Electrical Impedance Tomography Algorithm Research Articles

PDE-solved by boundary element method for electrical impedance tomography

In this article a new version of the algorithm for Electrical Impedance Tomography is presented. By describing the problem with differential equations brought to integral equations, the algorithm can be used for many types of tomography. The approach used is particularly useful where it is not possible to formulate boundary conditions at the outer boundary of the region. Influence of the proximity effect on precision of imaging was considered.

Comparison second order versus zero order boundary element method for tomography imaging

In this article a new version of the algorithm for Electrical Impedance Tomography is presented. By describing the problem with differential equations brought to integral equations the inverse problem for tomography has been defined. This algorithm can be used for many types of nonclassical tomography. This approach is particularly useful where it is not possible to formulate accurately the boundary conditions at the outer boundary of the region. The influence of the order of BEM effect on precision of imaging was shown.

Supershape Augmented Reconstruction Method Based on Boolean Operations in Electrical Impedance Tomography

This paper presents a supershape augmented shape reconstruction algorithm for Electrical impedance tomography, aiming at high-quality reconstructions with respect to multiphase conductivity distributions. Within the proposed algorithm, the reconstructed inclusions are composed of basic shape primitives expressed through a supershape formula. To allow automatic topological evolution, multiple Boolean operations, including three basic Boolean operations and compound Boolean operations, are employed so that the candidate shape primitives can be intersected, subtracted and merged to form different shapes. The proposed algorithm is tested using simulations and water tank experimental data. Moreover, robustness studies considering varying initial guesses and differing signal to noise ratios are performed. It is demonstrated that the proposed algorithm is able to preserve detailed features of inclusions under detection and provide reliable estimates to unknown conductivity values and the interface properties.

A Three Dimensional Calderon-Based Method for EIT on the Cylindrical Geometry.

Electrical impedance tomography (EIT) is an imaging modality in which voltage data arising from currents applied on the boundary are used to reconstruct the conductivity distribution in the interior. This paper provides a novel direct (noniterative) 3-D reconstruction algorithm for EIT in the cylindrical geometry. The algorithm is based on Calderón's method [Calderón, 1980], and is implemented for data collected on two or four rows of electrodes on the boundary of a cylinder. The effectiveness of the method to localize inhomogeneities in the plane of the electrodes and in the z-direction is demonstrated on simulated and experimental data. The results from simulated and experimental data show that the method is effective for distinguishing in-plane and nearby out-of-plane inhomogeneities with good spatial resolution in the vertical z direction with computational efficiency.

Optimization of Bio-Impedance Techniques-Based Monitoring System for Medical & Industrial Applications

ABSTRACT At present, Electrical Impedance Tomography (EIT) is a simplified, non-invasive, cost-effective, vogue and standard technique to reckon the electrical properties of the interior of a biological tissue by the measurements of voltage and current signals from its boundary. The EIT system, consisting of 16 or 8 or 4 electrodes, is attached to the circumference of an object. A conventional EIT system consists of a precise current source that can generate a high-frequency, low-amplitude current signal (generally in order of mA) that is to be given in two electrodes of the electrode array which can be selected through fast multiplexer switching controlled by a controller. The current injected to these two electrodes produces the voltage drop to other remaining unconnected electrodes which can be measured in terms of induced voltages and this measurement cycle continues by changing the electrode. This designed module provides effective information in terms of relative voltage data to the Personal Computer (PC) equipped with the GUI based on MATLAB for the further analysis through a wired/wireless connection. This algorithm of all functions is related to image reconstruction, including the impedance plethysmography using a MatLab Graphical User Interface (GUI). Also, analysis part has been also done by using the same GUI to construct an image. Several simulation experiments have been performed to evaluate the performance of the proposed EIT system and algorithm. Thus, we conclude the proposed EIT system to improve for better image resolution. The designed EIT system would be useful in industrial and medical applications.

