A Virtual Electrode-Based Enhanced GREIT Method for Electrical Impedance Tomography

We read with interest the recent article by Zarantonello et al.1 on the physiologic effects of prone positioning on ventilation and perfusion distribution, oxygenation, and lung mechanics in COVID-19 acute respiratory distress syndrome patients. We would like to first congratulate the authors for the nicely conducted study that once again proved the clinical applicability of electrical impedance tomography for the assessment of ventilation–perfusion matching at the bedside. We acknowledge the clinical significance of the findings, but we wish to point out that several parts of the electrical impedance tomography methodology were incorrectly described in the article.In the Methods section, the authors described how the lung areas that were (1) perfused but not ventilated, (2) ventilated but not perfused, and (3) both ventilated and perfused were “divided by the sum of ventilated and perfused pixels” to calculate the corresponding relative fractions of the lung area in percentages, i.e., (1) “% shunt area,” (2) “% dead space area,” and (3) “% matched area,” respectively. However, the denominator must be the number of pixels that were ventilated or perfused, i.e., using the logical operator “or,” otherwise the calculated relative areas would be incorrect. The authors also determined “the percentage of total ventilated lung area that was located in the dorsal half of the thorax,” which they inaccurately termed as “dorsal ventilation.” According to the consensus electrical impedance tomography terminology and definitions,2 regional ventilation is determined as the sum of all pixel values of tidal impedance variation not as the pixel count, which defines just the ventilated area.The authors further introduced a new electrical impedance tomography parameter, the “homogeneity index,” which they “calculated as 1 – global inhomogeneity index,” based on the assumption of the global inhomogeneity index ranging from 1 to 0. However, the global inhomogeneity index values are commonly higher than 1 in patients with pronounced ventilation inhomogeneity, as shown already in some of the examined mechanically ventilated subjects in the original description of the global inhomogeneity index3 or recently in patients with exacerbated chronic lung disease.4 An example patient case is presented in figure 1, in which a global inhomogeneity index value of 2.59 was noted in the presence of pendelluft, which is a frequent cause of out-of-phase impedance variation both in spontaneously breathing and ventilated patients.5 The “homogeneity index” proposed by the authors would be negative in this case and assume the confusing value of –1.59. We therefore strongly advise against using the “homogeneity index” as a surrogate for the well established global inhomogeneity index.The authors pointed out that electrical impedance tomography perfusion assessment with saline bolus injection had been validated only in two animal studies. In fact, this technique of contrast-enhanced electrical impedance tomography has been studied in several other animal studies as well.6–9 Last, we agree with the authors that electrical impedance tomography images do not cover the whole lungs, but as summarized in the consensus paper on chest electrical impedance tomography,2 an electrical impedance tomography image does not originate from “only the area of the lung surrounded by the belt.”Electrical impedance tomography receives increasing attention due to its noninvasive bedside monitoring features. Correct description and implementation of the electrical impedance tomography technique and analysis procedures are crucial for further development and clinical use.Dr. Zhao receives a consulting fee from Dräger Medical (Lübeck, Germany). Dr. Frerichs reports funding from the European Union’s Framework program for Research and Innovation Horizon 2020 (WELMO, grant No. 825572).

An image reconstruction method is proposed based on Lagrange-Newton method for electrical impedance tomography (EIT) and ultrasound tomography (UT) dual-modality imaging. Since the change in conductivity distribution is usually accompanied with the change in acoustic impedance distribution, the reconstruction targets of EIT and UT are unified to the conductivity difference using the same mesh model. Some background medium distribution information obtained from ultrasound transmission and reflection measurements can be used to construct a hard constraint about the conductivity difference distribution. Then, the EIT/UT dual-modality inverse problem is constructed by an equality constraint equation, and the Lagrange multiplier method combining Newton-Raphson iteration is used to solve the EIT/UT dual-modality inverse problem. The numerical and experimental results show that the proposed dual-modality image reconstruction method has a better performance than the single-modality EIT method and is more robust to the measurement noise.

