A Krylov subspace type method for Electrical Impedance Tomography

T15. Imaging fast neuronal depolarization in 3D during seizures with electrical impedance tomography and scalp and intracranial depth electrodes

The aim of electrical impedance tomography (EIT) is to reconstruct the conductivity values inside a conductive object from electric measurements performed at the boundary of the object. EIT has applications in medical imaging, nondestructive testing, geological remote sensing and subsurface monitoring. Recovering the conductivity and its normal derivative at the boundary is a preliminary step in many EIT algorithms; Nakamura and Tanuma introduced formulae for recovering them approximately from localized voltage-to-current measurements in [Recent Development in Theories & Numerics, International Conference on Inverse Problems 2003]. The present study extends that work both theoretically and computationally. As a theoretical contribution, reconstruction formulas are proved in a more general setting. On the computational side, numerical implementation of the reconstruction formulae is presented in three-dimensional cylindrical geometry. These experiments, based on simulated noisy EIT data, suggest that the conductivity at the boundary can be recovered with reasonable accuracy using practically realizable measurements. Further, the normal derivative of the conductivity can also be recovered in a similar fashion if measurements from a homogeneous conductor (dummy load) are available for use in a calibration step.

In this chapter, we have discussed the physics of the common medical imaging techniques that are applied in the electromagnetic spectrum: electrical impedance tomography (EIT), magnetic resonance imaging (MRI), microwave imaging (MWI), and computed tomography (CT) scan. The EIT and MWI imaging techniques based on the electromagnetic theory and Maxwell's equations are specifically investigated with detail physics and imaging algorithms (BIM and DBIM) flowcharts. Then we explained the basic theories and structures of the machine learning and deep learning methods, and discussed their applications in medical imaging within the last decade. Particularly, we discussed the most recent deep learning network applications in medical imaging diagnosis, segmentation, and reconstruction. Furthermore, more advanced applications that combine the electromagnetic physics-based imaging methods with deep learning networks for imaging improvements are discussed in details through four recent EIT and MWI imaging studies published.

Recently, the image reconstruction study on EIT plays a vital role in the medical application field for validation and calibration purpose. This research article analyzes the different types of reconstruction algorithms of EIT in medical imaging applications. Besides, it reviews many methods involved in constructing the electrical impedance tomography. The spatial distribution and resolution with different sensitivity has been discussed here. The electrode arrangement of various methods involved in the EIT system is discussed here. This research article comprises of adjacent drive method, cross method, and alternative opposite current direction method based on the voltage driven pattern. The assessment process of biomedical EIT has been discussed and investigated through the impedance imaging of the existent substances. The locality of the electrodes can be calculated and fixed for appropriate methods. More specifically, this research article discusses about the EIT image reconstruction methods and the significance of the alternative opposite current direction approach in the biomedical system. The change in conductivity test is further investigated based on the injection of current flow in the system. It has been established by the use of Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EDITORS) software, which is open-source software.

Electrical impedance tomography (EIT) is a modality for spatially mapping the internal conductivity distribution of a domain and has recently been explored for potential application in embedded sensing and nondestructive evaluation (NDE) of moderately conductive materials (e.g., carbon fiber composites). The underlying supposition of this approach is that damage represents a loss of conductivity that can be detected, localized, and roughly shaped via EIT. Mathematically, EIT is an ill-posed inverse problem that requires regularization. To date, there have been many studies showing that EIT can indeed work on carbon fiber composites. However, the state of the art suffers from, among others, three important limitations that this manuscript seeks to address. First, the vast majority of these studies make use of overly simple shapes such as flat plates that are not representative of the geometric complexity of real engineering components. For EIT to be established as a viable embedded sensing and NDE modality, work needs to be done to show that it can indeed perform on complex shapes. Second, the state of the art overwhelmingly uses simple regularization methods (e.g., Tikhonov regularization, the smoothness prior, etc.). This is problematic because regularization markedly affects the final image quality. And third, more sophisticated EIT formulations making use of different error norm terms are very seldom explored. Because of the ill-posedness of the EIT inverse problem, formulations that are more robust to outlier data, such as using the ℓ1-norm on the error term, are essential. In light of these limitations, we herein make three contributions: First, we apply EIT to a complexly shaped carbon fiber truss structure produced by a novel additive manufacturing process for the detection of notch damage. Second, we implement a mixed regularization scheme that combines a focal prior with a smoothness prior. These results are compared to images produced using only the smoothness prior. And third, we implement the ℓ1-norm on the error term via the primal-dual interior point method (PDIPM) in order to demonstrate the effect of different error norms (i.e., ℓ1 versus the pervasively used ℓ2-norm) on image quality. It is shown that EIT does indeed work well on this complex shape, that the mixed prior significantly improves image quality, and the ℓ1-norm adeptly localizes damage.

