Statistical Inversion Based on Nonlinear Weighted Anisotropic Total Variational Model and Its Application in Electrical Impedance Tomography

Electrical impedance tomography (EIT) aims to reconstruct the conductivity distribution using the boundary measured voltage potential. Traditional regularization based method would suffer from error propagation due to the iteration process. The statistical inverse problem method uses statistical inference to estimate unknown parameters. In this article, we develop a nonlinear weighted anisotropic total variation (NWATV) prior density function based on the recently proposed NWATV regularization method. We calculate the corresponding posterior density function, i.e., the solution of the EIT inverse problem in the statistical sense, via a modified Markov chain Monte Carlo (MCMC) sampling. We do numerical experiment to validate the proposed approach.

Nonlinear Electrical Impedance Tomography Method Using a Complete Electrode Model for the Characterization of Heterogeneous Domains

This paper presents an electrical impedance tomography(EIT)method using a partial-differential-equationconstrained optimization approach.The forward problem in the inversion framework is described by a complete electrodemodel(CEM),which seeks the electric potential within the domain and at surface electrodes considering the contact impedance between them.The finite element solution of the electric potential has been validated using a commercial code.The inverse medium problem for reconstructing the unknown electrical conductivity profile is formulated as an optimization problem constrained by the CEM.The method seeks the optimal solution of the domain’s electrical conductivity to minimize a Lagrangian functional consisting of a least-squares objective functional and a regularization term.Enforcing the stationarity of the Lagrangian leads to state,adjoint,and control problems,which constitute the Karush-Kuhn-Tucker(KKT)first-order optimality conditions.Subsequently,the electrical conductivity profile of the domain is iteratively updated by solving the KKT conditions in the reduced space of the control variable.Numerical results show that the relative error of the measured and calculated electric potentials after the inversion is less than 1%,demonstrating the successful reconstruction of heterogeneous electrical conductivity profiles using the proposed EIT method.This method thus represents an application framework for nondestructive evaluation of structures and geotechnical site characterization.

Lung Ventilation Functional Monitoring Based on Electrical Impedance Tomography

Medically, electrical impedance tomography （EIT） is a relatively inexpensive, safe, non-invasive and portable technique compared with computerized tomography （CT） and magnetic resonance imaging （MRI）. In this paper, EIT_TJU_ II system is developed including both the data collection system and image reconstruction algo- rithm. The testing approach of the system performance, including spatial resolution and sensitivity, is described through brine tank experiments. The images of the thorax physical model verify that the system can reconstruct the interior resistivity distribution. Finally, the lung ventilation functional monitoring in vivo is realized by EIT, and the visualized images indicate that the configuration and performance of EIT_TJU_ II system are feasible and EIT is a promising technique in clinical monitoring application.

Advances in electrical impedance tomography-based brain imaging

Novel advances in the field of brain imaging have enabled the unprecedented clinical application of various imaging modalities to facilitate disease diagnosis and treatment. Electrical impedance tomography(EIT) is a functional imaging technique that measures the transfer impedances between electrodes on the body surface to estimate the spatial distribution of electrical properties of tissues. EIT offers many advantages over other neuroimaging technologies,which has led to its potential clinical use. This qualitative review provides an overview of the basic principles,algorithms, and system composition of EIT. Recent advances in the field of EIT are discussed in the context of epilepsy,stroke, brain injuries and edema, and other brain diseases. Further, we summarize factors limiting the development of brain EIT and highlight prospects for the field. In epilepsy imaging, there have been advances in EIT imaging depth,from cortical to subcortical regions. In stroke research, a bedside EIT stroke monitoring system has been developed for clinical practice, and data support the role of EIT in multi-modal imaging for diagnosing stroke. Additionally, EIT has been applied to monitor the changes in brain water content associated with cerebral edema, enabling the early identification of brain edema and the evaluation of mannitol dehydration. However, anatomically realistic geometry,inhomogeneity, cranium completeness, anisotropy and skull type, etc., must be considered to improve the accuracy of EIT modeling. Thus, the further establishment of EIT as a mature and routine diagnostic technique will necessitate the accumulation of more supporting evidence.

Lorentz force electrical impedance tomography using pulse compression technique

Lorentz force electrical impedance tomography （LFEIT） combines ultrasound stimulation and electromagnetic field detection with the goal of creating a high contrast and high resolution hybrid imaging modality. In this study, pulse compression working together with a linearly frequency modulated ultrasound pulse was investigated in LFEIT. Experiments were done on agar phantoms having the same level of electrical conductivity as soft biological tissues. The results showed that：（i） LFEIT using pulse compression could detect the location of the electrical conductivity variations precisely; （ii） LFEIT using pulse compression could get the same performance of detecting electrical conductivity variations as the traditional LFEIT using high voltage narrow pulse but reduce the peak stimulating power to the transducer by 25.5 dB; （iii） axial resolution of 1 mm could be obtained using modulation frequency bandwidth 2 MHz.