Electrical brain imaging (EBI) refers to a set of techniques that exploit either the spontaneous electrical activity of the central nervous system, as in electroencephalographic (EEG) source reconstruction, or make use of external current injections, as in electrical impedance tomography (EIT) , to image the structure or function of the brain. When compared to other brain imaging methods used in research or in the clinical setting, such as computed tomography (CT), magnetic resonance imaging (MRI), functional MRI (fMRI), positron emission tomography (PET) and single photon emission computed tomography (SPECT), EIT and EEG source localization instrumentation offer the advantages of portability, low cost, high temporal resolution [ms] and quick setup. The downsides are a low spatial resolution [cm], high computational cost of the image reconstruction process and high sensitivity to imperfections of the electrical model of the head.
\nIn this work, a new special purpose reconstruction algorithm for EIT is presented and validated wth experimental measurements performed on a cylindrical phantom and on a simulated human head. The algorithm focuses on the quick detection of compact conductivity contrasts in imperfectly known in 3D domains. The performance of the proposed algorithm is then compared to the one of a benchmark reconstruction method in the EIT field, Tikhonov regularized reconstruction, with stroke detection and classification as a case study. Moreover, the possible application of EIT imaging to the detection of epileptic foci with intracranial deep electrodes (stereoelectroencephalography or SEEG) is explored.
\nFinally, EEG source reconstruction algorithms are implemented on a heterogeneous multi-CPU and multi-GPU computing system to significantly reduce the reconstruction time.

Peatland management, conservation, and restoration rely on a thorough understanding of peatland hydrogeology and carbon dynamics. To date, most of the information about peatland subsurface properties is derived from laboratory analyses of borehole samples, which allow direct measurement of hydrogeological and geochemical parameters but provide only point-wise information. Here, we present the use of the low-frequency electrical impedance tomography (EIT) to investigate hydrogeological properties and carbon dynamics in alpine peatlands in an imaging framework. In particular, we aim to map biogeochemical hotspots and to delineate flow paths controlling surface-groundwater interactions and nutrient cycles. The EIT method is an extension of the widely-used electrical resistivity tomography (ERT), which deploy electrodes (placed on the ground) to inject current to resolve the conductive (conductivity) and capacitive (polarization) properties of the subsurface along 2D planes or 3D volumes. While the electrical conductivity (due to migration of charges in the pore space) has been commonly used to investigate variations in saturation, porosity and fluid electrical conductivity (EC); the polarization (i.e., capacitive effect, resulting from accumulation and polarization of charges in the fluid-grain interface), provides a unique opportunity to gain information about changes in pore-space geometry, cations exchange capacity and soil organic carbon (SOC). To resolve the frequency-dependence of the electrical properties, imaging measurements were collected in the range between 0.1 and 75 Hz, while vertical soundings were conducted between 0.1 and 1000 Hz. This information is needed to discriminate between SOC and clay content and quantify changes in hydraulic properties. The geophysical investigations are supported by the analysis of material extracted from boreholes. The EIT surveys were conducted across six alpine peatlands in Austria to characterize the variability in electrical properties at both local (site-specific) and regional (inter-site) scales. The investigated peatlands mainly originated through terrestrialisation of lakes that had formed in glacially eroded depressions at the end of the Last Glacial Maximum. Accordingly, substratum is dominated by lacustrine fines in direct proximity to glacial sediments and various types of alpine bedrock.Our results reveal that the electrical conductivity and polarization are consistent for data collected across the different peatlands, supporting the relevance of the EIT method for peatlands investigations. We demonstrate that incorporating polarization as an additional parameter alongside electrical conductivity improves the resolution of peat thickness compared to interpretations based solely on electrical conductivity. Moreover, the polarization response reveals clear spatial variations related to geochemical variations in the organic soil. While the electrical properties are consistent, important changes in the polarization response can be observed in degraded peatlands, demonstrating the potential of the EIT method for the design of remediation and conservation strategies. Ongoing tracer experiments aim to validate petrophysical models connecting electrical and hydraulic properties in an imaging framework.