As implied by its name, electrical impedance tomography (EIT) is to reconstruct an impedance distribution in an object of interest from electrical measurement on the boundary of the object. Because of its non-invasiveness, portability and practical utilities, EIT has been actively studied since 1970s and led to many useful and inspiring results. There are already two books on this subject. One is a general textbook published in 1990 [1]. The other is a monograph from a conference on biomedical applications in 1992 [2]. Given the steady development in EIT theory, technology and applications over the past decade, the book under review is indeed overdue to provide an overview of such a fascinating field. This book consists of four parts on algorithms, hardware, applications, and directions, along with two introductory appendices on bioimpedance and biomedical EIT, respectively. The first and only chapter in the first part of the book formulates the problem and describes associated reconstruction methods. The second chapter addresses instrumentation issues, which is the only chapter in the second part. The third through seventh chapters form the third part to cover various biomedical applications, including imaging of the thorax, brain, breast, gastrointestinal tract, hyperthermia, intra-pelvic venous congestion, and so on. Finally, as the fourth part the subsequent six chapters are respectively dedicated to three unique modes of EIT (magnetic induction tomography, magnetic resonance EIT, industrial process tomography) and professional perspectives from three leading groups (Sheffield and Oxford Brookes Universities in UK as well as Rensellaer Polytechnic Institute in USA). The two appendixes are very educational for non-experts to appreciate the ideas and features of EIT. There are 141 formulas and 183 figures in the book. While generally speaking is in high quality, the formatting and compiling work could have been done better. For example, some formulas carry no indexes; a number of figures are not given captions; full bibliographic information is not given to few cited references; and there are some minor typos. All the chapters are well written by established authorities, whose opinions on the future directions are also included. There is no doubt that the book serves its purpose well, which I read with pleasure and satisfaction. Clearly, the book provides a solid foundation to understand the big picture, technical contents and open problems of EIT and to prepare a mathematician, an engineer, or a technologist for research and development in various aspects of EIT, and a biomedical researcher or a clinician for applications of EIT techniques. Nevertheless, in my opinion, the theoretical and algorithmic aspects could have been covered more systematically and more thoroughly. For example, the book would be even more valuable if a more comprehensive review has been presented on Maxwell's equations, more rigorous discussions been given on existence, uniqueness and stability of the EIT solution, and representative reconstruction algorithms described in more details. An insightful comment on the current status of this field was made by Dr. Holder, the editor of this book, that it doesn't clearly work, so we can reap the fruits of its images, or not work, so we can change direction; usually almost works, which is an incitement to redouble our efforts. I believe that many active researchers who handle highly ill-posed problems may more or less share his feeling, and that is exactly why these kinds of problems are attractive to motivated investigators. The advice and lessons given in the book are numerous, covering improvement of data acquisition, regularization of algorithms, incorporation of a priori knowledge, avoidance of tweaking algorithmic parameters, use of different meshes, simulation of realistic noise and errors, fusion of complementary modalities, etc. Interestingly, I notice a substantial similarity between EIT and some molecular imaging modalities, such as fluorescence/bioluminescence tomography [3,4]. The interaction between these two research areas should be mutually beneficial. From that perspective, this book is helpful for further research not only on EIT but also on other highly ill-posed inversion problems; for example, fluorescence/bioluminescence tomography. With the momentum of the EIT research, seems very likely that this technology will gain much wider acceptance in clinical scenarios, along with other emerging biomedical imaging methods. Hence, I highly recommend this masterpiece for imaging scientists and engineers who are interested in EIT, and sincerely suggest that all those who are involved with tomographic imaging and noninvasive testing would be benefited by reading such an excellent text, even just some chapters.