Use of 3-D magnetic resonance electrical impedance tomography in detecting human cerebral stroke: a simulation study

We have developed a new three dimensional (3-D) conductivity imaging approach and have used it to detect human brain conductivity changes corresponding to acute cerebral stroke. The proposed Magnetic Resonance Electrical Impedance Tomography (MREIT) approach is based on the J-Substitution algorithm and is expanded to imaging 3-D subject conductivity distribution changes. Computer simulation studies have been conducted to evaluate the present MREIT imaging approach. Simulations of both types of cerebral stroke, hemorrhagic stroke and ischemic stroke, were performed on a four-sphere head model. Simulation results showed that the correlation coefficient (CC) and relative error (RE) between target and estimated conductivity distributions were 0.9245±0.0068 and 8.9997%±0.0084%, for hemorrhagic stroke, and 0.6748±0.0197 and 8.8986%±0.0089%, for ischemic stroke, when the SNR (signal-to-noise radio) of added GWN (Gaussian White Noise) was 40. The convergence characteristic was also evaluated according to the changes of CC and RE with different iteration numbers. The CC increases and RE decreases monotonously with the increasing number of iterations. The present simulation results show the feasibility of the proposed 3-D MREIT approach in hemorrhagic and ischemic stroke detection and suggest that the method may become a useful alternative in clinical diagnosis of acute cerebral stroke in humans.

Electrode models in electrical impedance tomography

This paper presents different views on electrode modelling, which include electrode electrochemistry models for modelling the effects of electrode-electrolyte interface, electric field electrode models for modelling electrode geometry, and electrode models for modelling the effects of electrode common mode voltage and double layer capacitance. Taking the full electrode models into consideration in electrical impedance tomography (EIT) will greatly help the optimised approach to a good solution and further understanding of the measurement principle.

Electrical impedance tomography using adaptive mesh refinement

In electrical impedance tomography （EIT）, distribution of the internal resistivity or conductivity of an unknown object is esti- mated using measured boundary voltage data induced by different current patterns with various reconstruction algorithms. The reconstruction algorithms usually employ the Newton-Raphson iteration scheme to visualize the resistivity distribution inside the object. Accuracy of the imaging process depends not only on the algorithm used, but also on the scheme of finite element discretization. In this paper an adaptive mesh refinement is used in a modified reconstruction algorithm for the regularized Err. The method has a major impact on efficient solution of the forward problem as well as on achieving improved image resolution. Computer simulations indicate that the Newton-Raphson reconstruction algorithm for Err using adaptive mesh refinement performs better than the classical Newton-Raphson algorithm in terms of reconstructed image resolution.

New Regularization Method in Electrical Impedance Tomography

Image reconstruction in electrical impedance tomography(EIT) is a highly ill posed inverse problem. Regularization techniques must be used in order to solve the problem. In this paper, a new regularization method based on the spatial filtering theory is proposed. The new regularized reconstruction for EIT is independent of the estimation of impedance distribution, so it can be implemented more easily than the maximum a posteriori(MAP) method. The regularization level in our proposed method varies spatially so as to be suited to the correlation character of the object's impedance distribution. We implemented our regularization method with two dimensional computer simulations. The experimental results indicate that the quality of the reconstructed impedance images with the descibed regularization method based on spatial filtering theory is better than that with Tikhonov method.

Improve Spatial Resolution of Electrical Impedance Tomography Image Based on Non-uniformity Fine Mesh

In electrical impedance tomography (EIT) an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. Several difficulties have been identified in EIT, where the main problem is the low spatial resolution. This paper presents a fining mesh method based on finite element method (FEM), by fining the sensitive element, the most actual signal is obtained in certain electrode number. Newton-Raphson reconstruction algorithm improves the spatial solution of image. The advantages of this method are the improvement of spatial resolution and ease of implementation.

Locating Impedance Change in Electrical Impedance Tomography Based on Multilevel BP Neural Network

Electrical impedance tomography(EIT) is a new computer tomography technology, which reconstructs an impedance (resistivity, conductivity) distribution, or change of impedance, by making voltage and current measurements on the object's periphery. Image reconstruction in EIT is an ill-posed, non-linear inverse problem. A method for finding the place of impedance change in EIT is proposed in this paper, in which a multilevel BP neural network (MBPNN) is used to express the non-linear relation between the impedance change inside the object and the voltage change measured on the surface of the object. Thus, the location of the impedance change can be decided by the measured voltage variation on the surface. The impedance change is then reconstructed using a linear approximate method. MBPNN can decide the impedance change location exactly without long training time. It alleviates some noise effects and can be expanded, ensuring high precision and space resolution of the reconstructed image that are not possible by using the back projection method.