A multifrequency time-difference electrical impedance tomography algorithm using spectral constraints

This study aims to propose a multifrequency time-difference algorithm using spectral constraints. Based on the knowledge of tissue spectrum in the imaging domain, the fraction model was used in conjunction with the finite element method (FEM) to approximate a conductivity distribution. Then a frequency independent parameter (volume or area fraction change) was reconstructed which made it possible to simultaneously employ multifrequency time-difference boundary voltage data and then reduce the degrees of freedom of the reconstruction problem. Furthermore, this will alleviate the illness of the EIT inverse problem and lead to a better reconstruction result. The numerical validation results suggested that the proposed time-difference fraction reconstruction algorithm behaved better than traditional damped least squares algorithm (DLS) especially in the noise suppression capability. Moreover, under the condition of low signal-to-noise ratio, the proposed algorithm had a more obvious advantage in reconstructions of targets shape and position. This algorithm provides an efficient way to simultaneously utilize multifrequency measurement data for time-difference EIT, and leads to a more accurate reconstruction result. It may show us a new direction for the development of time-difference EIT algorithms in the case that the tissue spectrums are known.

Adaptive $L_{p}$ Regularization for Electrical Impedance Tomography

Owing to its low cost, fast response, non-invasiveness, and non-radiation, electrical impedance tomography (EIT) has been applied to numerous fields. However, its spatial resolution is low due to the inherent ill-posed problem and the “soft field” effect. The $L_{p}$ regularization ( $0 ) is effective for overcoming these disadvantages, and efforts have been made to use regularization from the most popular $L_{2}$ to its variants $L_{1}$ and $ L_{1/2}$ . Nevertheless, $L_{p}$ regularization is generally difficult to be solved fast and efficiently, and the selection of p yielding the best result is also a problem. In this paper, an adaptive re-weighted (ARW) algorithm with a general frame is presented to solve the $L_{p}$ regularization for EIT, with p for each pixel determined adaptively in iterations. Experiments were carried out to validate the proposed algorithm. Results show that compared with other EIT algorithms, the ARW algorithm had a higher spatial resolution. Moreover, it can provide a wider range of selection for regularization parameter, which increases the practicality of the proposed algorithm.

A Bilateral Constrained Image Reconstruction Method Using Electrical Impedance Tomography and Ultrasonic Measurement

Electrical Impedance Tomography (EIT) reconstructs the conductivity distribution in a sensing area through an array of boundary electrodes and has received increasing attention in bio-impedance measurement. To provide accurate image reconstruction of irregular conductivity distribution in large sensing area, we propose an efficient and accurate bilateral constrained dual modality reconstruction algorithm using EIT and ultrasonic measurement, where the EIT pre-reconstruction helps to select the time of flight (TOF) time window and the ultrasound reflection information of boundary points contributes to joint iterative reconstruction. In the simulations and phantom experiments selecting abdomen tumor as the object of interest, the proposed method successfully reconstructed the small inclusions. Quantitatively, the proposed bilateral constrained method has improved the reconstruction performance in terms of boundary preservation and robustness compared with single modality EIT and ultrasonic algorithms.

A modified L1/2 regularization algorithm for electrical impedance tomography

A more approximate solution can be obtained when the regularization technique is used to solve the ill-posed and nonlinear problem of electrical impedance tomography (EIT). However, due to the distribution of the ill-posed sensitivity matrix and sharp changes in preserving boundary information, commonly used regularization algorithms have their own limitations, such as filtering out the effective data and reconstructing images with unclear edges. In this paper, a modified algorithm based on L1/2 regularization (MA1/2) was proposed with the L1/2-norm as the form of the penalty term due to its better sparse characteristic. In addition, characteristics of the gradient in eight neighborhoods were utilized to retrieve reasonable data which might be filtered out. Two different dimension operators for the reconstruction quality were adopted accordingly. Both simulation and static experimental results demonstrated that the MA1/2 method significantly decreased the effect of measurement noise and improved the quality of reconstructed images.

Influence of reconstruction settings in electrical impedance tomography on figures of merit and physiological parameters

