at a frequency of 1 kHz are 0.1 S/m and 0.02 S/m respectively. We designed an anatomical head-shaped phantom to test these algorithms in 3D condition. 32 sliver electrodes and a ground electrode were positioned based on the distribution proposed by (Avery 2014). Electrodes were addressed using the protocol eeg31b, in which current is preferentially applied to diametrically opposing electrodes (Tidswell et al 2001). The same potato perturbation was placed in posterior (x: 4.5 cm y: 0 cm z: 0 cm), middle (x: 8 cm y: 0 cm z: 0 cm) and anterior (x: 13 cm y: 0 cm z: 0 cm) positions, with the origin set to the posterior boundary (figure 7). All phantom experiments were undertaken at room temperture.
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Multifrequency methods for Electrical Impedance Tomography

Multifrequency methods for Electrical Impedance Tomography

Initially developed for geophysical studies, EIT was first applied to clinical research in 1987 by the Sheffield University research group, led by Barber and Seagar in the Department of Medical Physics and Clinical Engineering at Royal Hallamshire Hospital. The Sheffield Mark 1 EIT system had a ring of 16 electrodes, and a single current source [17]. Using a multiplexer, current was injected and voltages were measured at adjacent pairs of electrodes. Most early clinical studies were made with the Sheffield Mark I, and many research groups still use systems based on this first example (see section 2.1.2) [72, 82, 26, 35]. The first algorithm for imaging conductivity changes in a 2D cross-section, the so-called "Sheffield algorithm", was based on a backprojection method [6]. The Sheffield group is also accredited with proposing to reference measurements taken at different frequencies against each other [16, 41]. Three-dimensional imaging methods and realistic electrode models were initially developed at the Rensselaer Polytechnic Institute [23, 104, 74], and statistical approaches to image reconstruction and regularization were pioneered by researchers at the Universities of Helsinki and Kuopio (now University of Eastern Finland) [111, 113, 59, 60]. Electrical Impedance and Diffuse Optical Reconstruction Software (EIDORS) is a freely available MATLAB toolbox for EIT imaging [86, 66] based on software developed at the Universities of Manchester and Kuopio [114, 112].
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Digital biomedical electrical impedance tomography based on FPGA

Digital biomedical electrical impedance tomography based on FPGA

A sine current signal with small amplitude and fixed frequency is applied to a pair of electrodes. The differen- tial voltages on the other neighboring electrodes are col- lected in sequence. Each measured voltage is amplified and filtered through the signal processing circuits firstly. Then, the voltages are converted to 14 bits digital signals by analog-to-digital converter AD9240 secondly. Through orthogonal sequence demodulation, the real and imagi- nary parts of the measured voltages are acquired and sent to reconstruction computer for imaging finally. As adja- cent incentive measure working mode is used, the meas- ured voltages are 208. The excitation electrodes and the measured electrodes are chosen by multiplexed switches controlled by FPGA.
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Discrete mathematical models for electrical impedance tomography

Discrete mathematical models for electrical impedance tomography

Electrical Impedance Tomography (EIT) is a non-invasive, portable and low-cost medical imaging technique. Different current patterns are injected to the surface of a conductive body and the corresponding voltages are measured also on the boundary. These mea- surements are the data used to infer the interior conductivity distribution of the object. However, it is well known that the reconstruction process is extremely ill-posed due to the low sensitivity of the boundary voltages to changes in the interior conductivity distribution. The reconstructed images also suffer from poor spatial resolution. In tomographic systems, the spatial resolution is related to the number of applied current patterns and to the number and positions of electrodes which are placed at the surface of the object under examination. Two mammographic sensors were recently developed at the University of Mainz in collaboration with Oxford Brookes University. These prototypes consist of a planar sensing head of circular geometry with twelve large outer (active) electrodes arranged on a ring of radius 4.4cm where the external currents are injected and a set of, respectively thirty six and fifty four point-like high-impedance inner (passive) electrodes arranged in a hexagonal pattern where the induced voltages are measured. Two 2D reconstruction methods were proposed for these devices, one based on resistor network models and another one which uses an integral equation formulation. The novelty of the device and hence of these imaging techniques consists exactly in the distinct use of active and passive electrodes.
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Cardiac mapping of electrical impedance tomography by means of a wavelet model