Realistic forward and inverse model mesh generation for rapid three-dimensional thoracic electrical impedance imaging

This thesis is a reconciliation between multiple bodies of work with a shared objective that is ``to identify the active support" under different environment settings. The applications of focus within this thesis will be placed on electrical impedance tomography (EIT) and direction-of-arrival (DOA) estimation. The term ``active support" or only ``support" is commonly used in compressed sensing and sparse signal recovery communities which is essentially referring to ``the most contributing parameters" in a system of linear equations. Although with a common objective shared among the works that have been done within this thesis, this thesis can be divided into two major parts based on applications’ environment. The first part is the support identification under a process expressible by Fredholm integral equation of the first kind. For this problem, a research topic that is known as ``Electrical impedance tomography (EIT)," is chosen as a representative application for a collection of problems expressible by this integral equation. The physical laws (Physics) of EIT can be explained by Maxwell's equations under quasi-static environment. Under such condition, the energy dissipated from the source is spread throughout the region (domain) in a non-linear fashion. Together with the absent of phase or time delay information, the image reconstruction task for EIT usually faces the issue of low signal-to-noise-ratio (SNR) and support ambiguity. Multiple real-life applications typically fall under this category of problems such as medical and geophysical subsurface imaging, deconvolution, and image deblurring. The EIT is an imaging technique that estimates a distribution of electrical admittivity $\gamma$ of a ``subject under test (SUT)" sometimes called as ``medium" based on an inference from data captured from the medium's boundary. Although the name would suggests the value of `impedance' to be measured, in most practical scenario its reciprocal which is `admittance' (admittivity value) is commonly calculated instead. The admittivity value $\gamma$ encapsulates the information of medium's conductivity ($\sigma$) and permittivity ($\epsilon$) with the following expression $\gamma = \sigma + i\omega\epsilon$, where $\omega=2\pi f$ is the angular frequency (rad/s) and $f$ is frequency in Hz. The ``tomographic reconstruction" or ``the process of estimating the medium's internal admittivity distribution" can be accomplished by solving a mathematical problem that is commonly known as an ``inverse problem." Due to a quasi-static nature of this imaging modality, the image reconstruction of the EIT is known to be one of the most severely ill-posed inverse problems. The image reconstruction problem of EIT will be analyzed through two different viewpoints. Firstly, this problem will be analyzed through the lens of a discrete ill-posed inverse problem from the applied mathematics community viewpoint. Secondly, this problem will be re-analyzed through the lens of array signal processing/beamforming framework from the signal processing community viewpoint. While exploring the EIT image reconstruction techniques, it was observed that although the EIT system can be implemented economically, the implementation process is not completely straightforward. Therefore, a framework of a simple and reliable EIT prototyping system that could provide means to collect different data format (e.g. single measurement vector (SMV) and multiple measurement vectors (MMV)) were implemented in this thesis. This robust, economical, and straightforward implementation framework was developed with an aim that it could be beneficial for those who are interested in image reconstruction and inverse algorithms without the access of a full functioning commercialized EIT system. The second part is the support identification for DOA estimation under Gaussian and $\alpha-$stable distributed noises. Several improvements of a robust beamforming technique called MUSIC-like algorithm had been further investigated which helps improve the algorithm's performance. The main focus of this part is the performance improvement of the algorithm that can be used for support identification task under different noise scenarios. Three different approaches for estimating a relaxation parameter, an essential parameter used in the MUSIC-like algorithm, are presented. By experimenting with different approaches, an adaptive framework for relaxation parameter was observed to have the potential for further improvement. The performance of the MUSIC-like algorithm was then further explored through the directional adaptive framework under both Gaussian and $\alpha-$stable distributed noise. It was also compared with the conventional MUSIC algorithm coupled with a pre-conditioned covariance matrix.