Electrical Impedance Tomography (EIT) is a promising application that displays changes in conductivity within a body. The basic principle of the method is the repeated measurement of surface voltages of a body, which are a result of rolling injection of known and small-volume sinusoidal AC current to the body through the electrodes attached to its surface. This method finds application in biomedicine, biology and geology. The objective of this paper is to present the applications of Electrical Impedance Tomography, along with the method's capabilities and limitations due to the electrical properties of the human body. For this purpose, investigation of existing literature has been conducted, using electronic databases, PubMed, Google Scholar and IEEE Xplore. In addition, there was a secondary research phase, using paper citations found during the first research phase. It should be noted that Electrical Impedance Tomography finds use in a plethora of medical applications, as the different tissues of the body have different conductivities and dielectric constants. Main applications of EIT include imaging of lung function, diagnosis of pulmonary embolism, detection of tumors in the chest area and diagnosis and distinction of ischemic and hemorrhagic stroke. EIT advantages include portability, low cost and safety, which the method provide, since it is a noninvasive imaging method that does not cause damage to the body. The main disadvantage of the method, which blocks its wider spread, appears in the image composition from the voltage measurements, which are conducted by electrodes placed on the periphery of the body, because the injected currents are affected nonlinearly by the general distribution of the electrical properties of the body. Furthermore, the complex impedance of the skin-electrode interface can be modelled by using a capacitor and two resistor, as a result of skin properties. In conclusion, Electrical Impedance Tomography is a promising method for the development of noninvasive diagnostic medicine, since it is able to provide imaging of the interior of the human body in real time without causing harm or putting the human body in risk.

Electrical impedance tomography (EIT) seeks to image the electrical conductivity of an object using electrical impedance measurement data at its periphery. Ultrasound reflection tomography (URT) is an imaging modality that is able to generate images of mechanical properties of the object in terms of acoustic impedance changes. Both URT and EIT have the potential to be used in various medical applications. In this paper we focus on breast tumour detection. Both URT and EIT belong to soft field tomography and suffer from the small amounts of available data and the inherently ill-posed nature of the inverse problems. These facts result in limited achievable reconstruction accuracy and resolution. A dual bio-electromechanical tomography system using ultrasound and electrical tomography is proposed in this paper to improve the detection of the small-size tumour. Data fusion techniques are implemented to combine the EIT/URT data. Based on simulations, we demonstrate the improvement of detection of small size anomalies and improved depth detection compared to single modality soft field tomography.

Root biomass is one of the most relevant root parameters for studies of plant response to environmental change. In this work, a dynamic and adjustable electrode array sensor system is designed for developing a cost-effective, high-speed data acquisition system based on electrical impedance tomography (EIT). The developed EIT system is found to be suitable for in situ measurements and capable of monitoring the changes in root growth and development with three-dimensional imaging by measuring impedances in multiple frequencies with the help of an EIT sensor. The designed EIT sensor system is assessed and calibrated by the inhomogeneities in both water and soil media. The impedances are measured for multiple tap roots using an electrical impedance spectroscopy (EIS) tool connected to the sensor at frequencies ranging from 1 kHz to 100 kHz. The changes in conductivity are calculated by obtaining the boundary voltages from the measured impedances for a given stimulation current. A non-invasive imaging method is utilized, and the spectral changes are observed accordingly to evaluate the growth of the roots. A further root analysis helps us estimate the root biomass non-destructively in real-time. The root size (such as, weight, length) is correlated with the measured impedances. A regression analysis is performed using the least square method, and more than 97% correlation is found for the biomass estimation of carrot roots with an RMSE of 4.516. The obtained models are later validated using a new and separate set of carrot root samples and the accuracy of the predicted models is found to be 93% or above. A complete electrode model is utilized, and the reconstruction analysis is performed and optimized by utilizing the impedance imaging technique in difference method. The tomography of the root is reconstructed with finite element method (FEM) modeling considering one-step Gauss–Newton (GN) algorithm which is carried out using an open source software known as electrical impedance and diffuse optical tomography reconstruction software (EIDORS).