Cardiac mapping of electrical impedance tomography by means of a wavelet model

2.1.1. EIT Data Acquisition in an Animal Experiment EIT data were collected using the Enlight ® (Timpel SA, Sao Paulo, Brazil). The electrical current used in the electrodes was 5 mA at 125 KHz. Each EIT image con- sisted of a matrix of 32 × 32 pixels and was acquired at an image acquisition rate of 50 frames per second. An ECG-gated image set was generated to represent the car- diac cycle and was synchronized with the peak of the R-wave of the ECG signal [6]. The wavelet transform was applied to the EIT signals of perfusion images, ob- tained by means of the ECG-gated temporal averaging of the EIT raw data. During the experiment, the pig was submitted to mechanical ventilation assistance, and three positive end-expiratory pressure (PEEP) ventilation pa- rameters were used: 18 cm H 2 O (PEEP18), 12 cm H 2 O
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Optimized breath detection algorithm in electrical impedance tomography

Optimized breath detection algorithm in electrical impedance tomography

Data collection is performed within an ongoing observational clinical study as part of the CRADL project. Infants with a body weight less than 600 g, postmenstrual age less than 25 weeks at inclusion, electrically active implants or those suffering from thorax skin lesions were excluded from the study. Informed written consent was obtained from the parents of the neonatal study participants. The raw EIT data were acquired by the CRADL study EIT device (Swisstom, AG, Landquart) with 32 textile electrodes at the frame rate of 48 Hz. This system is specially designed for infants who had thorax diameters as small as 17.5 cm [27, 28]. Current injections with amplitude of 3 mA rms at a frequency of 200 kHz were applied using a skip 4 injection pattern. The resulting voltage differences were measured by the remaining electrode pairs after each current injection, then DC and system related voltage changes were removed. The GREIT reconstruction algorithm [20] was then used to reconstruct the images. EIT image data were filtered using a bandpass filter with cut-off frequencies of 0.15 Hz and 1.8 Hz in order to remove cardiac related impedance changes.
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Electrical Impedance Tomography of Fast Neural Activity In The Brain

Electrical Impedance Tomography of Fast Neural Activity In The Brain

Impedance was recorded using a crab nerve suspended on an array of electrode hooks, where the nerve was stimulated to induce action potentials. At the same time, a square wave current was injected into the nerve using two of the electrode hooks and impedance was measured via another two electrodes (figure A1-3). The impedance was measured whilst injecting various current levels and varying the spacing of the current injection electrodes It was important that the applied current did not change the characteristics of the measured compound action potential. This could be ensured if both measuring electrodes (R1 and R2) were a significant distance from the excitation. Electrode R2 was so distant (7.5cm) from the stimulus that measurement from this electrode, although affected by the excitation, could not contribute significantly to the overall action potential. Also R1 was proximal to the current injection electrodes. However, the distance of electrode R1 from the excitation current was limited by the need for the excitation electrodes to be as close to the stimulus as possible in order to reduce the effect of dispersion of the compound action potential, which would make the resistance change small at distances more than about 16 mm from the stimulus. The radius of each nerve was about 0.5 mm, and the predicted length constant in previous modelling was about 0.6 mm (Boone, 1995). Thus the closest voltage electrode to the excitation was around 5 length constants from its nearest current electrode and current densities at these distances were proven to be insignificant by Boone.
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A novel time-difference electrical impedance tomography algorithm using multi-frequency information

A novel time-difference electrical impedance tomography algorithm using multi-frequency information