Delayed detection of an internal hemorrhage may result in serious disabilities and possibly death for a patient. Currently, there are no portable medical imaging instruments that are suitable for long-term monitoring of patients at risk of internal hemorrhage. Electrical impedance tomography (EIT) has the potential to monitor patients continuously as a novel functional image modality and instantly detect the occurrence of an internal hemorrhage. However, the low spatial resolution and high sensitivity to noise of this technique have limited its application in clinics. In addition, due to the circular boundary display mode used in current EIT images, it is difficult for clinicians to identify precisely which organ is bleeding using this technique. The aim of this study was to propose an optimized strategy for EIT reconstruction to promote the use of EIT for clinical studies, which mainly includes the use of anatomically accurate boundary shapes, rapid selection of optimal regularization parameters and image fusion of EIT and computed tomography images. The method was evaluated on retroperitoneal and intraperitoneal bleeding piglet data. Both traditional backprojection images and optimized images among different boundary shapes were reconstructed and compared. The experimental results demonstrated that EIT images with precise anatomical information can be reconstructed in which the image resolution and resistance to noise can be improved effectively.

Electrical impedance tomography aims at reconstructing the internal conductivity of a physical body from boundary measurements of current and voltage. In this work, the conductivity is modelled as a log-normal random field with a known (prior) distribution, and the reconstruction task is reformulated as a Bayesian inference problem. Combining the prior information with a stochastic Galerkin finite element method, an explicit parametrized approximation is written for the posterior distribution of the conductivity, i.e. for the conditional probability distribution given the boundary measurements, which enables efficient computation of point estimates for the posterior. The feasibility of this approach is demonstrated by two-dimensional numerical examples in the framework of the complete electrode model, which is the most accurate model for practical impedance tomography.

The trust region (TR) method is an effective algorithm for image reconstruction of electrical impedance tomography (EIT). Aiming at the drawback of the traditional TR method, an improved method named the nonmonotonic and self-adaptive trust region (NSTR) method is proposed in this paper, in which three kinds of modified techniques are shown that help in improving the computational precision and convergence speed of the algorithm. The comparisons with image reconstruction are carried out between the NSTR, Levenberd–Marquardt (LM) and TR methods. Simulation experiment results indicate that for both the LM and TR methods it is difficult to accurately reconstruct concave and multiple boundaries. However the NSTR method cannot only realize accurate reconstruction, but also provide faster convergence speed. A noise simulation test is carried out and results show that the NSTR method also has strong stability in image reconstruction for EIT. This new method presents a feasible and effective way to research on image reconstruction for EIT.

A singularity image method is applied to the electrical impedance tomography ofgas–liquid flows in a two-dimensional circular domain. Algorithms that useanalytic complex functions, dipoles and the Milne-Thomson circle theorem aredescribed. Numerical experiments are provided to demonstrate the robustness ofthis technique. Numerical results show excellent reconstruction properties.

Electrical impedance tomography and microwave imaging methods for monitoring the temperature distribution during hyperthermia treatment is discussed. The numerical models, primarily finite element based, are described for each with attention to the differences in the governing partial differential equations. The reconstruction algorithms for determining the tissue properties are discussed. Finally, preliminary results using electrical impedance tomography to map conductivity changes during hyperthermia are shown. >