Electrical Impedance Tomography Based on Direct Search Method

Solution to impedance distribution in electrical impedance tomography （EIT） is an ill-posed nonlinear inverse problem. It is especially difficult to reconstruct an EIT image in the center area of a measured object. Tikhonov regularization with some prior information is a sound regnlarization method for static electrical impedance tomography under the condition that some true impedance distribution information is known a priori. This paper presents a direct search method （DSM） as pretreatment of image reconstruction through which one not only can construct a regularization matrix which may locate in areas of impedance change, but also can obtain an initial impedance distribution more similar to the true impedance distribution, as well as better current modes which can better distinguish the initial distribution and the true distribution. Simulation results indicate that, by using DSM, resolution in the center area of the measured object can be improved significantly.

An Algorithm for Cavity Reconstruction in Electrical Impedance Tomography

We consider the inverse problem of finding cavities within some object from electrostatic measurements on the boundary. By a cavity we understand any object with a different electrical conductivity from the background material of the body. We give an algorithm for solving this inverse problem based on the output nonlinear least-square formulation and the regularized Newton-type iteration. In particular, we present a number of numerical results to highlight the potential and the limitations of this method.

Anisotropic TV Regularization in Electrical Impedance Tomography: An Experimental Study

Total variation (TV) regularization method is a typical method to preserve the discontinuities structure in EIT. Isotropic TV and anisotropic TV are two well-known variants of TV. The main differences between them are that the latter tends to distort the reconstructed internal inhomogeneities along the coordinate axis. In this article, we adopt the alternating direction method of multipliers (ADMM) to overcome the non-differentiability of the anisotropic TV and verify the characteristics of anisotropic TV regularization by the tank experiments.

Positive End-expiratory Pressure Titration after Alveolar Flecruitment Directed by Electrical Impedance Tomography

Background： Electrical impedance tomography （EIT） is a real-time bedside monitoring tool, which can reflect dynamic regional lung ventilation. The aim of the present study was to monitor regional gas distribution in patients with acute respiratory distress syndrome （ARDS） during positive-end-expiratory pressure （PEEP） titration using EIT. Methods： Eighteen ARDS patients under mechanical ventilation in Department of Critical Care Medicine of Peking Union Medical College Hospital from January to April in 2014 were included in this prospective observational study. After recruitment maneuvers （RMs）, decremental PEEP titration was performed from 20 cmH20 to 5 cmH20 in steps of 3 cmH20 every 5-10 min. Regional over-distension and recruitment were monitored with EIT. Results： After RMs, patient with arterial blood oxygen partial pressure （PaO2） ＋ carbon dioxide partial pressure （PaCO2） 〉400 mmHg with 100% of fractional inspired oxygen concentration were defined as RM responders. Thirteen ARDS patients was diagnosed as responders whose PaO2 ＋ PaCO2, were higher than nonresponders （419 ± 44 mmHg vs. 170 ±73 mmHg, P 〈 0.0001）. In responders, PEEP mainly increased-recruited pixels in dependent regions and over-distended pixels in nondependent regions. PEEP alleviated global inhomogeneity of tidal volume and end-expiratory lung volume. PEEP levels without significant alveolar derecruitment and over-distension were identified individually. Conclusions： After RMs, PEEP titration significantly affected regional gas distribution in lung, which could be monitored with EIT. EIT has the potential to optimize PEEP titration.

A New Design of Electrical Impedance Tomography Sensor System for Pulmonary Disease Diagnosis

As an advanced process detection technology, electrical impedance tomography(EIT) has wide application prospects and advantages in medical imaging diagnosis. However, a series of issues need to be addressed before applying EIT for bedside monitoring. Medical diagnosis and bedside monitoring are dynamic measuring process, where the positions of measuring electrodes and the shape of the detected field are changing dynamical. Due to the inability to cope with the changeable electrode positions and various dynamic fields, existing EIT systems are mainly used for industrial detection in condition of static measurement and visualization. In this paper, we investigate the dynamic measurement and visualization of human breast in EIT field, describe the design of the measuring sensor system, and expound the measuring principle. The main component of the hardware system is a builtin servo electrical resistance tomography sensor with capacitive sliding rod, which can adapt to the crowd of different chest contour and the change of chest shape in the dynamic process of breathing.The corresponding measuring principle is extracting all real-time positions of measuring electrodes,then obtaining the dynamic boundary, finally dividing the detection field rapidly. Experimental results confirmed that the proposed system can obtain real-time location of boundary sensor and dynamically solve the problem of arbitrary-shape boundary measurement. The imaging results validate the availability of designed sensor system and the effectiveness of the corresponding measuring principle.