In the numerical validation, SC and DLS were applied to synthetic data, and the recon- structed images were compared. The generation of synthetic data is based on a circular mesh model with a radius of 300 pixels divided into 800 elements and 441 nodes. Fur- ther, 16 electrodes are evenly placed on the edge (Fig. 11a). A current of peak amplitude 1 mA was injected into two electrodes placed polarly, and the difference between the voltages on all adjacent pairs of electrodes not involved in delivering the current was measured, for a total of 192 measurements per frequency. The ground point was fixed at the center of the mesh. After generating the boundary voltage data, two levels of Gauss- ian noise were added, with SNRs of 60 dB and 80 dB, respectively.
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A REVIEW ON BREAST ELECTRICAL IMPEDANCE TOMOGRAPHY CLINICAL ACCURACY

A REVIEW ON BREAST ELECTRICAL IMPEDANCE TOMOGRAPHY CLINICAL ACCURACY

Electrical Impedance Tomography (EIT) is a non-invasive procedure using electrical impedance to image the human breast. Due to its mobility and using non-compression technique it is appealing to patients. This scanning device does not emit any ionizing radiation thus it can be done on pregnant women by means of no age limit. Since the EIT has play some supplementary function in the breast imaging, a lot of research on its clinical accuracy has been done. Therefore, the aim is to carry out a review of EIT clinical accuracy and assess the quality of journal by using Quality Assessment of Diagnostic Accuracy Studies (QUADAS) criteria. The journals that assess the sensitivity were search through various databases and the clinical accuracy of EIT in each journal is recorded. The review shows that the range sensitivity (S n ) of
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New Solutions for the Three-Dimensional Electrical Impedance Equation and its Application to the Electrical Impedance Tomography Theory

New Solutions for the Three-Dimensional Electrical Impedance Equation and its Application to the Electrical Impedance Tomography Theory

Still, recent works have shown that the convergence speed of the Taylor series in formal powers is very good (see e.g. [6]), compared to other classical methods for expanding functions. Remark 15: When considering the two-dimensional case of (20), by virtue of Theorem 10, the procedures exposed in this work will allow us to obtain the general solution of the two- dimensional Electrical Impedance Equation (1). This implies that, for the two-dimensional case, the present work poses an alternative method to the one exposed in [20].

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Modern Trends in Development of Electrical Impedance Tomography in Medicine

Modern Trends in Development of Electrical Impedance Tomography in Medicine

With that, the main areas of research are the following: optimal placement of electrodes and lead system; effective materials for electrodes; optimal amperage; optimal frequency; defining necessary and sufficient number of electrodes; use of the finite element method and of nonlinear optimization; studying feasibility of using internal electrodes for improving accuracy; calibration of information and measurement systems; numerical interpolation methods; combined influence of electrical impedance tomography with ultrasound 37 ; studying sensitivity and modeling

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Electrical impedance tomography as a tool for phenotyping plant roots

Electrical impedance tomography as a tool for phenotyping plant roots

Electrical impedance tomography (EIT) shares the same concepts as ERT. Although the imaged property remains the same (resistivity, or its inverse conductivity), EIT injects an alternating current rather than a direct current. his provides extra versatility as it can exploit diferent modalities (time diference, frequency difer- ence, multi-frequency) and expands the opportunities to characterise plant-soil interactions. he conduction of current in RSAs depends highly on the characteristics of the AC injected with the potential to better discriminate between soil and root tissues. Recent advances in this area [28, 36], show that the use of spectral EIT in com- bination with induced polarisation techniques are capa- ble of discerning the presence of high-density roots and some physiological processes. Moreover, studies such as [37], show the capability of EIT to identify the pres- ence of pathogenic agents in trees. his ield is still under continuous development, and new approaches are being established. For instance, Rao et  al. [38] suggest a com- bined use of ERT and plant-water-low models to further understand their pedophysical interactions with soil.
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