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.

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.

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.

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.

EIT Image Reconstruction by Modified Data

Electrical impedance tomography (EIT) is a radiation-free imaging method. Canoni-cally, in lung EIT, 16 electrodes are placed horizontally on the thorax skin. By inject-ing currents through electrodes attached to the skin, a set of induced voltage measure-ments can be collected. The conductivity distribution on the chest plane can be ob-tained from these electrical boundary conditions. It has been reported that the adjacent current injection pattern is sub-optimal for EIT reconstruction. However, this adjacent current injection pattern is commonly used in commercially available EIT devices. In this study, we modify the boundary conditions according to the superposition principle of the electrical field. As a result, boundary conditions of the adjacent current pattern will be transformed to those corresponding to “skip-3” current injection pattern. Simulation results indicated that reconstruction benefits from the modified boundary conditions.

Comparison of Image Reconstruction Algorithms in EIT Imaging

Electrical Impedance Tomography (EIT) is a medical imaging technique which can be used to monitor the regional ventilation in patients utilizing voltage measurements made at the thorax. Several reconstruction algorithms have been developed during the last few years. In this manuscript we compare a well-established algorithm and a re-cently developed method for image reconstruction regarding EIT indices derived from the differently reconstructed images.

NUMERICAL LOCALIZATION OF ELECTROMAGNETIC IMPERFECTIONS FROM A PERTURBATION FORMULA IN THREE DIMENSIONS

This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms： the Current Projection method, the MUltiple Signal Classification （MUSIC） algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.

Finite Element Modeling of Human Thorax Based on MRI Images for EIT Image Reconstruction

Electrical impedance tomography(EIT)image reconstruction is a non-linear problem.In general,finite element model is the critical basis of EIT image reconstruction.A 3D human thorax modeling method for EIT image reconstruction is proposed herein to improve the accuracy and reduce the complexity of existing finite element modeling methods.The contours of human thorax and lungs are extracted from the layers of magnetic resonance imaging(MRI)images by an optimized Otsu’s method for the construction of the 3D human thorax model including the lung models.Furthermore,the GMSH tool is used for finite element subdivision to generate the 3D finite element model of human thorax.The proposed modeling method is fast and accurate,and it is universal for different types of MRI images.The effectiveness of the proposed method is validated by extensive numerical simulation in MATLAB.The results show that the individually oriented 3D finite element model can improve the reconstruction quality of the EIT images more effectively than the cylindrical model,the 2.5D model and other human chest models.

An image reconstruction algorithm of EIT based on pulmonary prior information

Using a CT scan of the pulmonary tissue,a human pulmonary model is established combined with the structure property of the human lung tissue using the software COMSOL.Combined with the conductivity contribution information of the human tissue and organ,an image reconstruction method of electrical impedance tomography based on pulmonary prior information is proposed using the conjugate gradient method.Simulation results show that the uniformity index of sensitivity distribution of the pulmonary model is 15.568,which is significantly reduced compared with 34.218 based on the round field.The proposed algorithm improves the uniformity of the sensing field,the image resolution of the conductivity distribution of pulmonary tissue and the quality of the reconstruction image based on pulmonary prior information.

Artificial intelligence for closed-loop ventilation therapy with hemodynamic control using the open lung concept

Purpose–The purpose of this paper is to develop an automatic control system for mechanical ventilation therapy based on the open lung concept(OLC)using artificial intelligence.In addition,mean arterial blood pressure(MAP)is stabilized by means of a decoupling controller with automated noradrenaline(NA)dosage to ensure adequate systemic perfusion during ventilation therapy for patients with acute respiratory distress syndrome(ARDS).Design/methodology/approach–The aim is to develop an automatic control system for mechanical ventilation therapy based on the OLC using artificial intelligence.In addition,MAP is stabilized by means of a decoupling controller with automated NA dosage to ensure adequate systemic perfusion during ventilation therapy for patients with ARDS.Findings–Thisinnovativeclosed-loop mechanicalventilation system leadsto a significant improvement in oxygenation,regulates end-tidal carbon dioxide for appropriate gas exchange and stabilizes MAP to guarantee proper systemic perfusion during the ventilation therapy.Research limitations/implications–Currently,this automatic ventilation system based on the OLC can only be applied in animal trials;for clinical use,such a system generally requires a mechanical ventilator and sensors with medical approval for humans.Practical implications–For implementation of a closed-loop ventilation system,reliable signals from the sensors are a prerequisite for successful application.Originality/value–Theexperiment with porcine dynamics demonstrates thefeasibility and usefulness of this automatic closed-loop ventilation therapy,with hemodynamic control for severe ARDS.Moreover,this pilot study validated a new algorithm for implementation of the OLC,whereby all control objectives are fulfilled during the ventilation therapy with adequate hemodynamic control of patients with ARDS.