In vivo Detection and Imaging of Intraventricular Hemorrhage in Neonatal Piglets Using Electrical Impedance Tomography

Intraventricular hemorrhage(IVH) is one of the most severe medical emergencies in neurosurgery. Early detection or diagnosis would significantly reduce the rate of disability and mortality, and improve the prognosis of the patients.Although present medical imaging techniques have high sensitivity to identify bleeding, the use of an additional, non-invasive imaging technique capable of continuously monitoring IVH is required to prevent contingent bleeding or re-bleeding. In this study, electrical impedance tomography(EIT) was applied to detect the onset of IVH modeled on 6 piglets in real time, with the subsequent process being monitored continuously. The experimental IVH model was introduced by one-time injection of 2 ml fresh autologous arterial blood into the ventricles of piglets.Results showed that resistivity variations within the brain caused by the added blood could be detected and imaged in vivo using the EIT method, and the magnitude and the size of region of interest on EIT images may be linearly associated with the volume of the blood. In conclusion, EIT has unique potential for use in clinical practice to provide invaluable real-time neuroimaging data for IVH after the improvement of electrode design, anisotropic realistic modeling, and instrumentation.

An Electrical Impedance Imaging System Towards Edge Intelligence for Non-Destructive Testing of Concrete

In the construction industry,to prevent accidents,non-destructive tests are necessary and cost-effective.Electrical impedance tomography is a new technology in non-invasive imaging in which the image of the inner part of conductive bodies is reconstructed by the arrays of external electrodes that are connected on the periphery of the object.The equipment is cheap,fast,and edge compatible.In this imaging method,the image of electrical conductivity distribution(or its opposite;electrical impedance)of the internal parts of the target object is reconstructed.The image reconstruction process is performed by injecting a precise electric current to the peripheral boundaries of the object,measuring the peripheral voltages induced from it and processing the collected data.In an electrical impedance tomography system,the voltages measured in the peripheral boundaries have a non-linear equation with the electrical conductivity distribution.This paper presents a cheap Electrical Impedance Tomography(EIT)instrument for detecting impurities in the concrete.A voltage-controlled current source,a micro-controller,a set of multiplexers,a set of electrodes,and a personal computer constitute the structure of the system.The conducted tests on concrete with impurities show that the designed EIT system can reveal impurities with a good accuracy in a reasonable time.

Electromagnetic Model and Image Reconstruction Algorithms Based on EIT System

An intuitive 2D model of circular electrical impedance tomography （EIT） sensor with small size electrodes is established based on the theory of analytic functions. The validation of the model is proved using the result from the solution of Laplace equation. Suggestions on to electrode optimization and explanation to the ill-condition property of the sensitivity matrix are provided based on the model, which takes electrode distance into account and can be generalized to the sensor with any simple connected region through a conformal transformation. Image reconstruction algorithms based on the model are implemented to show feasibility of the model using experimental data collected from the EIT system developed in Tianjin University. In the simulation with a human chestlike configuration, electrical conductivity distributions are reconstructed using equi-potential backprojection （EBP） and Tikhonov regularization （TR） based on a conformal transformation of the model. The algorithms based on the model are suitable for online image reconstruction and the reconstructed results are aood both in size and position.

Primary Research of EIT Inverse Problem Based on CS （Compressed Sensing） Technique

EIT （electrical impedance tomography） problem should be represented by a group of partial differential equation, in numerical calculation： the nonlinear problem should be linearization approximately, and then linear equations set is obtained, so EIT image reconstruct problem should be considered as a classical ill-posed, ill-conditioned, linear inverse problem. Its biggest problem is the number of unknown is much more than the number of the equations, this result in the low imaging quality. Especially, it can not imaging in center area. For this problem, we induce the CS technique into EIT image reconstruction algorithm. The main contributions in this paper are： firstly, built up the relationship between CS and EIT definitely; secondly, sparse reconstruction is a critical step in CS, built up a general sparse regularization model based on EIT; finally, gives out some EIT imaging models based on sparse regularization method. For different scenarios, compared with traditional Tikhonov regularization （smooth regularization） method, sparse reconstruction method is not only better at anti-noise, and imaging in center area, but also faster and better resolution.