Recent studies have shown high correlation between pulmonary perfusion mapping with impedance contrast enhanced Electrical Impedance Tomography (EIT) and standard perfusion imaging methods such as Computed Tomography (CT) and Single Photon Emission Computerized Tomography (SPECT). EIT has many advantages over standard imaging methods as it is highly portable and non-invasive. Contrast enhanced EIT uses hypertonic saline bolus instead of nephrotoxic contrast medium that are utilized by CT and nuclear Ventilation/Perfusion (V/Q) scans. However, current implementation of contrast enhanced EIT requires induction of an apnea period for perfusion measurement, rendering it disadvantageous compared with current gold standard imaging modalities. In the present paper, we propose the use of a wavelet denoising algorithm to separate perfusion signal from ventilation signal such that no interruption in patient's ventilation would be required. Furthermore, right lung to left lung perfusion ratio and ventilation ratio are proposed to assess the mismatch between ventilation and perfusion for detection of Pulmonary Embolism (PE). The proposed methodology was validated on an ovine model (n=3, 83.7±7.7 kg) with artificially induced PE in the right lung. The results showed a difference in right lung to left lung perfusion ratio between baseline and diseased states in all cases with all paired t-tests between baseline and PE yielding p <; 0.01, while the right lung to left lung ventilation ratio remained unchanged in two out of three experiments. Statistics were pooled from multiple repetitions of measurements per experiment.

Image reconstruction for Electrical Impedance Tomography (EIT) is a highly nonlinear and ill-posed inverse problem. It requires the design and employment of feasible reconstruction methods capable to guarantee trustworthy image generation. Deep Neural Networks (DNN) have a powerful ability to express complex nonlinear functions. This research paper introduces a novel framework based on DNN aiming to achieve EIT image reconstruction. The proposed DNN model, comprises of the following two layers, namely: The Stacked Autoencoder (SAE) and the Logistic Regression (LR). It is trained using the large lab samples which are obtained by the COMSOL simulation software (a cross platform finite elements analysis solver). The relationship between the voltage measurement and the internal conductivity distribution is determined. The untrained voltage measurement samples are used as input to the trained DNN, and the output is an estimate for image reconstruction of the internal conductivity distribution. The results show that the proposed model can achieve reliable shape and size reconstruction. When white Gaussian noise with a signal-to-noise ratio of 30, 40 and 50 were added to test set, the proposed DNN structure still has good imaging results, which proved the anti-noise capability of the network. Furthermore, the network that was trained using simulation data sets, would be applied for the EIT image reconstruction based on the experimental data that were produced after preprocessing.

Magneto-acousto-electrical tomography with magnetic field measurement technique (MAET-MI) is a hybrid imaging method that brings high spatial resolution of ultrasound imaging in electrical impedance tomography. This study investigates the impact of the quality factor of circular and figure-of-eight coils on the imaging performance of MAET-MI. Induced MAET signals on the circular coil are accurately obtained by modeling a circuit representation of an air-cored circular coil and deriving its transfer function through impedance measurements. The study demonstrates a significant improvement in signal-to-noise ratio (SNR) using high-quality factor coils compared to unity quality factor coils. Additionally, a 16-element linear phased array (LPA) ultrasound transducer, an air core circular coil, and a figure-of-eight coil are numerically modeled to obtain sector scan images of two-dimensional conductivity distributions. Point spread function (PSF) is characterized, and the lateral resolution of sector scan conductivity images is enhanced through two-dimensional deconvolution with PSF. The combined use of circular and figure-of-eight coils provides comprehensive imaging coverage. Notably, this research presents a practical method for estimating both circular and figure-of-eight coils' transfer functions, achieving 12.9 dB SNR improvement with high-quality factor coils. A simplified breast model is rotated 16 steps, and sector scan conductive boundary images are reconstructed for both coils. A two-dimensional image of a breast model is obtained by combining images from two different coils. These findings offer significant advancements in MAET-MI imaging, particularly in low SNR environments.

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that displays changes in conductivity within a body. This method finds application in biomedical and geology. EIT finds use in medical applications, as the different tissues of the body have different conductivity and dielectric constants. In this paper a phantom model is designed considering Finite Element Model (FEM). AC current of amplitude 1 mA and frequency 1 KHz is applied considering adjacent protocol with noise less and noisy cases. From the computed voltage data image is reconstructed using Kalman algorithm. For noisy case noise levels equal to Signal-to-Noise Ratio (SNR) 30 dB, 15 dB and 7 dB were considered. Kalman algorithm is studied for EIT image reconstruction in noise free and noisy case, in terms of shape, size, spatial location of the target object.