Objective: Electrical impedance tomography (EIT) is a non-invasive and relatively cheap imaging technique allowing continuous monitoring of lung function at the bedside. However, image reconstruction and processing are not yet standardized for clinical use, limiting comparability and reproducibility between studies. In addition, optimal reconstruction settings still have to be identified for different clinical applications. In this work (i) a systematic way to select ‘good’ EIT algorithm parameters is developed and (ii) an evaluation of these parameters in terms of correct functional imaging and consistency is performed. Approach: First, 19 200 reconstruction models are generated by full factorial design of experiment in 5D space. Then, in order to quantify the quality of reconstruction, known conductivity changes are introduced and figures of merit (FoM) are calculated from the response image. These measures are further used to select a subset of reconstruction models, matching certain FoM thresholds, and are then used for in vivo evaluation. For this purpose, EIT images of one piglet are reconstructed to assess changes in tidal impedance and end-expiratory lung impedance, at positive end expiratory pressure of 0 and 15 cmH2O. From ground truth spirometry measurements, physiological criteria are formulated and the subset of models is further reduced. Finally, the remaining reconstruction models are evaluated on physiological data gathered from published data in the literature to assess the generalization possibilities. Main results: Parametrization of EIT image reconstruction has a strong influence on the resulting FoM and the derived physiological parameter. While numerous reconstruction models showed reasonable values for a single parameter, in total only 12 matched all simulation and physiological criteria. After validation on further physiological data, only a single reconstruction model remained with a noise figure of 0.3, target size of 0.08, weight radius of 0.3, normalized voltage and strong weighting of lung and heart regions. Furthermore, the relationship between the reconstruction settings and some FoM could be partly explained by using a linear statistical model. Significance: The quest for standard reconstruction settings is highly relevant for future clinical applications. Simulation measures might help to assess the quality of the reconstruction models, but further evaluation of more data and different experimental settings is required.

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

BackgroundElectrical impedance tomography (EIT) is a noninvasive, radiation-free, and low-cost imaging modality for monitoring the conductivity distribution inside a patient. Nowadays, time-difference EIT (tdEIT) is used extensively as it has fast imaging speed and can reflect the dynamic changes of diseases, which make it attractive for a number of medical applications. Moreover, modeling errors are compensated to some extent by subtraction of voltage measurements collected before and after the change. However, tissue conductivity varies with frequency and tdEIT does not efficiently exploit multi-frequency information as it only uses measurements associated with a single frequency.MethodsThis paper proposes a tdEIT algorithm that imposes spectral constraints on the framework of the linear least squares problem. Simulation and phantom experiments are conducted to compare the proposed spectral constraints algorithm (SC) with the damped least squares algorithm (DLS), which is a stable tdEIT algorithm used in clinical practice. The condition number and rank of the matrices needing inverses are analyzed, and image quality is evaluated using four indexes. The possibility of multi-tissue imaging and the influence of spectral errors are also explored.ResultsSignificant performance improvement is achieved by combining multi-frequency and time-difference information. The simulation results show that, in one-step iteration, both algorithms have the same condition number and rank, but SC effectively reduces image noise by 20.25% compared to DLS. In addition, deformation error and position error are reduced by 8.37% and 7.86%, respectively. In two-step iteration, the rank of SC is greatly increased, which suggests that more information is employed in image reconstruction. Image noise is further reduced by an average of 32.58%, and deformation error and position error are also reduced by 20.20% and 31.36%, respectively. The phantom results also indicate that SC has stronger noise suppression and target identification abilities, and this advantage is more obvious with iteration. The results of multi-tissue imaging show that SC has the unique advantage of automatically extracting a single tissue to image.ConclusionsSC enables tdEIT to utilize multi-frequency information in cases where the spectral constraints are known and then provides higher quality images for applications.

An iterative damped least-squares algorithm for simultaneously monitoring the development of hemorrhagic and secondary ischemic lesions in brain injuries.

Electrical impedance tomography (EIT) is a non-invasive and real-time imaging method that has the potential to be used for monitoring intracerebral hemorrhage (ICH). Recent studies have proposed that ischemia secondary to ICH occurs simultaneously in the brain. Real-time monitoring of the development of hemorrhage and risk of secondary ischemia is crucial for clinical intervention. However, few studies have explored the performance of EIT monitoring in cases where hemorrhage and secondary ischemia exist. When these lesions get close to each other, or their conductivity and volume changes differ greatly, it becomes challenging for dynamic EIT algorithms to simultaneously reconstruct subtle injuries. To address this, an iterative damped least-squares (IDLS) algorithm is proposed in this study. The quality of the IDLS algorithm was assessed using blur radius and temporal response during computer simulation and a phantom 3D head-shaped model where bidirectional disturbance targets were simulated. The results showed that the IDLS algorithm enhanced contrast and concurrently reconstructed bidirectional disturbance targets in images. Moreover, it showed superior performance in decreasing the blur radius and was time cost-effective. With further improvement, the IDLS algorithm has the potential to be used for monitoring the development of hemorrhage and risk of ischemia secondary to ICH. Graphical abstract (a) and (b) are simulation images of bidirectional disturbance targets with different change ratios of volume (Vr) and conductivity (σr) based on the damped least-squares (DLS) algorithm and iterative damped least-squared (IDLS) algorithm, respectively. (c) shows the performance metrics of blur radius and temporal response with different volume ratio (corresponding to Vr). (d) shows the performance metrics of blur radius and temporal response with different conductivity change percentage (corresponding to σr).