Detection of indentation damage in carbon fiber/epoxy composites via EIT during the application of bending loads

Electrical impedance tomography (EIT) is a promising technology to visualize the conductivity distribution within a closed domain by injecting electric currents and measuring the corresponding voltages at its boundary. Due to the advantages of non-radiative, high-speed and low-cost, EIT has been widely used in industrial and biomedical fields. However, the image reconstruction of EIT is a nonlinear ill-posed inverse problem, which greatly limits its spatial resolution and noise robustness. Although many efforts have been devoted to developing the EIT imaging method, the improvement of EIT spatial resolution and noise robustness is still a focus of current research. Inspired by multimodal information fusion, an ultrasound reflection guided EIT imaging method is proposed to simultaneously reconstruct the inclusion boundary and conductivity. The local structural information obtained from ultrasound reflection measurements will provide a good initial guess and prior constraint on inclusion boundary reconstruction of EIT under the Bayesian inversion framework. The Maximum A Posterior (MAP) estimation combining with alternative optimization strategy is used to solve the inclusion boundary and conductivity simultaneous estimation problem. The numerical and phantom experimental tests are carried out and show that the proposed method has better imaging accuracy and noise robustness than traditional single-modality EIT method.

Electrical Impedance Tomography (EIT) is an imaging technique with wide applications in medical imaging and industrial monitoring. EIT uses the boundary voltage- current data from the surface of the body under testing to reconstruct the tomography of the object. Though the technique is non-invasive and is cheaper compared to traditional imaging modalities, overall spatial resolution is much less. In this paper, we are reviewing different electrode configurations, sensing techniques and various current injecting schemes. Varied hardware setups have different impacts on the resolution of the final reconstructed image. This review will go in depth over these techniques and their effects on the reconstructed image.

Electrical impedance tomography(EIT) can produce functional images with conductivity distributions associated with physiological events such as cardiac and respiratory cycles. EIT has been proposed as a clinical imaging tool for the detection of stroke and breast cancer, pulmonary function monitoring, cardiac imaging and other clinical applications. However EIT still suffers from technical challenges such as the electrode interface, hardware limitations, lack of animal or human trials, and interpretation of conductivity variations in reconstructed images. We improved the KHU Mark2 EIT system by introducing an EIT electrode interface consisting of nano-web fabric electrodes and by adding a synchronized biosignal measurement system for gated conductivity imaging. ECG and respiration signals are collected to analyze the relationship between the changes in conductivity images and cardiac activity or respiration. The biosignal measurement system provides a trigger to the EIT system to commence imaging and the EIT system produces an output trigger. This EIT acquisition time trigger signal will also allow us to operate the EIT system synchronously with other clinical devices. This type of biosignal gated conductivity imaging enables capture of fast cardiac events and may also improve images and the signal-to-noise ratio (SNR) by using signal averaging methods at the same point in cardiac or respiration cycles. As an example we monitored the beat by beat cardiac-related change of conductivity in the EIT images obtained at a common state over multiple respiration cycles. We showed that the gated conductivity imaging method reveals cardiac perfusion changes in the heart region of the EIT images on a canine animal model. These changes appear to have the expected timing relationship to the ECG and ventilator settings that were used to control respiration. As EIT is radiation free and displays high timing resolution its ability to reveal perfusion changes may be of use in intensive care units for continuous monitoring of cardiopulmonary function.

Cross modality generative learning framework for anatomical transitive Magnetic Resonance Imaging (MRI) from Electrical Impedance Tomography (EIT) image.

In this paper we present a new pipeline for the fast and accurate segmentation of impedance images of the lungs using Electrical Impedance Tomography (EIT). EIT is an emerging promising non-invasive imaging modality, which produces real-time poor-spatial but high temporal resolution images of impedance inside a body. Recovering impedance itself constitutes a non-linear ill-posed inverse problem, therefore the problem is usually linearized which produces impedance-change images rather than static impedance, and the images are highly blurry and fuzzy along the object boundaries. We provide a mathematical reasoning behind the high suitability of the Kalman filter when it comes to segmenting and tracking conductivity changes in EIT lung images. Next, we use a two-fold approach to tackle the segmentation problem. First, we construct a global lung shape to restrict the search region of the Kalman filter. Next, we proceed by augmenting the Kalman filter by incorporating an adaptive foreground detection system to provide the boundary contours for the Kalman filter to carry out the tracking of the conductivity changes as the lungs undergo deformation in a respiratory cycle.