Toward Electrical Impedance Tomography Coupled Ultrasound Imaging for Assessing Muscle Health.

This paper establishes for the first time that a coupled ultrasound (US) and electrical impedance tomography (EIT) system can serve as a non-invasive, spatially localized approach to extract clinically relevant muscle properties. The US/EIT system represents a potential enhancement to electrical impedance myography (EIM), which has shown promise as a non-invasive technology that may have important clinical use in indicating neuromuscular disease status and as a diagnostic tool. A 2.5D EIT algorithm evaluated on simulation, measured phantoms, and measured patient data was studied to evaluate US/EIT's ability to distinguish different aspects of muscle tissue. Simulated and phantom experiments revealed the depths of distinguishability of 3.2 and 4.2 mm in simulation for 10% and 20% changes in muscle properties, respectively, and 3.6 mm in measured phantom experiments assuming a 12% muscle conductivity change. Reconstructions from the patient data established that there were consistent differences 1) between longitudinal (along) and transverse (across) muscle conductivity reconstructions at frequencies of 40 and 80 kHz and 2) side-by-side comparison between healthy and diseased tissue in terms of conductivity, permittivity, and phase at 40 and 80 kHz. Comparisons were made between the EIT reconstructed values and electrical impedance spectroscopy (EIS) measurements (an available surrogate in place of standard EIM measurements) made with the US/EIT system, wherein 1) EIS and EIT show similar sensitivity to longitudinal and transverse differences and 2) EIT showed a more consistent ability to differentiate healthy and diseased tissue. These results suggest that US/EIT appears very promising for non-invasive and spatially localized diagnosis of muscle health.

An image reconstruction algorithm for electrical impedance tomography using Symkaczmarz based on structured sparse representation

Electrical impedance tomography (EIT) is a new medical imaging technology that is used to estimate changes in the internal conductivity based on measurements of the border voltage disturbance. However, the generalized inverse operator of image reconstruction for EIT is ill-posed and ill-conditioned. In order to improve reconstruction quality, the structured sparse representation is integrated into the iterative process of the Symkaczmarz algorithm for EIT image reconstruction in this paper. The sparsity prior and the underlying structure characteristics of conductivity reconstruction are considered in the proposed algorithm. Both simulation and experiment results indicate that the proposed method has feasibility for pulmonary ventilation imaging and great potential for improving the image quality.

Combing signal processing methods with algorithm priori information to produce synergetic improvements on continuous imaging of brain electrical impedance tomography

Dynamic electrical impedance tomography (EIT) promises to be a valuable technique for monitoring the development of brain injury. But in practical long-term monitoring, noise and interferences may cause insufficient image quality. To help unveil intracranial conductivity changes, signal processing methods were introduced to improve EIT data quality and algorithms were optimized to be more robust. However, gains for EIT image reconstruction can be significantly increased if we combine the two techniques properly. The basic idea is to apply the priori information in algorithm to help de-noise EIT data and use signal processing to optimize algorithm. First, we process EIT data with principal component analysis (PCA) and reconstruct an initial CT-EIT image. Then, as the priori that changes in scalp and skull domains are unwanted, we eliminate their corresponding boundary voltages from data sets. After the two-step denoising process, we finally re-select a local optimal regularization parameter and accomplish the reconstruction. To evaluate performances of the signal processing-priori information based reconstruction (SPR) method, we conducted simulation and in-vivo experiments. The results showed SPR could improve brain EIT image quality and recover the intracranial perturbations from certain bad measurements, while for some measurement data the generic reconstruction method failed.

Image Reconstruction for Electrical Impedance Tomography Using Enhanced Adaptive Group Sparsity With Total Variation

A novel image reconstruction algorithm for electrical impedance tomography using enhanced adaptive group sparsity with total variation constraint is proposed in this paper. The new algorithm simultaneously utilizes the prior knowledge of regional structure feature and global characteristic of the conductivity distribution. The regional structure feature is encoded by using an enhanced adaptive group sparsity constraint. Meanwhile, the global characteristic of inclusion boundary is considered by imposing total variation constraint on the whole image. An enhanced adaptive pixel grouping algorithm is proposed based on Otsu's thresholding method, which demonstrates good noise immunity. An accelerated alternating direction method of multipliers is utilized to solve the proposed problem for a faster convergence rate. The performance of the proposed algorithm is thoroughly evaluated by numerical simulation and experiments. Comparing with the state-of-the-art algorithms, such as the L1 regularization, total variation regularization, and our former work on adaptive group sparsity, the proposed method has demonstrated superior spatial resolution and better noise reduction performance. Combined with the total variation constraint, distinct boundary of inclusions has also been obtained.

An Image Reconstruction Algorithm for Electrical Impedance Tomography Using Adaptive Group Sparsity Constraint

Image quality has long been deemed a key challenge for electrical impedance tomography (EIT). High-quality image is of great significance for improving the qualitative and quantitative imaging performance in biomedical or industrial applications. In this paper, a novel image reconstruction algorithm for EIT using adaptive group sparsity constraint is proposed to obtain enhanced image quality. The proposed algorithm takes both the underlying structure characteristics and sparsity prior of the conductivity distribution into account to promote a solution with group sparsity structure and reduce the degree of freedom. Specifically, an adaptive grouping method is incorporated for efficient and dynamic pixel grouping when the conductivity distribution does not have a fixed structure or the prior knowledge of the structure is unavailable. Numerical simulation and phantom experiments are performed to validate the proposed algorithm. The results are compared with those using the Landweber iteration, total variation regularization, and $l_{1}$ regularization. Both simulation and experiment results confirm the significantly improved tomographic imaging quality using the proposed algorithm, which demonstrates great potential for multiphase flow imaging and biological tissue imaging.

Comparison of distribution of lung aeration measured with EIT and CT in spontaneously breathing, awake patients1.

Both Electrical Impedance Tomography (EIT) and Computed Tomography (CT) allow the estimation of the lung area. We compared two algorithms for the detection of the lung area per quadrant from the EIT images with the lung areas derived from the CT images. 39 outpatients who were scheduled for an elective CT scan of the thorax were included in the study. For each patient we recorded EIT images immediately before the CT scan. The lung area per quadrant was estimated from both CT and EIT data using two different algorithms for the EIT data. Data showed considerable variation during spontaneous breathing of the patients. Overall correlation between EIT and CT was poor (0.58-0.77), the correlation between the two EIT algorithms was better (0.90-0.92). Bland-Altmann analysis revealed absence of bias, but wide limits of agreement. Lung area estimation from CT and EIT differs significantly, most probably because of the fundamental difference in image generation.

Distributed Pressure Sensing Using Carbon Nanotube Fabrics

A nanoengineered fabric capable of densely distributed pressure sensing is presented. Piezoresistive carbon nanotube-latex thin films were spray-coated and integrated with fabric to form robust, flexible, and deformable sensors. Spatial pressure sensing was achieved and validated experimentally using an electrical impedance tomography algorithm, which was able to estimate the resistivity distribution of the fabric and its changes due to applied pressure at different locations.

Self-sensing concrete enabled by nano-engineered cement-aggregate interfaces

The objective of this study was to design a multifunctional cement composite that could not only bear loads but also possessed electromechanical properties that are sensitive to damage. A mainstream approach is to disperse large quantities of conductive additives in the cement matrix, which can be costly, involve complex procedures, difficult to scale-up, and degrade concrete’s inherent mechanical properties. Instead, this research proposes a new method to design multifunctional and self-sensing concrete, which is achieved by altering the cement–aggregate interface using conductive, nano-engineered coatings. Here, a carbon nanotube–based ink solution was sprayed onto the surfaces of aggregates and then dried to form electrically conductive, thin film-coated aggregates. Then, the film-coated aggregates were used as is for casting concrete specimens. It was demonstrated experimentally that this procedure yielded concrete specimens that were not only conductive but also had electrical properties that varied in response to applied physical damage. An electrical impedance tomography algorithm was also implemented and used for estimating their spatial resistivity distributions. Since the electrical properties at every location of the film-enhanced concrete were sensitive to damage, electrical impedance tomography was able to produce electrical resistivity maps that indicated the locations and severities of damage. Multiple concrete cylinder, plate, and beam specimens were cast and tested for validating the self-sensing properties of film-enhanced concrete and the spatial damage detection capabilities of the electrical impedance tomography algorithm.